IT would hare been ufelefs in the preceding part of this work to have enumerated, or to havenbsp;arranged under any claffical order, the various bodies of the univerfe; fince the properties whichnbsp;formed the fubjeft of that part, belong ihdifcri-niinately to bodies of every denomination. In treating of one of thofe properties, viz. of the mobilitynbsp;of matter, and particularly of the collifion ofnbsp;bodies, one difference only was noticed, namely,nbsp;that which exifts between claflic and non-elafticnbsp;bodies; but that difference neither demanded anbsp;particular difcrimination of bodies, nor could itnbsp;quot;'ith propriety be introduced in any other part ofnbsp;fhe work. We alfo, in explaining the doftrine ofnbsp;n^'^don, applied its laws to folids only, not becaufenbsp;VOL. II.nbsp;nbsp;nbsp;nbsp;gnbsp;nbsp;nbsp;nbsp;jhulds

fluids arc �xempt from thofe laws, as far howeVef as their nature admits of their being placed in cir-cumftances fimilar to thofe of the folids �, but be�nbsp;caufe the mechanic of fluids contains certain othernbsp;laws which arc not applicable to folids; hence thenbsp;particular examination of the equilibrium and ofnbsp;the motion of the fluids, was referved for the pre-fent part.

We are now going to treat of the peculiar properties of bodies, viz. of fuch as render one piece of matter, or fet of bodies, difi�rent from anothernbsp;piece of matter, or other fet of bodies; and ofnbsp;fuch properties there are fome which belong to anbsp;great number of bodies, though not to all; othersnbsp;which belong to a few; and, laftl'y, there are othernbsp;properties, which belong to tingle bodies only.nbsp;Thus water, oil, fpirit Ol wine, and air, are allnbsp;fluid fubllances, fo that by that fluidity they arenbsp;dillinguilhed from ftones, metals, wood, bones,nbsp;amp;c. which are all folid fubftances. But, thoughnbsp;water, oil, fpirit of wine, and air, be all callednbsp;fluids; yet the firfl; three are dillinguilhed fromnbsp;the lall, by this, viz. that tliey are not compref-fible into a narrow'er fpace by the application ofnbsp;any mechanical force, at leall not in any remarkable degree; whereas air may be eafily comprelTednbsp;into a narrower fpace. Hence water, oil, and fpiritnbsp;of wine, are faid to be non-elaftic fluids j but air isnbsp;faid to be an elallic fluid. Farther, though water,nbsp;oil, and Ipirit of wine, be all three non-elaftic

fluids, yet the firft may' be diftinguKhed from the other two, by its not being capable of inflammation ; whereas oil and fpirit of wine may be eafilynbsp;inflamed and burned away. Yet though thefe twonbsp;agree in the property of being inflammable, theynbsp;may however be eafily diftinguilhed flora eachnbsp;other by means of other peculiar properties ; common oil, for inftance, is much lefs fluid thannbsp;fpirits; it dfo feels clammy to the fingers, whichnbsp;fpirit of wine does not �, it is lefs inflammable, andnbsp;lefs evaporable than fpirits, amp;c.

This Ihort Iketch of the nature and variety of the natural properties of bodies, will fufficientlynbsp;manifeft the multiplicity of particulars which muftnbsp;be noticed in the prefent part of thefe elements;nbsp;and will, at the fame time, point out the neceffitynbsp;of preferving as much order and perfpicuity, as thenbsp;intricate nature of the fubjed can admit of.

With this view we (hall begin by making a flight, but general, furvey of the Univerfe, or rather, of the bounds of human knowledge relativenbsp;to the number and variety of natural bodies;nbsp;quot;whence the reader may form fome idea of the extent, variety, and importance, of the fubjeft. Butnbsp;previous to this, it will be proper to make the following obfervation.

It is a rule in elementary eompofitions, to explain thole articles firft, which may elucidate what follows;�to take nothing for truth, unlefs it hasnbsp;been previoufly proved; and not to mention any

thing which has not been already defcribed. But the ftrld: adherence to this rule is impra�ticable iiinbsp;natural philofophy, wherein hardly any thing cannbsp;be mentioned, which does not owe its exiftcncenbsp;to the previous exiftence of feveral other things,nbsp;which cannot have been all previoufly defcribed.nbsp;Thus, in fpeaking of the fufibility of metals, wenbsp;muft naturally mention the thermometer; and innbsp;defcribing the thermometer, we, muft naturallynbsp;fuppofe the previous knowledge of the fufibilitynbsp;of glafs, and of the nature of quickfilver, whichnbsp;is the metallic fubftance moftly ufed for the con-ftrudlion of that very ufeful inftrument. Thenbsp;reader, however, need not be under any apprehen-fion of being mifled or confufed; for whenever anynbsp;article is mentioned without its having been previoufly explained, he may be allured, in the firftnbsp;place, that the particular defcription of that article is not neceffarily required in that place; andnbsp;fecondly, that the proper defcription �f that article will be found in feme other more appropriatenbsp;part of the work.

CONTAINING AN ENUMERATION OF THE VARIOUS KNOWN BODIES OF THE UNIVERSE, UNDER GENERAL AND COMPREHENSIVE APPELLATIONS.

The moft dlftant obje�ls, that are at all perceivable by any of our fentes, are the luminous coeleftial bodies, amongll ivhich the Sun is the grandefl; and the moft admired of the creation.nbsp;Its fplendor, its heat, and its beneficial influence,nbsp;have always excited the particular Attention of thenbsp;human fpecies, and have obtained the adoration ofnbsp;all thofe nations, which have not been bleffed withnbsp;the light of Revelatiop. Next to it is the Moon,nbsp;whofe apparent fiv-e nearly equals that of the Sun ;nbsp;blit its fplendor is vaflly inferior. The other numerous bright objedts of the heavens differ fromnbsp;each other in fize and luftre but in thofe refpedfsnbsp;they all appear greatly inferior even to the Moon.nbsp;Amongft them there are fix, which are feen tonbsp;move with apparent irregularity, but under certainnbsp;determinate laws, through certain parts of thenbsp;heavens whilfl; the others appear to rerpain at thenbsp;f^me unalterable diftance from each other.�Thenbsp;oriiierare called Planets, and their particular namesnbsp;are. Mercury, Venus, Mars, Jupiter, Saturn, and thenbsp;B 3nbsp;nbsp;nbsp;nbsp;Georgian

Georgian Blanet: but it will be fliewn hereafter, that the Earth we inhabit is likewife a planet, whichnbsp;renders the planets feven in number. The latternbsp;are called Stars, the principal of which have like-wife obtained particular names; but they are toonbsp;numerous to be inferted in this place.

Belides the Stars properly fo called, and the planets, which are always vifible to the inhabitants of the Earth, feveral other luminous objeds are atnbsp;times feen in the heavens, which appear for a con-fiderable time, move in a manner apparently morenbsp;irregular than the planets, then difappear, and perhaps make their appearance again after a longnbsp;period of years. Thefe are called Comets.

By means of the telefcope it has been difcovered, that four fmall luminous objeds revolve at certainnbsp;diftances round the planet Jupiter; feven fuchnbsp;bodies revolve round the planet Saturn, and fixnbsp;revolve round the Georgian Planet. Thofe fmallnbsp;revolving bodies are called Satellites, or Moons; fornbsp;in fad the Moon itfelf will be (hewn to be a Satellite, which moves round the Earth, in the famenbsp;manner as the abovementioned fatellites revolvenbsp;round their relpedive planets in ftated periods.

The fcience which enumerates thofe coeleftial objeds, which defcribes their peculiar appearances,nbsp;which examines and calculates their movements,nbsp;and which renders that knowledge ufeful to thenbsp;human fpecies, is called AJtronomy, the elements of

The celeftial bodies which have been juft mentioned, and fuch as fall under the cognizance of Aftronomy, do all move under certain laws, which,nbsp;even with rel'ped to the Comets, have been in a greatnbsp;nieafure inveftigated and afeertained. But therenbsp;are feveral other objefts, either luminous or opaque,nbsp;which appear in the Iky at uncertain times, andnbsp;which d� not follow any known regularity of motion; fo that they very feldom appear twice in thenbsp;fame place, and of precifely the fame fhape. Thefenbsp;are, for very ftrong reafons, fuppofed to be muchnbsp;nearer to us than the Moon, which is the neareftnbsp;to us of all the celeftial bodies that have a knownnbsp;regularity of motion. They .are collectively callednbsp;Meteors.^ whence the particular examination of theirnbsp;origin, of their appearances, and of their influence,nbsp;or of their efteCfs, forms the fubjeCt of Meteorology.,nbsp;which is a very confiderable branch of Naturalnbsp;Philefophy.

The principal objeCts of Meteorology' are, i. Thofe luminous appearances, which are commonly callednbsp;Falling Stars, or Shooting Stars, the largeft of whichnbsp;are more particularly callednbsp;nbsp;nbsp;nbsp;2. The quick

moving light, which is feen at times in the Iky, ^fpecially about the North and South Poles, andnbsp;'vhich has hence been denominated the Auroranbsp;Borealis, and Aurora Aujiralis, or Northern andnbsp;Southern Ughts, 3. The Rain-hw, 4. Halo's, ornbsp;B 4nbsp;nbsp;nbsp;nbsp;Corona's

Coronals, viz. thofe fteady white circles which are fometimes feen about the Sun and the Moon. 5,nbsp;Parhelia, or Mock Suns, and Parafelenae, or Mock--Moon. 6, Zodiacal Light. 7. Other luminousnbsp;appearances more irregular and lefs remarkablenbsp;than the preceding, which have obtained, from theirnbsp;more ufual (hapes, fituations, amp;c. the various namesnbsp;of Draco Folans, viz. Flying Dragon, or Flying Kite;nbsp;Luminous Arches-, Luminous Clouds-, Ignis Fatuus,nbsp;vulgarly called Will with a wifp, or Jack in anbsp;lanthorn, or Jack-a-lanthorn-, the Fata Morgana,nbsp;See, 8. Thunder Lightning. 9, Vapours, Fogs,nbsp;Mijis, and Clouds. 10. Rain, Hail, and Snow.nbsp;II. Water Spouts. 12. Winds, under the variousnbsp;names of Trade Winds, Monfoons, Gales, Whirlwinds,nbsp;See,. 13 . Storms, and Hurricanes.*

Some authors have reckoned the natural formation of ice, or the froft, as alfo earthquakes, volcanos, Stc.amongft the meteors j but it will be much better to confine the word meteor to its originalnbsp;lignification, viz. to fomething that takes placenbsp;in the fky above us, but nearer to us than thenbsp;Moon.�The nature, origin, and effedls of thenbsp;above enumerated meteorogical objedfs, as alfo ofnbsp;volcanos, of earthquakes, amp;c. will be deferibed innbsp;different parts of thefe elements.

* Thofe objects of meteorology have been ufually faid to be of three kind?, viz. fiery, -watery, and airy, metears. Butnbsp;this diflindlipi) is both ufelefs and improper.

of the Unlverfe. nbsp;nbsp;nbsp;9

We muffc laftly enumerate the various bodies which form the Earth, or the planet we inhabit.

A variety of obfervations, experiments, meafure-ments, and incontrovertible arguments, the principal of which will be mentioned hereafter, have proved that this Earth is not a perfeft fphere; butnbsp;that it is' a little flattened on two oppofite parts,nbsp;which give it the figure of an oblate fpheriod; thenbsp;longeft diameter of which has been reckoned equalnbsp;to 41960862 Englith feet, or 7947 Englifh miles;nbsp;the fhortefl; diameter has been reckoned equal tOnbsp;41726516 Englifh feet, or 7902,7 Englifh miles;nbsp;the difference of the two diameters being 234345,6nbsp;feet, or 44,4 miles,*

* See De la Lande�s Aftronomy, voL III. De la Figure de la Terre et de fon applatilTemcnt; where, viz.in�. 2690, andnbsp;2693, the two diameters are fhewn to be equal to �562024,nbsp;and 6525376 French toifes, from which the above-mentionednbsp;lengths have been derived; a Ftench toife being equal tonbsp;^gt;3945 Englifh feet.

Sir Ifaac Newto.n, fuppofing the earth to be of uniform denfity, afligned for the difference betv.'een the equatorialnbsp;and polar diameters part of the former. Bofeovieb,nbsp;taking a mean from all the meafures of degrees, found thenbsp;difference of the two diameters equal tonbsp;nbsp;nbsp;nbsp;From other

tneafurements made in various parts and calculated by different able rnathematicians, this difference has been reckoned equal to 34-. or ^ by de La Lande; to hy de Lanbsp;Place; to ^ by Sejour.�Thefe latter refults agree prettynbsp;well with the obfervations of the length of the pendulum

The furface of the Earth confifts of land and water varioufly intermixed. The land is ufuallynbsp;divided into, i. Continents, or very large tradsnbsp;comprehending feveral countries, ftates, amp;c. 2.'nbsp;Ifands, or fpots of dry land, having water all round.

3. Peninfulas, or fpots of dry land furrounded by water, excepting a fmall neck or communicationnbsp;with fome other land. 4. Ifthmufes, or necks ofnbsp;land, which join the peninfulas to other land.nbsp;5. Promontories, or high landsextending themfelvesnbsp;into the fea, the extremities of which are callednbsp;Ca'pes or HeaJ-lands. And lallly. Mountains, whichnbsp;are parts of the land conliderably elevated abovenbsp;the adjacent country; the fmalleft of which arenbsp;called Hills.

The watery part of the furface is ufually divided into, 1. Oceans, or vafl. colledions of fait water, viz.nbsp;the largeft divifions of the watery part of the furface. 2. Seas^ or parts of oceans, clofe to, or betweennbsp;.^bme countries. 3. Gulfs or Bays, which are feasnbsp;having land all round, except on one fide, by whichnbsp;made In different latitudes; fo that upon the whole or anbsp;fraftion not much differing from this, feems to be the neareftnbsp;to the truth. The caufes of difagreement between the re-fults of different meafurements, probably are the imperfection of inftruments, the partial attradlion of mountains, andnbsp;the unequal denfity of the materials within, and at no greatnbsp;diftance from the furface of the earth. See ProfelTor Playfair�s paper on the fig. of the Earth in the Tranf. of the.nbsp;R. S. of Edinburgh, vol. V. P. I.

4. Straits, or Friths, being narrow branches of the feabetween two contiguous lands, or narrow paffagesnbsp;from One fea to another. 5. Lakes, or colledtionsnbsp;of water m fome inland place. And 6. Rivers, ornbsp;Streams of Water.

The particular defcription of thofe parts, as alfo of the political divifion of the Earth, form the fub-jefts of Geography and Hydrography.

There are feveral hollows or natural pits in the Earth; but they either do not defcend, or could notnbsp;be examined, to any great depth. Deep pits havenbsp;alfo been made by human art j but the deeped ofnbsp;them do not exceed 2400 feet, or lefs than half anbsp;mile; fo that the induflry of man has not been ablenbsp;to penetrate fo far below the furface of the Earthnbsp;as half a mile, which is a very flrort diftance indeed,nbsp;when compared with the abovementioned lengthsnbsp;of the diameters. So that whatever lies below that

The materials which have been extradled from thole excavations are not in general of a naturenbsp;different from thofe, which in fome particularnbsp;places have been found immediately upon the fur-face of the earth.

Upon that furface a vad variety of objedts is to fgt;e obferved; but thofe various objefts, togethernbsp;quot;'dh thofe that are dug, have been ufually arrangednbsp;under three grand divifions, which are naturally

which have been emphatically called the three Kingdoms of Nature-, viz. the Animal Kingdom,nbsp;which comprehends all thofe felf-moving, organized bodies, of which the human being forms onenbsp;Ipecies, The Vegetable Kingdom, which comprehends all thofe organized bodies called plants,nbsp;which grow by an enlargement of parts, have anbsp;certain period of life or of exiftence, but are at:-tached to a particular part of the foil, from whichnbsp;they derive the greatell part of their nouriflrment.nbsp;And laflly, the Mineral Kingdom, which compre^nbsp;hends all the other bodies of the Earth; for allnbsp;the others are fometimes found within the Earth,nbsp;whereas living animals and living plants are not tonbsp;be found buried at any confiderhble depth belownbsp;the furface of the Earth.

, Every one of thofe three grand divifions is fub-dlvided into a variety of fubordinate fubjedfs. Thus the particular enumeration and claflificationnbsp;of all living creatures, or organized bodies, whichnbsp;give marks of fenfation, which continue their kindsnbsp;according to invariable laws, and which are foundnbsp;in the ftate of embryo, infancy, maturity, old age,nbsp;or death, forms the lubjedt of Zoology.�Anatomynbsp;examines and defcribes the internal and externalnbsp;parts of the animal body, Medicine, or the Medical art, endeavours to preferve or to reftore thenbsp;health of animals, and is itfelf fubdivided intonbsp;other branches, .Sec,

Thus alfo with rcfpeft to the vegetable kingdom, the enumeration and regular arrangement of all the plants forms the fcience of Botany. Thenbsp;art of cultivating them is called Agriculture, HuJ-handry, amp;c.

In like manner with refped to minerals, the enumeration and arrangement of all their fpecies,nbsp;together with th.e defeription of fuch of their pro-*nbsp;perties as are neceflary to diferiminate them fromnbsp;each other, forms the fubjed of Mineralogy. Thenbsp;confideration of their original formation, and ofnbsp;their prefent natural difpofition in the body bf thenbsp;Earth, is denominated Geology. The particularnbsp;knowledge and management of one fort of minerals, viz. of metallic fubftances, is called Metalsnbsp;lurgy, and fo forth.

When the knowledge of thofe various fubjeds was not very extenfive, all the known particularsnbsp;could be ealily arranged under the general title ofnbsp;Natural Philofopy; but the progrefs of civilization, and the unremltted attention which has beennbsp;beftowed, particularly within the two laft centuries, on fcientific fubjeds, have increafed thenbsp;number of ufeful dlfcoveries to fuch a degree, asnbsp;to render the capacity of one man inadequate tonbsp;the comprehenfion of the whole ftock of know-ledge, and much lefs able fo treat of all thenbsp;above-mentioned fubjeds in a full and completenbsp;manner. Therefore, under the title of Elementsnbsp;of Natural Philofopby, we mean to explain the

principles, or the foundation of all thofe various branches of knowledge, which depend upon thenbsp;properties of natural bodies; whence the ftudentnbsp;may obtain a competent knowledge of the whole,nbsp;and particularly of the admirable connexionnbsp;which exifts between them all, upon which, asnbsp;upon a fteady foundation, he may extend hisnbsp;-knowledge of any particular branch, which his inclination or his profeffion may lead him to adopt.

Almofh all the bodies which come under the cognizance of our fenfes, viz. all the animals, allnbsp;the vegetables, and almoft all the minerals, arenbsp;compound bodies; viz. they evidently confifb ofnbsp;fubftances differing in weight, colour, and othernbsp;properties, which may be feparated more or lefsnbsp;eafily from each other; but when feparated to anbsp;certain degree, the human art is not able to de-compofe them any farther. Now thofe fubftancesnbsp;or components of animal, vegetable, and mineralnbsp;bodies, which appear of a uniform nature, andnbsp;which, at prefent, cannot be divided into morenbsp;limple fubftances, muft be reckoned elementarynbsp;or primitive, until a mode of decompofing themnbsp;be difeovered. Thus, for inftance, water was formerly reckoned an elementary fubftance; but itnbsp;has been of late years difeovered, that it confifts ofnbsp;quot;(for it maybe refolved into,) other fubftances, whichnbsp;poffefs properties very different from each other.nbsp;Hence, at prefent, water is no longer looked uponnbsp;as an elementary fubftance. It, therefore, naturally

turally appears that the number of elements muft have been always fluftuating, and that k is likelynbsp;to continue fo for ages to come, fince the ingenuity of man continually difcovers new fubftances,nbsp;and at the fame time finds means of reducing intonbsp;fimple fubftances feveral fuch bodies as had before paffed for fimple, primitive, or elementary.

The fcientific perfons of the prefent time acknowledge the fubftances of the following lift, as the elements or components of all animals, vegetables, and minerals; yet it will prefently benbsp;fhewn that fome of thofe elements are merely hypothetical, and that they have been admitted as

Calorific, or caloric The Eledric fluidnbsp;The Magnetic fluidnbsp;Oxygennbsp;Hydrogennbsp;Azotenbsp;Carbonnbsp;Sulphurnbsp;Pholphorusnbsp;P^adical muriaticnbsp;Radical boracicnbsp;Radical fluoric

Of tJie hwtvn B�dieS

Radical fach-ladtic	Zinc
Radical formic	Lon
Radical Prufllc	Tin
Radical febacic	Lead
Radical bombic	Copper
Radical laccic	Mercury
Radical fuberic	Silver
Radical zoonic	Platina
Arfenic nbsp;nbsp;nbsp;.	Gold
Molly bdenite	Silica
Tungfleri	Argill
Chrome	Baryt
Titanite	Strontian
Sylvanite	Lime
Uranite	Magnefia
Manganefe	Jargonia, or Zirgonia
N ickel	Pot-afli
Cobalt	Soda, and
Bifmuth Antimony	Ammoniac

The firft four of* thofe elements may with propriety be called hypothetical. Thefe are Lights or that fluid which renders dbjedls perceivable bynbsp;our eyes; Caloric, viz. the fluid which is fuppofednbsp;to produce the phenomena of heat, or to affefl: usnbsp;with the fenfation of heat; the Ele5lric Fluid,nbsp;which is fuppofed to produce the phenomenanbsp;called ekBrical, and the Magnetic Fluid, to whichnbsp;the properties of the magnet are attributed i for,

in fa6t, the phenomena which fall under each of thofe four denominations, are only fuppofed to bgnbsp;the effecSls of a fingle fluid refpe�ling the nature ofnbsp;which, however, various opinions are entertained.

fhall treat at large of thofe four very remarkable natural agents in the third part of this Work; yet fome of their properties mull unavoidably be mentioned in treating of the properties of

With refpeft to the latter, it may likewife be obferved, that fome of them are only fuppofed tonbsp;^xifl from analogy. Thus it is known that thenbsp;fnlphuric acid confifts of fulphur and oxygen ; fornbsp;It may be formed by combining thofe two fubflaa-ces together, and it may be reduced into tholenbsp;fubftances. It is likewife known, and for the likenbsp;reafon, that the carbonic acid confifts of carbonnbsp;aud oxygen; but the components of the muriaticnbsp;acid are not known with certainty ; yet from thenbsp;analogy of other acids, the muriatic acid is fup-Pofed to confift of oxygen joined to fomethingnbsp;_ '''^lich fomething elfe has been called the bafenbsp;Ihat acid, or the ^nuriatic radical. The like ob-*^r^tion may be applied to fome other radicals.

four, has been acquired by the aftual decom-pofition of o � nbsp;nbsp;nbsp;1nbsp;nbsp;nbsp;nbsp;^

uc 1 as ate vifually found j and likewife by the

c nbsp;nbsp;nbsp;aftual

a�lual re-compofition or formation of feme bodies in a great meafure fimilar to the natural, fromnbsp;a combination of fome of the elementary fubftan-ces. The art of decompofing natural bodies isnbsp;called Analyjis',�the art of formmg compoundsnbsp;is called Syntkefis-, and both the art of analyfing,nbsp;and the fynthetical art, together with the knowledge of the principal fads which have been af-certained by thofe mearfs, form the fcience ofnbsp;Chemi/lry.

Having thus far given a general idea of all the bodies, which either are known to exift, or are, fornbsp;very flrong reafons, fuppofed to exift ; I foall nownbsp;fubjoin a flrort but comprehenfive view of theirnbsp;properties; and foall, at the fame time, point outnbsp;the order m which the particular defeription ofnbsp;thofe properties will be arranged in the followingnbsp;chapters.nbsp;nbsp;nbsp;nbsp;'

It has been foew'ii in the firft part of this work, that matter in general is polfeffed of extsnfon, di-.vifibility, impenetrability^ mobility, vis inertiac, a?ndnbsp;p-avitation.�Upon the mobility and the vis iner~nbsp;tiae of bodies, the extenfive doctrine of motion ornbsp;the mechanical laws, have been eftablifoed; but thatnbsp;dodrine cannot be fufficiently elucidated, unlefsnbsp;it be particularly adapted to each of the threenbsp;principal ftates of bodies, viz. to folids, to non-elaftic fluids, and to elaftic fluids; therefore, having already explained the mechanical laws withnbsp;refped to folids, it will be nccefiary, in the next

t^lace, to treat of the mechanical properties non-ekftic fluids, under the title of Bydrofaiics,

then of the mechanical properties of elaftic flji s, under the title of Pneumatics; and lallly, ofnbsp;ether peculiar properties, behdes the mechanical,nbsp;which belohg to each of them, viz. to iohd andnbsp;fluid, to Ample and to compound, bodies, undernbsp;the title of Chemiftry,nbsp;nbsp;nbsp;nbsp;_nbsp;nbsp;nbsp;nbsp;^

� The properties of bodies may be faid to be eit of a fajjive or of an ai�ive nature. The formernbsp;are extenfion, figure, diviftbUity, impenetrability, mobility^ vis inertia?, denfity 3.v.d rarity, haidnefs, [oftnbsp;uefs, fluidity, rigulity,flexibility, elafticily, opacity, andnbsp;1-ranfparency ; which have been fufficiently definednbsp;in the preceding pages, and will be farther explained in the following; or their meaiiing isnbsp;commonly too well known to require any particularnbsp;definition. The latter, or thofe ofan aftive nature,nbsp;are attraction and repulfion.

Befides what relates to light, heat, electricity, and magnetifm, there are four lorts of attraftion,nbsp;viz. I ft. The attradion which every known bodynbsp;has towards all the reft, and which is called gravitation ; zdly. The- attraction which homogeneousnbsp;parts of matter have towards each other, or bynbsp;which they adhere to each other, and which isnbsp;called the attraction of aggregation ; and fuch is thenbsp;power by which two fmall drops of quickfilver,nbsp;when placed contiguous to each other, rufli, as Itnbsp;were, into each other, and form a Angle drop;nbsp;c 1

jdly. The attraEiion of cohefon, or that power by ^which the heterogeneous particles of bodies adherenbsp;to each other without any change of their naturalnbsp;properties 5 fuch as the adhefion of water to glats,nbsp;of oil to iron, amp;c. 4thly. The attraStion of com-pofition or of affinity, which is the tendency thatnbsp;parts of heterogeneous bodies have towards eachnbsp;other, by which they combine, and form a body,nbsp;differing mor� or lefs from any of its components.*

�Repulfion' takes place either between the homogeneous, or between the heterogeneous, parts of bodies; but the exiftence of the former is withnbsp;great reafon much doubted.

It is remarkable that of all thofe properties we only know their exiftence, and fome of the lawsnbsp;under which they adl; but we are otherwife utterly ignorant of their nature and dependence.

*� The inveftigation and the knowledge of this laft fort of attraction, or affinity, is the moft ufeful and extenfive,nbsp;it being the foundation of chemiftry and of various arts.nbsp;Its inveftigation is likewife very intricate, for it is differentnbsp;between any two bodies from what it is between any tw'onbsp;others, and it fluctuates according to a vaft variety of cir-cumftances. Thus, for inftance, a certain body A has anbsp;greater tendency to mix with another body B in a particular temperature, than in any another. The fame body Anbsp;has a greater affinity to another body B, than to a thirdnbsp;body C, and it may have no affinity at all, or even a repul-fion, towards a fourth body D. Yet when D and C arenbsp;mixed fo as to form one compound body, then A may havenbsp;an affinity .to that compound.

chapter II.

JiJYdrost:at:ICS is the fcience which treats of the preffure and equilibrium of non^nbsp;elaflic fluids*; Hydrodynamics is the fcience whichnbsp;treats of fluids in motion; and Hydraulics treats ofnbsp;the conftruftion of certain machines or engines innbsp;which fluids are principally concerned. But wenbsp;Ihall now treat of what relates to non-elaftic fluids,nbsp;without taking any farther notice of thofe nominalnbsp;diftinftions. ^

* This fcience began to be cultivated by the great Archimedes.nbsp;nbsp;nbsp;nbsp;'nbsp;nbsp;nbsp;nbsp;, n -j or�.

W to be nbsp;nbsp;nbsp;ot �,�-lt;�/.�#'lt;. �gt;��nbsp;nbsp;nbsp;nbsp;�

relative to the preffures, movements, aird other properties thofe fluids.nbsp;nbsp;nbsp;nbsp;�

The ingenious Mr. Canton, in the year 176I3 difcoverv, the compreflibiiity of water, ofoil,amp;c. in the followingnbsp;ner. He took a glafs tube having a ball at one end, muchnbsp;the (hape of a thermometer glafs; filled the ball and part o,nbsp;^he tube with water, which had been deprived of air as

C 3

22 nbsp;nbsp;nbsp;Of Hydrojlatics.

A perfeSifluid is that whole parts may be moved from each other by the lead force. But fuch anbsp;fluid is not to be fou;id; for. independent of itsnbsp;gravily, or Wfeiglit, or tendency towards the centrenbsp;of the earth, every non-elaftlc fluid is pofiefied of

much as it v/as pofEb'.e ; then placed it under the receiver of an air-pump, and on exhaufting the receiver, (viz. onnbsp;removing the preffure of the atmofphere from over thenbsp;water and the glafs in which it was contained) the waternbsp;rofe a little way into the tube, viz. expanded itfelf. And,nbsp;on the contrary, when he placed the apparatus under thenbsp;receiver of a condenfing engine, and by condenfing the a1frnbsp;in the receiver, increafed the preffure upon the water, anbsp;diminution of bulk took place, for the water defcended anbsp;little way into the tube. � In this manner,�� he fays, � I have

found by repeated trials, when the heat of the air has been � about 50�, and the mercury at a mean height in the baro-� meter^ that the water will expand and rife in the tube bynbsp;� removing the weight of the atmofphere, one part innbsp;� 21740; and will be as much compreffed under the weightnbsp;� of an additional- atmofphere. Therefore t])e compreflionnbsp;� of water by twice the weight of the atmofphere is onenbsp;� part in 10870.�

�t Water has the remarkable property of being more �t comprelhble in winter than in fummer, which is contrarynbsp;� to what I have obferved both in fpirit of wine and oil ofnbsp;� olives.�

� Mr, Canton likewife fubjedfed other fluids to the like ^periments, and found them fufceptible of compreflionnbsp;ai-id expanfion in the following proportions:

' nbsp;nbsp;nbsp;Compreflion

tlie attraction of aggregation (viz. of tbe mutual attraction between its parts) in a particular degree ; of the attraction of cohefion, which is likewifenbsp;ip a particular degree, towards other bodies, andnbsp;of the attraction of aflinity. Befides which anbsp;fort of obftruCtion or want of perfect freedom may.

obferved more or lefs in all fluids. For in-ftance, a fmall drop of water placed upon a dry and clean glafs plate, does not aflum,e an horizontal furface, but remains nearly of a globularnbsp;form j its attraction of aggregation, which drawsnbsp;every part of it towairds its centre, being greaternbsp;' than its gravity; and its attraftion of cohefionnbsp;towards the glafs being jufl fufficient to let thenbsp;drop adhere to the glafs, tvhen the latter is turnednbsp;upfidedow'n. But if the drop be fpread over thenbsp;luiface of th� glafs, then the film of water willnbsp;adhere to the glafs with greater force, nor will it

Compreffion lt; of rain water - - 46 gt; millionth parts. � of fea water - - 40nbsp;(_ of mercury - - - 3J

Mr. Canton was of opinion that this fmall degree of compreffibility is not owing to the compreffion of anynbsp;air which might be lodged within thofe fluids; for, havingnbsp;vaufed a quantity of water to imbibe more air than it contained in a preceding trial, he found tliat its compreffibility wasnbsp;not thereby increafed.�Canton�s Papers in the Phil. Tranf,nbsp;�0I. 52d and 54th.

recover

recover its former globular form ; becaufe by the fpreading, its particles have been brought nearer tonbsp;the glafs, and the whole drop has been brought intonbsp;contafl: with a much' greater furface of the glafs;nbsp;hy which means the attraction of cohefion, or attraction towards the glafs, has been rendered muchnbsp;greater than the mutual attraction between thenbsp;particles of water (for either of thofe attractions isnbsp;increafed or diminilhed by bringing the partsnbsp;nearer to, or by removing them farther from eachnbsp;other), and, it has likewife been rendered muchnbsp;greater than the attraction of gravitation.

If the fame experiment be tried with a fmall drop of quickfilver, inftead of water, this alfo willnbsp;aflume a globular form, in confequence of itsnbsp;attraction of aggregation j and it will adhere to thenbsp;glafs, if the latter be turned upfide down, on accountnbsp;of its attraction'of cohefion. But it will be foundnbsp;impoffible to fpread it over the glafs, becaufe itsnbsp;attraction of aggregation is much greater than itsnbsp;attraction of cohefion towards the glafs.

When the quantity of fluid is confiderable, as a cup nearly full of water, then the attraction of cohefion is much fmaller than its gravitation, and thenbsp;greatefl: part of the fluid lies too far from the fidesnbsp;of the cup, to be fenfibly affeCted by its attraction.nbsp;Hence the furface of the water, in confequence ofnbsp;its gravitation, (as will prefently be thewn) will benbsp;horizontal, jexcepting that part of it which lies nearnbsp;the fides of the cup, which will be attracted, and,'nbsp;*nbsp;nbsp;nbsp;nbsp;afcending

amending a certain way, will drag part of the contiguous water in confequence of its attraction of aggregation, fo as to form a concave furface; Onnbsp;the other band, by a little care, more water maynbsp;be put in the cup than its abfolute capacity, or,nbsp;fpeaking more juftly, the water may be made tonbsp;projeft above the edge of the cup, and then nearnbsp;the edge it will affume a furface vifibly convex;nbsp;it being prevented from falling over to a certainnbsp;degree, by both the attraction of aggregation, andnbsp;the attraction towards the fides of the cup.

Thus much may be fufficient to tliew that both the quiefcent ftate of fluids, and their movements,nbsp;are influenced by a variety of powers: but as gravitation is the principal afting power, when thenbsp;quantity of fluid is not very fmall, we fliall therefore proceed to ftate and to explain the laws of hy-droftatics, upon the fuppofition that fluids arenbsp;actuated only by the power of gravity; for we fliallnbsp;afterwards endeavour to point out the principalnbsp;deviations from thofe laws, which are occafioned bynbsp;the interference of other caufes.

I fliall however juft mention, previoufty to the ftatement of the necefiliry propofttions, that thoughnbsp;much mention is made of the particles of fluids,nbsp;yet by this expreflion we only mean indefinitelynbsp;fmall parcels of fluid; for ive are not acquaintednbsp;^ith the fliape or lize of thofe particles, nor indeednbsp;'�''fth that dlfpofition which renders them fo verynbsp;pioveable from each other. Our eyes, either naked

or ivheii afllfted by the moft powerful microfcopes. cannot difcover any component particles ofnbsp;fluid. Some fmail bodies are indeed to be feen innbsp;certain natural fluids, as in blood, milk, amp;c. i butnbsp;thofe are not the parts which conftitute the fluid;nbsp;they are folid or compadt fmail bodies, which fwimnbsp;in, or are mixed with the fluid.

Propofition I. Every body, or fyjiem of bodies, endeavours to defend with its centre of gravity towards the centre of the earth, and that as near as it lies in itsnbsp;power.

The truth of this propofition is fully manifefted by alb that has been already faid relatively tonbsp;the centre of gravity, and to the mechanicalnbsp;povVers: but as it is the foundation of the doftrinenbsp;of hydroftatics, it will be of uie to render it ftill

� Thus if a folid body BD (fig. i. Plate X.) be left at liberty, it will fall towards the ground, and if itnbsp;happen to hit the ground with one end B firft, innbsp;the oblique diredlion in which it is reprefented, itnbsp;w'ill not remain in the fituation which is indicatednbsp;by the dotted reprefentation, but it will fall flatnbsp;upon the ground, as at BC; for in that ftate itsnbsp;centre of gravity A will come as near as it pofliblynbsp;can to the ground, fince the gravitating power willnbsp;force the body to move on until a fufficient impediment is interpofed between the centre of the Earthnbsp;and the centre �f gravity of the body.

Now imagine that the abjovementionetl boay be very foft, and it is plain that if the eohehon of itsnbsp;parts be lefs powerful than the gravity of thofe particles, the body will not remain in the fituationnbsp;ABC, but will fpread itfelf very flat and clofenbsp;to the flat fluface of the ground, in order that itsnbsp;centre of gravity may come as near as poffible tonbsp;the centre of the earth.

Farther, let the body AB, (fig. 2. Plate X.) con-: flftlng of two equal balls faftened to an inflexiblenbsp;rod AB, be placed upon the fulcrum D, whilft itsnbsp;centre of gravity is at C, viz. in 'the middle of thenbsp;rod and it is evident that the end B will defeendnbsp;until the body remains in the fituation of the dottednbsp;reprefentation EG; for in that cafe its centre ofnbsp;gravit5f C is as low as the obftacies at D and G wdlinbsp;permit it to defeend.

The defeent of this body AB may be prevented by applying a hand, or fome other obftacle at F;nbsp;but in this cafe the obftacle at F will fuffer a pref-fure upwards, which preflure is equal to the excefsnbsp;of the momentum of the end B above the momentum of the end A; viz. to the w^eight of Bnbsp;multiplied by BD, minus the w'eight of A multiplied by AD ; for if that difference were added tonbsp;the end A, the centre of gravity would then be removed from C to D, where it would be fupportednbsp;by the fulcrum D, and of courfe the two parts ofnbsp;the body on either fide of D would balance eachnbsp;other j fo that in this cafe one end of the body

preffes upwards, becaufe the greater momentuin of the other end tends downwards j and the latter can-n�t adl without producing the former.

'PiOpofition II. A fluid which is kept in any vejfel 6pen at top, will acquire, and will remain at reftnbsp;a flat jurface parallel to the horizon, as tong as it isnbsp;not difiurhed.

This is a natural confequence of the preceding principle; for in that cafe the centre of gravity ofnbsp;the fluid will lie as low as it poflibly can. Thusnbsp;let ABDC (fig. 3. Plate X.) reprefent one fide of anbsp;redangular veflel containing water as high as EF,nbsp;whofe centre of gravity is G ; now we fhall provenbsp;that when the furface of the water is flat and hori-2onta1, as EF, then the centre of gravity of thenbsp;Ivater lies loweft; but that if the water be cleVatednbsp;on any part of that furface, and of courfe lowerednbsp;on any other part, then rhe centre of gravity willnbsp;be removed to fome place higher than G.

Imagine that the water be difpofed in the fitua-tion DKBC, viz. that the portion KEH be removed to the place BHF ; and in this cafe the centre of gravity L of the quantity of water KE)I-Inbsp;FC remains in its Original fituation, whilft thenbsp;Centre of gravity of .the quantity of water KEH hasnbsp;been removed higher, viz. from I toS. Nowfincenbsp;the comriion centre of gravity of two bodies is in anbsp;flraight line between the refpective centres of gravity of thofe bodies; therefore, the common centrenbsp;of gravity of both the quantities of water formerly

ftood at G in the line IS ; whereas it now ftandsat O in the line LS, vis. evidently higher than thenbsp;. level of G, which is the line zr.

This reafoning, which has, for the fake of brevity, been applied to one fide of the vetielgt; inay be eafity adapted to any fedion of the water andnbsp;veflel, as alfo to veflels of any thape, and to anynbsp;irregularity which the furface of the water may�^nbsp;be fuppofed to acquire for in any cafe the con-clufion is exaftly the fame, namely, that thenbsp;centre of gravity of a given quantity ot fomenbsp;uniform fluid, like water, which is contained innbsp;an open veflel of any lhape, ftands at the lowefl;nbsp;poffible fituation, when the whole furface of thenbsp;fluid is in the fame horizontal line.

It is an evident confequence of this propofition, that if a vejfel confifi of two pipes perpendicular tonbsp;the horizon, and open at top, osgt; in fig. Platenbsp;or if it confifi of various pipes communicating zvith eachnbsp;other, (how fever they may be inclined to the horizon,nbsp;but open at top), as, in fig. 5. Plate X. and a qnan-tity of xvater, or of other fiuid, be poured into anynbsp;of them, the water will rife to the fame horizontalnbsp;line Or level in all the pipes which communicate asnbsp;above; for in that cafe only the centre of gravitynbsp;of the whole quantity of water will lie as low asnbsp;the veffel can admit of.

Thofe perfons who may think it ftrange that the fluid going down one pipe flrould drive a partnbsp;�f the fluid upwards in the other pipe, muft con-

fider that this is analogoijs to the preffure upwards �f the folid, fig. 2. Plate X. as explained in pagenbsp;2^5nbsp;nbsp;nbsp;nbsp;fh-iid is driven upwards in one pipe^

in order that the greater quantity of fluid in the other pipe may defcend lower down.¹

Though the application of prop. 2d. to theabove-men-tioned cafe of pipes, amp;c. be very obvious; yet to prevent any poffible difficulty iu the mind of the novice, I thallnbsp;inftance it in the cafe of fig. 4. by which example the attentive reader may be fully enabled to apply it to any othernbsp;cafe.

GD and FC reprefent two equal cylindrical pipes open at top, communicating with each other at the bottom, andnbsp;containing water as high as AB; the height AD, or BC,nbsp;being 10 feet; it is evident that the centre of gravity ofnbsp;all the water which is contained in thois' pipes muft benbsp;at K, viz. five feet above DC, and midway between thenbsp;two pipes; whilll the centre of gravity of the water innbsp;each pipe is at Y and Z refpedlively. Now fuppofe itnbsp;poffible to remove tw'o feet height of water from the pipenbsp;GD into the pipe f C ; then, bccaufe the pillar of waternbsp;DE which remains in the pipe GD, is eight feet high, itsnbsp;centre of gravity muft be at S, 4 feet above D; and be-caufe the pillar of water .Cf in the other pipe now is 12nbsp;feet high, its centre of gravity T muft be fix feet above C;nbsp;fo that the centre of gravity ot the water In GD has beennbsp;lowered as much as tne centre of gravity of the water innbsp;FC has been elevated; hence, the ftraight line ST muftnbsp;pafs through the point K, which is the common centre ofnbsp;gravity of both the pillars of water when they'were equal.

quot;Propofition III. ^he prejj'ure of tke .Janiz jluul is in tlis proportion of its perpendicular height, and isnbsp;exerted in everv direefion. So that all parts of thenbsp;fame fluid, at the fame depth, prefs each other withnbsp;ecpital force in every diretd/on.

In fig. 5. Plate X. it is evident that the quantities of water in' the different pipes prefs equally againft each other; for if a quantity of water benbsp;removed from anyone of thofe pipes, the furfacenbsp;of the water will defeend to a lower level in all th�nbsp;other pipes; and that the preflure is exertednbsp;equally in every diredtion is proved by obfervingnbsp;that, however the pipes are connected at B, thenbsp;water rifes to the fame level in them all.

In order to prove that the preflure is exadriy proportional to the perpendicular height of thenbsp;water, let ABE,GHD, be (fig. 6. Plate X.) two cylindrical pipes of equal diameter, fituated perpendicular to the horizon ; and let them contain equalnbsp;quantities of water, which of courfe mull be

But now the quantity of water CF is to the quantity of water ED, as 12 to 8, or as 3 to 2 ; therefore (fee p. 75. 'dol. I.)nbsp;rhe diftance of their common centre of gravity O from S,nbsp;muft be to its diftance from T, as 3 to 2, viz. it muft benbsp;nearer to T than to S, or nearer to T than the point K is;nbsp;for K is midway between S and T ; therefore, by remov-'ng part of the water from one pipe to the other, the centrenbsp;gravity of the whole has been raifed; hence that centrenbsp;'^f gravity lies loweft: when the' furface of the water innbsp;pipes is in the fame level, or horizontal line, AB.

equally high in both pipes, viz. AB equal to CD } and the preffures on the bottoms BE, ED mufl:nbsp;evidently be equal. Now let the water AFBE benbsp;poured into the other pipe, where it will occupy thenbsp;{pace GHFC, To as to jnake the whole perpen-.dicular height HD double the height CD. Andnbsp;it is alfo evident that the quantity of water GHFCnbsp;mufl prefs as much upon the furface of the waternbsp;FCED, as it did upon the bottom BE j thereforenbsp;the pretTure on the bottom ED is uow double ofnbsp;what it was before, viz. a double perpendicularnbsp;height occafions a double prelfure. In the famenbsp;manner it is proved that a treble perpendicularnbsp;height occafions a treble preflure; or, univerfally,nbsp;that the preffure is as the perpendicular height.nbsp;And the fame thing is evidently true with refpeftnbsp;to any other uniform fluid.

Notwithftancling the evidence of this demon-ftratlon, fome of my readers may ftill wonder that a fmall quantity of water, fuch as is contained innbsp;the pipe AB, (fig. y. Plate X.) Ihouid balance thenbsp;large quantity of water in the pipe DC; and tonbsp;thofe it may be of ufe to fee this property exhibited in another light.

Suppofe then that the capacity of the cylindrical vefTel EDC be equal to loo times the capa-^ city of the other cylindrical vefTel AFB. Now ifnbsp;the water were to rife one inch above ED in thenbsp;large vefTel, it is evident that it would neceffarilynbsp;faU 100 inches below AF in the fmall vefTel; To

that the fpaces, through which thofe two quantities of water move, or their velocities, are inverfelynbsp;as their quantities, or their weights; hence theirnbsp;momentums are equal, and of courfe they balancenbsp;each other, in the fame manner as the twonbsp;weights R and Z of fig. 8. Plate X. balance eachnbsp;other, when the arms of the rod on either fide ofnbsp;the prop S are inverfely as the weights.

It is an evident confequence of this propofition, that the prejfttre on any determined part of the bottom,nbsp;or of the fides, of any vejfel containing a uniform fluid,nbsp;like water, is equal to the weight of a pillar �f thatnbsp;fluid having a bafe equal to that part of the bottom,nbsp;or fide, and the altitude equal to the perpendicularnbsp;height of thefluid above it.

Whence we may calculate the preffures upon, and of courfe the ftrength required for, dams,nbsp;pensjcifterns, aquedufts, dikes, flood-gates, amp;c. (i.)

(i.) The practical application of this corollary to fuch fur-faces as are parallel to the upper furface of the fluid, is eafy and obvious �, for we need only multiply the given furfacenbsp;hy the perpendicular altitude of the fluid above it. Thus ifnbsp;it be required to determine the preffure upon two fquarenbsp;feet of the flat bottom of a veffel which contains three feetnbsp;perpendicular depth of water, we multiply 2 feet by 3, andnbsp;fbe ptoduft is 6; viz. the propofed part of the bottomnbsp;fiiftains a preffure equal to the weight of fix cubic feet ofnbsp;water; but one cubic foot of water weighs about 1000 avoir-VOL. II.nbsp;nbsp;nbsp;nbsp;jjnbsp;nbsp;nbsp;nbsp;.nbsp;nbsp;nbsp;nbsp;dupoife

^4. nbsp;nbsp;nbsp;Of Hydrojlatics.

Before we proceed any farther, it is neceflary to obferve, that the furface of the water, or of anynbsp;other fluid, has been faid to aflume a flat horizontal furface, or to come to the fame horizontal line,

dupoife ounces; therefore the above-nientioned prefTure is equal to 6000 ounces, or to 375 pounds.

But the application of it to oblique or curve furfaces is not equally obvious; for every point of fuch furfaces is at anbsp;different diftance from the upper furface of the fluid: wenbsp;flialJ, therefore, endeavour to elucidate it in a more particular manner; and for this purpofe it will be neceflarynbsp;to premife the following propofition, which is demonllratednbsp;in aneafy and perfpicuous manner, as given by Mr. Cotesnbsp;in his Hydroftatical Lectures.

If any indefinitely /mail part or point of a furface, tr num-her of Jurfaces, be multiplied by its perpendicular dijiance from any given plane ; the fum of the produSis �will be equalnbsp;to the product of the -whole furface, or number of furfaces,nbsp;multiplied by the perpendicular difance of the centre of gravity of the fngle furface, or of the common centre of gravitynbsp;of the whole number of furfaces, from the fame plane.

In fig. 17. Plate X. let any number of quantities a, b, e, dl reprefent as many weights, hanging at their centres ofnbsp;gravity, a, b, c, d, by the lines ao, bo, co, do, fixed to artynbsp;horizontal plane 0, 0, 0, a; and let z be the common centrenbsp;of gravity of all the weights, and za its perpendicular diftance fram that plane: I fay that agt;Cao-i-bxbo-j-cXconbsp;~f-dxdoz= a^f c dxzo.

For' let the common centre cf gravity of the weights a, Ps be the point k, tind to the line xo, drawn parallel to the

�f Hydrojiatks. nbsp;nbsp;nbsp;35

!;n fuch pip�s as communicate together, on the fuppofition that the force of gravity a�ls in thenbsp;direction of parallel lines; and fuch appears to benbsp;the cafe with fmall furfaces of water, as for in-

reft, let am and bn be perpendiculars. Then by the fimilac triangles mxa, nxb, we have mx : nxnbsp;nbsp;nbsp;nbsp;(xa �. xb \ ) b �.

by the known property of a centre of gravity. Hence a Xmx�b X nXy or a X mo � xo�b^xo�no, or, axmonbsp;lt;iy.xo�bxxo � bxno: whence axmo bxno ~ a-ybnbsp;X xo; which was to be proved in the fimpleft cafe of the

Now let a weight x�a b, be fufpended by a line xo, in the common centre of gravity of a and b; and likewife anbsp;Weight y A? c, in the common centre of gravity of x and c ;nbsp;and alfo a weight z a? in the common centre of gravitynbsp;of y and d; Then z is the common centre of gravity ofnbsp;all the weights a, b, c, d, firft propofed.

Confequently, by what has been proved in the firft cafe, Vft\iZVtaxao-\-bxbo�xXxo-,zr\�\\ktvrlkxXxo-{-cXcozznbsp;yxyo-, and likewife yXyo dxdo�zXzoi confequently,nbsp;a Xao bxbo cXco=yXyo-, zndlikewiCe a Xao bxbo nbsp;cXco dxdo � fzXzo:pJ a b^c dxzo-, which was tonbsp;be proved.

Hence if a furface or number of furfaces of any kind be confidered as equally ponderous in every equal part, and asnbsp;divided into indefinitely fmall parts, fufpended by linesnbsp;drawn from their centres perpendicularly to any horizontalnbsp;plane; it is manifeft that if every part be multiplied refpec-'nbsp;tively into its perpendicular line, the fum of the produ�lsnbsp;Will be equal to the produft of the whole furface multipliednbsp;D Xnbsp;nbsp;nbsp;nbsp;into

2 6 nbsp;nbsp;nbsp;Gif Mydrofatics,

ftance, a fmall pond, a cittern, amp;c. But fince the force of gravity tends to the centre of the Earth,nbsp;every point of the furface of the water, or of anynbsp;other fluid, when quiefcent,mufl; be equidiftantfrom

into the perpendicular diftance of its centre of gravity from the faid plane; and that this equality of the products willnbsp;fubfift even if the faid lines be perpendicular to any plane,nbsp;though not parallel to the horizon.

This being premifed, the method of determining the prefllire of a fluid upon any giyen furface becomes evidentnbsp;and genera!; for confldering the upper furface of the fluidnbsp;as the above-mentioned plane, in the firfl: place we find thenbsp;area of the given furface (by common menfuration); fe-condly, we find the centre of gravity of the fame (by thenbsp;rules of chap. VI. P. I.): then multiply the area of the givennbsp;furface by the perpendicular diftance of its centre of gravity from the furface of the fluid, and the produdt willnbsp;exprefs the preffure. Thus the preflure on the furface ofnbsp;an hemifphericai veffel full of water, is equal to the pro-du�l; of its furface multiplied by its radius.

Thus alfo the preflure upon the fide ABCD of the reftangular vefi'el, fig. i8. Plate X.; full of water, is equalnbsp;to the produdl of the area ABCD multiplied by, half thenbsp;depth of the water; viz. by the diftance of the centre ofnbsp;gravity E of the propofed furface from the furface of thenbsp;water.

It appears from what has been faid above, that the preffure of a fuperincumbent fluid bn the fide of a vcflel, or, in general, on any furface which is not parallel to the furfacenbsp;of the fluid, muft be unequally diftributed over it. Thus,nbsp;for inftance, if through the centre of gravity E of the fide

ABCD,

Of Hydrofa�cs, nbsp;nbsp;nbsp;37

that centre: hence that fluid mull alTume a fphe-roidlcal furface, like that of the Earth; and this curvature is both vifible and meafurable in largenbsp;furfaces of water, as that of the fea,

AB CD, fig. 18. Plate X, an horizontal line be drawn, which divides that fide into two equal parts; it is evidentnbsp;that the preiTure on the lower half is greater than the pref-fure on the upper half, becaufe the former lies deeper intonbsp;the Water. Therefore there muft be an horizontal linenbsp;lower than the middle E, which divides the fide ABCDnbsp;into two fuch unequal parts, as that the prefTure of the fluidnbsp;upon one of thofe parts be equal to the preflure of the fluidnbsp;upon the other. Hence if the whole preflure of the fluidnbsp;Were colle�ed upon that line, it would have the fame efredlnbsp;Upon the plane, as when it was diftributed unequally uponnbsp;it.

It may be likewife eafily conceived, that in the laft mentioned line there mull be a point, in which if the whole preflure were colledtcd, it would have the fame elFedl uponnbsp;the plane as when the preflTure was unequally diftributed all �nbsp;over it.

It follows, that if exaiSlly againft that point, but on the oppofite fide of the plane, a force be applied equal to thenbsp;whole prelTure of the fluid upon that plane, this force wouldnbsp;exadlly counteradl that preflure, and the plane would remainnbsp;perfedlly at reft, viz. it would not incline to any fide. Nownbsp;that point in any furface is called the centre of freffurt ofnbsp;that furface^ and may be inveftigated by meansof a fluxion-sry calculation. But for this inveftigation, which goes rathernbsp;beyond the limits of an elementary treatifc, I muft refer my

2 8 nbsp;nbsp;nbsp;Of Hydrojlatics.

Since fluids prefs in every diredtion, and that preflure is as their perpendicular heights j therefore,.,nbsp;at the fame depth, the particles of the fluid prefsnbsp;equally againft each other. Alfo, fince equal bulksnbsp;of a uniform fluid are of equal weight, therefore nonbsp;motion can take place in a fluid without fome external caufe j but if one parcel of the fluid becornesnbsp;lighter or heavier than the reft, then that portionnbsp;will afcend or defcend in the fluid, giving way tonbsp;other parcels of the fluid that are heavier or lighternbsp;than itfelf.

When the bottom, or one fide of a veflel full of inquifuive readers to the works of other writers. It is,nbsp;llecellary however to add the following obfervations.

In this cafe the plane, which fuftains the preflure of the, fluid, is fuppofed to be an inflexible plane, or the furface of a,nbsp;very fubftantial folid; for if the plane be the thin fide of anbsp;vell'el, or any other very flexible fubftance, the preflure coknbsp;ledled in one point would not produce the fame effedl: asnbsp;when it is diflrributed over the whole plane. It may benbsp;fuftained in the latter cafe, whereas it might bend or burfl;nbsp;the plane in the former.

Various writers have concluded, that if a plane immerfefl in a fluid be fuppofed to be extended until it cuts the fur-face of the fluid, and if that fedtion be confidered as thenbsp;axis of motion of a pendulum whofe hob, or fufpendednbsp;body, is the propofed plane; the centre of ofcillation ofnbsp;flich a pendulum coincides with the centre of preflure of,nbsp;that plane. But Profeflbr Vince Ihews, in his principles ofnbsp;hydroftatics, Seil. !� Prop* XII. that thofe points feldoninbsp;coincide.

Suid is heated, the fluid which is contiguous to the heat, is thereby rarefied, viz. its bulk becomes enlarged, and of courfe it becomes,lighter than an equalnbsp;bulk of the fame fluid which is not fo rarefied; hencenbsp;it afcends in it, amp;c.�And this is the caufe of thenbsp;motion which takes place in fluids that are heatingnbsp;or boiling.

The fame thing which has been faid of fluids in fluids, or of the parcels of a fluid, is applicable tonbsp;folids, viz. a folid at any depth is preffed in proportion to the perpendicular altitude of the fluid overnbsp;it; but as that preiTure adts on every fide, the bodynbsp;�will not afcend nor defcend in the fluid, unlefs itsnbsp;weight is fmaller or greater than that of an equal

If the imraerfed body be compreffible, fuch as a bladder full of air, then the preflure of the fuper-incumbent fluid, according to its perpendicularnbsp;height, will be rendered manifeft; for the deepernbsp;the body is conveyed, the more will its bulk be

Sailors at tea frequently Ihew the following experiment; They cork an empty bottle, (viz, a bottle full of tie it to a rope, to which is added a leaden weight,nbsp;and let the whole down,into the fea to a certain depth;nbsp;they then pull up the apparatus, and generally find thatnbsp;either the cork is driven into the bottle, or the bottle isnbsp;broken, flyt experiment be tried with a bottle fullnbsp;of Water, or of wine, and corked as before, no alteradon.

If, when a folid is inimerfed in a fluid, the preflure of the fluid on one fide of the body be prevented,nbsp;then the preflTure on the other fides of it will benbsp;rendered manifeftj and by this means a bodynbsp;aftually heavier than an equal bulk of water, maynbsp;be caufed to be prefled upwards by the water; and,nbsp;on the other hand, a body adtually lighter than annbsp;equal bulk of water may be caufed to be prelfednbsp;downwards by the water.

Take a glafs tube about 18 inches long, as AB fig. 20. Plate X. open at both ends, and let itsnbsp;lower end be ground quite flat and fmooth. Let anbsp;brafs plate C, a little larger than the diameter ofnbsp;the tube, be ground likewife very flat, and fix anbsp;little hook to its middle, to which a firing D 0 multnbsp;be tied. Place the brafs plate againft the aperturenbsp;of the tube, and by pulling the firing at D, keep

will take place. This difference of effedt is owing to the bottle being full of a compreffible fluid in the former cafe,nbsp;and of a non-comprefEble fluid in the latter.

At the depth of 32 feet below the furface of the fea, a diver has been calculated to be preffed with the weight ofnbsp;about 28000 avoirdupoife pounds; yet as that prefTure isnbsp;diftrfbuted all over his body, and the human body confiftsnbsp;moflly of non-claftic fluids or of folids, he does not feel anynbsp;remarkable inconvenience from it.�This prefTure is calculated in the following manner.

The furface of the body of a middle fized man is reckoned equal to about 14 fquare feet j therefore a diver fituated 32nbsp;9nbsp;nbsp;nbsp;nbsp;feet

plate tight againft the tube. In this fituation tninaerge the tube in the water, until the plate isnbsp;below the furface to the depth of more than 8 ornbsp;lo times its thicknefs. Then if the ftring be letnbsp;SO, the plate will not fall off, but will remainnbsp;adhering to the glafs tube; the reafon of which is,nbsp;tiiat now the water prefles only againft the undernbsp;part of the brafs plate. And, in fa�f, if vvaterbenbsp;poured into the tube, then the plate will b� immediately feparated from the tube, and vyill fall to thenbsp;bottom of the vetPel EF.

A brafs plate ac^ fig. 21. Plate X. very flat and i fmooth, muft be cemented to the bottom of a veflelnbsp;EF; a fimilar fmooth brafs plate, to which a largenbsp;cork is cemented fo as to form a compound bodynbsp;lighter than an equal bulk of water, muft be laidnbsp;�upon the former plate, and in very clofe contaft with

feet below the furface of the fea is prefled by a pillar of �water v^hofe bafe is i4fquare feet, and altitude 32 feet. Nownbsp;fuch a pillar contains (14X32 = ) 448 cubic feet of water,nbsp;and as acubic foot of water weighs about 1000 avoirdupoifenbsp;ounces; therefore the weight of fuch a pillar is (448 X 1000nbsp;=a) 448000 ounces, or 28000 avoirdupoife pounds.

In this calculation the furface of the body of the diver has been confidered as being all at an equal diftance fromnbsp;the furface of the fea, which is not really the cafe; but atnbsp;foe depth of 32 feet the difference of perpendicular diftancenbsp;of the various parts of the body is not confiderable ; fo thatnbsp;foe refult of the calculation is very near the truth, efpeciallynbsp;if the depth be reckoned from the middle of the body.

it. Then by applying a hand, ora ftick to the upper part of the cork, keep it down until the veflbl EFnbsp;be filled with water. This done, remove the handnbsp;or flick from over the cork, and it will be foundnbsp;that, though fpecifically lighter than water, thenbsp;cork and brafs plate will not afcend to the furfacenbsp;of the water. The reafon of which is, that thenbsp;�water cannot in this cafe prefs on the lower furfacenbsp;of that brafs plate. And in faft, if by means of thenbsp;ftick or hand, the upper brafs plate be feparated anbsp;little front the lower one, fo that the water maynbsp;enter between them, then the upper plate wiih thenbsp;cork will immediately afcend to the furface of thenbsp;water.

Propofition IV. When fluids of different fpecifle gravities mutually prefs againfl each other, their fur~nbsp;faces cannot tie in the fame level; but their perpendi^nbsp;cular altitudes above the level of their junElion arenbsp;hiverfely as their fpecifle gravities. .

The weights of equal bulks of different bodies are called their fpecifle gravities, or their relativenbsp;weights. Thus, for inftance, if you fill a veffelnbsp;with w'ater, and weigh it; then remove the water,nbsp;fill it equally full with quickfilver and weigh itnbsp;again, you will find it to weigh, in the latter cafenbsp;�4 times as much as it weighed in the former¹:nbsp;therefore the fpecific gravity of quickfilver is faid to

be 14, whilft the fpecihc gravity of water is faid to be one; and fo of the reft. Hence the weightsnbsp;of bodies, or their abjolute weights, are exprefled bynbsp;the -produfts of their bulks multiplied by theirnbsp;Tefpeftive fpecific gravities; for, in the above-mentioned inftance, if the weight of quickfilver is 14nbsp;pounds, when that of an equal bulk' of water isnbsp;one pound, it follows that 4 times that bulk ofnbsp;quickfilver mufl; weigh 4 times 14, or 56 po.unds;nbsp;that 10 times that bulk of quickfilver muft weighnbsp;140 pounds; that twice that bulk of water muftnbsp;weigh twice one, viz. 2 pounds ; and fo forth.

Now let the part ECDF of the cylindrical bent tube, fig. 9. Plate X. be filled W'ith quickfilver,nbsp;the furface of which will come to the fame levelnbsp;EF in both legs. Then fuppofe that one inchnbsp;height of quickfilver, viz. GE, be removed fromnbsp;the pipe CS, and that inftead of it fourteen inches of water, viz. GS, be added; it is evidentnbsp;that fince quickfilver is fourteen times as heavy asnbsp;Water, the perpendicular pillar of w�ater G S muftnbsp;prefs upon the furface of the quickfilver GV, asnbsp;itiuch as the perpendicular. pillar of quickfilvernbsp;Eg : hence the preflure againft the quickfilver in-the pipe BD remaining the fame, its furface muftnbsp;remain at F. But the furface of the water is at S,nbsp;'�iz. 14 inches above the level GZ of the jumftionnbsp;of the two fluids, whilft the furface F of thenbsp;quickfilver is one inch above the faid level. Therefore the perpendicular heights of thole fluids above

the

the level of their jundion are inverfely as their fpecific gravities.�The like reafoning may evi-'nbsp;dently be applied to all other fluids, and to veflelsnbsp;of any other fliape ; therefore the propofition isnbsp;univerfally true.

Propofition V. A body floating in a fluid dif-places a quantity of the fltiid, the weight of which is equal to the weight of the body.

Thus the body- DB, fig. lo. PI. X. floating on the fluid FHG, weighs as much as the quantitynbsp;of that fluid which would exadly fill up thenbsp;fpace ABCE; for the body DB is kept in thatnbsp;place by the preflure of the furrounding water,nbsp;which fame preflure, previoufly to the immerfionnbsp;of the body, was juft fuflicient to keep in thenbsp;fame place a quantity of the fame fluid equal tonbsp;the fpace ABCE: therefore the weight of thatnbsp;quantity of the fluid is equal to the weight of thenbsp;body.

The following confequences, or corollaries, are naturally deduced from this propofition,

1. nbsp;nbsp;nbsp;If the fame body be fuccefiively placed onnbsp;fluids of different fpecific gravities, it will difplacenbsp;different quantities of thole fluids; that is, it willnbsp;fink deeper in the lighter than in the heaviernbsp;fluid.

2. nbsp;nbsp;nbsp;If the weight of the body be equal to that ofnbsp;an equal bulk of the fluid, then that body will remain at reft in any part of that fluid below the

3- If a body heavier than an equal bulk of a certain fluid, be placed on the furface of that fluid, it will link with the excefs of weight by whichnbsp;the Weight of the body exceeds the weight of annbsp;equal bulk of the fluid. Thus, if a body whichnbsp;Weighs tliree pounds be put in water, and a quantity of water equal in bulk to that body weighsnbsp;two pounds; then the' body will defcend in thenbsp;water with the force of one pound ; the meaningnbsp;of which is, that if that body be tied by means ofnbsp;a firing to one fcale of a balance, and be weighed,nbsp;firfl; out of the water, and then in water, as innbsp;fig- 11. PI. X. it will be found to weigh threenbsp;pounds out of the water, and one pound in water:nbsp;whence it follows, that if the weight of a body benbsp;divided by that weight which it lofes in water, thenbsp;quotient fliews its fpecific gravity; viz. it (hewsnbsp;how many times that body, is heavier than annbsp;equal bulk of water.

4. If a body lighter than an equal bulk of a certain fluid be placed at the bottom of a veffelnbsp;full of that fluid, that body will afcend withnbsp;more or lefs force, according as the difference ofnbsp;�weight between the body and an equal bulk of thenbsp;fluid is greater or fmaller; � becaufe a quantity ofnbsp;the fluid equal to it in bulk, but heavier than thenbsp;body, will continully take its place, until part ofnbsp;the body projeds above the furface of the fluid;

and only fuch a part of it will remain in the fluidi as can difplace a quantity of the fluid whofe weightnbsp;equals the w'eight of the body. Therefore in ordernbsp;to keep that body below the furface of the fluidgt;nbsp;3'ou muft prefs it with a weight equal to the difference between the weight of the body and thenbsp;W'eight of an equal bulk of the fluid.

If a body be cauled to float fucceffively on two different fluids, the quantities of thofe fluids,nbsp;which are difplaced by that body, and likewife thenbsp;parts of that body which are immerfed in the twonbsp;fluids, tvil! be inverfely as the fpecific gravities ofnbsp;thofe fluids. Thus, fuppofe that a folid bodynbsp;w'eighs 5 lbs. that an equal bulk of water weighsnbsp;JO lbs. and that an equal bulk of another fluidnbsp;weighs 15 lbs. in which cafe the fpecific gravitiesnbsp;of the folid body, of the water, and of the othernbsp;fluid, are as t, 2, and 3 : Then that body, whennbsp;floating upon water, will difplace a quantity of water which is equal to one half of its bulk, andnbsp;when floating upon the other fluid, it will difplacenbsp;a quantity of that other fluid, which is equal tonbsp;one third part of its bulk. But one half is to onenbsp;third, as 3 is to 2, and thofe numbers are inverfely as the fpecific gravities of water and of thenbsp;other fluid.

6, When a folid is floating upon a fluid, the part immerfed is to the whole folid, as the fpecificnbsp;gravity of the folid is to the fpecific gravity of thenbsp;fluid ; for when the fpecific gravity ot the folid is

equal to that of the fluid, then the folld^.lil'places a quantity of fluid equal in bulk to Itfelf; whennbsp;the fpecifle gravity of the fplid is the half of thatnbsp;of the fluid, then it difplaces a quantity of fluidnbsp;the bulk of ^ which is equal to the half of its ownnbsp;; and lb forth.

7- All bodies retain their whole gravity, when irnmerfed in a fluid �, but that' gravity is eithernbsp;partly or entirely, counterafted by the preflfure ofnbsp;the fluid, according as the' gravity of the im-merfed body is equal to, or difl�rent from, that ofnbsp;an equal bulk of the fluid.

Propofition V|. If a lighter fluid refl upon a heavier, and a body vohoje Jpecific gravity is greaternbsp;than that of the upper, and lefs than that of thenbsp;lower fluid, � remain between them j the part ofnbsp;it ivhick ftands in the upper fluid is to the part of itnbsp;'which Jiands in the lower fluid, as the difference between the fpecific gravity of the lower fluid and thenbsp;fpecific gravity of the body, is to the difference between the fpecific gravity of the upper fluid and thenbsp;fpecific gravity of the body.

The demonftrations of this and of the following propofitions will be found in the notes; to thatnbsp;the reader may, according to his capacity, eithernbsp;examine them, or take the propofitions for granted. (2.)

Cor.

1^8 nbsp;nbsp;nbsp;Of Bydrofat�cf.

Cor. The part L is to the tvhole body, as the dif-ference betzveen the fpecific gravities of the folid and lighter fluids is to the difference between the fpecificnbsp;gravities of the heavier and lighter fluids. (3.)

Propofition

vity is 0; EFG the heavier, whofe fpecific gravity is�r UL is the body, whofe fpecific gravity is c, and which remains with the part U in the upper, and with the part Lnbsp;in the lower, fluid.

It has been fhewn in cor. 3. of prop. V. that if the �weight of a body be divided by the weight which it lofesnbsp;in a fluid (which is the weight of an equal bulk of thatnbsp;fluid) the quotient \yill exprefs the fpecific gravity of thatnbsp;body in comparifon with that of the fluid, which will benbsp;called unity. - Therefore if the weight of the body out ofnbsp;the fluid be divided by its fpecific gravity^ the quotient willnbsp;be the weight of a quantity of that fluid equal in bulk tonbsp;the body. Hence it appears that the weight of the body

is f X U L, that the weight of that quantity of the lower fluid which is difplaced by the part L, is L b, and thenbsp;weight of that quantity of the upper fluid which is dif-piaced by the part U, is U a i therefore nbsp;nbsp;nbsp;nbsp;x

(2.) The laft analogy, by inverfion and compofition, becomes L ; L U :; r � a : b � a.

Confideri�ng that we are furrounded by a thin and invi-fible fluid called air, (as will be more particularly (hewn in the fcquel) in �which we conftantly move and live; itnbsp;follows that a body v/hen weighed in the common way,nbsp;that is, in air, weighs lefs than if it were weighed in vacuo,

Propofitlon VII.' If t%vo fluids he mixed together the bulk of the heavier fluid is to the hulk of �nbsp;lighter, as the difference between the fpecific gravitiesnbsp;cf the mixture and of the lighter fluid, is to tJie

viz. where there is no air j � alfo, that if any fnb � float upon the furface of a fluid in vacuo, upon a

ting the air, the floating body will rife higher above t e � furface, fo that the proportion' of the part immerfed tanbsp;� the whole will be fomewhat lefs than before. The dif-� ference of the parts of a folid immerfed in a fluid, whennbsp;in vacuo, and in open air, may be eftimated in generalnbsp;�nbsp;nbsp;nbsp;nbsp;� Atwood's Dejcrip. of Experiments for a Caurfe

B = the part immerfed when in vacuo; a � the fpecific gravity of the fluid in which thenbsp;folid is immerfed;nbsp;g � the fpecific gravity of air.

xsTnr

_50 nbsp;nbsp;nbsp;Of HydroJiaticS.

ture and of the heavier fluid. �Then as the bulk of the heavier fluids midtiplied by its fpeciflc gra^nbsp;vity, is to the hulk of the lighter fluid midtiplied bynbsp;its fpeciflc gravity, fo is the vo�ight of the heaviernbsp;fluid to the weight of the lighter fluid (3).

The fame thing muft be underftood of two

The fpeciflc gravity of air (viz. j-) is abcfut 0,0013; hence,, by making the computation, it wall appear that thenbsp;exiftence of the air over a fluid in which a folid floats,nbsp;produces a very fmall dift�erence wdth refpecl to the partnbsp;of the folid which is immerfed in the fluid; fo that itnbsp;needs not be regarded, unlefs the utmoft preciflon be required ; in which cafe the adlual fpeciflc gravity of the air,nbsp;as indicated by the barometer, mull be taken into the computation ; for the gravity of the air is continually varying,nbsp;and its aflual quantity is (hewn by the barometer, as willnbsp;be explained hereafter.

It follows likewife, that if two bodies, of different fpe-cific gravities, balance each other in a pair of fcales, their weights are not exactly equal; for if the air were removed,nbsp;that body whofe fpeciflc gravity is leaft would preponderate.

(3.) Let A and B reprefent the bulks of the two fluids, a and h their fpeciflc gravities, and c the fpeciflc gravity ofnbsp;the compound. Then the weight of the compound isnbsp;reprefented by c xA B; the weight of A is reprefentednbsp;by A a, and the weight of B is reprefented by B ; therefore Ac Bf =: Aa-f-; and Be � 'Qb � ha � hc%

folids

This propofition is, however, true only when the bulk of the compound is equal to the fumnbsp;of the bulks of the two components previoully tonbsp;their being mixed, which feldom is the cafe j experience (hewing (as will be particularly mentioned in the fequel) that when two or more bodiesnbsp;are mixed together, a fort of incorporation, andnbsp;fometimes an expanfion, frequently takes place,nbsp;which is attended with a diminution or increalenbsp;of bulk; thus, a pint of fpirit of wine mixed withnbsp;n pint of water, forms a compound which mea-fures lefs than two pints. And a cubic inch of tinnbsp;incorporated, by means of fufion, with a cubicnbsp;inch of lead, will form a mafs which meafuresnbsp;more than two cubic inches.

When fuch increafe or decreafe of bulk does not take place, then we may, by the laft propofition,nbsp;find out the weights of two ingredients whichnbsp;form a compound body, having given the fpecificnbsp;gravities of the ingredients, and of the compound.

CHAPTER III.

T has been already mentioned that the fpecific gravity of a body is the proportion wiiieh itsnbsp;weight bears to the weight of another body ofnbsp;equal bulk.- Thus the fpecific gravity of mercurynbsp;is fakl to be to the fpecific gravity of \vater as 14.nbsp;to one; the meaning of which is, that if a quantity of mercury, which exadly fills a certain veffd,nbsp;and a quantity of water which likevvife exactlynbsp;fills the fame veffel, be weighed feparately, thenbsp;former will be found to weigh 14 times as muchnbsp;as the latter; fo that if the water weighs onenbsp;pound, or one ounce, amp;c. the mercury will benbsp;found to weigh 14 pounds, or 14 ounces, amp;�c.�nbsp;Thus alfo the fpecific gravity of mercury is to thenbsp;fpecific gravity of zinc as two to one; viz. if anbsp;a cubic inch, or a certain veflel full, of mercurynbsp;weigh 14 pounds, a cubic inch, or the fame veffeinbsp;full, of zinc will be found to weigh 7 pounds.nbsp;Or, if the former weigh Too grains, the latter willnbsp;be found to weigh 50 grains; and fo on.

But though bodies may be thus compared in-difcriminately together, yet conveniency has ef-tabliflied the cuftom of comparing all bodies with water, the fpecific gravity of which is reckoned

Of the Specific Gravities of Bodies. 5S-

one, or unity j fo that, fpeaklng of the above-men tioned bodies, the fpecific gravity of mercuiy isnbsp;fald to be 14, and that of zinc, to be 7gt; meaning that equal quantities of -water, of mercury, andnbsp;of zinc, weigh refpeftiveiy J, I4gt;nbsp;nbsp;nbsp;nbsp;7, be they

Nor does this mode of expreffing the fpecific gravities alter the proportion between any two or ' more bodies; for inhance, it has been fald abovenbsp;that the fpecific gravity of mercury is to that ofnbsp;zinc as two to one, and by the laft exprefiion thofenbsp;fpecific gravities have been ftated as 14 and 7 ,nbsp;but thofe two numbers are to each other esaclly

The reafons for which water has been generally adopted as the ftandard with which all othernbsp;bodies are compared, are, ill, that by weighingnbsp;the fame body out of water and in water, the fpecific gravity of that body may, in general, be morenbsp;eafily afcertained than by any other means; andnbsp;adly, that water of the fame purity and of thenbsp;fame fpecific gravity, may be eafily procured in

But the fpecific gravity of water is liable to be altered by two caufes, viz. by the admixture ofnbsp;other fubfiances, and by an alteration of temperature;� water, for Inftance,- at 100� of temperature, is lighter than water at 60�and ftHl lighternbsp;than Water at 40quot;. Therefore .the waier, whichnbsp;ts to be ufed for the purpofe of alcertaining the

fpecific gravities of bodies, muft be free from heterogeneous fubftances, and muft be ufed always at the fame degree of temperature.

Diftilled water, and rain water, are fufficiently pure, and equally ufeful for the above-mentionednbsp;purpole, as they have not been found to differ innbsp;fpecific gravity.

The moft natural ivay of determining the fpecific gravity of bodies is to weigh in a pair of fcales, or by means of a fteelyard, bodies of differentnbsp;forts, but o^ precifely the fame dimenfions; andnbsp;this, indeed, is a very good pradical method fornbsp;fluids, which may be put fucceflively into thenbsp;fame phial, amp;c. j but the difficulty of formingnbsp;folids exadly of the fame dimenfions is fo very'nbsp;great, that their fpecific gravities are generally determined by' weighing each body both out of water and in water, in the manner which will be particularly deferibed in this chapter; excepting fomenbsp;powdery fubftances, which, in this relped, maynbsp;be treated like fluids.

It appears, therefore, that a common pair of fcales, or balance, is the principal inftrument whichnbsp;is required for determining the fpecific gravitiesnbsp;of bodies. It only requires to have a hook affixednbsp;under one of the fcales. This balance, when innbsp;life, might be held in the operator�s hand : but asnbsp;thofe experiments. require a certain time, andnbsp;much accuracy, therefore it is advifable to havenbsp;them fet upon a ftand, fuch as is reprefen ted innbsp;*

%� 14. of Plate X. The whole apparatus, then, for determining fpecific, gravities, which goes under the name of the Hydroftatical Balance and itsnbsp;apparatus^ confifts of the following parts. A ba-lance, fuch as ABCD, fig. H- I�fote X. whichnbsp;foould be fo fenfiblequot; as to turn at leaf! w'ith thenbsp;2oth part of a grain when each fcale is loaded withnbsp;3. Weight of two or three ounces. An accurate fetnbsp;of weights, efpecially of grains, fuch as weightsnbsp;of 10 grains and of' 100 grains, befides the finglenbsp;grains; it being much more commodious to makenbsp;the computation entirely in grains, or at moil innbsp;Ounces and grains, than to be encumbered withnbsp;weights of different denominations. A glafs jarnbsp;E, about 7 or 8 inches high, which is to contain the diftilled or rain-water. A glafs ball, ofnbsp;about an inch, or an inch apd a half in diameter,nbsp;with a bit of fine platina wire, about three inchesnbsp;long, affixed to it¹, A fmall glafs bucket G, with

This ball may be either of folid glafs, or of hollow glafs partly filled with quickfilver, or with fome othernbsp;heavy fubftance. In the latter cafe it generally has a fliortnbsp;perforated llem, into the perforation of which the platinanbsp;wire is faftened with cement. But if it be a folid glafs ball,nbsp;a hole of about fh of an inch in length muft be drillednbsp;in it, wherein the wire is to be faftened. For the fake ofnbsp;expedition in making the computation, it would be propernbsp;to make this glafs ball of a certain weight expreflible by anbsp;round number j for inftance, pf 100, or 5^'^� lOOQnbsp;grains,

a glafs handle. A fmall phial or two, as H; viz. of fuch a lhape as to admit of their being eafilynbsp;filled, emptied, and cleaned. And a thermometer I.

This hydroftatical balance and apparatus is commonly made by the philofophical inftrument-makers of a very compa�: form, fo as to admit ofnbsp;its being packed up in a pretty fmall box; butnbsp;when in ufe, it muft be fet upon a table, as isnbsp;reprefented in fig. 14, where, it muft be remarked,nbsp;that the balance may be moved a little way up ornbsp;down, either by means of the firing which goesnbsp;along the ftand, in the common way, or by fomenbsp;other mechanical contrivance which needs not benbsp;particularly defcribed.

We fhall now proceed to ftate the praftical methods of determining the fpecific gravities of bodies of various fpecies; which methods are nothing more than pradfical applications of the Propofi-tions of the preceding chapter, as will appear bynbsp;obferving at the end of the Rules, the quotationnbsp;of the Propofitions upon which thofe rules depend.

Problem I. To afcerlain the fpecific gravity of a pretty large folid, which is heavy enough to fink innbsp;water.

Rule. Sufpend the folid by means of as flender a thread as may be juft fufficient to hold it, to thenbsp;hook under the fcale C, fo as to hang at the dif-tance of fix or feven inches below that fcale, andnbsp;9nbsp;nbsp;nbsp;nbsp;hy

by putting -ft'eights in the oppo�te fcale D, find out its exaft weight in air, that is out of the water.nbsp;Then place the jar E, about three-quarters fullnbsp;of rain or diftiiled water, juft under the fcale C,nbsp;which is the cafe aitually reprefented in thenbsp;%ure; let the folid body be immerfed in the water, and either by removing fome of the weightsnbsp;from the fcale D, or by putting weights in thenbsp;fcale C, find out its exadt weight in water. Subtract the latter weight Irom the former, and notenbsp;the remainder. Laftly, divide the weight of thenbsp;folid out of the water by that remainder, and thenbsp;quotient will exprefs its fpecific gravity. (Prop.nbsp;T.) � See the precautions which follow the example.

Examp/e, A piece of filver was found to weigh in air (that is, out of the water) 136 grains, andnbsp;in water 123,73 grains. The latter weight beingnbsp;fubtradled from the former, there remained 12,21;nbsp;grains. Laftlyi 136 was, divided by 12,25, andnbsp;the quotient 11,091 expreffed the fpecific gravity of the piece of filver.

Before we proceed any farther, it is neceftary to prevent any poffible niiftake, by the ftatement ofnbsp;the following

General precautions. The water in which the folid is to be weighed, befides its being either dif-or rain water, muft be quite clean.� Itsnbsp;temperature, as well as that of the folid, muft benbsp;^s;iear as poffible to 6 2� of Fahrenheit�s thermometer.

meter; for which purpofe the ball of the thermometer mull be placed in the water, and the temperature is adjufted by the addition of hot or cold water.� If the folid body be foluble in water, ornbsp;if it be porous enough to abforb any water, thennbsp;it muft be varnifhed, or fmeared over with fomenbsp;oily or greafy fubftance ; but in that cafe fome allowance muft be made on account of the varniflr,nbsp;he. �When the folid is weighed in water, its upper part ought to be a little way below the furfacenbsp;of the water; for inftance, about an inch j and itnbsp;muft by no means be buffered to touch the fidesnbsp;or bottom of the jar.�Care muft be had thatnbsp;no bubbles of air adhere to the folid under water;nbsp;for they would partly buoy it up. Thefe may benbsp;eafily removed by means of a feather. � The folidnbsp;muft be of a compa�t form, and tree from accidental or artificial vacuities, fo as not to harbournbsp;any ait; for otherwife its fpecific gravity cannotnbsp;be afeertained by weighing in water, amp;c. Thus ^nbsp;piece of filver, which is much heavier than w'ater,nbsp;may be formed into a hollow fphere, which will appear to be much lighter than w'ater; for if thisnbsp;fphere were immerfed in water, it w'ould difplacenbsp;a quantity of water w'hich is equal not only to thenbsp;filver, but alfo to the fpace which is contained innbsp;the fphere^. � Thefe precautions muft be attended

to * It is for this reafon that a fliip might be made of iron,nbsp;or of copper, or, in fhort, of any fubftance whofe fpecific

well as of the following problems of this chapter, as tar as they may be concerned in them.

Problem II. to afeertain the fpecific gravity rf folids., or compact bodies, that are fufficientlynbsp;heavy to fink in %vater, which are not Joluble in thatnbsp;fluid, hut are too fmall to be tied by means of anbsp;thread.

Rule. Sufpend the glafs bucket G by the interpolation of a thread, to the hook of the fcale C, and find its wfeight in air; then place the fub-ftance, which is to be tried, in it, and weigh itnbsp;3-gain. The former weight fubtrafted from thenbsp;latter leaves the weight of the fubftance in air.nbsp;T! his being done, the fame operation muft be repeated in water; that is, let the loaded bucket benbsp;weighed in water, then remove its contents, andnbsp;Weigh the bucket alone in water. Subtract thenbsp;latter weight from the former, and the quotientnbsp;is the weight in water, of the fubftance undernbsp;examination. Having thus obtained the weightsnbsp;of that fubftance in water and out of water, younbsp;'''ill then proceed according to the precedingnbsp;problem; viz. fubtraft its weight in water fromnbsp;Us weight in air, and note the remainder. Dividenbsp;Us weight in air by this remainder, and the quo-gravity far exceeds that of water; and yet it would floatnbsp;as tydl as a fhip which js made of wood, in the ufual way.

tient

tient will exprefs its fpecific gravity. (Pr�p. V.) � .. Obferve the general precautions at the end ofnbsp;Problem I. p. 57.

By this meads the fpecific gravity of diamonds and other fraall preciou�^ ftones, aamp; alio of grainsnbsp;of platina, of filings of metal, of mercury, See.nbsp;may be afeertained.

Example. The gl'afs bucket being fufpended from the hook of the fcale C, was counterpoifednbsp;by weights in the oppofite fcale D. Some gold-dull; was then placed in it, and by adding morenbsp;weights into the fcale D, its weight (viz. of thenbsp;gold-dufl; alone) vvas found to be 460,6 grains.nbsp;The loaded bucket was then weighed in water,nbsp;and was found to weigh 736,1 grains; and afternbsp;having removed the gold-duft from the bucket,nbsp;the latter by itfelf was found to weigh in waternbsp;300 grains; which being fubtraded from 736,1,nbsp;left 436,1 grains for the weight of the gold innbsp;water. Then this weight of the gold in waternbsp;(viz. 436,1) was fubtraded from its weight in airnbsp;(viz. 460,6) and the remainder was 24,5. Laftly^nbsp;the weight of the gold in air, viz. 460,6 was di-' vided by the remainder 24,5, and the quotient �nbsp;18,8 exprelfed the fpecific gravity of the gold-duft.

Problem III. 'To afcertain the fpecific gravity of a folid body lighter than an equal bulk of voaier, viz.nbsp;fuch as will not fmk in it, ,

Of the Specific Gi'avlties of Bodies. 6i

Rule. Take another body of a compaft form, fgt;ut much heavier than an equal bulk of water, fonbsp;that when this body is conneded with the bodynbsp;in queftion, they may both fink in water. Thisnbsp;prepared, afcertain the weight of the lighternbsp;body in air, and the weight of The heavier bodynbsp;in Water. Then tie, by means of thread, bothnbsp;bodies together, but not fo clofely as to excludenbsp;the water trom, or to harbour bubbles of air, between them; and weigh them both in water.nbsp;Now fince the heavy body is partly buoyed up bynbsp;the lighter body, the weight of both in water willnbsp;be lefs than the weight of the heavier body alone,nbsp;Subtrad the former front the latter, and add thenbsp;remainder to the weight of the lighter body in air ;nbsp;for this fum is the w'eight of a quantity of waternbsp;equal in bulk to the lighter body. Therefore thenbsp;weight of the lighter body in air muft be dividednbsp;by the laft-mentioned fura, and the quotient willnbsp;exprefs the fpecific gravity of the lighter body.nbsp;(Prop. V. Cor. 3, and 4) � Obferve the generalnbsp;precautions at the end of Prob. 1. p. 57.

Example. A 'piece of elm, being varnifned in �rder to prevent its abforbing any w^ater, wasnbsp;found to weigh in air 920 grains. A piece ofnbsp;lead, which was chofen for this purpofe, was foundnbsp;to Weigh in water 911,7 grains. The piece ofnbsp;and the piece of lead were tied together, andnbsp;being fufpended from the hook of the fcale C,

amp;;c.

See. in the ufual manner, were found to weigh in water 331,7 grains, viz. 580 grains lefs than thenbsp;lead alone; therefore 580 was added to 920 (vi2.nbsp;to the weight of the elm in air) and made up thenbsp;fum of 1500. Laftly, 920 was divided by 1500,nbsp;and the quotient 0,6133 expreffed the fpecificnbsp;gravity of the piece of elm.

It is almoft fuperfluous to obfer\'e, that the fpe-cific gravities of bodies that are lighter than water, are lefs than unity.

Problem IV. To afeertain the fpecfic'gravities of fmall bodies (fuch as faline powders, i^c.) which arenbsp;foluble in, or abjorb, water, and are not capable ofnbsp;being varnfiied.

Rule. The fubftance in queftion muft be reduced into fine powder, unlefs it be already in that fliape. Take a clean glafs phial, fuch as H, fig.nbsp;14, put it in one of the fcales of the balance, andnbsp;counterpoife it by placing weights in the oppofitenbsp;fcale ; then fill the phial w'ith the pow'd;r in queftion, ramming it as clofe as poflible, and quite upnbsp;to the top. This done, replace the phial in thenbsp;fame fcale in which it flood before, and by addingnbsp;niore weights in the oppofite fcale, find out thenbsp;exaft weight of the powder alone. Now removenbsp;the powder from the phial, fill the latter with dif-tilled or rain water, and placing it in the fcale asnbsp;before, afeertain the weight of the water alone.nbsp;By this means you have the weights of equalnbsp;quantities of the powder and of water, which

lt;:ific gravity of water is not in this cafe exprefled hy unity ; therefore fay, as the weight of the water IS to the weight of the powder, fo is unity tonbsp;s tourth proportional, which is the fpecific gravitynbsp;the powder when that of water is reckonednbsp;^nity; that is, divide the weight of the powdernbsp;hy the weight of the water, and the quotient willnbsp;exprefs the fpecific gravity of the powder.

In certain cafes the faline fubftances or other fmall bodies, if the reducing them to powder benbsp;objefted to, may be weighed in the bucket, according to Problem II. but inftead of water theynbsp;muff be weighed in fome other fluid, in which theynbsp;are not foluble, and whofe fpecific gravity is already known i for the fpecific gravities thus foundnbsp;may be eafily referred to that of water.

Example. The phial H full of a certain fait was fouird to weigh 630 grains (meaning the faitnbsp;alone, independent of the phial) and the fame phialnbsp;full of rain-water was found to weigh 450 grains,nbsp;(viz. the water alone) ; therefore 630 was divided

Rule. This may be done either by the method ^aft-mentioned, which indeed is the moft proper.nbsp;It being the moft accurate, for nice experiments jnbsp;or in the following manner ;

Sufpend the glafs ball F, fig. 14, or a piece of metal, to the hook of the fcale C, and find fuc-ceffively its weight in air, its weight in water, andnbsp;its weight in any other fluid you wifli to try. Sub-trad: its weight in water from its weight in air,nbsp;and the retnainder is its lofs of weight when weighed in water. Alfo fubtrad its weigiit in the othernbsp;fluid from its weight in air, and the remainder isnbsp;its lofs of weight in the other fluid. Novy- thofe 'nbsp;two laft weights are exadfly as the fpecific gravities of the two fluids refpeedively. But the fpecific gravity of water is not, in this cafe, expreflednbsp;by unity; therefore fay, as the lofs of weight innbsp;water is lo the lofs of weight in the other fluid,nbsp;fo is unity to a fourth proportional; that is, dividenbsp;the lofs of weight in the other fluid by the lofs ofnbsp;w'eight in water, and the quotient will exprefs tirenbsp;fpecific gravity of the-Other fluid.

For this purpofe a glafs ball with a bit of platina wire, are preferable to other fubftances, becaufe-amongft all the variety of fluids there are fewernbsp;that have any adion upon glafs and platina thannbsp;upon any other-folid; yet they are corroded bynbsp;one or two fluids, and therefore when thefe are tonbsp;be tried, the method of Problem IV. mull benbsp;adopted j but^the phial muft confitl of fuch a fub-ftance as is not liable to be corroded by the fluidnbsp;c]ueftion; or the glafs phial may be lined in

Of the fpecific Gravities of Bodies, 65 done by warming the phial ; for this film will

Example. A glafs ball which weighed 100 grains in air, was found to weigh 60 grains in water, and 70 grains in another fluid ; fo that thenbsp;lofs of weight in water was 40 grains, and the lofsnbsp;of Weight in the other fluid was 30 grains; therefore 30 was divided by 40, and the quotient 0,75nbsp;exprelTed the fpecific gravity of the other fluid.

The knowledge of the fpecific gravities of bodies is of the utmoft confequence in philofophy, 3nd in other fciences, as alfo in the feveral arts,nbsp;which depend on thofe fciences. Independent ofnbsp;thofe bodies which are pretty unifornii, and whofenbsp;fpecific gravities are well known, it frequentlynbsp;happens in chemiftry, in the practice of feveralnbsp;arts, and in fome departments of civil fociety,nbsp;that the fpecific gravities of various bodies, efpe-cially of compounds, muft be a�tually afeertainednbsp;on particular fpecimens. The ftrength and adi-vity of divers chemical articles is accompanied withnbsp;a proportionate degree of fpecific gravity; there-

* The fpecific gravity of air, and other elaftic fluids analogous to air, is afeertained by firfl: filling a phial withnbsp;Water and weighing it, then filling the fame with the

daftic fluid in queftion, and weighing it again, after the Wanner of Problem IV, j but the phial which is necef-fary for the purpofe of confining elaftic fluids, as alfo thenbsp;mode of filling it, will be deferibed hereafter,

66 C)f the Jpeeific Gravities of Bodies, fore the knowledge of the latter is ufed as an indication of the former. The ftrength of fpirits isnbsp;determined both in diftilleries, and by the officersnbsp;of the excife, from their fpecific gravities. Thenbsp;aflayers and the refiners of filver and gold frequently make ufe of the fame means for determining the quality of their articles, and fo forth.

This extenfive ufe of the knowledge of fpecific gravities has produced a variety of contrivances,nbsp;under the names of Ejfay infrument. Hydrometer,nbsp;Areometer, Gravimeter, and Pefe-liqueur, for the pur-pofe of afcertaining the fpecific gravities of differentnbsp;bodies in an expeditious manner.

The conffruftion of all thofe inftruments depends upon the principle of the 5th Propofition of the preceding chapter, viz. that if a body wholenbsp;fpecific gravity is lefs than that of certain fluids,nbsp;be caufed to float fucceffively upon thofe fluids,nbsp;it will fink deeper into the lighter than into thenbsp;heavier fluid. Or that a greater addition ofnbsp;weight is required to keep the fame part of thenbsp;floating body below the furface of a heavier, thannbsp;of a lighter, fluid.

The fimplefl hydrometer is reprefented in fig. 13. of Plate X. It confifts of a graduated rod or ftem,nbsp;CA, about 4 Inches long, which is fixed to thenbsp;bulb A. From the loweft part of A another flemnbsp;proceeds a fliort way, and terminates in a fmallernbsp;bulb B. The bulb B is partly or entirely fillednbsp;with fomc metallic fubftance, generally quickfilver,

Of the fpecijic Gravities of Bodies. 67 ^hich anfwers two purpofes^ it renders thejnftru-tnent juft heavy enough to fink as far as fome part ofnbsp;the ftem CA below the furface of the fluid whichnbsp;is to be tried by it; and it ferves to keep the in-fl-tunient upright in the fluid j hence it is placedjnbsp;as ballaft, in the loweft part of the inftrument.

Now when the fpeciflc gravity of a fluid is to determined, the fluid is put into a glafs jar,nbsp;or other convenient veflel, and the hydrometer isnbsp;fet to float in it; then the fpeciflc gravity of thenbsp;fluid is indicated by the number of the divifionsnbsp;of the ffcem AC which remain above the furfacenbsp;of the fluid j or (which amounts to the famenbsp;thing) by thofe which remain below that furface ;nbsp;thofe divifions being made, by trial and adjuft-ment, to reprefent parts of the whole bulk of tlienbsp;inftrument, Suppofe, for inftance, that the bulknbsp;of the whole inftrument be equal to 1000 cubicnbsp;tenths of an inch, and that each of the divifionsnbsp;�of the ftem reprefencs one of thofe parts. Thennbsp;if this inftrument be placed firft in one fluid andnbsp;flien in another, and if it be found to fink as farnbsp;the 40th divifion (counting from the top) innbsp;one fluid, and as far as the 30th in the other fluid.

It is evident that of the 1000 parts of the bulk, have been funk in the former fluid, and 970nbsp;in the latter; therefore, fince the fpeciflc gravitiesnbsp;of thofe fluids are inverfely as the parts immerfed,nbsp;tee fpeciflc gravity of the former is to that ol thenbsp;Utter as 570 is to 960. If water be one of the

fluids, for inflance the former j then fay, as 970 is to 960, fo is one to a fourth proportional, whichnbsp;is the fpecific gravity of the other fluid when thatnbsp;of water is called unity. But the divifions on mofl;nbsp;of thofe inftruments are numbered fo as to indicate immediately the fpecific gravity of a fluid innbsp;comparifon with that of water, which is reckonednbsp;one.

Hydrometers of the above-mentioned fort have been made of glafs for fuch fluids as corrode metals ; and of metal, which is more durable, fornbsp;fuch fluids as have no adion upon it. But its pe- �nbsp;culiar imperfedtions are two in number; ifb. It cannbsp;ferve only for thofe fluids which differ very littlenbsp;in fpecific gravity; for if die divifions of the flemnbsp;reprefent fmall portions of the bulk of the inftru-ment, then the whole length of the ftem will like-wife reprefent no great part of the whole bulk;nbsp;hence very little difference of fpecific gravity cannbsp;be indicated by all the divifions which are upon -it; and if the divifions. reprefent confiderablynbsp;large portions of the inftrument, then the Inflru-ment will not indicate fmall differences of fpecificnbsp;gravity, adly. The inequalities of the ftem, and .nbsp;the fmall quantity of fluid, which in the commonnbsp;manner of ufing the inftrument can hardly be ;nbsp;prevented from adhering to that part of the ftemnbsp;which is juft above the fluid, render it inaccurate 'nbsp;in a greater or lefs degree.

The

The removal of the firft t)f thofe imperfections has been attempted either by adapting differentnbsp;ftems to the fame inflrumenc; fo that a heaviernbsp;or a lighter item might be put on, according tonbsp;the nature of the fluid under examination; or bynbsp;affixing certain weights to the inftrument, and al-tering the value of the divifions accordingly.

The fecond imperfeCtion has been removed by removing the divifions from the ftem, and indeednbsp;by this means the firft imperfedion is in greatnbsp;meafure removed j viz. the ftem contains one mark,nbsp;about its middle, and the inftrument is caufedtonbsp;fink always to that mark in different fluids, by thenbsp;addition of different weights. Then the fpccificnbsp;gravities are indicated by thofe weights.

The weights in fome hydrometers are fcrewed to, or fimply laid in a cup fit to receive them atnbsp;the bottom of the inftrument. In others thenbsp;weights are placed in a cup which is fixed on thenbsp;top of the ftem, and which of courfe remains outnbsp;of the fluid. But as the laft method is apt to render the inftrument top-heavy; therefore fome of,nbsp;them have been conftruefed with two cups, viz.nbsp;one at top and another at their lower part; andnbsp;proper weights are to be placed in both, viz-, thenbsp;ooarfcft or Urged in the lower, and the minuted innbsp;*^be upper cup,

buch inftruments have alfo been ufed for determining fpecific gravities of fmall folids. In

this cafe the folid is placed in the lower cup, and fuitable weights are put into the upper cup.

. Another inftrument has alfo been ufed for expe-ditioully determining the fpecific gravities of fluids. It confifts of a feries of glafs bubbles, increafingnbsp;and decreafing in fpecific gravity from thenbsp;ftandard fluid, in a known ratio. When a fluid isnbsp;to be tried, thofe balls, which are all numbered,nbsp;mufl; be placed fucceffively in the fluid, and it willnbsp;be found that fome of them will fink to the bottomnbsp;of the veflel, whilfl; others will remain on the furfacenbsp;of the fluid; but that bubble which is precifely ofnbsp;the fame fpecific gravity with the fluid, will remainnbsp;in any part of it, without fhewing any tendencynbsp;either to afcend or to defcend.

All thofe inftruments muft be reckoned Inferior to the hydroftatical balance and apparatus, and thatnbsp;on various accounts, which will eafily occur to anynbsp;reflecting mind. Expedition of operation, andnbsp;portability, are the only circumftances wdiich havenbsp;recommended them. But the ufe of the balancenbsp;is by no means long and intricate; and it is un-queftionably the leall equivocal. With refpeft tonbsp;portability, it muft be obfep'cd that no Angle hydrometer, even 6f the beft fort known, can be ufednbsp;for afcertaining the Ipecific gravities of all forts ofnbsp;bodies; and if many of them mufl; be had in rea-dincfs, then the bulk of them all will more thannbsp;eoual that of a tolerably ufeful balance and apparatus. Therefore we may conclude with affirming�

that the hydroftatical balance and apparatus is upon the whole the moft accurate, the moft durable, and the moft portable apparatus for the purpofenbsp;of afcertaining fpecific gravities in general; andnbsp;that the ufe of hydrometers may be recommendednbsp;to fuch perfons only as are obliged to try a greatnbsp;Variety of fluids which do not vary much in gravity; viz. to diftillers, to. officers of the excife, amp;c.

Thus far I have endeavoured to give a Ihort but comprehenfive account of the inftruments, which,nbsp;befides the balance, have been contrived for thenbsp;purpofe of afcertaining fpecific gravities. A particular defcription of them all is incompatible withnbsp;the nature and limits of this work. But if the reader be defirous of examining the particular con-ftrudtions and ufes of fuch inftruments, he maynbsp;confult the books which are mentioned in thenbsp;note¹.

In determining fpecific gravities of bodies, diffe-I'ent experimenters have ufed water of various, and Sometimes of unknown temperatures; generally how-

Boyle�s Works, quarto edition of iyya, vol. IV. p. aOij.�piii], Tranfaftions, vol. 36,'vol. for 1793, p- 164.

'�Memoirs of the Adanchefter Society, vol. i.�Ramfden�s Account �f Experiments to determine the Spec. Grav. ofnbsp;�^luids; London, 1792.�Annales de Chimie, vol. 21.�.nbsp;Bauni�s Elem. de Pharmacie.�Nicholfon�s Journal ofnbsp;Alat, Phil. No, I. III.�^De Prony�s Architecture Hydrau-hquc, from � 614 to � 626,

ever, between the 50th and 65th degree of Fahrenheit�s thermometer. But the beft tables of fpecific gravities have been formed at the temperature eithernbsp;of about 5 5� or 60�.

A confiderable difference does frequently appear in thofe tables between the ftatements of the fpecific gravities of the fame bodies. This differencenbsp;fonietimes affeds even the firft decimal figure; innbsp;one table, for inftance, we find that a certain body isnbsp;2,135, and in another table that it is 2,245.nbsp;evident that this difference cannot be attributed tonbsp;the different fpecific gravities of avater at thofe temperatures ; for that difference will not affed evennbsp;the third decimal figure ; but it mull be attributednbsp;to other caufes, the principal of which are the ini-perfedion of the inftruments with which the bodiesnbsp;are weighed, and the various qualities of the bodiesnbsp;themfelves, which are occafioned by innumerablenbsp;and often apparently trifling circumftances. Hencenbsp;it follows that in forming a table of fpecific gravities the greateft care fhould be had to attain thenbsp;utmoft degree of accuracy; but in the ufe of fuchnbsp;a table, fome latitude muft be allowed to the pofli-ble error in the ftatement of the fpecific gravities, innbsp;proportion as the conftitutions of the bodies arenbsp;more or lefs variable.

The following table has been formed by comparing the beft tables of fpecific gravities now extant ; by confulting the works of the beft authors who have treated of particular fubftances; and by

OJ the Specific Gravities of Bodies. 73

*^peating feveral of their experiments. But after it muft be acknowledged, that the difBculty ofnbsp;reconciling the different difcordant ftatements, and

obtaining genuine fpecimens for aftual experiments, is fo very great, that the utmoft diligence ^'11 not be fufficient to obtain certainty and pre-cifion*. The reader will find the fubftances arranged in the following manner. The metallicnbsp;fubftances occupy the firft place; thefe are followednbsp;by the earths and ftones �, then come the inflara-mable, the vegetable, the animal, and laftly thenbsp;fluid fubftances,�When a fubftance is ftated withnbsp;two fpecific gravities, the meaning is that the fpe-cific gravity of that fubftance is various, viz. fome

� If the reader be defirous of examining this fubjecl in a �nore particular manner, he may confult Dr. Davis�s excellent Paper on Specific Gravities, in the Phil. Tranf.nbsp;vol. XLV. p. 416; or in the Abridg. vol. X. p. 206. Thisnbsp;paper contains all that which had been done previous to thenbsp;year 1747, relative to the fubjelt;a.�M. Briffon�s Tables ofnbsp;Specific Gravities.�M, de Prony�s Archit. Hydr.�Mr.nbsp;Gilpin�s excellent Tables of the weights, amp;c. of mixtures ofnbsp;fpirit and water in different proportions in the Phil. Tranf. fornbsp;the year 175^, page 275.�Kirwan�s Mineralogy, fecondnbsp;edit�I do not refer the reader to a vaft number of othernbsp;tables, whfth are either lefs correft, or copied from thenbsp;abovementioned works. With refpetft to the gravity ofnbsp;^ir under different degrees of preffure, as alfo of heat, amp;c.nbsp;be may perufe a moft valuable paper of Col, |ioy, in thenbsp;i'bil. Tranf. vol. LXVlI.

fpecimens of it are heavier than others, but between the annexed limits. When that variation is notnbsp;very great, then the mean fpecific gravity alone isnbsp;expreffed. In felefting the articles for the followingnbsp;table, I have reje�led moft of tiiofe which occurnbsp;lefs frequently, or whofe fpecific gravity is toonbsp;fiudjiating; and for a fimilar reafon the expreffionsnbsp;of the fpecific gravities have been extended to anbsp;greater number of decimals with certain fubftancesnbsp;than with others.

TABLE of the Specific Gravities of different Subftances at the Temperature of 6o� Fahr.nbsp;Therm.; unlefs fome other Temperature be ex-prefsly mentioned,,

tlie fame formed into a plate by being compreflcd through thenbsp;[ rollers of a flatting-mill -nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;22,069

of the Engllfii ftandard, being 22 carats fine, fufed, but not hammered ------nbsp;nbsp;nbsp;nbsp;- - 18,888

of the Englifli guinea nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;17,629

of the ftandard of the French coin in Gold/nbsp;nbsp;nbsp;nbsp;being 21^ carats ^

of the French ftandard for trinkets in the 3fear 1780 being 20 carats .nbsp;fine, fimply fufednbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;'nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;15,709

the fame hammered nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;_nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;,nbsp;nbsp;nbsp;nbsp;15,774

of the Spanifti coin in the year 1780 17,655 of the Portugal coin in. the yearnbsp;^nbsp;nbsp;nbsp;nbsp;1780nbsp;nbsp;nbsp;nbsp;-------- 17,966

The finenefs of gold, or the proportion of alloy (that �s, of other metal) it contains, is reckoned by imaginarynbsp;'^'eights, called carats. The whole mafs is conceived tonbsp;divided into 24 equal parts, viz. 24 carats, and the pu-'��T of the fpecimen is-expreffed by the number of caratsnbsp;�f pure gold it contains. T- hus gold of i8 carats fine,nbsp;�^eaiis a compound of 4¹ ths of pure gold, and ths ofnbsp;fome other metal; � gold of 22 carats fine, containsnbsp;v|ths of pure gold and _\ths of alloy; and pure gold isnbsp;Calfd gold of 24 carats fine.

Of the, Specific Gravities of Bodies.

*3.375

lt; '

Brafs, being a compound metal, varies between -------

� The fpecific gravity of mercury varies a little with various fpecimens ; but the proportion at different degreesnbsp;of heat is nearly the fame; the bulk of mercury increafingnbsp;by the quantity 0,000102. for every degree of heat; itsnbsp;bulk at 32� being called one or unity.

f Such is the ufual fpecific gravity of copper, reckoned pure; but it is frequently found of fuperior gravity. Bergman found the fpecific gravity of Swedift copper to benbsp;9.3243; but this may poffibly be a mifiake ; for he like wifenbsp;fets the. fpecific gravity of iron at 8,3678, which is con-fiderably higher than the beft ftatements.

the pureft from Cornwall, limply f 7,170 fufed-f ------nbsp;nbsp;nbsp;nbsp;- 2 75291

The expanfion of fteel in hardening, befides its being indicated by the decreafe of fpecific gravity, is alfo de-cifively fljewn by the following experiment of Adr. Robertnbsp;I^enniiigton. � A piece of fteel which when foft mea-Lred in length 2,769 inches, after being hardened bj'nbsp;plunging it red-hot in cold water, was found to meafurenbsp;^gt;7785; and after having been letdown to a blue temper,nbsp;mcafured 2,768 inches.

t Gellert affetts that the fpecific gravity of the tin of Lallicia in Spain is 7,063.

This fp. gr. has been ftated on the authority of Muf-chenbroek and Bergman ; but Briffon ftates it at 5,7633.

t This fpecific gravity refts upon the authority of Elhuyari. It may poffibly be a miflake. See Kirwan�snbsp;Mineralogy, fecond edit. vol. 2, p. 308,

Lapis lazuli - nbsp;nbsp;nbsp;--nbsp;nbsp;nbsp;nbsp;--nbsp;nbsp;nbsp;nbsp;--nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;Snbsp;nbsp;nbsp;nbsp;2.,76o

Hyalite or Lava Glafs nbsp;nbsp;nbsp;- -nbsp;nbsp;nbsp;nbsp;- _nbsp;nbsp;nbsp;nbsp;.nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;a,no

Barofelenite - - - - _ Lapis hepaticus , - - _nbsp;Talk, common, or Venetian �'

Oriental pearls - nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;- -nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;��2,683

- 1 , f native - nbsp;nbsp;nbsp;--nbsp;nbsp;nbsp;nbsp;--nbsp;nbsp;nbsp;nbsp;--nbsp;nbsp;nbsp;nbsp;- 2,035

white flint nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;_ about 3,306

common plate - nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;- about 2,760

PorcelainSeres - nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;- - -2,145

Plaftic gum, or Caoutchouc, commonly ) q go., called India rubber ----- 9nbsp;Camphornbsp;nbsp;nbsp;nbsp;- 0,988

Gum arabic - nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-1,452

Gum tragacanth nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;,-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;- 1,316

Pry ivory - nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-1,825

Heart of oak, 60 years old - nbsp;nbsp;nbsp;�nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;- 1,170

Trunk of afh - nbsp;nbsp;nbsp;--nbsp;nbsp;nbsp;nbsp;--nbsp;nbsp;nbsp;nbsp;--nbsp;nbsp;nbsp;nbsp;-- 0,845

Beech wood - -- -- -- -- 0,852 Alder wood -nbsp;nbsp;nbsp;nbsp;--nbsp;nbsp;nbsp;nbsp;--nbsp;nbsp;nbsp;nbsp;--nbsp;nbsp;nbsp;nbsp;-- 0,800

, nbsp;nbsp;nbsp;5

Foplar wood - nbsp;nbsp;nbsp;--nbsp;nbsp;nbsp;nbsp;--nbsp;nbsp;nbsp;nbsp;--nbsp;nbsp;nbsp;nbsp;-- 0,383

�^hitc Spanifir poplar wood - - - -0,529 �nbsp;nbsp;nbsp;nbsp;�nbsp;nbsp;nbsp;nbsp;Apple

Quince tree nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;--nbsp;nbsp;nbsp;nbsp;--nbsp;nbsp;nbsp;nbsp;--nbsp;nbsp;nbsp;nbsp;--nbsp;nbsp;nbsp;nbsp;cgt;j793

Dlftilled

Sea Water ¹ - nbsp;nbsp;nbsp;--nbsp;nbsp;nbsp;nbsp;--nbsp;nbsp;nbsp;nbsp;--nbsp;nbsp;nbsp;nbsp;--nbsp;nbsp;nbsp;nbsp;1,026

^3-phtha - nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;--nbsp;nbsp;nbsp;nbsp;--nbsp;nbsp;nbsp;nbsp;--nbsp;nbsp;nbsp;nbsp;0,814.7

SS PJ the Specific Grcnnties.of Bodies�

Ewe�s milk - nbsp;nbsp;nbsp;--nbsp;nbsp;nbsp;nbsp;--nbsp;nbsp;nbsp;nbsp;--nbsp;nbsp;nbsp;nbsp;--nbsp;nbsp;nbsp;nbsp;1,04�'

* The rectification of fpirits (whether from wine, or rum, or malt-liquor, for it feems to be all the fame thing)nbsp;has been carried to a very great degree of perfection, bynbsp;means of repeated How diftillations, together with the addition of alkaline falts, which have a very great power ofnbsp;abforbingthe aqueous part of the liquor.. The lighted: fpirit,nbsp;which I find recorded, was ufed in France, by Chauflier, thenbsp;� fpecific gravity of which is ftated at 0,798, See 1�Ency-clopedie M�thodique, art. Alcohol, In England it has beennbsp;obtained, not without extraordinary care and attention, ofnbsp;the fpccific gravity 0,813.nbsp;nbsp;nbsp;nbsp;Tranf. vol. for 179c,

p. 324. But with moderate attention it may be conftantly obtained of the fp. gr. 0,82514, and of this quality was thenbsp;fpirit which was ufed by Mr. Gilpin in his experiments fornbsp;the conftru�tion of his very accurate Tables, wherein, fornbsp;conveniency�s fake, the trifling fracSHon 0,00014 was omitted (fee the Phil. Tranf. for the year 1790, article XVIII;nbsp;for the year 1792, art. XXII; and for the year 1794, art.nbsp;XX.); from which the above fpecific gravities of water, ofnbsp;fpirit, and of the mixtures of water and fpirit, have been ex-tracSled.

Of the Specific Gravities of Bodies. 89

Spirit xafed for tire Tables which are in-1 o 82c ferted in the Phil, Tranf. for 1794 - J

Proof-fpirit, according to the Englifli Ex-. cife Laws* - nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;--nbsp;nbsp;nbsp;nbsp;--nbsp;nbsp;nbsp;nbsp;--nbsp;nbsp;nbsp;nbsp;0,916

Specific Gravities, at different Temperatures, of Spirit, whofe Specific Gravity at 60� is 0,825.

^^5� nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;--nbsp;nbsp;nbsp;nbsp;--.....0,83214

S5� nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;--nbsp;nbsp;nbsp;nbsp;-- --nbsp;nbsp;nbsp;nbsp;-- - 0,82736

The laft-mentioned gentleman having procured a fpcci-nren of fpirit of fuperior levity, its fpecific gravity being �5814196 at 60� of temperature, endeavoured to afcertainnbsp;what addition of water it might require in order to equal hisnbsp;ftandard fpirit j and upon trial found that when 1000 grainsnbsp;of it were mixed with 45 grains of water, the fpecific gra-�vity of the compound was 0,825153, which maybe confider-as exadlly equal to that of his ftandard fpirit. Phil.nbsp;Pranf. for 1790^ p.

* From the beft interpretation of the exifting Adis �f Parliament, it feems that the fpecific gravity of what isnbsp;Called prsoffpirit-, is 0,916; and that it coiififts of iconbsp;parts of redtificd fpirit of the fpecific gravity o,8255,and 62nbsp;parts of water by meafure, or 75 by weight; the whole atnbsp;60� of heat. (Dr. Blagdcn�s Report, Phil, ft rani, for I79^gt;

P' 3390

90 Of the Specif c Gravities �f 'Bodies.

Real Specific Gravities of Mixtures of Spirit (of the above-mentioned Quality) and Diftillednbsp;Water, at different Temperatures.¹

By'reul fpedjic gravitle^y are meant the fpecific gravities found by actual tri.il, and not thofe which might have been computed from the quantities of the ingredients. The latter do not agree with the former, on -C¹ count of the incorporation or lofs of bulk which takes place. See page 51.

Of the Specific Gravities of Bodies. 91

52 nbsp;nbsp;nbsp;0/ the Specific Gravities of Bodies.

Heat.

Of the Specific Gravities of Bodies. 93

Heat.	55grains of fpirit	5ograinsof fpirit 45 grains of fpirit		4.0 grains of fpirit
Heat.	to lOO grains of water.	to 100 grains i of water.	to 100 grains of water.	to 100 grains of water.
30�	0,96470	0,96719	0,96967	0,97200
35	0,96315	0.56579	0,96840	0,97086
40	0,56159	0,96434	0,96706	0,96967
45	0.95993.	0,96280	0,96563	0,96840
5�	0,95831	0,96126	0,96420	0,96708
55	0.05662	0,95966	0,96272	0,96575
60	0,95493	0,95804	0,96122	0.96437
65	0,9531�	0.9563s	0,95962	0,96288
70	0,95139	0.95469	0,95802	0=96143
75	0,94957	0,95292	0,95638	0,95987
80	0,94768	0,95111	0,95467	0,95826
85	0.94579	0,94932	0,95297	0,95667
90	0,94389	0.95748	0,95123
95	0,94196	0,94563	0,94944	0,95328
100	0,93999	0.94368	0,94759	0.95152

Of the Specific Gravities of Bodies. 9^

Niuriatic ether - nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;0,7296

�'at 0� of heat 0,001393 at 32� of heat 0,001299nbsp;ry in the barometer j at 60� of heat 0,001220nbsp;eing 29,75 .high,nbsp;nbsp;nbsp;nbsp;212� of heat 0,000938

The fpecific gravity of common air is not conftantly the fame. It increafes when the mercury rifes in the barometer, and vice verfa. Air is alfo expanded by heat, and

Azotic gas¹ ² - Sarometer at 29,75 Oxygen gas² - barometer at 29,75nbsp;Hydrogen gas² - barometer-at 29,75 ²��

Carbonic acid gas² barometer at 29,75 Nitrous gas² - barometer'at 29,75nbsp;Ammoniacalgas² barometer at 29,750,000706

Befides fliewing the comparative gravities of bodies, which are to be feen by bare infpeftlon, the great ufc of a table of fpecific gravities is for afcer-taining the real weights of bodies, and that without adlually weighing them, when their dimenfionsnbsp;are known, according to what has been alreadynbsp;explained in page 43. But for this purpofe it isnbsp;neceffary to know the real weight of a determi-

is contracted by cold, -though not regularly ; the greatefi; expanfion taking place between the degrees 52� and 72� ofnbsp;Fahrenheit�s thermometer, and the leaft at about aiaquot;.nbsp;But the expanfion for the fame degrees of heat alfo variesnbsp;according to the quantity of moifture in the air, and to thenbsp;altitude of the mercury in the barometer. When this altitude is 29gt;75 ^�^'1 the air' is in a mean Hate of moifture,nbsp;it then receives an addition of 0,484 to its bulk by the heatnbsp;of 212�; viz. a given meafure of air at 0� becomes 1,484nbsp;nieafureat 212% in which cafe the mean rate of expanfion

Thofe gaffes, or artificial airs, are, befides the influence of prefl'ure and heat, more fludfuating in their fpecific gravities. The above ftatements muft be underftood of theirnbsp;pureft ftates. �

nate bulk, of one of the fubftances that are mentioned in the table. Now finee water has been af-tumed as the ftandard of comparifon for the Iped-fic gravities of all other bodies, it will be more convenient to know the real weight of a certain,nbsp;^tiantity of water, v'vi.. a cubic inch, or a cubicnbsp;of than of any other body.

Though at firft fight it may appear eafy to determine the real weight of a certain bulk of water, yet the reader may reft affured, that this determination is attended with very great difficulties,nbsp;which arife from the imperfeeftions of the balance,nbsp;of the weights, of the meafures which are employed for meafuring the bulk, amp;c.� From the moftnbsp;accurate experiments, performed with the beft in-ftruments, and with all the precautions which thenbsp;prefent ftate of philofophical knowledge can fug-gefl:, it has been afeertained that a cubic inch ofnbsp;thftilled water at the temperature of 60� weighsnbsp;^52,576 grains troy; 5760 of which grains arenbsp;equal to one pound troy.¹

This weight has been calculated- for the temperature of boquot;, from the ftatement of Sir George Shuckburg Evelyn�s elaborate paper in the Phil. Trans, for the year 1798;nbsp;where, after the recital of his numerous experiments, thisnbsp;author exprefles himfelf thus � � In conclufipn if appearsnbsp;� then that the difference of the lengths of two pendulums,nbsp;� fuch as Mr. Whitehurft ufed, vibrating 42 and 84. timesnbsp;� in a minute of mean time, in the latitude of London, at

- The general rule for determining the real weight of any fubftance which is mentioned in thenbsp;preceding table, when its bulk is known, and isnbsp;exprefled in cubical inches, or by any other di-rnenfion which may be reduced into inches, is asnbsp;follows. Multiply the weight of a cubic inch ofnbsp;water by the number of cubic inches which ex-fnbsp;prelTes the bulk of the body in queftion, and multiply the produft by the fpecific gravity of thenbsp;body in queftion. The laft produft exprefles thenbsp;real weight of the body.

Thus if it be propcfed to determine the weight lof 10 cubic inches of carbonic acid gas, which isnbsp;the laft fubftance but two in the table, and w^iofe ,nbsp;fpecific gravity is 0,001682; multiply the weightnbsp;of a cubic inch of water by ten, and the produdtnbsp;will be 2525,76 ; then multiply this produdt bynbsp;0,001682, and the product 4,2483283, will exprefsnbsp;the weight in grains of ten cubic inches of carbonic acid gas, .viz. 45 grains nearly, at the temperature of 60quot;, and when the barometer ftands atnbsp;29,75 inches.

113 feet above the level of the fea, in the temperature of 60�, and the barometer at 30,inches, is = 59,89358 in-� ches of the parliamentary llandard; from whence all thenbsp;9 rneafures.of fuperficies and capacity are deducible.�

That agreeably to the fame fcale of inches, a cubic inch of pure diftilled water, when the barometer is atnbsp;29,74 inches, and thermometer at 66�, weighs 252,422nbsp;lt;5 parliamentary grains; from whence all the other weightynbsp;�f ajay be deriyed.�

Hitherto we have explained the equir librium of fluids, or the properties of fluidsnbsp;a quiefcent ftate. It is now neceffary to ex-^�Tilne the laws which relate to the fame when innbsp;niotion.

Fluids, like follds, are pofleffed of the general properties of matter, fuch as have been ftated andnbsp;^huftrated in the firft part of this work; andnbsp;amongft thofe general properties the inertia, andnbsp;the force of gravity have been fliewn to form thenbsp;foundation of the dodrine of motion. It hasnbsp;been obferved that in pradical cafes the theoretical laws of motion cannot be verified to a- greatnbsp;degree of exadnefs, on account of the fluduatingnbsp;^Tfiftance of the air, and of the fridion betweennbsp;various moving parts of contiguous bodies.nbsp;Fut befides thefe, fluids are.obftruded in their mo.-dons by the attradlon, adhefion, or vifcidity,nbsp;amongft their own particles; by their adhefion ornbsp;^ttradion to other bodies, and likewife'by fomenbsp;other circumftances which have not yet been fuf-hciently inveftigated.

The extenfive application of the fubjed, agd the imperfe(5t ftate of knowledge relatively to it,nbsp;w 2nbsp;nbsp;nbsp;nbsp;fug-

fuggefl. to perfons of fdence the neceffity of in-ftituting a long and ferious experimental invefti-gation, which, in addition to the difcoveries and, experiments that have been already made by manynbsp;able perfons, would much contribute to the advancement of the theory, and would prove verynbsp;beneficial to mankind in various refpeds, as innbsp;the conftruftion of hydraulic machines, conftruc-tion of (hips, navigation, amp;c.

The only plan which we can at prefent adopt, is, to ftate in a compendious manner the principalnbsp;propofitions which relate to the motion of fluids jnbsp;then to point out fonie of the deviations from thenbsp;theoretical rules which experience has clearly fhewn ;nbsp;and, laftly, to refer the inquifitive reader to thenbsp;works of the beft authors who have written pro-,nbsp;fefledly on the fubje�t.

Propofition. I. ^he forces of a fluid medium on a 'plane cutting the direBion of its motion with differentnbsp;inclinations fuccejflvely, are as the fqtiares of the finesnbsp;ff thofe inclinations.

Let IKCH, fig. 15. Plate X. reprefent a fluid, for inftance, the water of a river moving from IKnbsp;towards GH ^ and let GB reprefent the edge ornbsp;feftion of a plain furface, fituated in the water,nbsp;perpendicular to the furface of the water, but inclined to the direftion of its motion, fo as to makenbsp;an angle DBG with it, which is called the angle ofnbsp;incidence, or of Inclination,

Draw

Draw the quaclrantal arch ABF, make AG perpendicular to the direftion of the fluid, andnbsp;from B drop BD perpendicular to AG. Thennbsp;or its equal GB is the radius, and GD is thenbsp;of the angle of inclination DBGi Now w�nbsp;have to prove that the force of the moving fluidnbsp;^Pon the plane is as the fquare of the fine DG jnbsp;that if, in the fituation which is reprefentednbsp;hy the figure, the fine or line GD meafure fournbsp;and the preflTure of the water upon the planenbsp;he equivalent to 21^ pounds} then, when the planenbsp;fituated at another inclination GT, where thenbsp;hiie GS meafures 3 feet, the pretTure of the waternbsp;Ppon the plane will be equivalent to la pounds jnbsp;frgt;r the fquare of 4 is 16, the fquare of 3 is 9, andnbsp;iS is to 9 as 21 .f is to 12. Alfo when the planenbsp;hes in the fituation GF, which is in the diredtionnbsp;the motion of the fluid, then the preffure uponnbsp;Vaniflies, or becomes equal to nothing.

In order to prove this propOfition it muft be re-^olledted, that, according to the laws of oblique ^tnpuKes, the force is to the efledt as radius is tonbsp;the hue of inclination, (fee chap. VIII. of Part I.).nbsp;'Therefore in the prefent cafe, if the fame quantitynbsp;�f Water fell upon� the plane in the fituation AG,nbsp;in the fituation GB, the preflures upon the planenbsp;tn thofe two fituations would be as AG to GD.

it is evident that in the fituation AG a greater ^�nantity of the fluid falls upon the plane, than in thenbsp;tuation GB} for in the latter fituation the part

ADBC

ADBC of . the ftream does not meet the plane: hence it is farther evident that the quanties of water which fall upon the plane in thofe two fitua-tions, are as AG to GD, and thofe different quantities of fluid muft prefs forward with forces pro- -portionate to their quantities-; viz. as AG to GD :nbsp;but the preflures on the plane are, on account ofnbsp;the inclinations only, as AG to GD : therefore, innbsp;confequence of both thefe caufes combined together, the prefTures on the plane in the two fitua-tions are as AG multiplied by AG, to GD multiplied by GD; viz. as the fquare of AG (which isnbsp;the radius, or fine of the perpendicular diredion)nbsp;to the fquare of the fine GD. And the famenbsp;reafoning is evidently applicable to any other inclination of the plane.

It is alfo evident that the efFedt or preflfure on the plane is the fame, whether the ^lane ftands ftiflnbsp;and the fluid moves, or the fluid is at reft and thenbsp;plane is moved towards IK in a diredion parallelnbsp;to its original fituation; viz. with the fame in-,nbsp;clination.

Now in this explanation we have omitted feveral interfering circumftances; we have not taken noticenbsp;of the particles of w'ater after they have touchednbsp;the plane; for thofe particles, after that meeting,nbsp;muft go fomewhere. They cannot return towardsnbsp;IK, for that would be prevented by the currentnbsp;of the fluid; yet they form fome oppofition otnbsp;impediment to the current, and that oppofition

Varies according to the velocity of the current, and the inclination of the' plane. The water thereforenbsp;'vhich falls upon the plane muft flow over the edgenbsp;of the plane at B, and-in a direlt;5tion which croflesnbsp;the original- dire�lion of the ftream, as is indicatednbsp;'oy the figure; and it thus forms another impedi-�^vnt to the motion of the ftream, which contributes to alter the law which is expreffed in thenbsp;Pmpofition. The effect of this laft fort of ob-ftru�tion is fubjed to very great variations, whichnbsp;'^^pend upon the diftance of the bottom and fidesnbsp;of the veffel, or banks �f the river, from the plane ;nbsp;^pon the quality of the fluid; but, principally,uponnbsp;the velocity of the ftream; for when the ftreamnbsp;tnoves with very great velocity, the water, which,nbsp;after having flruck the plane, flows over the edgesnbsp;6f it, has no time to go quite behind the plane,nbsp;but is preffed forward by the water that follows,nbsp;^ud, inftead of going behind the plane, it tends tonbsp;Carry away, by the adhefion or vifcidity of itsnbsp;parts, the water which it already finds behind thenbsp;plane, (fee fig. 16, Plate X.) ; hence the preffurenbsp;the plane is increafed confiderably ; becaufe innbsp;that cafe, the plane, befides its being preffed on onenbsp;hde, is alfo fupported lefs on the other fide.

We have alfo omitted to take into the account the effed of fridion, which arifes from the adhe-hon of the water to the plain furface, and fromnbsp;the attradion amongft the particles of the water:

but thofe caufes of obftruflion cannot be eafily fubjeded to calculation, fince they depend uponnbsp;Qther fluduating 'caufes; fuch as the nature,nbsp;purity, and temperature of the fluid, the naturenbsp;of the plane, and the velocity of the motion.�nbsp;It is in Confequence of this adhefion or fridion,nbsp;that the plane fuffers fome degree of preflure, evennbsp;when it ftands in the diredion GF, viz. in the di-redion of the ftream.

It therefore evidently appears, that the theory of the motion of fluids depends on fome certain,nbsp;and upon other fluduating caufes, which rendernbsp;the inveftigation of it extremely difficult and perplexing.

Thefe remarks on the various caufes which render the refult of experiments different from the dedudions of the theoretical propofitions, are alfonbsp;applicable in a greater or lefs degree to the follow-ing profitions;

Propofition II. If inclimtian of the plane^ in. the conJiru8ion of the preceding propofition, remain thenbsp;fame, and the velocity of the fluid varies, then thenbsp;prejfure on the plane varies as the fqiiare. of the velocity.

Thus, if, when the water moves at the rate of 2 feet per fecond, the preflure on a certain fixednbsp;plane is equivalent to 10 pounds; then, wffien th^nbsp;water moves at the rate of 5 feet per fecond, thenbsp;preflure will be equivalent to 625 pounds j for the

Square of 2 is 4, the fquare of 5 is 25, and 4 is to 25, as 10 pounds are to 621 pounds.

If in equal times the fame quantity of water ftruck the plane with different velocities, the pref-fures would be as the velocities; viz. a double velocity would produce a double effedt, a treble velocity a treble effefl; gt; becaufe the momentum isnbsp;^qual to the produd of the quantity of matter bynbsp;the velocity j and, according to this fuppofition, thenbsp;quantity of water is the fame. But it is evidentnbsp;that when the velocity is double, a double quantity of water will ftrike againft the plane in annbsp;equal portion of time; hence the preffure isnbsp;doubled on account of the velocity, and againnbsp;doubled on account of the double quantity of water ; fo that upon the whole the preffure becomesnbsp;as 2 multiplied by 2, or as the fquare of 2. � Fornbsp;the fame reafon, when the velocity of the water isnbsp;trebled, the preffure is as three times 3,' or as thenbsp;fquare of 3 ; when the velocity is quadrupled, thenbsp;preffure is as the fquare of fourand, in ihort, thenbsp;preffure on the, plane will be as the fquare of thenbsp;Velocity.

However, on account of the above-mentioned caufes of obftruftion, this increafe of preffure, innbsp;proportion to the fquare of the velocity, is by nonbsp;uieans very regular, nor will it proceed beyond anbsp;certain limit.

The refult of this propofition is evidently the fame, whether the plane be fuppofed to remain

fixed and the fluid to move, or the fluid be fup-pofed to be at reft and the plane to be carried through it with the fame invariable inclination.nbsp;� The fame thing muft likewife be underftood ofnbsp;heavy bodies defcending in fluids.

Propofition III. If planes of different dimenfi-ons move with like inclinations, but with different velocities, and in different fluids; the preffiire upon each plane ^vill be as the produEl zvhich arifes by multiplying thefquare of the velocity by the area of the plane,nbsp;and by the denjity of the flidd belonging to that plane.

For it is evident from the preceding Propofition that when the areas of the planes and the fluidsnbsp;are alike, the preffures are as the fquares of thenbsp;velocities j and it is alfo evident, that, if the furfacenbsp;of the plane be doubled, (which makes it equal tonbsp;twice the original plane,) or trebled, (which makesnbsp;it equal to thrice the original plane,) amp;c. the pref-fure, or its equal, the fquare of the velocity willnbsp;likewife be doubled or trebled, amp;c. Alfo thisnbsp;doubled or trebled fquare of the velocity muft benbsp;again multiplied by thedenfity of the fluid ; for .anbsp;fluid which weighs twice, or three times, or anynbsp;other number of times, as much as another fluid,nbsp;muft produce a double,.or treble, or other proportionate, effeft.

In praftical cafes of this fort the refult of experiments has been found to differ confiderably from the theoretical calculations, which differencenbsp;is produced by the above-mentioned fluduatingnbsp;caufes.

Ncn-elqflic Fluids in Motion. . 107 Tims far we have confidered the quantity ofnbsp;Preffure which fluids in motion exert upon planes,nbsp;planes in motion receive from fluids at reft.nbsp;The particulars relative to the elFefts which arenbsp;produced by that preflure, may be eafily fuggeftednbsp;die recolleftion of wnat has been already ftatednbsp;and explained in the firft part, refpeding the effects of dired and oblique impulfes; yet it will benbsp;of ufe to afllft that recollecfion, by briefly obferv-pig, that a. body which receives an imprelTion fromnbsp;^ fluid, will be driven (or, which is the fame thing,nbsp;die body muft be fupported) in a diredion whichnbsp;either diredly oppofite, or differently inclined,nbsp;according as the diredion of the preflure is dirednbsp;or inclined in a greater or lefs degree.

Thus let ABHI, fig. i. Plate XI, reprefent a current of water from H to A; let D reprefent the upper edge of a body with a flat furface, lying perpendicularly into the water, and held by means of, ropesiat E. Now in this fituation, the current willnbsp;exert its full and dired force againfl the plane fur-face of the body; and if the ropes be let go at E,nbsp;die body will be driven down by the current,nbsp;'^�ithout deviating one way or the other. But ifnbsp;the faid body be fituated in a diredion oblique tonbsp;the ftream, as at Iq and be held by means of ropesnbsp;at G ; the force of the current will drive it againfl;nbsp;the fide of the river as at K, and a lelTer powernbsp;'vill be required at G to prevent the body beingnbsp;driven away with the ftream. In this cafe the

force of the ftream upon the body muft be re-f folved into two forces, viz. LM and MF, thenbsp;former of which is counteradled by the power atnbsp;G, whilft the latter, drives the body towards thenbsp;bank of the river, (fee chap. VIII. of Part I.). Butnbsp;if, when the body is at F, the ropes be let go at G,nbsp;then the body will be driven down by the current,nbsp;nor will it run towards the bank; for in this calenbsp;the body, by moving with the water, will be at reftnbsp;lelatively to it, and of courfe it will not receivenbsp;any impreffion from it.

It is in confequence of the fame principle that the fhip AB, fig. 2. Plate XL is impelled in the di-reftion from A towards C, by the wind which blowsnbsp;from W towards H, upon the oblique fails FG,nbsp;DE. But in this cafe of a fhip, it muft be remarked, that befides the fails, the wind blows alfo upon,nbsp;the body of the fhip, upon the ropes, mafts, amp;C;nbsp;which are not oblique to the diredion of the wind ;nbsp;in confequence of which the veffel is partly impelled towards H ; and, in fad, this will be found tonbsp;move in the line DK, though the diredion of thenbsp;body of the veffel be always parallel to AB. Thenbsp;diftance CK, viz. of the place in which the fhipnbsp;is adually found after a certain time, from that innbsp;which it ought to have been according to its original diredion AB, is called lee-way and thisnbsp;iee-way is proportionately greater, the more thenbsp;wind is inclined^ to the fails.

Non-elajiic Fluids iu Motion. nbsp;nbsp;nbsp;109

The fame principle likewife explains the aftlon �f the rudder in turning the fhip; for when thenbsp;ftip AC, fig. 3, Plate XL is in motion from Anbsp;towards C, if the rudder be fituated in the diredionnbsp;oblique to the keel, the water falling obliquely Upon it, impels it towards E, and of courfe thenbsp;^ead C of the Ihip will be turned towards D. Butnbsp;'vhen the thip is becalmed, the fetting of the rud-�^er aflant to the keel will have no power to turnnbsp;the fliip, becaufe the fliip being at reft with refpedbnbsp;to the water, no impulfe can take place, (i.)

(�.) The method of eftimating the force of the wind Upon the fails of a Ihip, or of a windmill} alfo the force ofnbsp;the water upon the rudder of a fliip in motion, or upon thenbsp;gates of a lock, or fluke in a river, amp;c.' is derived fromnbsp;Propofition IL of this chapter. But this force or prefliirenbsp;of the win^^upon the fails of a windmill, mull; not be mif-^ken for that force which turns the axis of the mill; nornbsp;tUufl: the force of the water upon the rudder of a ftiip benbsp;Uiiftaken for the force which actually compels the fliip tonbsp;turn; for the latter is only a part of the former, as will henbsp;^ewn by what follows.

Fhe force of wind^ which Jirtkes upon the fail, to turn the Pxis of a windmill-, or the force of the water which Jirikesnbsp;�goinJi the rudder, to turn the Jhip, is as the product of thenbsp;ffine multiplied by the fquare of the fine of the inclination ofnbsp;fail to the wind, or of the rudder to the dire�lion of the

Let AB, fig. 4. Plate XI. reprefent the axis of a wind-?ulll, and DC one ofits fails, fituated in the direction EC, inclined

Of the Aclions of

It is in confequence of the effeds which atifa from the different obliquity of impulfes, that bodies of the fame weight and bulk, but of differentnbsp;flrapes, will move through a fluid with more or

Through any point G in the line GC, draw a line GE perpendicular to CE, and through the point E, where GEnbsp;meets CE, draw EF perpendicular to GC. Then GC isnbsp;the radius, GE is the fine, and EC is the cofine of the angle GCE, viz. of the inclination of the fail to the wind.nbsp;Therefore, by Propofition II. of this chapter, the force ofnbsp;the wind upon the fail, when this is placed diredly oppofitenbsp;to it, is to the force of the wind upon the fail, when this is

placed in the oblique direction EC to it, as GCf is to G�!*. But the force in the diredlion GE is refolved into twonbsp;forces, viz. EF and GF, the latter of which being parallelnbsp;to the axis, cannot contribute to turn it round ; but thenbsp;force FE, being perpendicular thereto, is employed entirely in turning the axis or the fail round. Now the force

:: (making the radius GC equal one, or unity) (Jtf: GEfxEC^rthe cofine multiplied into the fquare of thenbsp;fine of the angle of inclination GCE; which produtSI,nbsp;therefore, expreffes that part of the force of the wind uponnbsp;each fail of the windmill, which contributes to turn thenbsp;axis of the mill round.

Non-elafiic Fluids in Motion. 111

freedom. Thus it has been calculated, that a cylinder going in the dired;ion of its axis, andnbsp;^ fphere of the fame diameter, move in the famenbsp;with the fame velocity, the refiftance to thenbsp;Motion of the the cylinder will be double to that

Since,'when th� fine of an angle increafes, the cofine de* '^feafes, and vice verfa; therefore there is a limit, at whichnbsp;produa of the cofine by the fquare of the fine is thenbsp;�'�sateft, or maximum. This limit, or this maximum, isnbsp;^^fily afcertained by the method of fluxions, and is donenbsp;�'� the following manner.

Making the radius=:i, and putting k for the cofine EC, be have, (Eucl. p. 47. B. I.) �g]�= i�which multiplied by the cofine x, becomes x�= to the force of thenbsp;Mnd upon each fail, to turn the axis of the mill. Sincenbsp;fluxion of a maximum is rto; therefore, when x�x� isnbsp;^maximum, its fluxion x�; or x~2,x^Xt whichnbsp;'lividcdby x, becomes i=3x�': hence x�^�\-, andxrav'IT

� 0,23856062 = 9,76143938, which is the logarithmic Cofine of 54�. 44'. 8quot;. Therefore the moft advantage-fituation of the fail with refpeft to the directionnbsp;the wind, or the fituation in which the wind has thenbsp;Si'eateft power to turn the fail and the axis of the mill round,nbsp;�s when the diredlion of the fail makes an angle GCE ofnbsp;54�- 44'. 8quot;, with the diredtion GC of the wind.

The fame fort of demonftration is applicable to the power which the impreflion of the water on the rudder of anbsp;in motion, has to turnthe fliip.nbsp;fig* 5. Plate XI. AD reprefents part of the ftip, B

iiz nbsp;nbsp;nbsp;Of the Actions of.

of the globe; which principally arifes from the former prefenting its flat bafe to the fluid; whereas the latter prefents a curve furface which receivesnbsp;the fluid obliquely. Bodies of the fame bulk, butnbsp;of other different fliapes, have been likewife fub-

its rudder fituated in the oblique pofition EC. The direction of the water is from G towards C, fmce the veflel moves in the contrary diredtion. Therefore the waternbsp;flrikes againfl: the rudder at an angle of inclination GCE,nbsp;which, fince the keel of the fliip is parallel to CG, is equalnbsp;to the angle SEC, which the rudder makes with the keel.

From any point G, in the line CG, drop GE perpendicular to CE, and from E drop EF perpendicular to CG. Then CG is the radius, GE is the fine, and CE the cofine,nbsp;of the inclination of the rudder to the keel, or to the direction of the water. Now the direct force of the water, is tonbsp;its oblique force upon the rudder, as (JGI^ is to GEV ; thenbsp;latter of which being refolved into the two forces EF and GF,nbsp;it is evident that EF is the only force which can contributenbsp;to turn the fhip ; for GF, being parallel to the keel, cannbsp;have no power upon it. Then GE : EF ;; GC : CE;

Non-elctj�ic Fluids in Motion. nbsp;nbsp;nbsp;113

je�led to calculator) with refpefl to the refinance quot;'hich they receive from moving fluids. Xhe fhapenbsp;of a body which will move through a fluid with thenbsp;greateft freedom poffible, has alfo been calculated ;nbsp;tiot the refults of aftual experiments have beennbsp;found to differ confiderably from the theoretical determinations j nor can we at prefent form any rulesnbsp;fufficient to afcertain thofe differences, fince they depend upon a variety of flu�tuating, and not, as yet,nbsp;fully afcertained caufes. If the reader be defirousnbsp;t^f examining the fubjedi: ftill farther, he may con-folt the works that are mentioned in the note *.nbsp;nbsp;nbsp;nbsp;.

51-�. 4-4.'. 8quot;.

For the fame reafons fuch muft likewife be the angles Bed, a CD, fig. 6. Plate XI. which the gates of thenbsp;lock C D E make with the fides of the canal A C B �, innbsp;urder that they may fuftain the greateft preffure they are capable of, from the water on the fide A CDE B.

* Archimedes de injidentibus humido. Mariotte on the rf^Ption of water and other fluids. Lamy de Pequilihre desnbsp;i'jueurs. Newton's principia. Gulielmini�s menfura aqua-fiuentmm. Gravefand�s phi!. Mnflchenbrock�s phil.nbsp;Bwitzej.gt;5 hydroft'. Varignon�s diflert. in the Mem. Acad,nbsp;^cien. The works on fluids of Belidor, Defoguliers, Clare,nbsp;rPorfon,, Boflu, D�Alambert, Buat, amp;c. De Prony�snbsp;Hydrauliq ue. The report of the committee ofnbsp;Society for the Improvement of Naval Architedlure.nbsp;Pndon 1794. Venturi's experimental enquiries on thenbsp;^�^eral communication of motion in fluids, Phil. Tr. amp;c.

I niall cpnelude this chapter by an obfervation relative to the fituation of the floating bodies them-felves.

It is of great confequence innavaj architedture, in navigation, amp;c. to determine not only the quantitynbsp;of a given floating body, which will remain im-merfed, and that which will remain out of the fluid ;nbsp;but likewife the pofition in which that body willnbsp;place itfelf. The full examination of this fubjednbsp;would require a great many more pages than we cannbsp;conveniently allot to itj we fhall therefore brieflynbsp;mention the two general principles only, upon which �nbsp;the fubjedt depends *,

I ft. A floating hody will remain at reft upon a fluid, with that part of its furface downwards which liesnbsp;near eft to its centre of gravity ] hence an homogeneous fphere will reiriain v.'ich that part of its furfacenbsp;downwards, with which it happens to be firft fituatednbsp;in the fluids for the centre of gravity of a fphere isnbsp;equally diftant from every point of the furface. Andnbsp;a cylinder will reft with its axis parallel to the furfacenbsp;of the fluid, amp;c.

ad. When a body floats upon n fluid, and remains at reft thereon, then the centre of gravity of the partnbsp;immerfed will lie perpendicularly under the centre ofnbsp;gravity of the part which remains out of the fluid.�nbsp;For if you imagine that the body is divided into

Non-elaftic Fluids b} Motion. � 15

parts, even with the furface of the fluid �, it is e vident that if the upper part be removed, the lowernbsp;part will afeend a little j and on the other hand, if thenbsp;^ower part removed, the upper will defeend anbsp;Httle into the fluid ; therefore thofe two endea,voursnbsp;Counteraft each other. And that they counteraftnbsp;^ach other in the fame perpendicular lipe paffingnbsp;through their centres of gravity, is alfo evident; fornbsp;otherwife the upper part would defeend on one fide,nbsp;and the lower would afeend on the other j that is,nbsp;^he body would not remain at reft, which is contrarynbsp;the fuppofition¹.

Upon this conhderation it may be eallly conceived that � amp;ny body, regular or irregular, might remain with that partnbsp;of its furface which is nearefl: to its centre of gravity, out ofnbsp;the fluid (contrary to the firft principle) provided that centrenbsp;^fid the centres of gravity of the two parts; viz. of thatnbsp;'vithin, and of that without the fluid, flood in the famenbsp;Perpendicular line. But the difficulty of placing and ofnbsp;P�'eierving them in that line is fo very great, that this caf?nbsp;inay .]jg reckoned impracticable.

OF THE ATTRACTION OF COHESION, OS. CAPILLARY ATTRACTION ; AND OF THE ATTRACTION OFnbsp;AGGREGATION.

Before we proceed any farther in the enumeration of the phenomena which relate to the motion of fluids, it will be neceifary to lay downnbsp;the refults of the principal experiments which havenbsp;been made concerning the attraftion of cohefion, asnbsp;alfo of aggregation, and to explain them in the beftnbsp;manner we are able; for by this means the readernbsp;will in fome meafure be enabled to comprehend hownbsp;far thefe attraflions are concerned in the movementsnbsp;of fluids, and how it happens that the a�lual motions of fluids through pipes, channels, holes, amp;c.nbsp;are confiderably different from thofe which mightnbsp;be derived from the general theory of motion.

The attraction of aggregation, is that which takes place amongft the homogeneous particles of thenbsp;fame fort of fubftance; and the attra�lion of cohefion,nbsp;is that which takes place between the particles ofnbsp;heterogeneous bodies. See the latter part of chap. I.nbsp;and the beginning of chap. II. of the prefent part.nbsp;_The principal fads which have been obferved relatively to thofe attractions, are as follows.

The globular form of the drops of rain ; the tuning of two drops of water into each other, when they

laid fo near as to touch, and a variety of other phenomena, render this attraftion very manifeft.

If. There is an attraction between water and glqfs, 'tvhich is increafed by cold, and diminijhed by heat; butnbsp;cateris paribus, proportionate to the quantity of thenbsp;S^�gt;face of contact.

If the breath from the mo�th be thrown upon a plate, it will be found to adhere to it longer innbsp;^old, than in hot, weather.

If a drop of water be laid upon glafs, it will pre-ferve a convex furface on the fide fartheft fronr the glafs, but on the neareft fide it will adapt itfelf tonbsp;*^he furface of the glafs, and will adhere to it with anbsp;certain degree of force �, but if the fame drop benbsp;fpread over the furface of the glafs, it will then lofe-Its convex furface, and will adhere to the glafs withnbsp;much greater force, as may be proved by endea-''^ouring to fbake it off in both cafes. By the dif-pstfion, the particles of water are placed much far-Ilgt;er from each othergt; hence their mutual attradtionnbsp;diminilhed ; and on the other hand the attraftionnbsp;l^ftween the water and the glafs is increafed bynbsp;leaving augmented the furface of contaft.

In either of thofe cafes the water is attradled by glafs on one fide only. But if another piece ofnbsp;glafs be placed facing the former, and in contaftnbsp;'''ith the film of water, then the water will be at-^^afted and retained with greater force j and if thenbsp;ater be encompaffed on every fide by glafs, as if itnbsp;be enclofed in a narrow glafs tube, then the attrac-

tiori will be ftronger Hill, becaufe the quantity df contaft in proportion to the quantity of water, i�nbsp;thereby confiderably increafed. By this means thenbsp;dttraftion is rendered fo very rnanifeft, that the denomination of capillary aitraSion has been fuggeft�dnbsp;by this more ufual mode of trying fuch experi-tnertts j which is by means of tubes, whofe bore isnbsp;about as fine as a hair, which in Latin is callednbsp;capillus.'

Put feme wat�r in a gkfs veflel, as in fig. 7. Plate XI and near the furface �f the glafs the waternbsp;Will be found to rife a little way, forming a curve,nbsp;as at A and B.�The like ef�eft will take place ifnbsp;yoii dip part �f a piece of glafs in water, as at Cnbsp;and D.�This efieft may be explained in the following manner;

Let AB, fig. 8. Plate XI. reprefent a feAion of the furface of a piece of glafs, having its lower part im-inerfed in the water BC. Imagine this furface to benbsp;divided into a niimbet of indefinitely fmall parts a, b,nbsp;c, d, amp;c. Then the paft a, next to the furface of thenbsp;water B C, will raife a quantity of water proportionate to its attractive force; but this quantity ofnbsp;water is thereby brought nearer to the part b of thenbsp;glafsi hnd is therefore attracted by it, whilfl: anothernbsp;quantity of water takes its place next to a. Again,nbsp;the firft quantity of Xvater being raifed to b, isnbsp;brought nearer to the part c of the glafs, hence it isnbsp;attracted by it, and is raifed to the place c, whilftnbsp;the quantity of watef at a takes its place, and an-7nbsp;nbsp;nbsp;nbsp;,nbsp;nbsp;nbsp;nbsp;Other

In confequence of this attraftion, the water ought form a film equally thick, or the quadrilateralnbsp;%urc ghas, on the furface of the glafs. But it muftnbsp;'^onfid'ered, that befides the attraftion towards glafs.nbsp;Water is poflTeiTed of the attradion of aggregation jnbsp;^iz. ofche attraftion of its particles towards each other jnbsp;confeqtience of which, when the firft quantity ofnbsp;'''^ter has been raifed to the place another quan-of water r is kept fufpended, in confequence ofnbsp;attraffion of water to water, between the waternbsp;and the water B C. When the glafs has at-^tafted the water to h, the part s will be enlargednbsp;into t z, becaufe the two quantities of water, a andnbsp;K can keep fufpended a greater portion of water,nbsp;than the quantity a by icfelf. Thus the water willnbsp;^feend along the furface of the glafs, and will re-tnain adhering thereto, in fuch quantity as to formnbsp;^ counterpoife to the attradfion of the glafs j viz.nbsp;the preflure of the water thus raifed, and the attrac-tion between it and the water B C, are all together anbsp;Counterpoife to the attradtion of the glafs.

The real afeent of the water, which in fig. 8. has ^oen enlarged for the fake of illuftratipn, when thenbsp;glafs is either flat, or not much bent, feldom exceedsnbsp;Cue tenth of an inch. But this altitude is increafednbsp;diminifhed by a variety of circumftances; viz. bynbsp;temperature and purity of the water, by the quality of the glafs, and moftjy by the polilh and clean-Hnefs of its furface,

I 4 nbsp;nbsp;nbsp;Place

Place a glafs bubble A (that is, an empty glafs ball) fig. i6. Plate XI. in a glafs veffel not quitenbsp;full of water. This bubble will float on the furfacenbsp;of the water, and it will be found to run fpontaneouflynbsp;�towards the fide of the veflel, as at B, to which itnbsp;will adhere with a certain force ; provided, however, the bubble, on being laid upon the water,nbsp;be not fituated too far from the fides of thenbsp;ve.fiel.

This efFedl is owing to the attradlion of the elevated water on the fide of the veffel, and that on the furface of the bubble. Thus the water at i is at-tradted both by the water at s and by the water at d,nbsp;which tends to bring thofe three parcels of waternbsp;together, and of courfe the glafs bubble alfo, whichnbsp;adheres to the water d. And this attradtion growsnbsp;ftronger and fironger in proportion as thofe pointsnbsp;come nearer to one another.

It is for the fame reafonthat if two glafs bubbles be placed upon w^ater, at no great diftance fromnbsp;each other, they will run towards each other, andnbsp;will adhere with a certain degree of force.

If the glafs veffel be filled, fo that the water may projedb above the edge of the vefftlj and a glafsnbsp;bubble be then laid upon it, as in fig. 17. Plate XI.nbsp;the bubble will be found to recede from the fides ofnbsp;the veffel. In this cafe the elevated water lt;2, whichnbsp;is contiguous to the fide A, is attradted lefs powerfully than the elevated water by the water of thenbsp;Veffel i for on account of the convexity at A, the

'''�a.ter between A and a, is not fo near to the elevi-t'on a, as an equal-furface b'Q o�water on the other fide of the bubble, is to the elevation h.

The perfendicular rife if water in glafs titles is ^^i'verfely as the diameter.� if glafs tubes opened atnbsp;both ends, be immerfed wit!� their lower aperturesnbsp;in Water, as in fig. 9. Plate XI. the water will in-ftantly rife fpontaneoufly into their cavities, and itnbsp;has been found that it will rife higher in narrowernbsp;than in larger tubes, by as much as the uiameter ofnbsp;^he larger tube exceeds that of the fmallcr ; the al-in a tube of one hundredth part of an inchnbsp;(viz. 0,01) in diameter, being about 5,3 inches.nbsp;Therefore in a tube of 0,02 in diameter, the altitude of the water will be the half of 5,3, viz 2,65nbsp;Inches in diameter, Alfo in a tube, whofe diameternbsp;is 0,1 of an inch (or ten times 0,01) the altitude ofnbsp;file water will be the tenth part of 5,3 ; viz. 0,53 ofnbsp;inch j and fo forth ¹.

Diveis

Since the diameters of the tubes are Inverfely as the al-*'ludes of the water within their cavities, it you call the dia-'Usters D, d. and the altitudes of the water A, rr, it will be d \ a �. k \ whence AD � ad\ that is, the produclnbsp;the diameter bv the altitude of the'water is always thanbsp;or the conftant quantity 0,053 of an inch ; for whennbsp;^he diameter is 0,01 of an inch, the water has been found tonbsp;file in It to the altitude of 5,3 inches; and 553x0,01 isnbsp;sq'Jal to 0,0^3,

Divers ingenious perfons who have examined thofe phenomena of capillary attraction, findingnbsp;that the bulks of the lufpended pillars of v/ater arsnbsp;not proportional to the furfaces of glafs with whichnbsp;they are in contad, have been induced to offernbsp;llrange hypothefesj which were neither warrantednbsp;by analogy, nor could they account for the phenomena. Dr. Jurin (Phil. Tranf. N. 355, and 363)nbsp;fuppofed that the real caufe of the fufpenfion ofnbsp;water in tubes is the attradion of the fmall annularnbsp;portion of the infide of the tube, to which thenbsp;upper furfice of the water is contiguous and coheres. Dr. Hamilton (in his Effays) fuppofes thatnbsp;the pillar of water is fupported by the attradioiinbsp;of the annulus contiguous to the bottom of thenbsp;tube.

Therefore, when you wilh to know how high will the water rife in a tube of a given diameter, you need only divide 0,053nbsp;nbsp;nbsp;nbsp;diameter, and the quotient expreffes the

altitude in inches, very nearly; for this altitude is alfo influenced by the various temperature, by the nature and clean-linefs of the glaf, amp;c.

The furface of a cylinder is as the produd of the diameter ' multiplied by the axis (or by the altitude j) but it has beennbsp;lliewn abovej that in the part oi the tube which is occupiednbsp;by the water, the proilud of the diameter by the altitude is anbsp;eonftant quantity ; therefore the furface of tlie glafs whichnbsp;is in contact with fuch a pillar of water, is likewifo a con-iliUit quantity^

pi'Oportionate to the whole furface of the ^ is in contaft with the column of water ; (fornbsp;point or particle of that furface is endowednbsp;an equal atcraftive power) and the preffure ofnbsp;^he fufpended water is equivalent to it; or it is anbsp;'-Ounterpoife to it. Without attempting to deter-the diftahcc from the furface of the glafs tonbsp;'''^ich the attraftive power may reach, it is cleatnbsp;^^3t a film of water of a certain thicknefs niuft benbsp;'^'ithin that attraftive power all round the inOde lur-of the tube, as high as the top of the pillar;nbsp;the reft �f the water which fills up the cavdty ofnbsp;tube, is attached to that film, and is kept fuf-pended by it, in confeqtience of the attrafldon ofnbsp;Water to water; yet the v/hole column of v/ater isnbsp;�Kept up by the attraftion of the glafs, and is a coun-terpoife to that force.

Thus if a piece of iron be fufpended to a mag-in virtue of their mutual attraftioni and a piece of lead is faftened to the iron ; it is evident thatnbsp;though the magnet has no attraftion whatever to-'''2rds the lead �, yet the piece of lead and iron together are kept up by the attractive force of thenbsp;^^gnet, and form a counterpoife to it ; hence, ifnbsp;the weight of the lead be increafed beyond anbsp;Certain degree, the whole will drop off from thenbsp;fnagner.

In the like manner the preiTi-re of the column of Water in the tube is equivalent, or it is a counter-i^oife, to the attractive force of the furface of the

elafsj which is in contaft wi h it; and of conrfe \t is proportionate to that furface. But in eftimatingnbsp;the quantity of that counterpoife, or of the preffurenbsp;of the column of water, we mufh take, befides thsnbsp;quantity, the altitude alfo, into the account; he-caufe, cteteris farihiis, fluids prefs in proportion to

varies, or in different cylindrical pillars, the preffures are as the produdls of the quantity of matter by thenbsp;altitude of each pillar refpedlively. Therefore thenbsp;preffure of the pillar of water in a glafs tube, whichnbsp;is a coun'erpoife to the attradlion of the glafs, isnbsp;the produft of the quantity of water by the altitude jnbsp;and in cylindrical tubes, this produdl is always proportional to the furface of glafs in contait withnbsp;the vrater ¹. This may be rendered more intelligible by means of an example.

Let the infide diameter of a tube BC, fig. 12. Flute XL be double that of the tube D F 5 then thenbsp;pillar of water FE will be two inches high whennbsp;the pillar AC is one inch high. Since the contentsnbsp;of cylitiders of the fame altitude are as the fquaresnbsp;of their refpedlive diameters, and their furfaces are

It has been fhew'n in the preceding note, that the furface of the glafs tube which is in contact with the pillar of water,nbsp;is a conftant quantity; therefore the produdi: of the quantitynbsp;of water by the a'titude of the pillar, muft likewifc be anbsp;conilant quantity; fince it is as the above-mentioned fur-face.

Of the AttraSlion of Cehefon, iAc, 125 finnply as their diameters, it is eafily calculated thatnbsp;the quantity of water in the pillar EF weigh?nbsp;^ gtains, that of AC mull weigh 4 grains, andnbsp;likewife that the furface of glafs in contact with thenbsp;P�^lar of water E F, is equal to the furface of glafsnbsp;''^hich is in contaft with the pillar of water AC ;nbsp;'''hence at firft fight it fhould feem that thofe equalnbsp;Surfaces ought to keep fufpended equal quantities ofnbsp;''�ater, whereas the quantity of water EF is the halfnbsp;the quantity of water AC ; but the pillar of waternbsp;is as high again as the pillar AC; hence itsnbsp;PtelTure which is equal to the produfl of the quantity of water by the altitude (viz. 1 grains bynbsp;^ inches) is equal to the preffure of the columnnbsp;Ac, viz. to the product of 4 grains by one

inch.

The above-mentioned phenomena of the. attradlion tif cohefion fhew, that what has been mentioned irinbsp;the preceding chapter concerning the rife of waternbsp;to the fame level in different pipes, which commu-tiicate together, is not ftriftly true. Indeed, whennbsp;the pipes are larger than an inch in diameter, thenbsp;difference of the altitudes becomes infenfible. Butnbsp;quot;'ith narrower pipes of different diameters, the waternbsp;tttay be plainly perceived to hand higher in thenbsp;ffnallcr than in the larger pipes.

IV. If a tube confift of two cylindersviz. ofthe narrow par;nbsp;nbsp;nbsp;nbsp;diameter is equal to that of

^^e tube A B, wherein the water would rife to the height A B j and of the larger fart C D, whofe diameter is

equal to that of the tube GH, wherein the water wouU rife to the height GH; and if this compound tube bcnbsp;placed with the narrow aperture in water, as atnbsp;the water will not rife in it higher than the altitudenbsp;G H, viz. to the fame altitude to which it zvould rifnbsp;if the tube were an uniforrn cylinder of the diameter ofnbsp;the large part.

Here, it might be ey.pefl:ed that the water would rife higher than D G ; but it muft be confidered thatnbsp;though the produdl of the piilars of water fiF bynbsp;its altitude, is lefs than a juft counterpoife to the at-tradlion of the furface E F of the glafs; yet thenbsp;overplus of attradlion of that furface, inftead ofnbsp;affifting to fjpporc the water in G E, will operate innbsp;a contrary way; that is, if we reckon the attraction 'nbsp;of the furface EF equal to 10, and if the preflfurenbsp;of the pillar of water in it, be equal to 8; thennbsp;the two remaining parts of attractive power willnbsp;tend to draw the water from the bafon, as much asnbsp;from the cavity D E, towards the furface E F ; fnnbsp;that by the addition of the narrow tube E F, the attraction of the larger part DI is diminilhed; at thenbsp;fame time that the water in it is partially fupportednbsp;by what may be called its perforated bafe IE.

V. If u compound tube, conftfting of a larger pciA LN, fig- 14- PI^.te XL wherein the water wouU.nbsp;rife fpontaneoufy Jo the altitude M. and of a narroivofnbsp;part OK, equal in diameter to the tube AB, whereatnbsp;the water would rife to the height A B ; filled withnbsp;tpsater as high as K, and then be placed with the largo

cperture in water as at N, the whole quantity of water will remainfujp.ended, filling the whole of the large tubenbsp;part of the narrow one. '�The fame thing will alfqnbsp;lake place with a veffei of any fijape, as P Q_S, pro -quot;Tided its upper part he drazm into a narrow cylinder�nbsp;fqual in diameter to the tube A B.

In thofe veflels the water is fupported partly by the attradlion of cohefion, and partly by the preffurenbsp;of the atmofphere. But not having as yet treated'nbsp;of the preffure and other properties of the at-^ofphere, it will not be poffible for the novice tonbsp;Onderftand at prefent the adtion of that preffure ; Inbsp;^hall therefore fubjoin the explanation of the abovc-naentioned phenomenon in the note, for the immediate perufal of thofe readers who are otherwifenbsp;acquainted with the properties of the atmofphere,

That this phenomenon is occafioned in great meafure W the preffure of the atmofphere, is'cvident from the foilow-obfervations ; firft, becaufe the water will not rife fpon-.taneoufly into the veffels ON, PS, to the height K andnbsp;^ s and fecondly, becaufe if thofe veffels, full of water asnbsp;^¹'gh as P, K, together with the bafon, be placed under thenbsp;receiver of an air-pump, on exhaufting the receiver of airnbsp;(''iz. on removing the preffure of the atmofphere), the vvaternbsp;'vill defcend in them, and will remain in them only as highnbsp;It would afcend fpontaneoufly ; whereas all the precedingnbsp;phenomena of capillary attradlion, or of attradlion of co-

VI. IVater rifes between contiguous glafs plates^ mid follows the fame law as it does with tubes j

hefion, and likewife all the others which are related in this chapter, will anfwcr as well in vacuo as in air ; unlefs thenbsp;contrary be mentioned.

How the water cpmes to be fupported in thofe vefTels, partly by the attra�ion ana partly by the atraofphere, willnbsp;be fliewn by the following example and calculation :

A column of water qf about 32 feet perpendicular altitude, is a counterpoife to a column of air of the altitude of the whole atmofphere. Therefore, if the perpendicularnbsp;height of the water in the vcflel PQS, be one foot, its preffurenbsp;will be equal to the 32'� part of the preffure of the atmofphere ; hence the atmofphere preffes on the, aperture ofnbsp;the tube P, with one 32'* part of its power; (fince the pref-fure of the atmofphere at the aperture Q_S, which otherwifcnbsp;would exadfly counteradt the preffure at P, is diminiflied bynbsp;the preffure of the water in the veffel P Q_S ;) and unlefs thenbsp;air comes in at the aperture P, the water will not defcendnbsp;In the veffel. Now let us fuppofe that the diameter of thenbsp;�aperture P be 0,00^ of an inch ; for it mud: be of aboutnbsp;that fize when the perpendicular altitude P Q_ of the waternbsp;is one foot. I he prefiure of the atmofphere upon a fquarenbsp;inch has been found to be about equal to the weight of 14nbsp;pounds, or 224 ounces, or 98036 grains; but the areanbsp;or aperture P, whofe diameter is 0,004^ of an inch,nbsp;is 0,0gt;:C0i256 of an inch; therefore, by the rule of proportion, we fay,'as one fquare inch is to the area 0,00001256;nbsp;fo is the preffure of the atmofphere upon a fquare inch (viz.

^8056 grains) to the prefiure of the atmofphere on the ;irea 0,00001256. And multiplying 98056 by 0,00001256,

Of the AttraBlon of Cohefion^ (Ac. 129

Namely^ the altitudes are inverfely as the diftances of plates.

If the glafs plates be parallel to each other, and placed with their lower edges in water, the waternbsp;^'11 rife between them, and will remain fufpcndednbsp;a certain height. This height is not fo great asnbsp;^^at of the water in a glafs tube, whofe diameter isnbsp;^^^^al to the diftance between the two plates; andnbsp;tliat for an obvious reafon; namely, becaufe in the

obtain the produdl 1,^3158336, viz. little more than ^ae grain, which is the, entire prefTure of the atmofphere onnbsp;farface of the water in the tube at Pgt; But it has beennbsp;^evvn above, that the atmofphere preffes upon that furfacenbsp;quot;'ith only the 32'* part of its entire force; therefore we mullnbsp;'iividc 1,23158336 by 32, and the quotient 0,03848698, ornbsp;of a grain nearly, is the real and aflual prefTure of thenbsp;atmofphere on the furface of the water at P; and this triflingnbsp;PrelTure will be eafily allowed not to be fufiicient to overcomenbsp;the attraction between the water and the furface of the tubenbsp;I* � hence the water remains fufpended in the veffels P Q_S,nbsp;fv ON.

This explanation is corroborated by the following experi-�hent.�Fill the velTel O N, or P Q_S, not entirely, but only t*? to the height T; which is done by lowering them in thenbsp;b'ater of the bafon ; and in that fituation touch the aper-ture O, or P, with a wet finger, fo as to introduce a littlenbsp;'''ster into it. Then if the veffel be drawn up, leaving itsnbsp;lower aperture only in the water of the bafon ; the column

Water T N, or T Q_, will remain fufpended in it, though there is no communication whatever between the water at T,nbsp;snd the water in the capillary aperture.

VoL. II. nbsp;nbsp;nbsp;ftnbsp;nbsp;nbsp;nbsp;tube

tube the water is furrounded by glafs on every fidej yet the proportion is the fame, that is, in two ornbsp;more pairs of glafs plates, the altitudes of the waternbsp;are inverfely as the diftances of the plates ; and thatnbsp;for the fame reafon as in glafs tubes. A C D F, andnbsp;B C D E, fig. 11. Plate XI. reprefent two flat glafsnbsp;plates, placed fo as to form, a fmall angle A C B,nbsp;and immerfed with their lower edges in water. Thenbsp;water will be found to rife between them, and tonbsp;remain fufpended in the fpace EFCDE, the outernbsp;edge of which, EFC, being a curve called an hyperbola. One extremity of this curve rifes as highnbsp;as the upper part of the glafs plates at C, and thenbsp;other extremity reaches as far as the edges of thenbsp;glailes contiguous to the water of the bafon at Fnbsp;and E.

The water between thofe plates rifes higher near the fide C D, and lower at a diftance from it. Innbsp;fhort, at any diftance from CD, as at ah, e d, ef,nbsp;the water rifes as high as it would rife betweennbsp;parallel plates, whofe diftance from each othernbsp;equalled the diftance between the plates of fig. 11.nbsp;at any of thofe particular places. Therefore thenbsp;altitudes of the water at different diftances from CDynbsp;are inverfely as the diftances between the two platesnbsp;at thofe places (I.)

(I.) In fig. 13. Plate XL. (which reprefents the fame elevation of water which is reprefented in fig. ii.) any tw'o or

Of the AtlraEiion of Cohefon, (^c. i_3i ABCE, ng. lo, Plate XL are two flat glafsnbsp;plates, forming a fmall angle with each other, likenbsp;^hofe of the preceding figure j the lowermoft ofnbsp;'^'kich is placed fo as tp form a fmall angle with thenbsp;korizon, having the edge AB a little elevated.nbsp;quot;� hofe plates may be kept feparate at E C, by thenbsp;�^terpofition of a bit of wax, or other fmallnbsp;body.

If a drop of water be introduced between thofe plates at EC, fo as to touch both plates, this dropnbsp;��'^ill be feen to move fpontaneoufly towards thenbsp;^pper part of the glafs plates, as far as the edgenbsp;AB.'�It will enfure the fuccefs of the experiment.nbsp;If the inner furfaces of the glalTes be previouflynbsp;damped with water.

*nore altitudes of water, ^sab, and cd, are inverfely as the 'liftances it, di, between the tw�o plates at thofe placesnbsp;''iz. ab : cd : : di : bt : : (by the fimilarity of the trianglesnbsp;Ddi,) Dd: Di; and this is the property of thenbsp;Common hyperbola, whofe afymptotes are the edge C D ofnbsp;*he glaffes, and the line DS, where the glafs plate cuts thenbsp;bjrface of the water in the velTel G.

It is evident that the water muft rife as high as the apex C 'whatever be the altitude of the plates, fince near the edgenbsp;C D the glafs plates come infinitely near to each other.

If the glafs plates, inftead of being fiat, be bent more or kis, then the edge of the water which rifes between themnbsp;'''ill not be an hyperbola, but it will vary according to thenbsp;Curvature of the plates. See Ditton�s Difcourfe on thenbsp;t'ew law of fluids.

K 2 nbsp;nbsp;nbsp;The

The drop of water will move towards the edge AB, even againft the diredtion of its gravity, be-caufe the attradlion of the glalTes towards the dropnbsp;is ftronger where the plates are clofer to each other,nbsp;as at d, than where they are farther afunder, as at ^ jnbsp;fo that the drpp at 0 is attradled more powerfully towards d, than towards e.

If the fide AB be gradually raifed higher and higher above the horizon, whilft the drop is moving j the latter will be feen to move flower andnbsp;flov/er towards AB, until at Jail the gravity of thenbsp;drop balances the attradtion of the glafles, and thenbsp;water remains at reft. After which, if the edge ABnbsp;be raifed ftill higher, the weight of the drop beingnbsp;greater than the attradlion of the giafs, will force itnbsp;to, defeend towards C E.

The preceding phenomena of attradtion take place not only between giafs and water, but likewife between almoft every fluid and every folid ,� even between fluids and fluids, or folids and folids. , Acon-fiderable difference is however occafioned by thenbsp;different degrees of force with which the particles ofnbsp;each body attract either one another, or thofe of another body.

Thus the attradtion of water to giafs is greatet than the mutual attradtion of its own particles; it isnbsp;alfo greater than that of any other fluid towardsnbsp;giafs, not excepting even the fpirituous liquors,nbsp;which are fpeciflcally lighter than water j hence water

hquor.

Mercury on the contrary is poflefled of a much greater degree of attraftion aarongft its own parti-'^les, than towards glafs; and it is owing to this that,nbsp;certain cafes, there feems to be a repulfion be-^Ween thofe tvro fubftances.

It is owing to th's attraftion of cohefion or capil-attraftion, that water rifes through the fine quot;'relfels of wood, and afcends to the tops of the higheftnbsp;trees;�that it infinuates itfelf through the poresnbsp;certain ftoncs, through fand, fugar, fait, amp;c,�nbsp;that in damp weather, (when the air depofites anbsp;�reatdeal of water) wood, glue, ropes, linen, paper.nbsp;Parchment, falts, amp;c. imbibe the water, and. arenbsp;dtereby fwelied, moiftened, foftened, and fome ofnbsp;t^iem acluodly diffolved.

It is in confequence of this attraction that metals a fluid {late rife and fpread themfelves betweennbsp;t^'e contiguous furfaces of other metals that are innbsp;^ folid ftate. And this indeed is the foundation ofnbsp;the art of foldering metals. Hence alfo mercurynbsp;^^adily infinuates itfelf through the , pores of goldnbsp;^^d tin i for the particles of mercury attradl onenbsp;Another much lefs than they do thofe of gold ornbsp;�

In fhort almoft all the innumerable phenomena are obferved in the common procelTes of na-in the arts and in' chemiftry, depend uponnbsp;*^hDle two forts of attraction, and their various

134 Of the AttraElion of Cohefon, amp;c. degrees in different bodies. When a metal for in-ftance is diffolved in aqua forth, that effedl isnbsp;owing to the particles of the metal having a greaternbsp;attraftion for thofe of the aqua forth, than for eachnbsp;other.

For the fake, however, of diftindtion and perfpi-cuity, when the attraction between two bodies is not fo powerful as to occafion a manifeft change ofnbsp;nature in either of the bodies, it is called aUra5lionnbsp;of cohtfion, and when :t produces a change, it isnbsp;then called attraSiion of ajfnity, or fpeajic at^nbsp;tra5Jion,

We fliall, therefore, treat of the attraftion of affinity in other chapters of this Vv^ork, and fhall confine theprefent merely to the attractions of cohefion

. The explanations of the phenomena, which have been already deferibed concerning glafs and water,nbsp;are fufficient to illuftrate, and to account for, thofenbsp;which may be obferved between other fluids andnbsp;glafs, or between other fluids and other folids jnbsp;allowing for the difference v/hich arifes from theirnbsp;different attraftive forces : yet, as quickfilver has anbsp;much ftronger attraftion of aggregation than of cohefion to glafs, it will be proper briefly to deferibenbsp;the principal experiments that have been made withnbsp;thofe two fubftances �, left the novice, furprifed bynbsp;the peculiarity of the phenomena, fhould be inducednbsp;to fuppofe that a repulfion exifts between thofe twonbsp;fubftances.

if a fmall globule of quickfilver be laid upon '^fean paper, and a piece of glafs be brought intonbsp;�'Contact with it; the mercury will adhere to it, andnbsp;''^dl be drawn away from the paper. If, whillb thenbsp;f�nal] globule of quickfilver is thus adhering to thenbsp;Si^fs, a larger quantity of quickfilver be brought innbsp;with the fmall globule, the latter will imme-diately forfake the glafs, and will incorporate with thenbsp;O'-her quickfilver; which fhews the greater degree ofnbsp;^^tra�lion between the particles of mercury thannbsp;l^etween them add glafs; hence it will be foundnbsp;^^practicable to fpread the quickfilver, like water,nbsp;the.furface of glafs. The fmall globule ofnbsp;^'Jickfilver adheres to the glafs with a little flatnbsp;fquot;rface, which renders the Drape of the mercury notnbsp;perfectly globular : but this little derangement ofnbsp;ftiape muft not be confidered as incompatible withnbsp;ftrong attraflion between the particles of thenbsp;'Mercury; for though this attrablion be greater thannbsp;attradion towards the glafs, yet the latter 'muftnbsp;produce a proportionate efteft; hence a fmall changenbsp;�^f ftiape; whereas if water were ufed in lieu ofnbsp;^riickfilver, the furface of contaft would be muchnbsp;greater.

Place a pretty large drop of quickfilver upon ^iean paper, and let two pieces of glafs touch it onnbsp;^Pp�fite Tides. On drawing the glafles gently fromnbsp;'^^ch other, the mercury will, in confequence of itsnbsp;adherence to the glalTes, be drawn from- a circulafnbsp;�Toto an oblong, or oval, Ihape.

If qiiickfilver be pur in a glafs, or wooden, or earthen veflel of upwards of an inch in width, thenbsp;furface of the quickfilver will be horizontal towardsnbsp;the middle, but convex towards the fides. Thisnbsp;alfo is the cafe w'hen a pretty large quantity ofnbsp;quickfilver is laid upon a table, or on a piece ofnbsp;paper, or other flat furface ; the gravity of it thennbsp;exceeding the attradtion ofcohefion.

If an iron ball (which will float upon quick-filver) be laid upon it, a depreflion of the quickfilver will be obferved all round the ba�1, as in fig. 18.nbsp;Plate XI. and the ball will run towards the fidenbsp;of the veffel, provided it be not fituated too farnbsp;from it. Alfo, if two fuch balls bq placed uponnbsp;tiuickfilver, but not very far afunder, they willnbsp;run towards each other. The reaibn of which is,nbsp;that where the cavities or depreffions of the quick-filver are joined ; that is, either between the ballnbsp;and the fide of the veffel, or betw^een the two balls,nbsp;there the preffure of the quickfilver upon the ball,nbsp;or balls, is diminiflsed by the attraction of thenbsp;quickfilver below ; and of courfe the balls are impelled that way by the fuperior preffure on the op-pofite fides.

If a fmall tube AB, fig. 19. Plate XI. open at both ends, be partly irnmerfed in mercury, thenbsp;mercury will be found to Hand lower Within thenbsp;tube than in the veffel �, and this depreflion has beennbsp;found to be inverfely as the diameters of the tubes.

Thus, if two tubes are immcrfed in quickfilver, and Ae diameter of one is double the diameter of thenbsp;Qther; then the difference of perpendicular altitudesnbsp;tgt;etween the furface of the quickfilver in the latternbsp;�^^'be and in the bafon, will be double to the likenbsp;difference with the former tube,

Quickfilver being an opaque body, it will be ne-uelTary to hold the tube AB near the -fide of the '^cffel, which is fuppofed to be of gla'fs, in ordernbsp;that the depreffion of the quickfilver within the tubenbsp;tiray be perceived.

The fame thing takes place between parallel glafs � Plates; viz. if they be immerfedin quickfilver, thatnbsp;fluid metal will (land lower between them than innbsp;flte reff of the veflelj and the depreffion is likewifcnbsp;Uiverfely as the diftances between the plates. If thenbsp;plates be fituated fo as to form a Imall angle;nbsp;*-^en the quickfilver, rifmg lefs near the angular edgenbsp;than at a diftance from it, will form a curve*.

If a glafs plate be laid in an horizontal fituation^ t�lth a largifh drop of quickfilver near one edge of it,nbsp;in ng. 20. Plate XL which reprefents a feclionnbsp;lb and another glafs plate, A B, be laid fo as tonbsp;f^fnn a fmall angle with it, and at the fame time tonbsp;UQmprefs the drop of quickfilver; the latter will benbsp;huund to move fpontaneoufly towards O, viz. towards

^ This Curve is an hyperbola, whofe afymptotes are the P^Tendicular edge or joining of the glalFe?, and the level ofnbsp;inercury in the bafcn.

^f a tube open at both ends, but having its lower end drawn out into a fine capillary aperture, be fillednbsp;with quickfilver to the altitude of about an inch ornbsp;two, no mercury will be found to run out of thenbsp;lower aperture 5 but if this lower end be fulTcred tonbsp;toitch other mercury, or if, by breaking off part ofnbsp;the fmall end, the aperture be enlarged, then thenbsp;quickfilver will readily run out.

Thofe phenomena with quickfilver are fo evidently dependent on its having a much greater at-tracli'on of aggregation than of cohefion to glafs j and they are fo evidt�ntly fimilar, though in a contrary way, to thofe which take place between waternbsp;and glafs, that after the particular explanations whichnbsp;have been given of thofe with water, it is needlefs tonbsp;dwell any longer upon thofe with quickfilver.

Thefe attradlions of cohefion and aggregation form a confiderable impediment to the thoroughnbsp;inveftigation of the laws of motion with refpedt tonbsp;fluids, as their influence is far from having been entirely afcert�ined. Even the laws of equilibrium arenbsp;affeded by them. Thus it frequently happens, that ifnbsp;two fluids of different fpeciP.c gravities, like waternbsp;and fpiritof wine, be mixed together, they will afterwards remain mixed ; whereas the lighter fluidnbsp;ought to al'cend and to float upon the heavier.

Thus alfo, if a fmall Heel needle, clean and dry, be gently laid upon water, the needle, though fpeci-

Of the AttraElion of Cohefan iSc. i39 This effcft is owing to the attraTion of thenbsp;particles of water to each other, which the fmallnbsp;'''eight of the needle is not fufncient to overcome.

weight of the needle deprelTes the particles of water which are direftlv under it,'and thefe, bynbsp;��^eir adhefion to the contiguous particles, draw themnbsp;below the ufual level; and thus a cavity ofnbsp;ooofiderable breadth is formed all round the needle,nbsp;quot;iiich cavity may be eafily perceived in a propernbsp;^ight.

This effecfl has been commonly attributed to a ^oppoled repulfion betv/een water and fteel, whichnbsp;�s not true ; for though the particles of water at-one another v/ith greater force than they donbsp;thofe of fteel; yet there is a degree of attraftionnbsp;between them and ifeel, which is flaewn by the

If any water happen to get over the floating needle the abovementioned experiment, then the latternbsp;immediately to the bottom.

The different degrees of the attrafiion both of Aggregation and of cohefion between the particlesnbsp;'^f the fame fubflance, or of diflerent fubftartces,nbsp;to form all the immenfe gradation from thenbsp;^oft fluid to the moft folid body, whether fimple ornbsp;'Compound, The ftates intermediate between thofenbsp;^gt;ttreines, are expreffed by the various names ofnbsp;ft�-'id, clammy, foft, glutinous,, tenacious, hard,nbsp;brittle, rigid, amp;c. But as thofe names are incapable

140 nbsp;nbsp;nbsp;Of the Attrahlicn of Cohefon, iAc.

pable of any precif� definitions, their meanings are; commonly ufed, and underftood with confiderablenbsp;latitude. The flate of a given body in this refpefl;nbsp;is afcertained, either by obferving the weight ornbsp;force which is required to difunite its parts j or bynbsp;comparing it with other bodies j as when it is faid,nbsp;that a ruby is fofter than a diamond, but hardernbsp;than the hardeft fteei, becaufe with it you maynbsp;fcratch the fteei but not the diamond*.

Various experiments have been inftituted for the purpofe of determining the force requifite to

* In the formation of feveral ftony concretions; in the cryftallization of falts, after having been diilblved in water jnbsp;in the cooling of certain metals after fulion, Sec. a regularnbsp;arrangement of parts is generally obferved ; the particles ofnbsp;bodies fltewing a tendency to join in a particular way. Itnbsp;has likewife been obferved, that in the formation of ftonynbsp;concretions, and in fome other proceffes, the flower the operation is performed, the harder the bodies are, which refuHnbsp;therefrom. Now all this has fuggefted the fuppofltion thatnbsp;the particles of the fame fort of matter have an atcradfion towards each other with certain ends, and a repulfion with thenbsp;oppofite parts. Hence, when they are placed in fuch a fitua-tion as may allow them to follow that natural inclination,nbsp;viz when they are rendered fluid by heat, or by folution innbsp;water, Sec. then they adhere to each other with their friendlynbsp;parts. Alio when the operation proceeds flowly, then thenbsp;particles have more time to arrange themfelves properly,nbsp;and confequenily form a harder body, than when thenbsp;operation proceeds more expeditioufly. See Higgins onnbsp;Ihght.nbsp;nbsp;nbsp;nbsp;'nbsp;nbsp;nbsp;nbsp;.

^ifunite folids from contiguous fluids, to difunitc folids from contiguous folids, and to break or tonbsp;'^ifunite the continuity of a given folid. But thenbsp;'^�rcumftances of temperature, purity of the bodies,nbsp;equality of fize, furface, amp;c. render fuch experiments fubjeft CO a confiderable uncertainty ; I fliall,nbsp;i^otwithftanding, fubjoin fome of the lefs equivocalnbsp;mfults of fuch experiments. The properties ofnbsp;^eilids do not belong to this part of my work;, butnbsp;^^ofe particulars, which relate to their hardnefs andnbsp;�^^nacity, could not with propriety be inlerted in anynbsp;'^drer part of thefe elements.

If fro m each of two leaden bullets a piece be cut widi a fliarp knife, and if then the two bullets benbsp;Pmfled with their flat bright furfaces againfl: eachnbsp;Other, (giving them a little twift), they ill be foundnbsp;m adhere fo firmly to each other, that fometimesnbsp;weight of 100 pounds will hardly be fufficientnbsp;m fcparate them. When feparated, a confiderablenbsp;'^^gtee of roughnefs will be found on their furfaces¹-'I'he bed; way of performing this experiment is re-Pmfented in fig. ai. Plate XI. which lliews two

The adhefion of the two bullets is certainly not owing the preffure of the furrounding air ,; for in the firft placenbsp;atmofpherical preffure is by no means fo great as tonbsp;P''oduce that degree of adhefion between fuch fmali furfaces jnbsp;in the fecond place, the two bullets thus prepared arenbsp;ound to adhere about as firmly in vacuo as they do in air.

prepared bullets adhering to each other, and each having a ring or bit of firing pafTing through anbsp;hole, lo that one of the rings may be faftened to anbsp;nail, or other fteady fupport, whiift the neceffiirynbsp;weight may be fufpendcd to the other ring. Thenbsp;flat and fmooth furfaces of other metals, of g1afs,nbsp;See. do alfo cohere to each odrer with confiderablenbsp;force; but with fuch bodies as are not fo pliable asnbsp;lead, a certain artifice is required for the purpofc}nbsp;namely, the interpofition of fome fluid as water,nbsp;oil, amp;c. or of fome lubflance which may be applied in a fluid ftate, though it may afterwards coagulate and grow folk!, as tallow, wax, or fluidnbsp;metals.

Two' brafs polifhed fiat furfaces, 2 inches in dia-� meter, fmeared over with greafe, and put togethernbsp;in a pretty hot flate, will, when cold, adhere tonbsp;each other fo firmly as to require nearly 600 poundsnbsp;weight to feparate th.em.

Every body knows ho'w firmly two pieces of metal adhere to each other, when they are foldered together ; that is, joined by the interpofition of another metal in a fluid ftate.

It muft be obferved, however, that in thefe laft experiments, where fomechtng is interpofed betweennbsp;the two furfaces, the adhefion feems to take place,nbsp;not between the furfaces of the two folids, lb muchnbsp;as between each of thofe furfaces and the interpofednbsp;fubftance; for, in the firft place, it feems ftrange thatnbsp;two iurfaces fltould have a greater attradion to each

other when fomething is interpofed, than other-'''�he j and fecondly, it has been found that the degree of adhefion differs according as different fub-^3nces, viz. oilj or water, or wax, greafe, turpentine, ^0. are interpofed between the furfaces of the verynbsp;^^gt;^0 fohds.

The adhefion in thefe experiments is partly attri-^tited to the preffure of the atmofphere, becaufe ^'^�rierimes the adhering plates are feparated in annbsp;^^haufted receiver. But, on the other hand, it feemsnbsp;hkely that the fcparation of fome of them in the ex-^^ufted receiver is occafioned rather by the extrication of air from the fubftance which is interpofed,nbsp;than by the removal of the armofpherical preffure.

The tenacity or ftrength of different fubftances is ttleafuredbythe force which is required to break them.nbsp;^0 a tepiperate degree of heat, it has been foundnbsp;that wires of the following metals, drawn throughnbsp;the fame hole, one tenth of an inch in diameter, andnbsp;fattened with one end to a nail, whilft v/eights werenbsp;^ufpended to the other, could not be broken by anynbsp;^orce lefs than the annexed weightsnbsp;Leadnbsp;nbsp;nbsp;nbsp;�nbsp;nbsp;nbsp;nbsp;�nbsp;nbsp;nbsp;nbsp;291

Brafs nbsp;nbsp;nbsp;�nbsp;nbsp;nbsp;nbsp;�nbsp;nbsp;nbsp;nbsp;360nbsp;nbsp;nbsp;nbsp;gt; Pounds.

. * If the metals, inftead of being formed into wire by be-paffed through a hole, be fimply caft in the fame mould cceffively, and be then broken by means of weights, theirnbsp;^nacity will be found fomewhat different from the ftatcmcntsnbsp;the above table.

A confiderable difference in tlie tenacity of me- ' tallic fubftances is occp.ffoned by their purity, temperature, manner of forming them, amp;c. But withnbsp;other fubftances, the fluftuation of their tenacity isnbsp;much greater than with metals, as will appear fromnbsp;the following obfervations of Mr. Emerfon.

� yard long, fuppOrted at both ends, will bear in �� the middle, for a very little time, about 330nbsp;pounds avoirdupolfe; hut will break with morenbsp;than that, weight. This Is at a medium; fornbsp;there are fome pieces that will carry fomethingnbsp;more, and others not fo muck. But fucli anbsp;piece of wood fhould net, in pradlice, be truftednbsp;for any length of time with above a third or fourthnbsp;part of that weight. For fince this is the extremenbsp;� weight which tlie bell: wood will bear, that of anbsp;� vvorle fort mull break with it. I have found bynbsp;experience, that there is a great deal of differencenbsp;In ftrength, in different pieces of the very famenbsp;tree ; feme pieces 1 have found would not bearnbsp;half the weight that others would do. The woodnbsp;of the boughs and branches is far weaker thannbsp;that of the body ; the vvood of the great limbs i.snbsp;ftronger than that of the fnal! ones; and the woednbsp;in the heart of a found tree Is ftrongeft of all. Inbsp;� have alfo found by experience, that a piece ofnbsp;timber, which has borne a great weight for a fmallnbsp;� time, has broke with a far lefs weight, wh.en left

Of the AttraEtion of Cobefton, iSc. 145 weaker when it is preen, and ftronj^eft when tho-

roughly dryed, and fhould be two or three years old at leait. If wood happens to be fappy, it,nbsp;will be weaker upon that account, and will like-wife decay fooner. Knots in w^ood weaken itnbsp;'^^ry much, and this often caufes it to breaknbsp;where a knot is. Alfo when wood is crofsnbsp;grained, as it often happens, in fawing, this willnbsp;Weaken it more or lefs, according as it runs morenbsp;or lefs acrofs the grain. And I have found bynbsp;Experience, that tough wood crofs the grain, fuchnbsp;as elm or afli, is feven, eight, or ten times weakernbsp;' than ftraighc; and wood that eafily fplits, fuch asnbsp;� fir, is 16, 18, or 20 times weaker. And for com-' mon life it is hardly pofiible to find wood, but itnbsp;' muft be fubjed to Ibme of thefe things. Befides,nbsp;' when timber lies long in a building, it is apt tonbsp;' decay, or be worm-eaten, which muft needs verynbsp;' much impair its ftrength. From all which itnbsp;' appears, that a large allowance ougkt to be madenbsp;' for the ftrength of wood, when applied to anynbsp;� vife, efpecially w�here it is defigned to continuenbsp;' for a long time.�

� The proportion of the ftrength of feveral forts ' of w'ood, and other bodies that I have tried, willnbsp;� appear in the following table:

�146 Gf the AttraElioH cf Cohefion, iAc.

� A cylindric rod of good clean fir, of an inch � circumference, drawn in length, will bear at thenbsp;� extremity 400 pounds, and a fpear of fir a inchesnbsp;diameter, will bear about feven tons; but notnbsp;� more.�

� A rod of good iron of an inch in circumference, � will bear near 3 tons weight.�

� A good hempen rope of an inch in circum-� ference,. will bear 1000 pounds at the extre-� mity.�

� All this fuppofes thefe bodies to be found and � good throughout; but none of thefe fliould benbsp;� put to bear more than a third or a fourth partnbsp;� of that weight, efpecially for any length ofnbsp;time.

The Viordjlrength has often been indifcrinninately ^�f�d for expreffing the tenacity', the brittlenefs, ornbsp;fite rigidity of bodies; but thofe qualities muft benbsp;diftinguiflied from eacli other, whenever any ofnbsp;^hem is to be uftd in mechanics, or in other circum-^^cices. Thus glafs may be broken incomparablynbsp;^'^fier than iron, and a glafs rod can fupporta muchnbsp;^'��'aller weight than what can be fupported by annbsp;iron rod : yet iron may be fcratched with glafsgt;nbsp;the latter cannot be fcratched with the former.

the following order, beginning with the hardefl:, 3nd ending widi the fofteft; iron, platina, copper,nbsp;filver, gold, tin, and lead.

The fame of the femi-metals, as far as it is known, ^anganefe, nickel, bifmuth, tungften, zinc, anti-�tiony, and arfenic.

With refpefl to the difference of elafticityy the �Petals (eem to follow the fame order as they donbsp;quot;'Uh refpecl to hardnefs ; except that perhapsnbsp;hopper might be placed before platina.

1 he rigidity and the elafticity of metallic fub-^^laces, are increafed by a variety of means, the Pdneipalof which are hammering, prefling, coolingnbsp;^^ddenly, and mixing fome of them together In duenbsp;proportions. And on the other hand, their rigiditynbsp;^nd elafticity are diminillied (except when they arifenbsp;from mixture) principally by heating and coolingnbsp;gradually.

Steel may be rendered harder than any other metallic fubftance. Thus if a piece of fteel be heated

red

red hot, and in that ftate be plunged in oil, it -wlil thereby become fo hard, that a file will hatdlynbsp;fcratch it �, and it Vv-ill be rendered ftill harder, if in-ftead of oil, the red hot fteel be plunged in water;nbsp;but if cold mercury be ufed inftead of either ofnbsp;thofe liquors, then the fteel will be rendered fonbsp;hard as to fcratch glafs nearly as well as a diamond.

The hardnefs of other natural folids, befides the metals, differs confiderably, according to the ftate ofnbsp;'purity and of various other circumftances. However, a ufeful gradation of the principal naturalnbsp;folids, with refpeft to hardnefs, is exhibited in thenbsp;following lift, which begins with the hardeft andnbsp;ends with the fofeeft.

The reader may naturally inquire whether the at-ti'adlion of cohefion, and the attradion of aggrega-follow any known law of increafe or decreafe, proportion to the did;ance ; but his inquiry willnbsp;^ot meet with any fatisfadory information-

The force of gravity has been fliewn to decreafe �nverfely as the fquares of the diftances. But thenbsp;^^tradion of cohefion, and that of aggregation, de-^'�^a-fe much fafter: for inftance, if a force of anbsp;^^oufand pounds weight be required to break a cer-folid, and if then the broken parts be placednbsp;Contiguous to each other, and fo clofely that thenbsp;cannot difcern the fradure; it will be foundnbsp;that they may be feparated with the utmoft fa*nbsp;eility.

It has been fuppofed, fhat thofc attradions decreafe inverfely as the cubes of the diftances j but ^10 fatisfadory experiments have as yet eftabliflrednbsp;this fuppofed law.

TH E effential fli�ts relative to the attraflions of cohefion and of aggregation having beennbsp;ftated in the preceding chapter, we inuft now explain the theory of the movements of fluids, tonbsp;which we fhall add feverai experimental obferva-tions, and fhall endeavour to point out the deviations of the refiilts of the latter from the determinations of the former.�The fubjedl is extenfive, and �nbsp;but imperfedlly known. We fhall therefore adoptnbsp;concifenefs as far as it may be compatible with per-fpicuity.

AFGB, fig. I. Plate XII. is a bent cylindrical tube, whofe parts A P�, BG, are perpendicular tonbsp;the horizon, and whofe diameter is too large to benbsp;confiderably affedfed by capillary attraction. Letnbsp;fome fluid, for inftance water, be put in itj and ifnbsp;this fluid be put in motion, by fhaking the tube oncenbsp;or twice, and then flopping it, the fluid will be foundnbsp;to continue to move fomc time longer j viz. it willnbsp;be found to afcend in one leg, and to defcendnbsp;in the other leg alternately. Thofe vibrations, ornbsp;(as they are ocherwife called) librations, becomenbsp;gradually fhorter and fhorter, on account of thenbsp;ffidion between the flijid and the tube, until at laft

Of the Motion of the Waves. nbsp;nbsp;nbsp;151

Ae fluid remaias perfedlly at reft. But thofe vibrations, whether longer or Ihorter, have been found to be performed in equal portions of time; andnbsp;thefe are equal to the times in which a commonnbsp;pendulum, the length of which is equal to half thenbsp;^^ogth of the fluid ENFGH, performs its fmalleftnbsp;''ibrations (i.)

(I.) That is, equal to the times in which a cycloidal pen-whofe length is equal to half the length of the fluid �-NPGH, performs its vibrations.

When the fluid in one leg {lands higher than in the other (which is the fituation adlually reprefented in the figure) di-'�ide the difference of altitude, E N, into two equal parts atnbsp;�The fluid adluated by its gravity defcends in the legnbsp;�^F, whilft it afcends in the oppofite leg B G; and when itnbsp;�'laches the fame height in both legs, which is at the level ofnbsp;it would remam there at refl j but having acquired anbsp;�-^rtain velocity by the defeent, it is thereby enabled to con-hriue its motion, until it rifes as high as the level of E,nbsp;the other leg B G, excepting a fmall dedudlionnbsp;^''^t tnufl; be made on account of the fridtion. Whennbsp;fluij tjjyg afeended in the leg BG, it will again de-^^�nd in that lejj, and will rife anew in the other, and fo on:

performing every one of its vibrations a little fhorter than preceding one, until its motion is entirely deftroyed bynbsp;^^2 fridlion, adhefion, amp;c.

quantity of fluid, or moving force E N, does evidently ' L 4nbsp;nbsp;nbsp;nbsp;increafe

r 5 '2 nbsp;nbsp;nbsp;Of the Motion of the TVaves.

. The principal ufe we (hall make of the above de-fcribed vibrations of a fluid in the bent tube, is for �nbsp;nbsp;nbsp;nbsp;explaining

jncreafe and decreafe, as the (pace which is to be run through by the fluid in order to reach the point of reft, or level of M ;nbsp;fince its length is always the double of that fpace. For infiance, when the upper paa of the fluid is at Z in the legnbsp;AF, it muft ftand at O in the other leg; then the differencenbsp;of altitude, or the moving force, is reprefented by Z Kgt;nbsp;�which is the double of Z M; and the fame thing may benbsp;faid of any other fituation of the fluid. But it has beennbsp;proved (in Prop. X. and XV. of the note N. i. to chap. X.nbsp;Part I.) that the vibrations, whether long or (hort, of a cycloidal pendulum are performed in equal portions of time,nbsp;for the very fame reafon, namely, becaufe the moving forcenbsp;is always proportionate to the arch which (lands betweennbsp;the point from which the pendulum begins to dcfcend innbsp;'every vibration, and the lowed point of the arch of vibration. Therefore the fame reafoning which demon-ftrates this property of the cycloidal pendulum, provesnbsp;the like property of the fluid moving in the tube

Since the moving force is equal to the difference of elevation between the furface of the fluid in one leg, and that of the fluid in the other; therefore, when the fluid is all innbsp;one leg, the moving force is equal to its entire weight ornbsp;gravity, which force will enable it to defeend perpendicularlynbsp;through a fpace equal to its whole length in a certain time ;nbsp;and ihnce this defeent is only a long vibration, and all the vi-brarions have been demonfirated to be performed in equalnbsp;times; therefore that alfo is the time in which the fluid willnbsp;perfotm each of its vibrations in the tube. But the time in

explaining the motion of the waves, to which they bear a great degree of analogy.

When the llirface of water is fnooth and at reft, gt;f any force (be it the aftion of the wind, as at Tea,nbsp;the fall of a heavy body, amp;c.) deprefs the fur-face of it in any particular place, as at A, fig. 2 andnbsp;Plate XII. (the former of thofe figures exhibitingnbsp;^ feiftion, and the latter a perpendicular view of thenbsp;fame objedt) the contiguous water will neccftarilynbsp;*^ifc all round that place, as at BBB ; fur if a certain quantity of water be depreiied below the ufualnbsp;f-vel, an equal quantity muft rife in fome othernbsp;place above that level, and the water which ftandsnbsp;lt;^lofert to the place of the original impreflion, willnbsp;�f courfe be moved.

The water which has thus been elevated, defeends fjon after in confeque.nce of its gravity ; and by thenbsp;it has reached the original level, it will .have

'''hich a cycloidal pendulum performs each of its vibrations '^^ecpial to the time that a body would employ in defeendingnbsp;P'-�rpendicularly by the force'of gravity through twice thenbsp;*��gth of the pendulum {fee the note N. i. to chap. X. ofnbsp;therefore the fluid in the tube A F G H, and anbsp;Cycloidal pendulum of h-alf the length of the fluid ENFGH,nbsp;'''�1 perform their vibrations in equal times.

If the reader be dcfirous of determining the time of v:-l^ration of a fluid in a tube which is not of equal diameter, whofe legs are not perpendicular to the horizon, he maynbsp;^onfult Newton�s Principia, B. 11. Prop. 44, 45, 46;

acquired a degree of velocity fufficient to carry it jower than that level; therefore .it now adls as another original moving force, in confequence ofnbsp;which the water will be raifed on both fides of it,nbsp;viz. at .A, and at CCC, fig. 3 and 4, Plate XII.nbsp;And for the fame reafon, thedefeent of thofe elevated parts will produce other elevations contiguous tonbsp;them, as at B B, D D, fig. 2 and 3, and fo forth.nbsp;Thus the alternate rifing and falling of the water innbsp;ridges will expand all round the original place ofnbsp;motion ; but as they recede from that place, fo thenbsp;ridges as well as the adjoining hollows, grow fmallernbsp;and fmaller, until they vanifh. This diminutionnbsp;of fize is produced by three caufes; viz. by thenbsp;want of perfedt freedom of motion amongft thenbsp;particles of water, by the refiftance of the air, and bynbsp;the further ridges being larger in diameter than thofenbsp;which are nearer.

It is likewile on account of the friftion, or ad-hefion, amongft the particles of water, and of the refiftance of the air, that in the fame place the alternate elevations and depreflions diminifti gradu-*nbsp;ally, until the water reaflumes its original tranquillity ; unlefs the external impreffion be renewed ornbsp;continued.

One of the abovementioned ridges, or elevations, together with one adjoining cavity, is called anbsp;�Wave.

The Breadth of the wave is the part of the horizontal line, which is occupied by a wave ; and this

is evidently equal to the diftance between the tops of two contiguous ridge?, or between the lowcft pointsnbsp;of two contiguous hollows.

A wave is faid to have run its breailh, when its elevated part is arrived at the place where the elevated part of the next wave flood before, or whennbsp;the elevated part B has moved as far as D ; or (^thenbsp;fituations of two contiguous waves being given)nbsp;when one of them is arrived at the place of thenbsp;other; and the time which is erripicyed in thisnbsp;tranfition is called the time of a vSave's-victicTi.

It muft not however be imagined that the w-ater is by this means carried progreiTively from A to-V'ards B, D, amp;c. it being only the fucceffive rifingnbsp;3nd falling, which is communicated from the original centre of motion to the next parts pro-greffively. This may be clearly perceived bynbsp;^'�lying fmall floating bodies upon the futface ofnbsp;die water, for they wdll be moved up and down, butnbsp;'''ill not recede from their original plac�s.

Now the alternate rifing of the water in two adjoining places, as at B and C, has been juftly confi-^'ored as analogous to the vibratory motion of the quot;'ater in the bent tube, fig. i. fo that the diflancenbsp;between the upper point of the ridge of a wave andnbsp;��^'0 loweft part of its hollow, is like the length ofnbsp;fluij jf, j-pig tube, fig. I. the difference at leafl isnbsp;^^ot Very great. Tdierefore the wave will performnbsp;'^Oe vibration, that is, the ridge of it will becoiuenbsp;hollow part, and the latter will be elevated, in

the Uime time chat a pendulum of half the length of the wave, (viz. half the length of the furface ofnbsp;the water between tlic upper part of the ridge andnbsp;the lowed part of the hollow) will perform one ofnbsp;its lead ofeiilations. Hence the motion of waves isnbsp;regular, or the rifings and fallings of the water in thenbsp;fame place are performed in equal portions of time,nbsp;as is the cafe with the fluid in the tube, fig, i.

But thio time of vibration is half the time in which a wave will run its breadth i for in order to run thatnbsp;breadth, the ridge mull come, not to the place wherenbsp;the next hollow Hood, but to the place where thenbsp;next ridge flood. Therefore a wave will,run itsnbsp;breadth in the fame time that a pendulum of half itsnbsp;length will perform two of its leafl. vibrations; or tonbsp;the time in which a pendulum equal to four timesnbsp;that length, (viz, equal to the length of the furfacenbsp;BCD) will perform one vibration; fince thenbsp;times, in which pendulums of different lengthsnbsp;perform their vibrations, are as the fquares of theifnbsp;lengths,'

When the -waves are broad and do not rife highj then the abovementioned length, BCD, will notnbsp;differ much from the breadth of the wave ; and ionbsp;chat cafe the wave will run its breadth in the famenbsp;time that a pendulum, whofe length is equal to thatnbsp;breadth, performs one of its vibrations. Hence, ifnbsp;the breadth of a wave be 39,1196 inches¹; then

Such being the length of the pendulum which vibrate¹ feconds. See page 1.9�. vol. I.

that wave will move on at the rate of 39,1196 inches per fecond of time; that is, at the rate of 195 feetnbsp;per minute, nearly.

It will eafily be conceived that the waves rife higher or lower, according to the power of the original moving force ; for the more water is difplacednbsp;by that force, the greater quantity of it mull be elevated above theiifual level; and of courfe the breadthnbsp;of the waves is likewife greater.

It feems to be pretty well determined from a variety of experiments and obfervations, tliat the ut-Rioft force of the wind cannot penetrate a great way Into the water; and that in great dorms the water ofnbsp;the fea is (lightly agitated at the depth of 2,0 feetnbsp;below the ufual level, and probably not moved at allnbsp;at the depth of 30 feet or five fathoms¹. Thereforenbsp;the a�lual difplacing of the water by the wind can-ftot be fuppofed to reach nearly fo low; hence itnbsp;fiiould feem that the greateft waves could not be fonbsp;Very high as they are often reprefented by accuratenbsp;and creditable navigators. But it muft be obfervednbsp;that in dorms, waves increafo to an enormous fizenbsp;^tom the accumulation of waves upon waves; for

the wind is continually blowing, its a�ion will '^atfe a wave upon another wave, and a third wav^nbsp;^pon a fecond, in the fame manner as it raifes a

Eoyle�s works, folio edition, vol. HI- Relations about the bottom of the Sea. Sect. Ill-wave

wave upon the flat furface of the water. In facfl:, at fea, a variety of waves of different flzes are frequently feen one upon the other, efpecialiy whilftnbsp;the wind is actually blowing. And when it blowsnbsp;frefh, the waves, not moving fufflcicntly quick,nbsp;their tops, which are thinner' and lighter, are iiTi-pelled forward, are broken, and turned into a whitenbsp;foam, particles of which, called the/prq)�, are carriednbsp;a vaft way.

Waves are circujar, or ftraight, or other wife bent, according as the original imprelllon is madenbsp;in a narrow fpace nearly circular, or in a flraightnbsp;line, or in other configurations. In open feas thenbsp;weaves generally are in the fhape of ftraight furrows,nbsp;becaufethe wind blows upon the water in a parallelnbsp;manner, at leaft for a long apparent traft.

When the water receives feveral impulfes at the fame time, but in different places, then the wavesnbsp;which proceed from thofe places muft neceffarilynbsp;crofs each other.�By this crofling the waves do notnbsp;difturh each other; but they follow their proper di-redions, by paffing one upon the other. Thus ifnbsp;two ftones be thrown upon the furface of ftagnantnbsp;water nearly at the fame time, but at a little diftancenbsp;from each other; the circular waves which proceednbsp;from thofe places will be clearly perceived to crofsnbsp;each other, and to follow their peculiar courfes.nbsp;The reaibn of which is, that the fame caufe whichnbsp;produces the alternate riling and falling of the waternbsp;upon the furface of otherv.nfe ftagnant water, muft

operate in the fame manner, and mufl; produce *^he like efFedt on the furface of another wave.

When a wave meets with an obftacle which is ftraight and perpendicular, fuch as a wall, a fteepnbsp;^ank, as RS, fig. 3. then the wave is refleded bynbsp;and the fhape of the refleded or retrogradenbsp;quot;''''ave, is the reverfe of what it would have been onnbsp;*^f^e other fide of the obftacle, had the obftacle notnbsp;^xifted. Thus in fig. 3. the reflefted wave vtvnbsp;^as the fame curvature as it would have had at xyx,nbsp;the obftacle had not refledted it; for the middlenbsp;part of the curvature muft naturally meet the obfta-^le, and muft be refledfed by it firft j fo that thisnbsp;part will be found at /, when the adjoining partsnbsp;'''hich are refledfed after it are at vv, amp;c.�And fincenbsp;^aves will'crofs without obftrudting each other, thenbsp;^ffledled waves will proceed from the obftacle, andnbsp;^�11 expand all round, Src.

When the bank or obftacle is inclined to the ho-^'2on, as is frequently the cafe on the Ihores of the ^'^a; then the refledtion of the waves is difturbed,nbsp;it is often abfolutely deftroyed by the friction ofnbsp;Water upon the ground.

Jf the obftacle be fuch as to refledb a part only of Wave, fuch as a ftone or a poft, which is fur-^�ounded by the water ; then the wave will be partlynbsp;fefledted in (hapes and diredtions which differ according to the form and fize of the obftacle, whilftnbsp;reft of the wave will proceed in its original di-

^cftion.

When a hole in an obftade permits part on]/ cf a wave to go through, as at Z, fig. 3. then circularnbsp;�waves will be formed on the other fide of the obfia-cle, whofe centre is the hole j for in faO; thofe wavesnbsp;owe their origin to the motion of the water in thatnbsp;place only.

The fame caufes which raife water into waves, mufl evidently produce the like efieft on othernbsp;fluids, but in different degrees, according as thenbsp;fluid is more or lefs lieavy, as its particles adherenbsp;more or lefs forcibly to each other, and probablynbsp;likewife accordincr as there is a greater or lefs de-gree of attradion between the fluid and the othernbsp;body, which gives it the impulfe.

When a ftone or other heavy body is dropped on the furface of oil, the waves are not nearly fo high,nbsp;nor fo quick, neither do they fpread fo far as thenbsp;waves of water. This effedt is evidently owing tonbsp;the claniminefs, or great degree of adhefion betweennbsp;the particles of the oil.

If the waves upon oil be attempted to be railed by the force of wind, it will be found very difficultnbsp;to fucceed even in a moderate degree. This diffi-culty is in a great meafure owing to the attraftionnbsp;between the particles of oil; but befides this, therenbsp;may be lefs attraftion between oil and air, than between the latter and water; for water always contains a certain quantity of air; and if it be deprivednbsp;of that air by means of boiling or otherwife, a flroi'tnbsp;2nbsp;nbsp;nbsp;nbsp;expofin'^

It is likevvife probable, that the furface of water, ^ven when ilagnant, roay not be fo fmooth as thenbsp;kirface of oil; fo that the wind may more eafilynbsp;^atch into the inequalities of the former than of thenbsp;latter.

It is remarkable that the effeft of the wind upon ^ater may in a great meafure be prevented or moderated, by fpreading a thin film of oil on the furfacenbsp;of the water.

No great quantity of oil is required for this pur-pofe; for, though oil be very clammy and adhe-five to almoft all other bodies ; yet w'hen dropped upon water, it w'ill inft ntiy fpread and extend itfclfnbsp;Over a vafi: furface of water ; and it will even drivenbsp;fmall floating bodies out of its way, acquiring, as itnbsp;feems, a repulfive property amongft its own particles.

This repulfion may be fhewn in the following ^tnufing manner : Cut a light {having .of wood, ornbsp;�f paper, in the form of a comma, or of the fize andnbsp;drape of fig. 5. Plate XII. fmear it with oil, thennbsp;place it upon the furface of a pretty large piece ofnbsp;Idaooth water �, and the bit of wood or paper will benbsp;to turn round in a dire�tion contrary to that ofnbsp;'�Ire point A, which is occafioned by the ftream ofnbsp;��ly particles iffuing from the point and fpreadingnbsp;'fernfelves over the furface of the water.�This experiment will not fucc,ecd in a bafon or other frnall

veflel full of water, wherein the particles of oil have not room enough to expand themfelves.

If a heavy body be dropped on the furface of water which is thus covered with a film of oil, the waves will take place in the fame manner as if therenbsp;were no oil. But the blowing of the wind will havenbsp;little or no efFeft upon it. In this cafe the oil feemsnbsp;to aft between water and air, in the fame mannernbsp;as it afts between the moving parts of mechanicalnbsp;engines; viz. it lubricates the parts, and rendersnbsp;the motion free and cafy.

But whether this be the real explanation or not, the faft is not lefs true than furprifing j and a verynbsp;ufeful confequence has been derived from it, namely, a method offtilling the waves of the fea in certain cafes.

It is exprefsly mentioned by Plutarch¹ and Plinythat the feamen of their times ufed to flill the waves in a ftorm, by pouring oil into the lea. Butnbsp;fince the revival of learning, though feveral obferva-tions relative to it are to be found in accounts ofnbsp;voyages, amp;c. yet I do not know that any noticenbsp;has been taken of this account by any philofophicalnbsp;writer, previous to the late celebrated Dr. Franklin�nbsp;who collefted feveral accounts relative to the fub-

Jeft, and made a variety of experiments upon itj the fum of vrhich is as follows*.

A fmall quantity of oil, for inftance, a quarter of ounce, will fpread itfelf quickly and forcibly uponnbsp;Water of a pond or lake, to the extent of morenbsp;than an acre ; and if poured on the windward fide,nbsp;the Water will thereby be rendered quite Imooth asnbsp;as the film of oil extends, whilfl; the reft of thenbsp;pond may be quite rough, from the adlron of thenbsp;'^'ind.

If the oil be poured on the leeward fide, then the force of the wind will in a great meafure drive it to-tvards the bank. Befides which, the experiment isnbsp;f'oftrated by the waves coming to chat fide alreadynbsp;formed; for the principal operatiort of the oil uponnbsp;Water is, as it feems, ift. to prevent the raifing ofnbsp;oew waves by the wind ; and adly. to prevent itsnbsp;driving thofe which are already raifed with fonbsp;�^uch force, as it would if their furface were notnbsp;�'ded.

Such experiments at fea are evidently attended ''^itn a great many difficulties; but in particularnbsp;oafes eflential advantages may be derived from thenbsp;^fo of oil, and feveral inftances of its having been

. See his paper oh the ftilling of waves by means of oil, ^ the Phil. Tranfactions, vol. LXIV. or in his mifcella-

164 Of the Motion of the Waves.

of very great fervice, are recorded¹. � We might/' fays Dr. Franklin, � totally fupprefs the waves innbsp;any required place, if we could come at thenbsp;windward place, where they take their rife.nbsp;This in the ocean can feldom if ever be done.nbsp;� But perhaps fomething may be done on particu-

Mr. Tengnagel, in a letter to Count Bentinck, dated Batavia, January the 5th, 1770, fays, � Near the Iflandsnbsp;Paul and Amfterdam, we met with a fiorm which had nothingnbsp;particular in it worthy of being communicated to you, exceptnbsp;that the Captain found himfelf obliged, for greater fafety innbsp;wearing the fliip, to pour oil into the fea, to prevent thenbsp;waves breaking over her, which had an excellent effccljnbsp;and fucceeded in preferving us.� Phil. Tranfadlions,nbsp;vol. LXIV. page 456.

It has been remarked in Rhode Ifland, that the harbour of Newport is ever fmooth whilft any whaling veflels are in it;nbsp;which is, in all probability, owing to the fifli-oil that maynbsp;come out of them.

It is faid to be a pradlice with the fifhermen of Lifbon when about to return into the river (jf they fee beforenbsp;them too great a furf upon the bar, which they apprehendnbsp;might fill their boats in palling) to empty a bottle or two ofnbsp;oil into the fea, which will fupprefs the breakers, and allovVnbsp;them to pafs fafely.

In various parts of the coaft of the Mediterranean, and elfewhere, it is a pradtice of the fifhermen, to fprinkle �nbsp;little oil upon the vt'ater, which fmooths the furface of thonbsp;water that is ruffled by the wind, and thus enables themnbsp;fee and to ftrike the fiih.

lar occafions, to moderate the violence of the waves, when we are in the midft of them, andnbsp;prevent their breaking, where that would be inconvenient.

quot; For when the wind blows frelh, there are con-' tinually rifing on the back of every great wave, a number of fmall ones, which roughen its fur-face, and give the wind hold, as it were, to puflinbsp;quot; it with greater force. This hold is diminifhednbsp;tgt;y preventing the generation of thofe fmall ones.nbsp;And poffibly too, when a wave�s furface is oiled,nbsp;Ae wind, in pafling over it, may rather in fomenbsp;degree prefs it down, and contribute to preventnbsp;Its rifing again, inftead of promoting it.�

Light, volatile, or etherial oils, like ether, fpirit turpentine, amp;c. do not pollefs the fame property as fat oils, fuch as olive oil, lin-feed, rape-feednbsp;train-oil, amp;c.

t i6� J

The infufficiency of the common theory to account for the phenomena which have beennbsp;obferved relatively to fluids in motion, fuggefts thenbsp;expedient of ftating the refults of the principal andnbsp;moft authentic experiments which have hithertonbsp;been made in this, branch of natural philofophy; itnbsp;being from a colledion of well eftablilhed fads, thatnbsp;a ufeful fet of theoretical propofitions, or naturalnbsp;lavvs, may hereafter be deduced. We fhall never-thelcis briefly prefix the leading propofitions of thenbsp;common theory, in order that the deviations of itsnbsp;refults from thofe of adual experiments, may benbsp;rendered more evident to the reader. And in thisnbsp;place it feems proper to obferve, that the imper-fedions of this theory, which in truth is partlynbsp;eftabliflied upon fads, mull be attributed not tonbsp;any deficiency in the mode of reafoning, but to thonbsp;want of adequate principles to eftablilh that reafoO'nbsp;ingupon.�The demonftration of any propofitio'��nbsp;whether in mathematics or in any other fubje*^'nbsp;does only fliew the natural, neceffary, and uncoU'nbsp;trovertable dependence of one idea upon the ne^t^�nbsp;throughout the whole chain of ideas, which

''^ene between the afTcrtion of the propofition, and �Certain principles or axioms. Therefore the de-*^onftration may be ftri�tly juft and proper, yetnbsp;propofition may be either true or falfe, accord-''�g as the principles upon which it is eftabiiflied arenbsp;^�'Ue or falfe �, and according as ail the principlesnbsp;tipon which that propofition depends, .or fome ofnbsp;only, have been taken into the account.

Now with refped to the theory of fluids in *^otion, the defe�l ariles from the imperfed; know-^*^dge of the principles, or the circumftances uponnbsp;'vhich the phenomena depend.

According to the common theory. I. When a fluid is conveyed through a pipe of an uniformnbsp;bore, or a channel of an uniform ftiape and capacity, as in fig. 6. Plate XII. the velocity of thenbsp;fluid is the fame in every fedtion of it; viz. in thenbsp;fame time an equal quantity of fluid will pafsnbsp;through AB, or through DC, or through EF, amp;c.nbsp;But if the fald channel or pipe be narrower at fomenbsp;places than at others, then the velocities of the fluidnbsp;^''^hich pafles through it will be different j viz. atnbsp;different fedlions the velocities will be inverfely asnbsp;*-he areas of the fedions. Thus, fuppofe that in thenbsp;channel, fig. 7. Plate XII. the aperture, or thenbsp;3rca of the fedion AB, is equal to half the area ofnbsp;^he fedion GD; then the velocity of the fluid atnbsp;AB will be double the velocity of the fluid at CD;nbsp;for fince the channel, or pipe, remains always full,nbsp;It is evident that in the fame time an equal quantity

of fluid m�fl pafs through CD, as through AB. But at AB the capacity of the pipe is half that atnbsp;CD; therefore the fluid muft move through AB asnbsp;quick again as it does through CD; fince, if itnbsp;moved with the fame velocity through both places,nbsp;the quantity of fluid which paffed through AB in anbsp;certain time, would be the half of what paflednbsp;through C D ; in which cafe the channel would notnbsp;remain equally full.

I�. If a fmall aperture be made in the bottom, cr in the fide of a veflfel full of water and open atnbsp;top ^ equal quantities of water will flow out of it innbsp;equal portions of time, provided the velTel be keptnbsp;continually full, by means of a proper fupply ofnbsp;water. But if the vefTel be not fupplied with waternbsp;(in which cafe the quantity of w^ater in it will benbsp;gradually diminilhed, until its furface arrives at thenbsp;aperture); then the water will flow out of the aperture with a velocity which is continually retarded;nbsp;and which has been found to be nearly equal to thenbsp;velocity which a body would acquire in fallingnbsp;tlirough a fpace equal to half the perpendicular altitude of the fluid above the aperture; hence thenbsp;velocity is as the fquare root of that altitude. (Seenbsp;what has been faid concerning the defeent of bodiesnbsp;in Chap. V. Part I.)

III. if in the bottoms or in the fules of eqiwl veflels containing water, equal apertures be made, butnbsp;at different diflances from the furface of the water;nbsp;then the quantities of water which will flow in ^

�given

given time, will be as the fqiiare roots of the altitudes of the water above the apertures refpedtivcly; fince, by the preceding paragraph, the velocities, arcnbsp;in that proportion.

IV. nbsp;nbsp;nbsp;In equal veflels full of water, if unequalnbsp;apertures be made at equal diftances below the fur-face of the water, then the quantities of water whichnbsp;flow in a given time, are nearly as the areas of thenbsp;apertures. , Hence, if cylindric veflels, full of water,nbsp;be equal in every refpedl:, except their having unequal apertures, the times in which they are emptiednbsp;�'vill be inverfely as the areas of their apertbres; andnbsp;if they are equal in every other refpeft, except innbsp;their diameter, then the times of emptying thera-felves will be as their contents refpedlively.

V. nbsp;nbsp;nbsp;Let a velTel of a cylindric or prifmatic formnbsp;be fet up perpendicularly to the horizon, and annbsp;aperture be made in its bottom ; then if the vcflelnbsp;be kept conftantly full by a fupply of water, twicenbsp;the quantity of water wjll flow out of the aperture

the fame time in which the veflTcl would empty bfelf if it were not fupplied with water.

The demonftration of thofe propofitions might hamp; cafily derived from the doftrine of motion al-feady explained¹ : but the determinations of thofenbsp;ptopofitions deviate more or lefs from the refultsnbsp;t^f afbual experiments; and this deviation is owing

to the following caufes or concurring circutn-ftances, which, on account of their uncertain or fiuduating nature, have not yet been fufficientlynbsp;invefligated.

Thefe are the peculiar natures of fluids, which vary, according to the temperature, purity. See.��nbsp;tire attraction of aggregation, or (as it is otherwifenbsp;called) the corpifcular attraSlionnbsp;nbsp;nbsp;nbsp;attraction of

cohefion; the friction againft the fldes of the veflels; the refiftance of the air �, the fize of the vefl�l innbsp;proportion to the aperture ; the fhape of the aperture j the-different directions in which the variousnbsp;parts, or (as they are otherwife called) the variousnbsp;filaments of the fluid of the fame veflel run towardsnbsp;the aperture ; and the vortices or irregular motionsnbsp;which are communicated to the fluid by a variety ofnbsp;caufes ; even by an obftacle to the ftream at fomenbsp;dillance from the aperture.

Actual experiments accurately performed, and obfervations attentively made on the motion ofnbsp;fluids, have fnewn the following faCts, which fornbsp;the fake of perlpicuity we fhali arrange under threenbsp;heads; viz. firlt, thofe which relate to fluids running through open channels j fecondly, thofe whichnbsp;relate to the running of fluids out of apertures; andnbsp;thirdly, thofe which relate to the jet itfelfout of thenbsp;aperture.

I. When water runs through a channel of an uniform fliape, and open ac top, as in fig. 6.nbsp;Plate XII. the water does not move with the famenbsp;2nbsp;nbsp;nbsp;nbsp;velocity

Velocity throughout the whole capacity or width of the channel j but its motion is fwifter throughnbsp;the middle of the upper furface, than nearer thenbsp;fiJes or the bottom, where its veloqity is partly-checked by the fridlion, adhefion, amp;c.

When the channel is not of an uniform lhape, or when it is interrupted by obltacles, the velocitiesnbsp;of the water at different tranfverfe feftions are notnbsp;inVerfely as the areas of thofe fe�lions; but theynbsp;differ more or lefs from that ratio, according to thenbsp;force of the dream, and tire peculiar configurationsnbsp;of the channel, and the obftacles which forced different parts or filaments of the ftream to run withnbsp;different velocities in different diredtions, whichnbsp;frequently crofs and check each other. Thus in thenbsp;ftream, fig. 8. Plate XII. the water in pallingnbsp;through the narrow part AB, will move with in-creafed velocity, and after having paffed that part,nbsp;its momentum will enable it to move on in thenbsp;ftraight diredlion ed-, but in confequence of thenbsp;attradlion of water to water, it will drag part of thenbsp;Water at e towards d, which occafions a deprefllon ofnbsp;the water about e-, hence the water from the adjacent parts fg, runs to fupply that defedt, andnbsp;thus a curvilinear or whirling motion dfg�, is produced.�Thefe whirling motions are called eddies.nbsp;�By this means the velocity of the ftream, in thenbsp;diredlioo e r/, is gradually checked, and its motionnbsp;ts communicated to the contiguous water in thenbsp;larger part ZR.�Farther on, the greateft part of

the ftream ftrikes againft the obftacle OS, which being aflant to its direflion, deftroys part of itsnbsp;force. With the other part of that* force, (agreeably to the law of the compofition and refolution ofnbsp;forces) the water runs in the diredtion OT, andnbsp;flrikes againft the bank at T, about which place itnbsp;meets the other part of the ftream, which runs innbsp;the diredlion d'V, and thus by crofting, they checknbsp;each other, amp;c.

The fame obfervations may be applied to the inequalities of the bottom. Thus, for inftance, let ABC, fig. 9. Plate XII. reprefent the bottomnbsp;of a channel which is hollowed at DB. EF re-prefents the furface of the water. Now the lowernbsp;part of the ftream, after having paflTed along thenbsp;hollow from D to B, will, agreeably to the laws ofnbsp;motion, tend to continue its motion in the laft di-redlion, viz. in the diredion from B towards Fjnbsp;and in faft at F, the furface of the water will benbsp;feen a little elevated above the reft. In this cafenbsp;two portions of the fame body of water run in different diredtions, viz. one part from B towardsnbsp;F, and another part from AE towards CF j hencenbsp;they muft partly obftrudt each other.

Such eddies and different diredlions may be clearly obferved in almoft any river or naturalnbsp;ftream of water, efpecially when the water containsnbsp;floating particles of earth and other folids. Bynbsp;pouring a fmall quantity of red wine, or of milk,nbsp;into a bafon full of water, a clear view of thofe

eddies, amp;c. may be exhibited in an eafy and familiar way. And the experiment may be varied by pouring the milk either in the dire�tion of the fide,nbsp;or towards the centre of the bafon; as alfo againfl:nbsp;^ fpoon, which may be made to reprefent an obfia-ole either againft the fide or at the bottom of thenbsp;VefTel.

The various changes and other phenomena ^hich take place in rivers, are almoft all dependingnbsp;opon the diretlions and the momenta of differentnbsp;parts of the ftream; fo that by a thorough examina-fion of the local caufes which produce them, thenbsp;Oaethods of ufing them advantageoufly, cr of re-��tedying the inconveniencies that arife therefrom,nbsp;may be frequently difeovered.�This is one of thenbsp;eflential advantages which mankind derives from thenbsp;knowledge of hydroftatics.

The water which runs in confequence of its gra-'^ity from a higher to a lower part of the furface �f the earth, in a channel generally open at top, isnbsp;Called a river.

A river which flows uniformly and preferves the l^rne height in the fame place, is faid to be in anbsp;Permanent ft ate. But fuch rivers are feldom if ever

From what has been faid above it is evident that the Water of a river does not flow with the fame ve-locity through the whole width of the river. Thenbsp;m which the water moves with the greateft ve-locity, is called the Fhread of the river, and this

174 Pf Motton of Fluids, amp;c. thread feldom lies in the middle of the river, but itnbsp;generally comes nearer to one fide than to the other,nbsp;according to the nature of the impediments, and ofnbsp;the configuration of the banks.

Rivers owe their origin to the natural fpiings, or mountains, or other elevated parts of the furface ofnbsp;the'earth, whence the water defcends through fuchnbsp;openings as nature, and fometimes art, offers to it.nbsp;I'lie waters of various fprings, by thus running towards the fame valley, frequently meet and form onenbsp;ftreaiTi, which, by paffing continually over the famenbsp;place, hollows the ground and forms itfelf a channel,nbsp;which, according to the nature and difppfition of thenbsp;ground, goes into various dire�tions, and alters itsnbsp;velocity, but always defcending from a higher to anbsp;lower place, until at laft it runs either into anothernbsp;river or into the fea, after having fometimes p'aflednbsp;over a tradt of fome thoufands of miles *.

The

* The proportional lengths of courfe of foine of the moft noted rivers in the world are flicwa nearly by the fobnbsp;lowing numbers.nbsp;nbsp;nbsp;nbsp;^

The velocity of the water of a river ought to in-cteafe in proportion as it recedes from its fource;

the numerous caufes of retardation, which occur in rivers, are produflivc of very great irreguiari-*^'^5; and it is impoffible to form any general rulesnbsp;determining fuch irregularities.

The unequal quantities of water (arifing from ��ains, from the melting of fnow, amp;c.) which arcnbsp;Conveyed by rivers at different feafons, enlarge ornbsp;^^ntradl their widths, render them more or lelsnbsp;^^pid, and change more or lefs the form of theirnbsp;^^ds. But independent of this, the fize and formnbsp;a river is liable to bq continually altered by the

ufual flowing of its waters, and by local peculiarities-The water conftantly corrodes its bed wherever h runs with confzderable velocity, and rubs off the fand,nbsp;br other not very coherent parts. The corrofion isnbsp;more remarkable in that part of the bottom, which isnbsp;under the thread of the river, or where the water de-feends, fucidenly from an eminence, as in a cajeade ornbsp;vjater-fall. The fand thus raifed is depofited in placesnbsp;where the water flacks its velocity, and there bynbsp;degrees an obftacle, a bank, and even an ifland, isnbsp;formed, which in its turn produces other changes.nbsp;Thus a river fometimes forms itfelf a new bed, or itnbsp;overflows the adjacent grounds.

In fome places we find that an obflacle, or a bent on one fide will occafion a corrofion on the oppofitenbsp;bank, by diredting the impetus of the ftream towards that bank. Thus, from divers caufes, whofenbsp;concurrence in different proportions, and at differentnbsp;times, forms an infinite variety, the velocity of riversnbsp;is never fteady or uniform.

� One of the pri.ncipal and mofl: frequent caufes,� fays the very able ProfeJJor Vlt;;nturi, � of retardationnbsp;� in a river, is alfo produced by the eddies whiehnbsp;are inceffantly formed in the dilatations of the bed,nbsp;� the cavities of the bottom, the in�qualities of tlgt;^nbsp;�� banks, the flexures or windings of its courfe, th^nbsp;� currents which crofs each other, and the flreai�**nbsp;which ftrike each other with different velocities. ^nbsp;� confiderable part of theforcc of the current is thn�

� employ

employed to reftore an equilibrium of morion, 'vhich that current itfelf does continually de-*' range * �

The ufe of rivers is immenfe.�They fertilize the ground ;�they fupply mankind and other ani~nbsp;with water, an article abfolutely necellary tonbsp;j�they ferve as tools for a variety of purpoles,nbsp;fuch as for giving motion to mills, pumps, and othernbsp;^^gines; they ferve for conveying the articles ofnbsp;Commerce, and for facilitating the intercourfe be-^'^fen inland countries. But I need not enlarge onnbsp;^ fubjedl, which is too obvious to need illuftration,nbsp;3nd which in the hands of many able writers, hasnbsp;^ften been adduced as a proper inftance of the infinite wifdom of Providence f.

JI. The running of water, or other fluid, out of a veflel, or refervoir, through any aperture, is like-'�^ife influenced by fome of the above-mentionednbsp;^aufes of retardation, as alfo by other peculiar cir-^Unaftances.

The ftream of water which ifllies out of a hole, '�Stids to carry aw'ay in its direftion any other fluid,nbsp;any fufficiently light folids, which may happen to

Exp. Enquiries on the lateral communication of motion to Fluids,nbsp;t For farther information refpedfing rivers, fee s�Grave-^ade�s Nat. Phil. B. III. chap. x. Rennell�s Account of thenbsp;Ranges, amp;c. in the Phil. Tranf. vol. 71�'. Guilislmini,nbsp;Natura de Flumi, amp;c.

be near it. This is what Profeffor Venturi calls the lateral communication of motion in fluids. But bynbsp;this lateral communication of motion to contiguous bodies, the celerity of the fluid itfelf isnbsp;checked more or lefs, and its, courfe is partlynbsp;diverted from the courfe which it would otherwifenbsp;follow.

Thus in fig. 10. Plate XII. which reprefeots the upper furface of two veflels contiguous to eachnbsp;other, and full of water, as high as the hole or aperture A.�If by pouring more water into the veflelnbsp;B, a ftream of water be caufcd to flow through A,nbsp;into the veflel C j this ftream will carry away thenbsp;water from the parts e e, towards C. But the de-preflron, or deficiency, of water at e e, is replacednbsp;by the water from the adjacent parts d d, which arenbsp;replenifhed from the next, and fo on. This produces eddies ?ci e d, e d. This phenomenon maVnbsp;be rendered more apparent if a little milk be atnbsp;times thrown into the velTel B, or if light andnbsp;fmall bodies float on the furface of the water.

When a ftream comes out of a hole, as at Agt; fig. II. Plate XII. if a thread, a feather, or othernbsp;light body be placed very near it, the tendency ofnbsp;the ftream to carry it away towards B, may benbsp;clearly perceived.�The following experim.ent willnbsp;fltew this property in a manner ftill more com

Let a veflel be made in the form of the lateral view A D B, fig. 12. Plate XII. viz. open at

and having one flant fide. Let a cylindrical pipe of about half an inch in diameterj and upwardsnbsp;a foot long, proceeding from a veffel C, comenbsp;ftraight down into the veflel AD B, and there letnbsp;termination F S, be bent in the direftion of thenbsp;^3nt fide BD. This done, fill the veflel ADBnbsp;'''ith water, then pour water into the velTel C ; fonbsp;that the water running down the pipe EFS, maynbsp;^orm the jet SK. It will be found that the waternbsp;of the veflel ADB, is carried away by the ftream,nbsp;^i^d this veflel is thereby almoft entirely emptied.

. The fanne communication of motion may be perceived within a tube; as is ftiewn by the following experiment of ProfeflTor Venturi.

, To an aperture on the fide of the veflel A B, fig. 13. Plate XII. a pipe CD, 1,6 inches innbsp;diameter, and little more than 5 inches long, wasnbsp;adapted in an horizontal direction. At E, diftantnbsp;0,71 inches from the fide of the veflTel, a bent glafsnbsp;tube EFG, was joined, whofe cavity was openednbsp;tnto that of the pipe, whilft its other extremity wasnbsp;inamerfed in coloured water, which was containednbsp;lit a fmall veflel G. When by pouring water intonbsp;velTel A B, a ftream was made to flow out at D,nbsp;i-hc coloured water was feen to rife confiderably innbsp;lower leg of the glafs tube.

This experiment being repeated, when the de-fccnding leg FG of the glafs tube was only 6,4 inches longer than the afeending leg EF. The colourednbsp;'�ater of the veflel G, rofe through the glafs tube,

l8o Of the Motion of Fluids^

and mixing with the other water, flowed with it out of the pipe at D and in a' fhort time the veflelnbsp;G was emptied.

This fort of fuftion or communication of motion takes place, whether the difcharging pipe C D, be diredted horizontally, or downwards, or upwards¹.

In a defcendlng ftream this power of communicating motion to the adjacent bodies, is rendered more active by, ornbsp;rather it may be better explained, on account of, the tendency that a defeending ftream has to divide itfelf into fe-parate portions, and of the prefllire of the atmofphere. Thisnbsp;tendency is owing to the acceleration of falling bodies.nbsp;Suppofe, for inftance, that there comes out of a hole at thenbsp;bottom of a veflel, an ounce of water per fccond of time;nbsp;then, when the firll ounce has been falling during two fe-conds, it muft have percurred a fpace equal to 4 times 16nbsp;feet nearly; whereas the fecond ounce of water having comenbsp;out one fecond later, has been falling during one fecondnbsp;only, and of courfe it muft have run through 16 feet only;nbsp;therefore the diftance of the firft ounce of water from thenbsp;next is equal to 3 times 16 feet.

At the end of three feconds, the firft ounce of water muft havepafled along 9 times 16 feet;/whilft the fecond ouncenbsp;of water has pafTed along 4 times 16 feet; fo that thenbsp;diftance between the firft ounce of water and the fecond,nbsp;now is 5 times 16 feet; which one fecond before was onlynbsp;3 times 16. Therefore the two ounces of water, or anynbsp;contiguous 'parts of the defeending ftream (for the fain�nbsp;reafoning may be evidently applied to any portions, or t�

Of the Motion of Fluids, ^c. nbsp;nbsp;nbsp;181

When wafer runs out of an aperture on the thin fide or bottom of a veflel, as at A, fig. 11. Platenbsp;the fize of the aperture being very fmall in

naiple particles, of a fluid, and to any portions of time) a conflant tendency to feparate, and they do adfuallynbsp;Pirate into irregular maffes, when the ftream defcendsnbsp;a fufflcient fpace ; and at the fame time the air forcesnbsp;3rgt;y contiguous bodies that are fufficiently moveable, ornbsp;��^'^toduces itfelf between the intcrftices, and is driven down-^3rds by the fucceeding parcels of water.

This is the reafon which, when a fluid, (fuch as beer, is poured out of one veflel into another in a longnbsp;team, mixes a confiderable quantity of air with the liquor,nbsp;��od produces the froth. Upon this principle the machinenbsp;blowing the fire of a furnace, by means of a fall of water,nbsp;conftrudled, ag will be deferibed in the fequel.

The refiftance of the air, the adhefion of water to water, the various fhape of the flream, render the feparation ofnbsp;'Is quot;parcels not very regular, and generally fpread or dividenbsp;longitudinal filaments.

The rain-water which in fome places flows from the tops ^^^houfes through fpouts, and falls in the flreets, in its fallnbsp;Pirates into parcels, and ftrikes the ground with diftinftnbsp;�''^s and ample furface.

� I Went,� fays ProfeJJor Venturi, to the foot of the cafeades ^dich fall from the glaciere of la Roche-Melon, on thenbsp;leaked rock at la Novalefe, towards Mount Cenis, andnbsp;^ound the force of the wind to be fuch as could fcarcely

^�'tried to the bottom, whence it rifes with violence^ and d'fperfes the water all round in the form of a mift.�^

proportion

proportion to the fide or bottom of the veflfel; the . ftream A B, is not throughout of the fhape of thenbsp;aperture, nor is it of an uniform fize. When thenbsp;aperture is circular, the diftance of the narrowednbsp;part of the ftream, from the infide furface of thenbsp;veffel, is about equal to the diameter of the aperture. This narroweft part of a ftream has beennbsp;called the contracted vein (vena contrast a by Newton) from which place forwards the ftream growsnbsp;larger, and fometimes divides itfelf into differentnbsp;parcels.

The diameter of the contrafted vein ; that is, of the narroweft part of the ftream, is fubjed to anbsp;little variation ; but from a mean of various mea-furements, it appears equal to 8i hundredths of thenbsp;aperture; fo that if the diameter of the aperture benbsp;one inch, the diameter of the vena contraSla willnbsp;be 0,81 of an inch

This contradion of the ftream is undoubtedly owincr to the various diredions in which the fluid

comes along the fides, and from every part of the veffel, towards the aperture, as is indicated by fig*nbsp;14. Plate XII. and in fad, when the aperture i*nbsp;very large in proportion to the fize of the velfthnbsp;the contradion of the ftr�am is not fo apparent-Alfo, if the aperture be not in a plate fufficiently

the vena contradla will not be perceived �, for fince the diftance of that contradlion front the innernbsp;Surface of the veflel is about equal to the diameternbsp;^f the aperture, if the thicknefs or rather the lengthnbsp;^^the aperture, exceed its diameter, as when a pipenbsp;added to the aperture; then the contraction, ornbsp;tendency to form the contradlion, takes placenbsp;that thicknefs, or within that length of

- The velocity of the water is not the fame in ^'^ery part of the ftream; for fince the famenbsp;T�antity of water muft pafs through every tranf-fedtion of it in a given time, the velocitynbsp;be inverfely as the area of each tranfverfenbsp;^^ftion. Therefore at the vena contraFa the ve-^ocity is greater than at the aperture. Now it hasnbsp;, *^*tennbsp;nbsp;nbsp;nbsp;fj-Qu, experiments, that the velocity of

fiuid at the aperture, fuppofirlg this to be cir-, nbsp;nbsp;nbsp;auj jg i^e made in a very thin plate, is very

quot;^3rly fuch as a body would acquire by falling perpendicularly from an altitude equal to half thenbsp;Perpendicular height of the fluid in the veflel,nbsp;^oove the centre of the aperture; and that the ve-^ocity ac the vena contraQa is fuch as a body would

acquire by failing perpendicularly from that whole height (a.)

If'to the circular aperture on the fide of a vefTel, there be applied a cylindrical pipe of the famenbsp;diameter, and whofe length is equal to from two to

(2.) The velocity of the fluid at the aperture maybe deduced from the quantity of fluid tvhich is found uponnbsp;trial to be difcharged in a given time ; and this is to be donenbsp;in the following manner.

Call the area of the aperture a; let ^ reprcfent the quantity of fluid which has been difcharged in the time f, which means the number of feconds of time; and let x exprefs thenbsp;velocity; that is, the fpace defcribed in one fecond of time.nbsp;Then imagining that all the fluid j is formed into a cylinder,nbsp;�whofe bafe is rr, and height we fhall have qzzahy

The proportion between the velocity at the vena con-iraSla-) and at the aperture, is found by faying, as the area of the former is to the area of the latter, fo is the velocity at thenbsp;aperture to the velocity at the vena contra�ia\viz. (fince thofenbsp;areas are nearly fimilar, and fimllar areas are to each other asnbsp;the fquares of their homologous fides, or of their diameters)nbsp;b,8ib tTl�; : 0,6561 : i ; : i ; 1,52, which, the readernbsp;is requefted to obferve, is nearly the ratio of i : / 2 jnbsp;fquare root of 2 being 1,414, amp;c.

four

^our times that diameter, as AB, fig. 15, Plate then a greater quantity of water will benbsp;^ifcharged through it than through the fimple aper-in an equal portion of tinie, every other cir-^^mftance remaining the fame; the quantities ofnbsp;fluid difcharged in thofe two cafes being as 133 tonbsp;*00 nearly.�The pipe A B, or any other prolongation of whatever fhape it may be, which is adapt-to the aperture of a veflel, amp;c. has been callednbsp;adjutage, probably from its property of promot-the difcharge of fluid.

ft has been alfo obferved, that the difcharge in a �'Ven time is the fame, whether the aperture benbsp;^titnilbed with the above-mentioned cylindric pipe,nbsp;with the pipe reprefented in fig. 16. Plate XII.nbsp;''^hich differs from the former only by its having,nbsp;to the fide of the veflel, a contraction nearlynbsp;the fhape of the contracted vein.

If the laft mentioned pipe be cut off at the con-*ta6tion, and the firfl: conical part only be left affixed lu the aperture, as in fig. 17. Plate XII. then thenbsp;difcharge of water is rather lefs than from a fimplenbsp;aperture j but it is probable that it would be quitenbsp;��flu fame, were it poffible to make the conical adju-exaftly of the fhape of the natural contraClednbsp;j excepting however the effedl of .fl'iflion.

If to this conical part a cylindrical tube of the diameter of the fmall part of the conical pipe, benbsp;applied, as in fig. 18. Plate XIl. the difchargenbsp;of fluid will thereby be diminiihed, and more fo

186 nbsp;nbsp;nbsp;Of the Motion of Fluids, (Fc.

a diverging pipe, viz. another conical tube be applied, as in fig. 19. Plate XII. thenbsp;difcharge of water will thereby be increafed withinnbsp;a certain limit ¹. And if between diofe two conical parts a cylindric tube be interpofed, as innbsp;fig. 20. then the difcharge is diminiamp;ed again;nbsp;but not nearly fo much as if the outer conical partnbsp;were removed�]�.

Experience, fiiews that the divergency of this' termination muft not be increafed beyond a certain degree, for in that cafe it will prove rather difadvantageous than ufefuh Itnbsp;appears that wlrcii the divergency is greater than an anglenbsp;of 16 degrees, the efFeift ccafes entirely; and that the greateftnbsp;effefl takes place; that is, the greateft quantity of fluid iSnbsp;difeharged, when the divergency is equal to an angle of aboutnbsp;three degrees.

f I he efredfs produced by the above-mentioned adjutages, and the exact quantity of water which is dif-charged through certain apertures, may be derived frcin the refults of ProfeTfor^Venturi�s Experiments, which arenbsp;concilely lubjoined.�The meafurcs 'arc Englifh, except thenbsp;contrary be expreircd,

'I'hc lame quantity of water (viz. 4 French cubic feet, equal to 4,845 Englifli cubic feet) flowed out of the famenbsp;veiTcI, or relcrvoir, which was kept confiantly full, throughnbsp;the following adjutage.s, in the annexed times, which are ex-prefled in feconJs. 'I'he aUitade of the water in the veflelnbsp;quot;nbsp;nbsp;nbsp;nbsp;'nbsp;nbsp;nbsp;nbsp;abovs

Of the Motion of Fluids', amp;c. nbsp;nbsp;nbsp;187

A remarkable advantage is derived from the knowledge of this faft, which is, tliac when water isnbsp;Conveyed through a flraight cylindrical pipe ofnbsp;'whatever length it may be, the difcharge of waternbsp;be increafed by only altering the drape of thenbsp;terminations of that pipe, viz. by making the end of

above the level of the centre of the outer aperture of the adjutage was always equal to 32,5 French inches, or 34,642 Englifli inches.

Through a fimple circular aperture, in a thin plate, the diameter of the aperture beingnbsp;equal to 1,6 inches, in �nbsp;nbsp;nbsp;nbsp;�nbsp;nbsp;nbsp;nbsp;41quot;.

as above, and 4,8 inches long. Fig. 15. in 31quot;. Through the tube, fig. 16. which differs fromnbsp;the preceding, by having the contradfion innbsp;the lhape of the natural contracted vein, in 31�fnbsp;Through the fliort conical adjutage, fig. 17.nbsp;which is only the firfl conical part of the pre-ceding, innbsp;nbsp;nbsp;nbsp;�nbsp;nbsp;nbsp;nbsp;�nbsp;nbsp;nbsp;nbsp;�* 42quot;.

Through the pipe, fig. 18. which confifts of a cylindrical tube, adapted to the fmall conicalnbsp;end of fig. 17. and of that diameter, ADnbsp;being 3,2 inches long, innbsp;nbsp;nbsp;nbsp;�nbsp;nbsp;nbsp;nbsp;� 42',5-

Through the like adjutage, but longer, AD being 12,8 inches, innbsp;nbsp;nbsp;nbsp;�nbsp;nbsp;nbsp;nbsp;� 45 ^*

Through the like, kill longer, A D being 25,6 inches, innbsp;nbsp;nbsp;nbsp;�nbsp;nbsp;nbsp;nbsp;�nbsp;nbsp;nbsp;nbsp;� 48''.

Through the adjutage, fig. 22. W'hich confifts of the fimple tube of fig. 15. placed over thenbsp;Conical part of fig. 17. innbsp;nbsp;nbsp;nbsp;��nbsp;nbsp;nbsp;nbsp;.� 32'',5.

the pipe, which is clofe to the refervoir, or the entrance to it, of the fhape of the contracEled vein, (as at A, fig. 21.) the dimenfions of.which havenbsp;been fiated in p. 182; and by making the othernbsp;extremity BC of the pipe, in the fhape of a truncated cone, whofe length BC may be equal to ninenbsp;times the diameter of the cavity at Bj and whofenbsp;aperture at C may be larger than the diameter at B,nbsp;in the ratio of 18 to 10.�By this means the quantity of water which is difcharged in a given time,nbsp;will be more than doubled j viz. the quantity ofnbsp;water difcharged by the fimple cylindric pipe, is tonbsp;the quantity of water which is difcharged by thenbsp;fame pipe with the above-mentioned conical terminations, as 10 is to 24 nearly.

The elfedl: of the above-mentioned adjutages is the fame, whether they be adapted to the fide or tonbsp;the bottom of the veffel, or in any other di-redtion, provided every other circumftance be thenbsp;iame; fuch as the capacity and form of the

Through the double cone, fig. 19. the dimenfions of which are, AB �EF=:i,� inches,

AC = 0,977 inches, CD = 1,376 inches, and the length of the outer cone =4,351nbsp;inches, innbsp;nbsp;nbsp;nbsp;�nbsp;nbsp;nbsp;nbsp;�

Through the adjutage, fig. 20. confifting of a cylindrical t�be 3,2 inches long, and 1,376nbsp;inches in diameter, interpofed between thenbsp;two conical parts of the preceding, innbsp;nbsp;nbsp;nbsp;��nbsp;nbsp;nbsp;nbsp;28quot;,5.

rtfervoir, the altitude of the water above the level of the centre of the outer opening of the adjutage, amp;c.

AH flexures, and all forts of internal contraflions, elongations, enlargements, and projedlions, of thenbsp;oendufting pipe, diminifla the quantity of difchargenbsp;tOore or lefs, according to the number and form ofnbsp;fuch irregularities, fliarp angular bendings hin-^ering the motion of the fluid, more than thofenbsp;of a regular curvature. The caufe of this retardation is undoubtedly owing to the eddies, and to thenbsp;orofllngs of .the various filaments of the fluid, which,nbsp;iiocording to what has been faid above, mufl: ne-ooflarily take place at thofe irregularities. This maynbsp;fio rendered fufficiently evident, if an irregular glalsnbsp;pipe be applied to a pretty large veiTel full of water,nbsp;with the water there be mixed fome particles ofnbsp;bounded amber, or other fubftance, whofe fpeclficnbsp;gravity differs but little from that of water.�All ed-and crofs diredtions mufl; unavoidably deftroynbsp;P3rt of the moving force.

Whenever an irregularity of the fliape of the aperture, or fome particular conformation of thenbsp;'^^flelj compel the particles of the fluid to run ob-towards an aperture, a circular motion isnbsp;f^on communicated to the fluid, and an hollownbsp;quot;quot;fiirl is formed above the aperture. By the circu-

_ ^notion the particles of the fluid acquire a cen-'�bfugai force, in confequence of which they tend to ^^cede from the centre or from the axis of motion,

where of courfe a hollow is formed, which is larger or fmaller, according as the rotation of the fluid isnbsp;more or lefs rapid. When this whirling motion isnbsp;pretty confiderable, if any light bodies float upon itgt;nbsp;thofe bodies will be readily drawn downwards to-^vards the aperture; for, fince the fpecific gravitynbsp;of the fluid is greater than that of the bodies, thenbsp;fluid will acquire a greater degree of centrifugalnbsp;force, and will recede farther than thofe bodiesnbsp;from ^he axis of the whirl. See chap. IX. ofnbsp;Part I.nbsp;nbsp;nbsp;nbsp;^

III. The laws of projeftilcs, which have been explained at the end of the firft part of thefe eie-raents, are applicable to fluids as well as to folidsgt;nbsp;excepting fome peculiarities which are eafily fug'nbsp;gefted by tlie nature of fluids. � Therefore the principal phenomena relative to the direflion, and thsnbsp;length of ,a ftream of fluid which ifllies out ofnbsp;aperture, may be determined by the laws of prO'

When fluids, like folids, are projefted in an oblique direblion, they defcribe parabolic paths; f-'�� tliey are at the fame time abled upon by the pt^'nbsp;jeflile force, and by the force of gravity, except^'nbsp;ing the deviation from that parabolic curve whiobnbsp;is occafioned by the refiflance or the air. But wh^^nbsp;they, are projebled perpendicularly upwardsnbsp;downwards, tl'.en they move in ilraight lines ;nbsp;yet thofe Ilraight lines might be confjdcred asnbsp;bolas grown infinitely nanow.

When a fluid comes out of a hole in the thin fide ^f a veflel, the velocity of � projedlion mufl; benbsp;��^clconed equal to that of the, z'-ena contraEla whichnbsp;'S very qear the aperture, and not to that of the fluidnbsp;the aperture itfelf. Therefore this velocity ofnbsp;projection is as the fquare root of the perpendicularnbsp;^hitude of the water above the centre of the orifice,nbsp;p. 183); whereas the velocity of the aper-ture itfelf is as the fquare root of half that altitude ;

Hut w'hen a pipe is adapted to the aperture, then tbe velocity of projedtion is nor fo great j for innbsp;��His cafe there is no contraclion of the ftream.

Independent �f this circumflance, the velocity of projedlion, and the diftance to which the jet cannbsp;feach, are influenced by other circumflances; viz.

By the fridlion againft the fldes of the pipe or Aperture. 2. By the refiftance of the air, in con-IHquence of which the jet is obltrudled throughout,nbsp;is divided at fome unafcerrainable diflancenbsp;j'oni the aperture. 3. By the v/eight of the fluid,nbsp;�helfj for when the highefl; particles of a perpendi-^ular jet ceafe to have motion, as alfo in their defcAit,

even of the edge of the aperture in a tirin' P'^te, Various parts of the fame jet acquire differentnbsp;'�^iocities, but in virtue of the attradlion of water

tion which arifes therefrom, the whole jet prefently acquires, and, for a certain length at leaft, proceeds with the fame velocity in every part of anbsp;tranfverfe fedion. But this velocity is a mean ofnbsp;the different velocities with which the variousnbsp;parts of the jet come out of the aperture ; for whilftnbsp;the filaments of greater celerity alTill; the motion ofnbsp;thole which have a lelTer celerity, the latter tend tonbsp;retard the former : therefore it fhould feem thatnbsp;' with a larger aperture, every thing elfe remainingnbsp;the fame, the velocity of projeflion mull be greaternbsp;than with a fmaller aperture; and this is true to anbsp;certain degree. But then another circumftance interferes, which is the refiftance of the air; for anbsp;larger jet, by prefenting an ampler furface to thenbsp;air, is liable to be divided by it, and by this divifionnbsp;the furface is increafed confiderably, which rendersnbsp;tire refiftance of the air much greater that refift-ance being, ceteris paribus, proportionate to thenbsp;furface.

Now all thofe circumftances, namely, the friction againft the Tides of the aperture j the divifion of thenbsp;ftream, which increafes not only according to thenbsp;fiz_e of the jet, but likewife according to its initialnbsp;velocity; and the refiftance of the air, are fo verynbsp;Iluftuating, that it is impofiable to fubject them tonbsp;calculation.

Experience only can inform us of the efFeffs W'hich may be expedled in certain circumftances:nbsp;yet as the experiments can hardly ever be repeated

^ftder the fame circumflances precifely, the laws '''hilt;-h are deduced from thpir general refults, muftnbsp;always be admitted with fonie latitude.

11quot; a velfel or refervoir of water be conftrudted lomevvhat like the reprefentation of fig. 22. PI. XII.

a hole be made in the thiiu fide at A, the water' � '''hich iflues out of it will afcend in a perpendicularnbsp;enlarging and dividing itfelf towards the top \nbsp;it will not rife fo high as the level of the-^furfacenbsp;^ of the water in the velfcl �, and it will rife fcillnbsp;Jofs high, if a pipe be adapted to the aperture, asnbsp;fig. 23, or if a bent pipe proceed from a veflcl, asnbsp;fig. 24. which is owing to the above-mentionednbsp;oaufcs of obftrudionj and in fad by removing thofenbsp;Caufes, at leaft in part, the height of the jet may benbsp;�^'oreafed ; obferving however that it can never benbsp;�^''ade to equal the height of the water in the re-fervoir,

*n proportion to the aperture, becaufe in that the water will move very flowly through thenbsp;in proportion to what it does out of the aper-and of courfe the fri�lion will be much lefsnbsp;'^^n if the pjpe ^he aperture vvere both of thenbsp;diameter. It is alfo for the fame reafon thatnbsp;will afcend higher when the conduit pipe isnbsp;n.nbsp;nbsp;nbsp;nbsp;onbsp;nbsp;nbsp;nbsp;fhorc

fhort than when it is long; and that the common figure of the pipes, from which the water fpoiits,nbsp;which is that of a truncated cone of confiderablenbsp;length, will not let the jet afcend fo high, nor be fonbsp;uniform and tranfparent, as if a large tube were covered with a flat plate, and a fmooth hole for thenbsp;exit of the water were made in the middle of thatnbsp;plate.

By enlarging the aperture, the friflion againfl: the fides is diminilbed ; but the friftion or oppofi-tion of the air is increafed. Therefore as long asnbsp;the former is diminifhed failer than the latter is increafed, the jet may be made to afcend higher andnbsp;higher by enlarging the aperture ; but beyond thatnbsp;limit the enlargement of the aperture will not in-creafe the height of the jet. Now it has been foundnbsp;from a variety of experiments, that this limit, ofnbsp;maximum of effedt, takes place when the diameternbsp;of the circular aperture is fomewhat lefs than annbsp;inch and a quarter ; fo that, cateris paribus, ths-height of the jet will be lefs, when the aperture i;*nbsp;either larger or narrower.

With a higher refervoir full of water, the perpendicular, or the nearly perpendicular, height of thfi^ jet is greater than with a lower refervoir ; but thi�nbsp;alfo has a limit; and it appears from a variety ofnbsp;experiments, that�a jet cannot rife higher thaf*nbsp;about too feet, be the height of the v/ater in thenbsp;refervoir ever fo great. For the higher the waternbsp;is in the refervoir, the greater is the velocity at th^

Aperture; and when that velocity has attained a �^��tain degree, the great refiftance of the air breaksnbsp;ftreafn into fmall drops, which prefent a vaftnbsp;^'^�I'face to the air, and are of courfe foon checked innbsp;^^eir motion *.

a femicircle, as A D M B, fig. 25. Plate XII. drawn upon the perpendicular fide A B (as anbsp;^'3rneter) of a veflel A K 1 B, wiiich is kept con-ftantly full of water ; and if a hole be made innbsp;thin fide of the vefiel, as at C ; alfo a line,nbsp;CD be

drawn parallel to the horizon from the hole the femicircle; then the fluid which iffues fromnbsp;hole C) will form a iet in the parabolic curvenbsp;and will fall upon the horizontal line B F, at a

156 nbsp;nbsp;nbsp;Of the Motion of Fluids, amp;c.

diftancc B E from the veffel, which is equal to twice the length of the line CD.�The dilfancenbsp;is called, as in folid projedtiles, the amplitude ofnbsp;the jeti

This however miift be underftood for refervoir� or veflels of fmall heights, ivhere the cfFedl of the re-fiftance of the air is inconfiderable ; otherwife thenbsp;deviation from the above-mentioned law is great andnbsp;uncertain (3.)

It evidently follows, that when the hole is mads at H, viz. in the middle of the altitude, then thenbsp;amplitude BF, or the diflance from the bottom B

(3.) In Prop. I. of the note to the laft Chapter of part I. it has been demonhrated, that the velocity of a pro-jeefile in any point of the-parabolic path, is the fame as itnbsp;'would be acquired by falling perpendicularly along on^nbsp;quarter of the paraineter belonging to that point as a vertex. It has alfo been fliown, that the fluid which conies outnbsp;of the hole C, deferibes the parabola C E, and that its veio'nbsp;city at the veha contraSia, which is very near the aperture,nbsp;is the fame as it would acquire by falling perpendicularly frottnbsp;A to C ; therefore A C is the fourth part of the parametetnbsp;which belongs to the vertex C of the parabola C E. No'''nbsp;one of the properties of the parabola is, that the fquare ofnbsp;ordinate is equal to the product of the correfponding abicifl-^nbsp;nniltiplied by the parameter; thcreforcTrEl'�=4 AC X CB�nbsp;Hence BE � 2 �?A C x C B ; and | B E = s/riC xnbsp;But by the property of the cirdu (Eucl. p. 35. Book iBdnbsp;v'A(r'gt;rc''B = C D. Therefore i B E = CD.�Ehi�nbsp;reafoning is evidently applicable to any point iu the

�^f�the veffd, where the jefwill fhrike the horizontal plane, is the greateft pofTible. Alfo that when anbsp;is made at an equal diftance from the bafe, asnbsp;that another hole is from the top of the refer-as at C j the amplitudes will be equal, viz. thenbsp;wi]] fti-ii^e tlie horizontal plane in the fame pointnbsp;^ gt; becaufe in that cafe the line C D is equal to thenbsp;line LM.

When the initial diredfion of the jet is neither P^' pendicular nor parallel, but oblique, to the hp-P2on, then its parabolic path differs in altitude,amp;c,nbsp;^'^cording to the angle of inclination. But the va-particulars which belong to it may be deter-^�'led from the theory of projedliles, which hasnbsp;delivered in the lafl; chapter of the firft partnbsp;thefe elements ; obferving however that thofpnbsp;^beoretical refults are nearly true for fhort diftancesnbsp;; but that when the diftances, fize of the jet,nbsp;are more confiderable, then nothing but adtuaJnbsp;^^Periments can determine the refult *.

� gt; De Prony�s Architeft. Hydraulique; Venturi 9a lateral communication of motion in fluids; Vince�snbsp;1 ��tiftatics, amp;c. as alfo moft of the other works whichnbsp;� Stationed in the note, p. 113. at the end of chap. IV,

[ �gs ]

OP PNEUMATICS, OR PERMANENTLY ELASTIC FLUIDS ; OF THE ATMOSPHERICAL AIR j AN�nbsp;OF THE BAROMETER.

The whole globe of the earth is furroundet^ by, or is involved in, a fluid, railed atrnbsp;which though not perceived by our eyes, is, however, manifefted in various ways. This fluidnbsp;up the fpace from the furface of the earth to thenbsp;height of feveral miles above it, and the wholenbsp;of it is called the atmojphere.

As filhes are furrounded by water, and live and move in water, fo are we human beings, and aflnbsp;other animals, furrounded by air, and live and moV^nbsp;in air.

A fifli which is taken out of the water, will di^ in a fnort time, and a human being, or any anifU¹'^^nbsp;taken out of the aerial fluid, will in general di^nbsp;much fooner.

Water gravitates towards the centre of the earth� and fo does the air¹. Hence, as a fifh or other bodfnbsp;in water is preflTed on every fide by that fluid, fo ar^nbsp;other animals, amp;c. prefled on every fide by the f�'''

The prefilire of the air was firft aiTerted by tbcGr¹^^ Galileus, and was fqon after illuflrated by his fcholar T�^'-ricellius.

�'Ouuding air, and this preflure (as will b� Ihewn in the fequel) is very confidcrable.

As the progrefTive motion of water from one plice towards another, is called a current of water;

the progrei�ive motion of the atmofpherical air is '^^lled in general wind, which according to the dif-ferent velocities of that fluid is more particularlynbsp;Specified by the appellations of breeze, gentle wind,nbsp;(Pc.

But the particulars in which air principally differs h'om water, arc 1 ft, that air weighs a vaft deal lefsnbsp;than water j and adly, that water is not compreffi-whereas a quantity of air may be forced into anbsp;hnaller fpace, by means of preflTure, or it may benbsp;Expanded by removing the preffure j and that ex-Piinfibillty, as far as we know, may be extended tonbsp;any degree j nor is it diminiftied by long continuednbsp;PtelTure.

Air is abfolutely necefTary to animal life, as alfo combuftion, to vegetation, and to ocher naturalnbsp;Ptoceftes. In all thofe procelTes the air either com-ttiunicates fomething to the fubftances concerned,nbsp;it receives fomething from them. But this property of receiving or giving is limited; for inftance,nbsp;^ Certain quantity of air is necefTary for the life ofnbsp;animal durinsr a mven time; now when the animalnbsp;has lived in it that length of time, the fame quantitynbsp;cf air will be unfit for the fupport of the li:e of thatnbsp;of any other animal. And the fame thing muftnbsp;04nbsp;nbsp;nbsp;nbsp;be

Thofe latter properties of the air are called its chemical 'properties, which will be explained when v/enbsp;corrte to treat of chemiftry �, whereas its other properties, fuch as its gravity, comprefiibility, amp;c. arenbsp;called Its mechanical properties, and thefe will be examined in the prefent chapter.

I fhall juft mention for the prelent, that befides the atmofpherical air, wi'.ich furrounds the earth,nbsp;there are other permanently elaftic fluids, the chemical properties of which are eflcntially differentnbsp;from thofe of air; though their mechanical properties are fimilar to thofe of that atmofpherical fluid ;nbsp;on which account they are all comprehended undernbsp;the general appellation o� aerial fluids, or oi peryna-yyently elaftic fluids j which expreftion means, that, asnbsp;far as we know, they are not convertible into a vift-ble fluid by means either of preffure or of cold j andnbsp;thence they are diftinguiflicd from vapours, as fromnbsp;the vapour or fleam of water, which is likewife annbsp;elaftic fluid, but not permanently fo j for either bynbsp;cooling, or by means of prcITure, that vapour is converted into water.

The principal mechanical properties of air are its weight and elafticity j but let us begin by manifeft-ing its exiftence.

When a perfnn blows upon a thread, or duft, ot Other light bodies that are placed at a fhort diAance

from his mouth, the light bodies are driven away 'from their places. Now it is the current of air,nbsp;ttiat being expelled from the lungs through thenbsp;^outii, drives the light bodies in its way.

turn it upfide dowm, and holding it in that Perpendicular pofition, immerfe it in water, as at A,nbsp;I. Plate XIII. it will be found that the waternbsp;not enter the glafs.�That fubftance whichnbsp;dvus prevents the entrance of the water into the ca-of the glafs, is a quantity of air. If you inclinenbsp;glafs a little, a bubble, viz. a certain quantitynbsp;�f air goes our, and an equal bulk of water takes itsnbsp;P^3ce. If the glafs be inclined ftill more, all the airnbsp;''�ill efcape from it, and the glafs will be entirelynbsp;filled with water.�The various parts of this expe-^'��rient may be explained in a more particular man-; thus, when the glafs is in the fituation A, thenbsp;in it, being the lighter fluid, is confined by thenbsp;quot;quot;^ater which occupies the aperture of the glafs j butnbsp;air being compreffiblc, the preiTure of the fu-P�rincunnbent water A B, (p. 31.) forces the airnbsp;a narrower fpace ; hence the water will benbsp;to afcend a little.way within the glafs at B, andnbsp;^*1^ lower you immerfe the glafs, the higher willnbsp;Water afcend within it. When the ^lafs is in-�incd, as at D, the furface of the water-fin it, whichnbsp;*'i^'nains alv/ays horizontal, ds, (p. 28.) and thenbsp;^11� occupies d;c fpace c, the lower part of which isnbsp;^'�^n with the edge d of the glafs. If the glafs be

The quantity of air. which thus cfcapes from the cavity of the glafs, being preffed on every lide bynbsp;the water, is forced to aluime a globular form, innbsp;winch lliape it is called a huhhle, which being lighternbsp;than an equal bulk of water, afeends to the furfacenbsp;of the latter, where it mixes with the common mafsnbsp;of atmofphericai air.

But frequently, when the bubble is fmall, it remains for a certain time on the furface of the water, enclofed in a film cr fhell of water; which is owingnbsp;to the vifeidity of the water, or to the attraftion mutual between the particles of water. In fadt, whatever increafss that vifeidity, fuch as a folution ofnbsp;foap, which is frequently praftifed by children, ornbsp;of any other glutinous matter, will increafe the durability of the bubbles, and in that cafe, by blowingnbsp;into the folution, the bubbles may be made verynbsp;large *,

Hence it appears that a bubble of air is not, according to the vulgar idea, an empty fpace, a mere nothing; but that it confifts of a fluid, which.

�*** Diftillers and other perfons that have occafion to tty fpecimens of fplrituous liquors, can ferm a tolerably accuratenbsp;idea of the flrength of thofe liquors, by fliaking the bottle,nbsp;and then obferving how foon the bubbles break on the fut'nbsp;face of the liquor ; for the thinner and purer the fpirit is,th�nbsp;iooner will the bubbles break.

Permanently Elaftic Fluids, ^c. nbsp;nbsp;nbsp;203

though invifible, has however weight and other qualities; and is, in fhort, a fubftance as muchnbsp;as any ocher fubftance which we feel or tafte *.

When by inclining the above-mentioned glafsfuffi-ciently in water, all the air is fufFcred to cfcape from Jtj then if this glafs be again turned with its aperture downwards, and in that pofition be drawn upwards, until its aperture remains a little below the

* The invifibility of air is what fuggefts the vulgar idea cgt;f its being nothing. But it muft be confidcred, that transparent bodies, viz. fuch as let the rays of light pafs freelynbsp;through them, cannot be feen. Thus water, glafs, air, amp;c.nbsp;cannot be perceived by an eye which is entirely furroundednbsp;hy any one of them. And even when that is not the cafe,nbsp;We can only perceive thofe fubftances by the heterogeneousnbsp;bodies which they may happen to contain, or by the inflexion,nbsp;tefraclion, amp;c. of the rays of light at their furfaces ; hence.nbsp;When fuch bodies are pure, and th�ir furfaces are removednbsp;bfom our fight, fo that we cannot obferve the bending of thenbsp;fays of light at thofe furfaces, then it is im'ioffible tonbsp;'bfcern the bodies themfelves.�If a glafs bbtde entirely filednbsp;quot;'bh pure water, be fituated againft a dark place, fo that nonbsp;objefts maybe feen through it, a perfon who looks diredblynbsp;b will not be able to fay whether the bottle be full ofnbsp;^ater or not.

f he particles which are feen moving about when light paffes through a hole in a rpon otherwife dark, are not the.nbsp;Pai tides of air, but they are particles of dull, fee. which floatnbsp;1*1 the air.

furface

furface of the water in the bafon, as at N, the glais will remain entirely full of water; the preffure ofnbsp;tlie atmofphere on the furface of the water of thenbsp;bafon forcing or keeping up the water which fillsnbsp;the glafs. Nor, in this cafe, can any air enter thenbsp;cavity of the glafs, becaufe air being fpecificallynbsp;lighter than water, cannot poffibiy defircnd from dnbsp;to e, in order to enter that cavity. But if the glafsnbsp;be raifed higher fill, fo that its aperture be elevatednbsp;above the furface of the water in the bafon, thennbsp;the air will immediately enter on one fide of thenbsp;aperture, whllfi; the water goes out at the oppofitenbsp;fide.

When the veffcl is Ihort, and its aperture left than a quarter of an inch in diameter, the water ornbsp;other fluid will not eafily run out of it, though thenbsp;velfei be fituated with the aperture' downwards.nbsp;This is owing to the actradtion of aggregation between the particles of water, which will not fuffernbsp;the fmall quantity of liquor in the neck of the velTelnbsp;to be divided fo as to give room for the entrance ofnbsp;the air: hence it appears why phials with fmall necksnbsp;are difficultly filled with any liquor, and difficultlynbsp;emptied.

A well known experiment, which is frequently fi-.ewn in a familiar way, depends upon the above-ir.entioned principle.�A wane glafs is entirely fillednbsp;w�.tii vyater or wine; then a flat piece of paper isnbsp;placed over it, and t'le palm of the hand is put overnbsp;the paper. Things being thus prepared, the glafs

the hand, amp;c. is turned upfide down, then the hand being gently' removed, the glafs will be foundnbsp;remain full of water, with the paper adheringnbsp;to it.

The followingex'periment is intended to foev/ the hgt;nie property; namely, the preffure of the at-tirofphere in a difierent and perhaps naore fansfac-tory way.

Take a glafs tube of a pretty uniform bore, and t^pen at both ends, as A B, fig. 2. Plate XIII. ficnbsp;^ cork dB to it, and let a flick or vvire Kd, benbsp;firmly cemented into the cork. In fhort, form anbsp;pifton, like that of a fyring

place this piflon even with the lovver end of the tuiae, reprefented at B, in the figure, and in that fituaiionnbsp;place the fame end of the tube in water, as in fig.nbsp;3- and holding the tube ftcadilyj pull up the piftonnbsp;Sradiially. It will be found that the water followsnbsp;the cork, and fills up all that part of the tube whichnbsp;below the pifton, as isfircwn in fig. 3. By thisnbsp;t^^cans the prefflire of the atmofphere is removednbsp;firom over that part of the water which is immediately under the tube ; therefore the preuure of thenbsp;^tinofpliere on the reft of the fuiTace of the water itinbsp;tfic bafon, forces that water into the tube, filling upnbsp;tts Cavity as far as the pifton.

But this preffure is limited; for if the tube be longer than 33 or 34 feet, and the pifton be pullednbsp;��ip to the higheft [)art of it, the water will not .rifenbsp;filgher than about 33 feet, and the reft of the tube

as far as the pifton, will retaain without either water or air: therefore the preflure of the atmofphere Isnbsp;equal to the preffure of a perpendicular column ofnbsp;water of the fame bafe, and about 33 feet innbsp;height.

if the fame experiment be tried with m^ercury inftead of water ; that is, if the end B of the tubenbsp;be immerfed in quickfilver, and the pifton be pullednbsp;upwards, the quickfilver will be found to rife notnbsp;higher than about 291 inches; which perpendicularnbsp;altitude of quickfilver is equivalent to the above-mentioned perpendicular altitude of water; fornbsp;quickfilver is about 13,6 times heavier than annbsp;equal bulk of water; therefore the column ofnbsp;water muft be 13,6 times as long as the column ofnbsp;quickfilver in order to balance it, or to balance thenbsp;preliure of the atmofphere which is equivalent to it jnbsp;and in fadt, if we multiply 291, or 39,75 inches,nbsp;by 13,6, the product will be 404,6 inches, or littlenbsp;more than 33 feet.

The remainder of the tube between the furface of the quickfilver in it and the pifton, when this isnbsp;pulled higher than the quickfilver will rife, or thenbsp;fpace which remains above the water when the ex- -periment is tried with water, is called a vacuum, ornbsp;empty fpace; meaning a fpace void of air, or othernbsp;ponderous fluid, as far as we know.

The lead reflection on the preceding experiments' of this chapter, v/ill evidently fliew, that whether anbsp;tube upwards of 30 or 31 inches long, clofcd at onenbsp;8nbsp;nbsp;nbsp;nbsp;end,

be filled with quickfilver, and then be im-naerfed with its aperture in a bafon of cjuickfilver¹;

a tube opened at both ends be furnilhed with a pifion, and the quickfilver be drawn into it by thenbsp;pulling up of the pifton ; or, laftly, a tube openednbsp;both ends, have one of its extremity immcrfednbsp;�u quickfilver, and the air be fucked out of it bynbsp;of an engine adapted to its other end ; the ef-and the caufe of that eficft, are always the fame,nbsp;''quot;�2. the quickfilver will rife to the perpendicular al-'^u^ude of about 29,75 inches, and will be kept upnbsp;the prefllire of the atmofphere on the furface ofnbsp;quickfilver in the bafon ; but in pracbice the firfl;nbsp;by far the eafieft and moft effectual way of per-^�rrning the experiment.

If a glafs tube, upwards of 31 inches long, be ^bus filled with quickfilver, and be left undiPeurbed,,nbsp;''��ith its aperture immerfed in a frnall bafon ofnbsp;'I'Jickfilver, the altitude of the mercury in it willnbsp;be found to be various, both at different times andnbsp;different places. In London its molt ufual alft-^ude is between 28 and 31 inches ; though it is fel-to be feen below 28,5, or above 30,5 inches.nbsp;This evidently (hews that the weight or gravity ofnbsp;^be atmofphere is of a variable nature; and hencenbsp;^be above-mentioned tube filled with quickfilver^ amp;c.

A finger miift be applied to the aperture in turning the which muft not be removed before that aperture benbsp;'^ttieifed into the bafon of mercury.

has been called a barometer or barojcope, viz. frdrrt its property of Ihewing the adual weight of the ac^nbsp;mofphere at any Articular place and time

No period or regularity has been as yet difcovered with refpeft to this change of gravity, or to the rifenbsp;and fall of the mercury in the barometer, which isnbsp;equivalent to that preffure; fo that it is impolTible tdnbsp;foretel the altitude of the quickfilver in the barometer for any particular time. But it has been ob-ferved, that the altitudes of the mercury in the barometer are frequently accompanied with certainnbsp;ftates of the weather, fuch as wind, rain, calms,nbsp;ftorms, amp;c. and frequently alfo a certain altitude ofnbsp;the barometer precedes that particular Hate of thenbsp;weather which is ufually conne�led with ir, onnbsp;which account barometers are often called weathernbsp;glajfes, and are commonly kept in houfes, on boardnbsp;of Ihips, amp;c. as indicators of the weather.

The principle upon which thofe barometers are confru�ted, has already been explained ; the othernbsp;parts which are annexed to the common con-ftruftion, are either ornamental, or they are intendednbsp;for the fecurity of the tube; of the quickfilver in

* This fufpenfion of the quickfilver in the barometer, of inverted glafs tube, not beyond a certain altitude, and the variations of that altitude, were firfi obferved by the celebratednbsp;Italian philoiopher 1 orrlcetli �, hence the barometer is oftennbsp;called the torriceUian tube-, and the vacuum in the uppernbsp;part of it, is called the Urricellian VMiuujn.

bafon, amp;c. they will be particularly defcribed hereafter. The words which are engraven on thenbsp;fcale of inches and tenths, which is annexed to thenbsp;'variable part of the altitude, are exprefiive of thenbsp;'''father, which has been obferved frequently tonbsp;Accompany thofe particular altitudes of the mercury.nbsp;They arc as follows:

The rifing and falling of the mercury in the ba-fometer muft not be confidered as fure indications of the weather which is to follow; yet in generalnbsp;they will enable the obferver to form a pretty goodnbsp;8'aefs of the change of weather which may be exposed. Numerous obfervations relative to thisnbsp;fubjeiSt have been made in various parts of thenbsp;'^'orld, and, from a colle�lion of thofe obfervations,nbsp;learned Dr. Halley deduced a fet of rules, ,nbsp;''^hich were publifhed in an early volume of thenbsp;Thilofophical Tranfa�lions, and to which not muchnbsp;addition has been made by fubfequent obfervers.

1 (hall now fubjoin thofe rules, or natural la\vs, together with the conjeftures relative to the caufesnbsp;upon which they depend, in Dr. Halley�s ownnbsp;words.

quot; To account for the different heights of the mercury at fevcral times, it will not be unnecef-fary to enumerate fome of the principal obferva-tions made upon the barometer.

� I. The nrft is, that in calm weather, when the air is inclined to rain, the mercury is commonly low.

�� 3. That upon very great winds, though they be not accompanied'with rain, the mercury finksnbsp;lowefl: of all, with relation to the point of the com-pafs the wind blows upon.

� 4. That, cateris faribus, the greatefl: heights of the mercury are found upon eafterly and north-eafterly winds.

� 6. That after very great flrorms of wind, when the quickfilver has been low, it generally rifes againnbsp;very faft.

� 7. That the more northerly places hav^ greater alterations of the barofeope than the morenbsp;foutherly.

own

own obfervations at'St. Helena, make very little or oo variation of the height of the mercury in allnbsp;'Weathers.

� Hence I conceive that the principal caufe of rife and fall of the mercury, is from the variablenbsp;''^inds which are found in the temperate zones, andnbsp;Whofe great inconftancy here in England is moltnbsp;Notorious.

quot; A fecond caufe is the uncertain exhalation and precipitation of the vapours lodging in the air,nbsp;whereby it comes to be at one time much morenbsp;oroiided than at another, and confequently heavier jnbsp;W this latter in a great meafure depends upon thenbsp;former. Now from thefe principles I fliall endea^nbsp;''^our to explicate the feveral pha^nomena of the barometer, taking them in the fame order I laid themnbsp;down.

I. The mercury�s being low, inclines it to rain, becaufe the air being light, the vapours are nonbsp;longer fupported thereby, being become fpecificallynbsp;Ireavier than the medium,wherein they floated j fonbsp;they defcend towards the earth j and, in theirnbsp;^^llgt; meeting with other aqueous particles, they incorporate together, and form little drops of rain,nbsp;^ot the mercury�s being at one time lower than atnbsp;toother, is the effedb of two contrary winds blowingnbsp;from the place where the barometer Hands, wherebynbsp;air of that place is carried both ways from it,nbsp;confequently the incumbent cylinder of air isnbsp;dlminifhed, and accordingly the rnercury links. As

for inflance, if in the German ocean it nioiild bIoW_ a gale of wefterly wind, and at the fame time annbsp;eafterly wind in the Irifli fea, or if in France itnbsp;fii nild blow a northerly wind, and in Scotland anbsp;foutherly, it muft be granted me that that part ofnbsp;the atiTiofphere impe dent over F-ngland wouldnbsp;thereby be exhaufted and attenuated, and the mercury would fubfide, and the vapours, which beforenbsp;floated in thofe parts of the air of equal gravitynbsp;with themfelves, would fink to the earth.

� 2. The greater height of the barometer is oc-cafioned by two contrary winds blowing towards the place of obfervation, whereby the air of other placesnbsp;is brought thither and accumulated j fia that thenbsp;incumbent cylinder of air being increafed both it^nbsp;height and weight, the mercury prefled therebynbsp;muft needs rife and ftand high, as long as the wind*nbsp;continue fo to blow ; and then the air being fpecih'nbsp;cally heavier, the vapours are better kept fufpend'nbsp;ed, fo that they have no inclination to precipita'^^nbsp;and fall down in drops; which is the reafon ofnbsp;ferene good weather which attends the greats*�nbsp;heights of the mercury.

� 3. The mercury finks the loweft of all by very rapid motion of the air in ftorms of wind :nbsp;the tradt or region of the earth�s fur face, whetc'''nbsp;thefe winds rage, not extending all round thenbsp;that ftagnant air which is left behind, as like''''

that the air muft necefTarlly be atrenuated when and where the faid wind, continue to blow, and thatnbsp;niore'or lefs, according to their violence ; add tonbsp;^hich, that the horizontal motion of the asr beingnbsp;quick as it is, may in all probability take offnbsp;^on-)e part of the perpendicular preffiire thereof, andnbsp;*^he great agitaiion of its particles is the reafon whynbsp;^he vapours are diffipated, and do not condenfe intonbsp;^rops fo as to form rain ; otherwife the natural consequence of the air�s r-arefaftion.

quot; 4. The mercury (lands the higheft upon an ^3fterly o'quot; north-eafterly wind, becaule in the greatnbsp;�Atlantic ocean, on this fide th � 35quot;' degree of northnbsp;^^titude, the weflerly and fouth- wefterly winck blownbsp;^hnoft always trade; fo that v. henever here the windnbsp;forties up at eaft and n .�rth-eaft, it is fure to benbsp;checked by a contrary gale as foon as it reaches thenbsp;*^cean; wherefore, according to what is made outnbsp;our fecond remark, the air muft needs be heaped over this ifland, and confequently the mercurynbsp;�^uft (land high, as oft n as thefe winds blow.,nbsp;his holds true in this country, but is not a gene-rule for others, where the winds are under dif-Serent circumftances; and I have fometimes feennbsp;*-he mercury as low as 2g inches upon an eafterlynbsp;but then it blew exceeding hard, and fo comesnbsp;be accounted for by what was obferved upon thenbsp;third remark.

quot; 5- In calm frofty weather, the mercury gene-(lands high, becaufe (as 1 conceive) it feidom p 3nbsp;nbsp;nbsp;nbsp;freezes

freezes but when the winds come out of the northern and north-eaftern quarters; or at leaft unlefs tho^e^nbsp;winds blow at no great diftance off; for the northernnbsp;parts of Germany, Denmark, Sweden, Norway?nbsp;and all that tract from whence north eaftern wind�nbsp;come, are fubjeCl to almoft continual froft all thenbsp;winter; and thereby the lower air is very muchnbsp;condenled, and in that ftate is brought hitherward5nbsp;by chofe winds; and being accumulated by the oppo-fition of the wefterly wind blowing in the ocean, thenbsp;mercury m.uft needs be preft to a more than ordinary height; and as a concurring caule, the Ihrink-jng of the lower parts of the air into leffer room bynbsp;cold, nnuft needs caufe a defcent of the upper partsnbsp;of the atmolpheregt; to reduce the cavity made bynbsp;this contraction to an aquilibrium.

� 6. After great (forms of wind, when the mercury has been very low, it generally rifes again very faft. I once obferved it to rife if inch in lefs thannbsp;fix hours, after a long continued ftorm of fouth-weft wind. The reafon is, becaufe the air beiog ;nbsp;very much rarefied by the great evacuations whichnbsp;fuch continued ftorms make thereof, the neighboor'nbsp;ing air runs in the more fwiftly to bring it to aOnbsp;^equilibrium; as we fee water runs the fafter for ha'^�'nbsp;ing a great declivity.

� y. Tiie variations are greater in the rnor� northerly places, as at Stockholm greater thannbsp;iParis (compared by Mr. Pafcall *) ; becaufe the

northerly parts have ufually greater ftorms of wind than the more foutherly, whereby the mer-^^ry fhould fink lower in that extream ; and thennbsp;northerly winds bringing the condenfed and pon-^'^tous air from the neighbourhood of the pole, andnbsp;�hat again being checked by a foutherly wind at nonbsp;Egt;�eat diftance, and fo heaped, muft of neceffitynbsp;^^ke the mercury in fuch cafe ftand higher in thenbsp;Other extream.

quot; 8 Laftly, this remark, that there is little or Variation near the equinoftial, as at Barbadoesnbsp;St. Helena, does above all others confirm thenbsp;^ypothefis of the variable winds being the caufc ofnbsp;^^lefe variations of the height of the mercury ; fornbsp;10 the places above-named, there is always an eafynbsp;S^le of wind blowing nearly upon the fame point,nbsp;'02. E. N E. at Barbadoes, and E. S, E. at St.nbsp;Helena, fo that there being no contrary currents ofnbsp;air to cxhauft or accumulate it, the atmofpherenbsp;i-^ntinues fnuch in the fame ftate : however, upon .nbsp;hurricanes (the moll; violent ftorms) the mercurynbsp;has been obferved very low, but this is but once innbsp;IWo or three yeart, and it foon recovers its fettlednbsp;ftate of about 29 inches.

� The principal objeftion^agaicft this doiflrine that i fuppole the air lometimes to move fromnbsp;ihofe parts where it is already evacuated below thenbsp;�^E^ilibrium, and fometimes again towards thpfenbsp;pstts where it is condenfed and crouded above thenbsp;flaean ftate, which may be thought eontraditftcry to

the law of ftatics, and the rules of the isquiUbrium of fluids. But thofe that fhall conflder how, whennbsp;once an impetus is given to a fluid body, it is capable of mounting above its level, and checkingnbsp;others that have a contrary tendency to defcendnbsp;by their own gravity, will no longer regard this as anbsp;material obftacle; but will rather conclude, that thenbsp;great analogy there is between the rifing and fallingnbsp;of the water upon the flux and reflux of the fea, andnbsp;this of accumulating and extenuating the air, is anbsp;great argument for the truth of this hypothefis.nbsp;For as the fea over againft the coaft of Effex rif�snbsp;and fwells by the meeting of the two contrary tidesnbsp;of f.ood, whereof the one comes from the S. W.nbsp;along the channel of England, and the other fromnbsp;the north, and on the contrary flnks below its levelnbsp;upon the retreat of the water both ways, in the tidenbsp;of ebb j fo it is very probable, that the air may ebbnbsp;and flow after the fame manner j but by reafon ofnbsp;the diverfity of caufes, whereby the air may be fetnbsp;in moving, the times of thefe fluxes and refluxesnbsp;thereof are purely cafual, and not reducible to anfnbsp;rule, as are the motions of the fea, dependingnbsp;wholly upon the regular courfe of the moon.� Sonbsp;far are Dr. Elalley�s obfervations.

eflabiiflied, fadt, that in the middle latitudes, ^ north or north-eaft wind conftantly raifes the barometer, and generally higher as its continuancenbsp;lon�^er. The contrary happens when a fouth oc

quot;Permanently Elajiic Fluids, iBc.. nbsp;nbsp;nbsp;217

fouth-weft wind blows; for I believe it is commonly loweft when the duration and ftrength of the windnbsp;from that quarter have been the greateft. 1�hu?nbsp;fhe north-eaft wind, by blowing for any length ofnbsp;btne, brings into the middle latitudes a mafs of airnbsp;fieavler than that which naturally 'appertains to thenbsp;��fgi�n, and raifes the barometer above its meannbsp;height. The continuance of a fouth -weftern carriesnbsp;the heavy air, depofits a much lighter body innbsp;Head, and never fails to fink the barometer be-low its mean height.�

The greateft alterations of the barometer gene-'��illy take place during clear weather, with a northerly wind ; the fmall changes generally take place during cloudy, rainy, or windy w'eather, with anbsp;fcutherlv vrind. The changes of the barometricalnbsp;altitude are greater in winter than in lummer; butnbsp;the mean elevation is greater in fummer than innbsp;- 'winter, and greateft at the equinox.

The barometer is generally lower at noon and midnight, than at any other period of thenbsp;hours,

To thofe we may ,add De Luc�s obfervation, viz. that a rapid movement of the mercury in the ba^nbsp;forneter, even when rifing, is an indication of badnbsp;'''father, but not of long duration.

Such are the indications which may be derived from the movements of the barometer alone; butnbsp;the obfervers of later times, having made a rationalnbsp;inveftigacion of the poilibie influence of the moon

upon the atmofphere, and upon the weather, have fhewn that we may form much more probable con-jeAures relative to the weather, by combining thenbsp;obfervations of the barometrical movements withnbsp;the fituations of the moon *. But of this more innbsp;the next chapter.

The movement of the mercury in the barometer about our latitude, has been already faid to amountnbsp;to about 3 inches. But it v/ill be of ufe to knownbsp;its more ordinary altitude, or its mean altitude.

It appears from the meteorological journals of the Royal Society, which are pubiilhed annually innbsp;die Philefophical Tranfaflions, that the mean altitudenbsp;of the barometer is 29,89 inches, and the mean altitude of the barometer for each fingle year, hardlynbsp;ever differs from the above, by more than ha.f anbsp;tenth of an inch ; as appears from the follov/ingnbsp;ftatement of the mean barometrical altitude of eachnbsp;year, commencing with the year 1787, from whichnbsp;time the barometrical obfervations at the apartmentsnbsp;of the Royal Society have been made with great at-?nbsp;tendon and regularity f.

The French reckon the mean altitude of the mercury in the barometer placed on the level ofnbsp;^he fea, equal to 28 French inches, which are equi-''^alent to 29,841 inches Engliili*-

It appears very clearly, from v/hat has been already faid in this chapter, that the air is a ponderous fubftance 5 but the particular weight of a givennbsp;^tiantity of air, or its Ipecific gravity, is afeertainednbsp;by adfually weighing it with a balance. For thisnbsp;Ptirpofe a glafs vefiel is weighed firft full of air,nbsp;�^hen exhaufted of air, and laftly, full of water,nbsp;by which means we obtain the weights of equalnbsp;bulks of air and of water; and dividing thenbsp;formef by the latter, the quotient will exprefsnbsp;^he fpecific gravity of the air F- Httt it muft be ob-ferved, that air, being very elaftic, its bulk, andnbsp;confequencly its fpecific gravity, is eafily increafednbsp;Or diminifhed by heat and cold, as alfo by an .aknbsp;^ration of the prefTure; therefore, whenever thenbsp;Specific gravity of an aerial fluid is to be flated, it isnbsp;slvyays proper to fet down the altitude of the merrnbsp;oury in the barometer, and the degree of heat, at

Royal Society at Sonierfct Hoafe, is fituated 81 feet above the river T hames, viz, the level of low water fpring tides.nbsp;quot;Ihe obf�rvations arc taken twice a day, viz. at 7 or 8 innbsp;the morning, and at 2 in the afternoon. The mean for thenbsp;tvhole year is obtained by adding'all the obf�rvations together, 2nd dividing the fum by the number ot obf�rvations.

* De Prony�s Architedirure Hyciraulique, p. 298. t The conftruflion of the veflel fit for this purpof�,nbsp;as alfo the manner of exhaufting it, will be deferibed

the

the time of weighing the air. And this precaution has been obferved in the table of fpecific gravities.nbsp;See p. 95.

The knowledge of the preflure of the atmofphere, and of the perpendicular pillar of quickfilver, whichnbsp;is equivalent to it, enables us to calculate the afttuinbsp;preflure of the atmofpliere upon the whole globe ofnbsp;the earth, upon the human body, or upon any othernbsp;body; and it appears that this preflure is prodigi-oufly great, yet we do not find it incommodious ornbsp;oppreflive, becaufe we are prefl'cd on every fidenbsp;by it, and the preflure on the furface of gur bodiesnbsp;is countera�led by the fluids and folids of our bodies,nbsp;which are aimoft entirely non eladic. If that pref-fure be removed from one fide, then it wfill be foundnbsp;to a6l with prodigious force on the other fide.

As the preflure of the atmofphere fupports a perpendicular pillar of quickfilver between 28 and 31 inches high, the weight of fuch a pillar, let its bafenbsp;be what it may, flrews the preflTure of the acmo-fphcre upon a furface equal to that bafe. Now anbsp;pillar of quickfilver, whofe bafe is an inch fquare, andnbsp;tvholb altitude is 28 or 31 inches long, w'dghsnbsp;or 15,23 pounds' avoirdupoife, the mean of winchnbsp;is 14,49 pounds; therefore at a mean the preffurenbsp;of the atmofphere upon every fquare inch, at thenbsp;furface of the earth, is about 14 | pounds avoirdu-poife ; then by the rule of proportion, or fimply bynbsp;multiplication, we may eafily find out the preflurenbsp;upon any given furface, Thus the preflTure of the

Permanently Elajlic Fluids, c. atrnofphere on a fquare foot, (which contains 144nbsp;Square inches) is equal to 144 times 14 | pounds,nbsp;'^gt;z. to 2088 pounds. The preffure' of the atmosphere on the body of a middle fized human beingnbsp;(reckoning its furface equal to 12 fquare feet) is 'nbsp;�2 times 2088 ; that is 25056 pounds, or upwardsnbsp;of eleven tons. The preffure on the furface of thenbsp;''�hole earth ^which, in round numbers, is equalnbsp;to 5 5*75680000000000 fquare feet,) is equal tonbsp;^bout 11642019840000000000 pounds.

If from a veffel full of water, part of the water be removed, then the cavity of that veffel will notnbsp;be entirely occupied- by water. Now the famenbsp;thing cannot be done with air ; for if from a veffelnbsp;full of air, half the air be removed by means of anbsp;proper engine, and the entrance of other air benbsp;prevented, the veffel will ftill remain entirely fullnbsp;of air, only the air in it will be half as denfe as itnbsp;Was before. If, inftead of the half, you remove anbsp;much greater portion of the air from the above-mentioned veffel, the veffel will ftill remialn entirelynbsp;full of air ; only the air in it will be proportionatelynbsp;lefs denfe. In (hort, by removing the preffure, anbsp;Quantity of air may always be expanded nor is itnbsp;known to what degree this expanfion will reach;nbsp;oonfeq'uently it is not in our power to determinenbsp;the extent of the atmofphere.

portionately, a quantity of air may be condenfed into any given fpace, however fmallthe denfitv of*nbsp;the compreffed air increafing according as the bulknbsp;is diminiHied. Nor has this condenfation an/nbsp;known limits, though it feems rational to fuppofenbsp;that a limit it muft undoubtedly have.

If a glafs veflel full of air be immerfed in water with its aperture downwards, the water immediatelynbsp;under it, which at firft lies even with its aperture,nbsp;will gradually rile in the velTel in proportion as thenbsp;veflel is conveyed deeper and deeper into the water;nbsp;the air in it being compreffed and condenfed by thenbsp;perpendicular altitude of the fuperincumbent water-On drawing the veffel upwards, the air in it will expand again.

This experiment lliews that air is compreffible; but the following experiment will fhew that the bulknbsp;of a given quantity of air is inverfely (and of courf�nbsp;its denfity is dire�tiy) as the compreffmg force; fornbsp;inftance, if a certain weight compreffes a quantitynbsp;of air into the half of its original bulk, twice thatnbsp;weight will comprefs it into a quarter of its originalnbsp;bulk; ten times that weight will force it into thenbsp;20quot;' part of its original bulk ; and fo on.

Take a cylindrical glafs tube bent in the forna of ABCD, fig. 4. Plate XIII. open at A, andnbsp;clofed at D, and place it with the bent part downwards ; pour as much quickfilver into the apertut�nbsp;A, as will barely fill the horizontal part B C, whichnbsp;will confine the air in DC, This air, like the an*

'vhich is about the apparatus, amp;c. is comprefied by �he ufual prefllire of the atmofphere, and this pref-fure is reprefented quot;by (fince it is equivalent to)nbsp;the aftual altitude of the mercury in the barometer.nbsp;Now, if you pour more quickfiiver into the aperture A, the air in C D will thereby be cpmprelTednbsp;into a narrower fpace ; as is indicated by the mercury riling into the part G D, and it will be found,nbsp;that the fpace D e, in which the air has been con-trafted by the prelTurc of the perpendicular pillar ofnbsp;Rlercury g/, (the altitude of which mull always benbsp;reckoned from the level of the furface of thenbsp;iTiercury in the part CD) in addition to the ufualnbsp;PrelTure of the amiofphere, is to its original bulknbsp;CD, as the ufual preffure of the atmofphere (or asnbsp;the a�tual altitude of the barometer) is to the fumnbsp;of'that adtual altitude, and the altitude^/. Thusnbsp;When gf is equal to the adlual altitude of the mercury in the barometer, then the preflbre on thenbsp;Confined air is twice as great as if it were prelTed bynbsp;the atmofphere only; therefore that air will be confined into the half of its original bulk, viz. De willnbsp;fie the half of D C. When the altitude^/ is madenbsp;^qual to twice the altitude of the mercury in thenbsp;fi^rometer, then the preffure on the confined airnbsp;will be three times as great as if it were preffed bynbsp;the atmofphere only; hence De v/iil be found equalnbsp;to a third part of D C; and fo on.

The expanfion of air in proportion to the diminution of the preffure, may be fliewn by a variety of

experiments., We fhali for the prefent, however, de-feribe only one which may be eafily performed.

Take a cylindrical glafs rube,, clofed^at one end and open at the other, fill it with quickfilver to anbsp;certain height, and leave the reft full of air (or, asnbsp;k would commonly be expreffed, leave it empty) gt;nbsp;put a finger upon the aperture of the tube ; turn thenbsp;tube with the aperture downwards �, immerge thatnbsp;aperture together with the finger, in a bafon ofnbsp;quickfilver, then remove the finger and it will benbsp;found that the air which was left into the tube, andnbsp;which now occupies the upper, that is the clofed,nbsp;part of the tube, has enlarged its dimenfions. Sup'nbsp;pofe, for inftance, that the tube be 30 inches long�nbsp;that it be filled with mercury, excepting 8 inches*nbsp;When the tube is inverted, as in fig. 5. Plate XlH*nbsp;the air will occupy the upper part A B, and thi^nbsp;mercury the lower part B C ; but the part Anbsp;which is occupied by the air, will be found tonbsp;longer than 8 inches; the reafon of which is, tha^nbsp;the original quantity, viz. 8 inches of air, whichnbsp;before the tube was inverted, was preffed by thenbsp;atmofphere, now fuftains a lower degree of prcf'nbsp;fure ; that is, the preflure of the atmofpherenbsp;partly counteradled by the pillar of ^mercury Bnbsp;Therefore, fince the buMcs of the fame quantitynbsp;air are inverfel'y as the prefiTures, it will alwaysnbsp;found that the difference of the adfual altitudenbsp;the mercury in the barometer, and the altitude

the aftual altitude of the mercury in the barometer, as 8 inches (viz. the original bulk of the confinednbsp;^�0 is to its prefent bulk AB; fo that if the aftualnbsp;altitude of the mercury in the barometer be 28nbsp;inches, CB will be found equal to 14 inches, andnbsp;equal to 16 inches; for in that cafe 28�14nbsp;(viz. 14) : 28 : : 8 : i6.

Air has been left for f�veral years very much CotTiprefled in proper veffels, wherein there was nothing that could have a chemical adion upon it;nbsp;and afterwards on removing, the unufual preflure,nbsp;and replacing it in the fame temperature, the airnbsp;has been found to recover its original bulk, whichnbsp;^ews that the continuance of the preflure had notnbsp;diminilhed the elafticity of it in the leafl. perceptible degree.

t 226 ]

Of THE DENSITY AND ALTITUDE OF THE ATMOSPHERE, TOGETHER WITH THE METHOD OF MEASURING ALTITUDES BY MEANS OF BAROMETRICAL OBSERVATIONS.

Experience fhews that the atmofphere, or the air, which furrounds the earth, is ofnbsp;different denfities at different diftances from thenbsp;centre thereof. Our direft experiments, however,nbsp;do not reach to any great heights into the regions ofnbsp;the atmofphere. But the numerous experiments,nbsp;which have been rnade on the comprefSon of air,nbsp;the moft convincing of which have already beennbsp;mentioned, prove that air is condenfed in proportion to the force which compreffes it, or that it expands in the inverfe ratio of that force, and that itnbsp;does not, lofe any portion of its elafticity by remaining long confined. We are, therefore, authorilednbsp;to fuppofe that the air, at all diftances from thenbsp;earth, is more or lefs denfe, according as it is fitu-ated nearer to, or farther from, it; or according asnbsp;it is preffed by a greater or leffer weight of fuperin-cumbent air. We may alfo conclude, that, notnbsp;knowing how far air may be expanded, we cannotnbsp;determine to what height the atmofphere is extended.

But the comprelRon arifing from the weight of fuperincumbent air, though by far the princi-is not the only caufe upon which the variousnbsp;�^cnfity of the atmofphere depends. In fhort, allnbsp;the caufes, which feem.to concur towards the pro-^^ftion of that effeft, are, i. The various quantity of fuoerincumbent air at different altitudes;

The decreafing attraftion of the earth, or the ^^creafing weight of bodies, iii proportion to thenbsp;^'luares of the diftances from the centre of thenbsp;^3rth 5 3. The influence of heat and cold j 4. Thenbsp;�iitnixture of vapours and other fluids; and, 5*nbsp;*Phe attradlion of the moon and other celeflialnbsp;bodies.

For the fake of perfpicuity, we fhall exanrtine ^^ch of thofe caufes fucceflively, and in the firftnbsp;Piace we fhall endeavour to explain the effcfts ofnbsp;Preffure.

Irnagine that ABCD, fig^ 6, Plate XIII. is ^ pillar, or veffel, full of air, reaching from thenbsp;^�rface A B of the earth, to the fartheft partnbsp;^ � of the atmofphere; for whatever is provednbsp;refpeft to the denflty of the air in thisnbsp;pillar. Or portion of the atmofphere, will evidentlynbsp;ligand good with refpedt to any other contiguousnbsp;pillar or portion of it, and, of courfe, with refpedt

Imagine likewife, that this pillar is divided by Partitions parallel to the horizon, into a vaftnbsp;i^itmber of equal fpaces, AB^/, efgh, ghihnbsp;amp;c.

Now as the denfity of the air is continually de-' creafing from the earth Upwaxds; therefore, ftriftlynbsp;Ipeaking, that denfity muft be various, even in dif-ferent parts of every one of thofe fpaces; yet asnbsp;thofe fpaces may be conceived to be infinitely fmallgt;nbsp;we may, without any fenfible error, fuppofe thatnbsp;the denfity of the air is uniform throughout the various parts of any one of them.

Since the denfity of the air is always as the force �which compreffes it j and fince the air in every paftnbsp;of the atmolphere is prefled by the weight of thenbsp;fuperincumbent air; it follows that the denfity ofnbsp;the air in A Be/, is to the denfity of the air in efgh,nbsp;as e/CD is to i-^CD. So that the difference between the preffures on lt;?/and on �(or betweennbsp;the quantities of air ABr/ and efgh^) is equal tonbsp;�the quantity of air efgh. For the fame reafon, thenbsp;difference between- the preffures on gh and on i^nbsp;(or between the quantities of air in efgh znd ghik)nbsp;is equal to the quantity of air ghik. Alfo the difference between the preffures on ik and on mn (ofnbsp;between the quantities of air ghik and ikmn), t*nbsp;equal to the quantity of air ikm,n; and fo on*nbsp;Therefore the quantities of air, or the denfities ofnbsp;air, in thofe fpaces, are proportional to the quantities of which they themfelves are the diffetquot;nbsp;ences. But when there is a feries of quantities�nbsp;whofe terms are proportional to their own differences, then both thofe quantities and theit

differences, are in geometrical progreffion * ; therefore the denfui�s, or quantities, of air in the equal fpac^s ABtf/inbsp;nbsp;nbsp;nbsp;ghik, iknin, amp;c. are in geo-

^t muff: likewife be obferved, that the heights of *^hole equal fpaces above the furface AB of thenbsp;^3Fth, are in arithmetical progreffion j viz. if thenbsp;f^cond fpace be one inch above the furface, thenbsp;^^xt will be two inches above that furface, the nextnbsp;'�o that will be three inches, and fo on ; or inftead ofnbsp;*fgt;ches their altitudes may be of any other dimenfion,nbsp;the one-hundredth, or the one-thoufandch partnbsp;an inch. From all which we derive a very remarkable conclufion; namely, that if the altitudesnbsp;dbo^jg the furface of the earth be taken in arithmeticalnbsp;Progreffion, the denjities of the air at thoje altitudes willnbsp;^0 in geometrical progreffion decreafmg.

Thus, for inftance, ff at a certain altitude the air half as denfe as it is immediately on the furfacenbsp;the earth j then at twice that altitude, the air willnbsp;four times lefs denfe than upon the furface of thenbsp;^arth; at three times that altitude, it will be eightnbsp;times lefs denfe; and fo forth.

Experience, afflffed by calculation, flicws that ^t the diftance of feven miles from the furface of thenbsp;^^tth, the air is about four times lefs denfe than it is

Let A, B, C, D, amp;c. be a feries of quantities, and if � quantities be proportional to their own differences, wenbsp;A ; A � B : ; B : B � C :: C : C ~ D, amp;c.nbsp;jnce converfely (Eucl. Cor. to Prop, 19. B. v.) A : B : ;

clofe to that furface¹. Now the knowledge of this fa6t will enable us to conftruft a table of denfitie¹nbsp;(or of prefTures) of the atmofphere at all altitudesnbsp;from the furface of the earth ; which may be donenbsp;in the following manner :

Take the altitudes in arithmetical progreffion� viz. 7 miles, 14, 21, 28, 35, amp;c. Then for thenbsp;denfities, fay, by the rule of three, as i is to fonbsp;is i to a fourth proportional, which is f-g, andnbsp;Ihews, that at the height of 14 miles the denfity ofnbsp;the atmofphere is the i6th part of what it is clofe tonbsp;the furface of the earth. Again, fay, as I is tonbsp;fo is f-g to a fourth proportional, which isnbsp;fhews, that at the diftance of a i miles the denfitynbsp;of the atmofphere is the 64th part of what it is clofenbsp;to the furface, amp;c. Thus you have the denfities (ofnbsp;the prefTures which are as the denfities) of the at¹nbsp;pioiphere at the undermentioned diftances.

Then, ih order to find the denfities correfpondent the intermediate altitudes, take an arithmeticalnbsp;t^ean proportional between 7 miles and 14 miles,nbsp;is I of- miles ¹ j allb, take a geometricalnbsp;t^ean proportional between the denfities of the airnbsp;7j and at 14 miles, viz. between f and whichnbsp;T t J and this is the denfity of the air at the al-titude of 10 f miles. Again, take an arithmeticalnbsp;^ean proportional between 14 and 21 miles, whichnbsp;^^171 miles; alfo, take a geometrical mean propor-*^ional between the denfities of the air at the above-�^entioned two altitudes, viz. between -rV andnbsp;quot;'hich is and it exprefles the denfity of the airnbsp;^t the height of 17 | miles. After the fame mannernbsp;you may take an arithmetical mean proportionalnbsp;between 17 | and '21 miles, and a geometricalnbsp;tUean proportional between the denfities at thofe al-�^'tudes. In Ihort, the like operation may be performed with any two altitudes, and their correfpond-^tit denfities j byquot; which means a table of denfities.

An arithmetical mean proportional between two num-is found by taking the half of the fum of the two ^'^'nbers. Thus the fiim of 7 and 14 is 21, the half ofnbsp;'^hich is lo -t.

t A geometrical mean proportional between two num-is found by extradling the fquare-root of the Ptodudl of the two numbers. Thus i multiplied by y'g,nbsp;S�ves gC ^ fquare root of which is f} and i is the geometrical mean between | and

anfwering to Certain altitudes, may be conftrufted* This laborious operation, however, may be avoid'�nbsp;ed i for the fame thing may be obtained by ufing anbsp;table of logarithms, which logarithms in fadt are anbsp;fet of numbers in arithmetical progreffion, annexednbsp;to another fet of numbers, which are in geometricalnbsp;progreffion; fo that the former may reprefent thenbsp;altitudes, whilfl: the latter reprefent the denfitiesnbsp;of the atmofphere correfpondent with thofe altitudes.

The principal ufe of fuch a table is for meafur-ing perpendicular altitudes above the furface of the earth, by means of barometrical obfervations, thenbsp;principle of which operation we ffiall endeavour tonbsp;explain.

The barometer, as has been ffiewn in the preceding chapter, fliews the aftual preffiire of the atmofphere, or the denfity of the air at the place where it is fituated j therefore the altitude of thenbsp;mercury in a barometer, placed at the top of anbsp;mountain, will not be fo great as the altitude of thenbsp;mercury in a barometer placed on the fea fhore.nbsp;Now thofe altitudes of the mercury being as thenbsp;denfities, and the denfity at the furface of the earth,nbsp;or on the fea Ihore, being called one in the table, wenbsp;fay, as the barometrical altitude at the furface is tonbsp;the barometrical altitude on the mountain, fo is onenbsp;to the denfity of the air at the top of the mountain �nbsp;and finding the denfity thus obtained in the table,nbsp;we have againfl it the correfpondent altitude, or

the

of the Atmofphere, fffr. nbsp;nbsp;nbsp;233

So far the operation would be eafy and ufeful, provided its refults were attended with fufficientnbsp;accuracy; but the other above-mentioned caufes,nbsp;quot;^hich af�e(5l the denfity of the atmofphere, rendernbsp;^ variety of correftions neceffary for the attainmentnbsp;t^f a uleful degree of accuracy in fuch meafure-tftents. The difficulty of inveftigating the peculiarnbsp;^ffefts of thofe caufes, as alfo of compenfating fornbsp;their effefls,, involve the operation in a good dealnbsp;Pf difficulty, on which account we fliall give a fullnbsp;examination of this fubjedl in the note (i.) �, and

(r.) The mechanical properties of the atmofphere are Analogous to the properties of a particular fpecies of curvenbsp;lines, called logarithmic curves hence the knowledge of thenbsp;Properties of the latter is of confiderable afliftance in eluci-'lating the properties of the former. But the nature ofnbsp;logarithmic curves is probably not fufflclently underftoodnbsp;I'y the greateft number of my readers : I fhall, therefore,nbsp;briefly fubjoin fuch of their properties as may fuffiee to illuf-frate the doctrine of the atmofphere.

^definitions. Upon an indefinite right-line AE, fig. 7) Plate XIII. make the intervals AB, BC, CD, amp;c. equal to onenbsp;Another; or (which is the fame thing) make the diftancesnbsp;AC, AD, amp;c. in arithmetical progreflion. From th�

2 34 nbsp;nbsp;nbsp;Of Denjity and Altitude

ihall here proceed to give a fliort idea of the inflU' ence of the above-mentioned caufes on the denfi-ties of the atmofphere, at different altitudes andnbsp;different times.

amp;c. parallel to each other, and in geometrical progrclllon gt; viz. making A F to B G, as BG to CH, as CH to DIgt;nbsp;and fo on. Then a curve line f GHI K, dravrn throughnbsp;the extremities of thofe parallel lines, is called a logarithmknbsp;curve. The indefinite right-line A E is its axis^ v^hichnbsp;will be fhewn to be an ajymptote to the curve, viz. it willnbsp;never meet the curve ; and the lines AF, BG, CH, DI, amp;c.nbsp;are the ordinates.

Since the ordinates may be taken in any geometrical proportion, it is evident that there is an infinite variety of logarithmic curves.

the next ordinate is of AF, and fo on without end; therefore no ordinate can ever be equal to O; for that 0 would be no part of the preceding ordinate; hence the axis and thenbsp;curve can never meet; though when produced towardsnbsp;the fhorfer ordinates, they come continually nearer to eachnbsp;other.

Prop. II. If a tangent and an ordinate he drawn from any point in a logarithmic curve; the fubtangent, or part of thenbsp;axis, which is contained between the interfe�iions of the ordi'nbsp;nate and the tangent, is a conjiant or invariable quantity.

In the preceding inveftigation of the decreafing denfity of the attnofphere, the force of gravity hasnbsp;Igt;een fuppofed to a�t uniformly ; whereas, in truth,nbsp;that force decreafes according as the fquares of

XIII. indefinitely near to each other, and through each �*^them draw a tangent and an ordinate to the curve; TE,nbsp;being the tangents, and BE, CF, the ordinates. Drawnbsp;another ordinate-D G, as diftant from CF as CF is fromnbsp;and through E and F draw E �, F r, both parallel tonbsp;axis.

Since the diftances B C, C D, are equal, we have, from *^he definition of the curve, DG:FC::FC;BE; bynbsp;^'vifion, DG �F C :FC : : FC�BE : BE; ; Gr:nbsp;E C : ; F � : B E.

It is evident from the parallelifm of the lines F r, E T D; as alfo of the lines D G, C F, BE, that the triangles F Gr, FVC, are fimilar, and fo likewife are the triangles F E �, E T B ; hence Gr:FC::Fr:VC; alfonbsp;E � : E B : : E � ; B T : ; G r : F C : ; F r ; V C. Butnbsp;E n is equal to F r; therefore the fubtangent B T muft benbsp;^fiual to the fubtangent C V.

equal to any other fubtangent of the lame curve ; or that tbe fubtangent is an invariable quantity.

fame ratio., viz. the fitfi be to the Jecond as the third to ^^efourth; and if through the extremities of the firf and thirdnbsp;^fecant be drawn., and another fecant be drawn through thenbsp;fgt;stremities of the fecond and fourth; then the part of the axis

236 nbsp;nbsp;nbsp;Of the Devftty and Altitude

the diftances from the centre of the earth increafe (p. 61. Part I.)i fo that the particles of air which arenbsp;at a diftance from the earth gravitate lefs than thofenbsp;�which are nearer to it j hence, on this account, the

which is contained between the interfeSiions of the firjl fecant and the firji ordinate, will he equal to that part of the famenbsp;axis which is contained between the interfedllons of the fecondnbsp;fecant and the fecond ordinate.

Thus, in fig. 9, Plate XIII. if A F : D I : : B G : E K, in which cafe, from the nature of the curve, AD^BE, andnbsp;AB~DE; and if the fecants G�'T, I^IV, be drawn jnbsp;then T A will be equal to V D.

'T hrough F and I draw FS, and IL, parallel to the axis* ThenfinceAF:pi::BG:EK, we have by alternation AF :BG;;DI:EK; inverfely, B G : A F ::nbsp;EK : PI; and, by divifion, BG � AF (=:GS);AFnbsp;;;EK � DI (i^LK) ; DI; inverfely, AF : GSnbsp;; : DI ; L K. But the triangles DI V, LKI, arc fimilar,nbsp;and fo likewife are the triangles AFT, F G S j thereforenbsp;,TA:FS:;AF;GS:: (from the above analogy) D Inbsp;: L K : : V D : IE. Then fince in the analogy TA : F Snbsp;; ; V D ; 1 L, the fecond and fourth terms are equal, viz*nbsp;FS=IL, or AB=:DE; the other two terms muft likewifenbsp;Be equal, viz. TA=V D.

Prop. IV. The fpace, which is circumferibed by any two, ordinates, and fuch parts of the curve and of the axis as Idnbsp;between thofe ordinates, is equal to the rebiangle of the fuhtan-gent and �the difference of the ordinates.

Thus, fig. 10, Plate XIII. the fpace GBEL is^er^ual to TE X SL 5 TL being the tangent at the point L,

cf the Atmqfpherei i�c. nbsp;nbsp;nbsp;2^7

lefs than if the force of gravity afted uniformly. Yet, fince the altitudes of the higheft mountainsnbsp;I'nake a trifling addition to the radius of the earth¹ ²

Imagine D I to be drawn infinitely near and parallel to and Ir to be drawn through the interfedflon I, pa-��ailel to the axis.

From the fimilarity of the triangles LIr, L T E, we I�ave EL:ET :;Lr:Ir; hence E T X.L r = EL Xnbsp;^ ^ the area D E I r = (fince, when ID is infinitely nearnbsp;*oEL, the triangle LIr vanilhes) DELI. And thenbsp;I^me thing may be faid of any other point very near I, andnbsp;another next to that, he. Therefore (the fubtangentnbsp;T being an invariable quantity) the fum of all the fmallnbsp;�es, fuch as DELI, between L E and B G; or thenbsp;Ipace BELG, is equal to E T X L S (L S being the funtnbsp;all the differences Lr).

Corollary I. The whole area, which is contained be-tween any oiJinate LE, the curve, the axis, and infinitely ^Jetended towards F A, is equal to the redtangle of that or-*^gt;nate and the fubtangent, viz. to L E X T E ; fince when

he area is infinitely extended towards A F, the laft ordinate ''aniflies, viz. EL becomes equal to the difference of ELnbsp;*gt;td the laft ordinate.

Cor. X. The fpaces, which begin at different ordinates, and are thus infinitely extended, are as the ordinates fromnbsp;which they begin to be reckoned.

Cor. 3. The fpace v.^hich lies between any two ordinates, ^ to the fpace which lies between any other two ordinates,nbsp;^ the difference of the firft two ordinates is to the differencenbsp;tgt;f the two others.

IJ 8 nbsp;nbsp;nbsp;Of the Denfty and Altitude

the diminution of the gravitating force will have no fenfible influence in our meafurements of altitudesnbsp;by means of the barometer. Thofe perfons, however, who wifh not to neglefl: that circumftance,

Prop. V . The dtjiances^ or parts of the axis, which lit hetween two equal ordinates in two, or more, different toga-rithmic curves, are as the Jubtangents of thofe curves �-fpeSIively.

Thus, if in the two logarithmic curves, FIG, QKS, F A be equal to P .Q_, aud B G be equal to H S ; then itnbsp;will be AB : T B : : P H ; V H; T G and V S beingnbsp;the tangents.

Draw two ordinates indefinitely near to G B and H S, and draw I n, K r, parallel to the axes ; then finee AF, Lljnbsp;B G, are refpedlively equal to P Q_, N K, H S, it will benbsp;(from the definition of the curve) A B : LB (or \n) : :nbsp;P H ; N H (or K r)} and alternately A B ; P H ; : In-Kr.

From the fimilarity of the triangles B G T, G I�, and H S V, S K r, we have BT;l�;:BG:�G;:HSinbsp;r S : ; H : r K; whence alternately B T : H V :;!��nbsp;K r : ; A B : P H; and inverfely, A B : B T : : P H tnbsp;H V.

Scholium. A table of logarithms is nothing more than a feries of numbers in arithmetical progreffion, annexed tonbsp;another feries of numbers that are in geometrical pro-greflion. Therefore, if the lengths of the abfeiflas A Bgt;nbsp;AC, AD, amp;c. of a logarithmic curve, fig. 7, Platenbsp;and the lengths of the correfponding ordinates A F, B G�nbsp;C H, amp;c. be exprefied in nunabers �, the former will be thenbsp;logarithms of the latter.

cf the AtmoJ^here, ^c. nbsp;nbsp;nbsp;239

Either in fuch meafurements, or in the inveftigation other properties of the atmofpheregt; will find thenbsp;^^ceflary explanations in the note below.

^ince the ratio of the ordinates as well as the lengths of abfcilTas may be various; it follows that differentnbsp;^�garithmic curves will reprefent different fyftems of lo-

In the curve which expreffes the common table of loga-called Briggs�s logarithms., the lengths of the ordi-are, i : 10 : 100 ; 1000, amp;c. or their ratio is 10, the abfciffas, or the logarithms, are i, 2, 3, 4, amp;c. ;nbsp;the fuhtangent (other wife called the module of that JyJiemnbsp;^��garithms) is equal to 0,43429448.

is evident that every ordinate is a geometrical mean ^��oportional between any two other ordinates equidiftantnbsp;it; whilfl its correfpondent abfciffa is an arithmeticalnbsp;proportional between the abfcilTas to the other twonbsp;^'^'^ioates. Thus C H, in fig. 7, is a geometrical meannbsp;�^�Ween B G, and D I i and A C is an arithmetical mean

� �n two equal parts in s, and find a mean geometrically P�'nportional between A F and B G, that mean will be thenbsp;quot;�th of the ordinate j fl; andAr is its logarithm.�-Thus

240 nbsp;nbsp;nbsp;Of the 'Denfity and Altitude

diminution of heat, contrafts, the bulk of air. this expanfion and contraftion are not regular, viz*nbsp;they are not exadly proportional to the degrees oinbsp;heat. Befides this, the rate of expanfion, by thenbsp;fame degrees of heat, differs according as the airnbsp;more or lefs denfe alfo according as it is more of

' lefs

if in one fyftem the module be M, and the logarithm of^ given number be L j whilft in another lyftem the modulenbsp;be m, and the logarithm of the fame number be / j thennbsp;will be M ; L ; : �2 : /; hence M.l= h m-, viz, the pro-dudl of the logarithm of a given number in one fylfetn�nbsp;multiplied by the module of another fyftem, is equal to thenbsp;produdl of the logarithm of the fame number in that othernbsp;fyftem, multiplied by the module of the firft fyftem.

If the module of one fyftem be reprefented by unity; thei^ � ; Lnbsp;nbsp;nbsp;nbsp;3 in which cafe L � = /.

Thus much will fuffice with refpedt to the properties of the logarithmic curves 3 we muft now proceed to explain'nbsp;by means of thofe properties, the conftitution of the at-mofphere, and the method of determining altitudes froiT*nbsp;barometrical obfervations. -

It has been already {hewn, that the denfities of the air at different diftances from the earth are in geometrical prO'nbsp;greflion decreafing, v/hilft the altitudes are in an increafio^nbsp;arithmetical progreftion 3 it is therefore evident, that ifnbsp;a ftraight line A M, fig. 12, Plate Xlil. the diftances Anbsp;at:, a D, amp;c. reprefent the altitudes, and the ftraight lio^*nbsp;AO, BF, C H, DI, amp;c. drawn perpendicular to A1^�

of the Atmoffhere, Csfc. nbsp;nbsp;nbsp;241

charged with moifturc. � The late General F.R.S. made a great variety of accurate ex-P^nments relative to this expanfio�i of air ; but thenbsp;*'�fults of his experiments will be ftated in anothernbsp;part of thefc elements.

The

quot;^^Prefent, or be made proportional to, the denfities of the at thofe altitudes; then a curve line OIN,nbsp;along the ends O, H, I, amp;c. of thofe lines, will be anbsp;''S^ithmic curve, and may be called the atmofpherical loga-; A M being its axis, and AO, B^, C H, amp;c, itsnbsp;''�'dinates. The area which lies between the firft ordinatenbsp;tlve curve, and the axis, and is infinitely extended towardsnbsp;^ may be confidercd as being equal to an infinite num-of ordinates, fituated extremely near to each other; butnbsp;reprefent the quantities of air at their refpec-fituations; therefore the abovementioned area will rc-P�'efent the whole quantity of air in the atmofphere. Ailbnbsp;area, or part of the abovementioned area, from any onenbsp;thofe ordinates upwards, will reprefent the whole quan-of atmofpheric air, which exifts beyond that altitude.nbsp;quot;Phis however would be the cafe if the force of gravitynbsp;Uniformly at all diftances from the earth, which is notnbsp;^fue. Therefore we muft now examine the real diminutionnbsp;denfity in the atmofphere on the true hypothefis, viz. ofnbsp;� Suavity�s decreafing according as the fquares of the dif-lt;nbsp;^'J'^ces increafe; in confequence of which the denfity of thenbsp;''t at any given altitude muft be greater than it -yvould be ifnbsp;force of gravity aifted uniformly, in order that a given

VOL. IJ.

242 nbsp;nbsp;nbsp;Of the Denfty and Altitude

The influence of the fun, and principally of fhC moon, upon the waters of the ocean, is too evidentnbsp;to need any particular examination. And it is evident from the laws of univerfal attradion, that thofc

Let PAZ, fig. 13. Plate XIII. reprefent the circumference of the earth, S its centre, m SM an indefinite right line pallingnbsp;through the centre S, and interfecling the circumference at A�nbsp;Let the altitudes SA, SB, SC, SD, differ indefinitely littlenbsp;from each other 5 but let them be in harmonical pro*nbsp;grelfion. Alfo let the ordinates AO, B F, C G, DH, benbsp;proportional to the denfities of the atmofphere at A, thenbsp;furface of the earth, and at the altitudes B, C, D ; but uponnbsp;the fuppofition that the force of gravity ads uniformly-Then the curve O F G H N, drawn along the extremitiesnbsp;of thofe ordinates, amp;c. is (from what has been faid above) *nbsp;logarithmic curve.

Now take S fi, a third proportional to S B and S A; take S f a third proportional to S C and S A ; alfo take S rf a thirilnbsp;proportional to S D and S A ; viz. let it be

SC, nbsp;nbsp;nbsp;SD, increafe) mull be in arithmetical progrelfionJnbsp;it being well known that the reciprocals of quantities that arsnbsp;harmonically proportional, are in arithmetical progreffion*nbsp;See Malcolm�s Arithmetic, B. IV. chap. 6.'

cf the Atmqfphere, ��f. nbsp;nbsp;nbsp;243

teleftial bodies muft aft upon the atmofpher� in a firniJar manner j that isj they muft occafion a fluxnbsp;and reflux of the atmofphere, as well as of thenbsp;'�cean. But the atmofpherical air being a fluid

the rea/ denfities of the air at A, B, C, D, refpeclively. quot;Through the points O, �, h, See. draw the curvenbsp;^fs h, amp;c. which will prefently be Ihewn to be a logarith-curve.

Trom the abovementioned analogiesj we have SD X = S C X Sc; hence Sc:Si^::SD:SC. Con-Sc :Sc �(z=cd) : : SD : SD �SC ( =nbsp;viz. ci/:CD::Sc:SD. Or, becaufe CDnbsp;indefinitely fmall, S C will be ultimately equal to S D :nbsp;^�nce, by fubftitution, the laft mentioned analogy becomesnbsp;CD;:Sc;SC::ScxSC:SCxSC::^�

Therefore c c/� D C x 5 ^tid by equal *^*^ltiplIcation, it will be cd X ~ CD x eg X

Tfow C D exprefles the bulk of the llratum C D G H (for as CD is very fmall, the air rnay, without any fenfiblcnbsp;be fuppofed to be Uniformly denfe throughout thenbsp;^tatum C D G H ) 5 egy by conftruftion, exprefles the

^he gravitation of each particle;' for fince the force of gra-is inverfely as the fquares of the diftances, if the gravity ^he furface A be called unity, we have S Cl��:nbsp;nbsp;nbsp;nbsp;; ; i :

R nbsp;nbsp;nbsp;,nbsp;nbsp;nbsp;nbsp;But

244 nbsp;nbsp;nbsp;Of the Oenfity and Altitude

much more variable than water, the aftion of fun and moon upon it becomes much lefs apparentnbsp;to us, fince tliey muft frequently concur with, ofnbsp;be counteradbed by, the much more powerful efFelt;^'^�

But the weight, or prefTure, of any flratum is as its bulk� as its denfity, and as its gravity conjointly i therefore CD X

Ta\^

quot;quot; TO

the ftratum CDGH. And the fame reafoning may h� adapted to any other fucceedirig ftratum. But the fum of allnbsp;fuch ftrata as cdhg (or cdxcg) from eg downward�s�nbsp;forms the area cmn g below eg-, therefore the whole prol'nbsp;lure upon C, arifing from the gravitation, or preflure, of aquot;nbsp;the air above it, is as the area cmng. But the denfitynbsp;of the air is as the preflure ; therefore any area 2.% cmanbsp;below any ordinate, as eg, is proportional to that ordinat^'nbsp;Now this is a charafteriftic property of the logarithm''^nbsp;curves; therefore it fbews that the curve Ofghn is a l'^'nbsp;garithmic curve. See Cor. 2. to Prop. IV. in page 221-

Farther it,appears, that this curve is exadly equal to curve OFGHN; for if B come continually near to A�nbsp;and ultimately coincide with it, the ultimate ratio of A Bnbsp;A b, and of B F to bf, muft be that of equality. Th'*�nbsp;the tangents OFK, O/k, form equal angles with thenbsp;dinate A O; confequently the fuhtangents A K, Ahnbsp;equal, and the curves OFGHN, Ofghn, are alfo eq*^^ 'nbsp;See Cor, to Prop. II. in page 235.

The diftances Si�, Sr, ^d, are in arithmetical Pf grefiion, and fo are the diftances Ab, Ac, Ad, becaufenbsp;latter are refpedively equal to SA � S SA � S r, .

of the Atmofphere, amp;c. nbsp;nbsp;nbsp;24^

heat and cold, of drynefs and moifture, of winds, (See the Abbe Mann�s Differt. on the Fluxnbsp;Reflux of the Atmofphere, in the fourth vol. ofnbsp;^he Tranf. of the Ac. of Sc. at Bruflds, or in the

Then fince Ofghn is a logarithmic curve, and the A^, Ar, Ai, are in arithmetical progreffion ; thenbsp;''��'^inates bf eg, dh, muft be in geometrical progreffion.nbsp;thefe ordinates reprefent the real denfities of the air atnbsp;gt; C, D ; therefore the deniities of the air at B, C, D, arenbsp;geometrical progreffion, on the true hypothclis of the de-^��eafeof gravity in proportion to the fquares of thediflancesnbsp;hom the centre of the earth.

^pon the whole then it appears that the difference be� ^'Veen the two hypothefes, viz. of an uniform, and of a de-^feafing gravity, is, that the ordinates b�, eg, d h, amp;c. whichnbsp;*^^Prefent the denfiti�s of the air at the places B, C, D, respectively, are a little longer than the correfponding ordi-BFyGG, DH. And they are longer, becaufe thenbsp;^^itiffas Ab, Ac, Ad, are fhorter than the correfpondingnbsp;^'^feiffas A B, A-C, AD; recolledting that the curvesnbsp;and Ofgn, have been deinonftrated to benbsp;^'l^ial. So that if the denfity. of the air, or the preffure ofnbsp;atmofphere, at a certain point, for inftance, D, is to benbsp;^^^'^'^ated on the fuppofition of an uniform gravity, ,vve muff ^nbsp;�^^tmine the value of the ordinate DH ; but upon the truenbsp;theory of a decreafing gravity, we muft determine the valuenbsp;the ordinate dh.�The method of calculating thofe ordi-is as follows.

The logarithmic area A O N M is equal to the reAangle ^ X AK (Prop, IV. in page 236, and its Corollaries) the

54^ nbsp;nbsp;nbsp;Of the Denfity and Altitude

Phil. Magazine, vol. V.) Hence the aftion of th� fun, and principally of the moon, upon the at-mofphere, has been long furmifed; but it is onlynbsp;of late years that it has been in fome treafut�

area B F N M is equal to BF x AK j the area C G N is equal to C G X A K, amp;c. Therefore the preffure at tbsnbsp;furface, which is proportionate to the area AONM, is equalnbsp;to A� X AK. But if the air were of a uniform denfify, equalnbsp;to its denfity at the furface A, and did not reach higher thannbsp;K, its whole quantify would be exprefled by AOx AK�nbsp;therefore the whole quantity of air A O N M, gradually de-ereafing in denfity, is equal to an homogeneous atmofphercnbsp;of the denfity A O, and altitude A K.

Farther, the quantity of air B F N M is to the quantity AONM, (or to A O x A K) as B F is to AO. Alfo tbsnbsp;quantity of air C G N M, is to the quantity AONMjnbsp;(or to A O X A K) as C G is to A O ; and fp forth.

Now let fig. 14. Plate XIII. reprefent the logarithmit^ curve of the common table of logarithms, where the fubtan-gent, or module A E, is equal to 0,43429; let AT be equalnbsp;to AO, (fee both figures) and DH to RY; then we havsnbsp;(by Prop. \f. in page 238.) AE:AK;;AR:AD*nbsp;Alfo, if VQ_be equal to B F, we have AE ; AK ; ; VR *nbsp;BD.

Thofe. two analogies are pf great pradlical ufe, viz. 1�*' finding out the preffures or the denfities of the atmofphei'S�nbsp;when the altitudes are given; and, on the other hand,nbsp;finding the altitudes, or the dift'erence between two altitude^�nbsp;when the denfities at thofe altitudes are (cnown.

ef the Atm�jphere, amp;c. nbsp;nbsp;nbsp;24gt;7

obferved, and rendered fenfible by means of very ^curate and long concinned barometrical obferva-^*ons; for it may be perceived only by taking a meannbsp;the obfervations of many years.

fliewn by the altitudes of the mercury in the barometer, (which are the counterpoifes to thofe prcflures) placed atnbsp;the correfponding fituations A, B, C, D, 6ic. The partsnbsp;^ U, A R, U R, are to be found in the common table ofnbsp;^'^�*rithms; AE is equal to 0 43479; and AK has beennbsp;�h:ertained, by the following means, to be equal to 26365nbsp;^^�t, or'five miles nearly,

R 4 nbsp;nbsp;nbsp;Tile

�48 nbsp;nbsp;nbsp;Of the Denfiiy and Altitude

Toaldo the learned aftronomer of Padua, after a variety of obfervations made in the courfe offeveralnbsp;years, found reafon to afl�rt, that cateris paribusy atnbsp;the time of the moon�s apogeum, the mercury in

The praflical application of the abovementioned analogies, to the method of meafuring altitudes by means of barometrical obfervations, will be illuftrated by one or tvVOnbsp;examples.

Example I. Suppofe that the mercury in the barometer at -A, fig. 13. viz. on the furface of the earth,,Hands at 30 inches�nbsp;at the fame time that the mercury of a fimilar barometernbsp;fituated on the top of a mountain at D, Hands at 29,34quot;nbsp;inches. It is required to deduce the altitude A D from thofenbsp;obfervations.

In the firft place it muft be recolledled, tliat the fame pref-fure of the atmofphere, which caufes a certain denfity of the air at any place A, or D, keeps up the mercury in the tubenbsp;of the baromer; therefore the altitudes of the mercury in thenbsp;barometers fituated at different altitudes above the furface ofnbsp;the earth, are proportional to the denfities of the air, or to thenbsp;ordinates of the atmofphcrieal logarithmic at thofe refpetSi'quot;^nbsp;altitudes. So that in the prefent inftance, 30 inches perpeO'nbsp;dicular altitude of mercury reprefents the ordinate AO, anlt;inbsp;^9,34 inches perpendicular altitude of mercury reprefent*nbsp;the ordinate D H.

Now in the logarithmic curve of the common tabular lo' garithms, fig. 14, Plate. XIII. AT and RY are t�'nbsp;ppedfively equal to A O and D H of the atmofphericalnbsp;logarithmic, fig. 13, Plate XIII.; therefore, taking froii*nbsp;the common logarithmic tables^ the logarithm of 30, whi'^^nbsp;3

cf the Atmofphere, amp;c. nbsp;nbsp;nbsp;249

tHe barometer rifes the 0,015 of an inch higher than at the perigeum; that at the time of the quadratures, the mercury ftancJs 0,008 of an inch highernbsp;than at the time of the fyziges and that it Hands

147712135 alfo the logarithm of 29,34, which is *4674601; and fubtraftirig the latter from the former, wenbsp;*�htain the remainder 0,0096612, which is equal to the portion A R of the axis.

This being obtained, we then fay A E : A K ; ; A R : �^0; viz. 0,4342945 ; 26057,675 : : 0,0096612 : to anbsp;tourth proportional, which gives the altitude A D equal tonbsp;^79,672 feet.

In finding this fourth proportional, according to the com-�^on rule of three, we may either multiply the third term by the fecond, and then divide the product by the firft ; or wenbsp;�t�ay firft of all divide the fecond ternt by the firft, and thennbsp;tonltiply the quotient by the third' term; the refult, as isnbsp;'''^11 known, turning out always the fame. But in thisnbsp;t^Peration the fecond method is attended with a pradlical ad-t'^ntage, which will be pointed out prefently.

Example 11. Suppofe the perpendicular pillar of mercury **gt; the barometer at B, to be 28,65 inches, and that of thenbsp;Mercury in a fimilar barometer at D, to be 26,97 inches.

Is required to determine thereby the perpendicular 'hftance BD, between the two ftations, or places of obf�r-Vation.

Suppofing the ordinates U Q__, R Y, to be refpedlively ^9nal to the above-mentioned mercurial altitudes 5 we takenbsp;*6e logarithm of 28,65, which is 1,4571246, and the lo-Sarithm of 26,97, which is 14308809 ; then fubtraifting the

Of the Deu/ity and Altitude

0,011 of an inch higher when the moon in each lunation comes neareft to our zenith (meaning thenbsp;zenith of Padua, where the obfervations were made)nbsp;than when it goes fartheft from it. quot;Journal desnbsp;Sciences Utiles.

26057,675 : : 0,0262437 : to a fourth proportionil, to find which, we divide the feepnd term by the firft, and �btain thenbsp;quotient 60000 ; then multiply the third term by this qun*nbsp;tient, and the: produft, viz. 1574,622 feet, is the dif-tance BD,

Here it is to be obferved, that the firft and fecond term* of the abovementioned analogy, are conftantly the fame, vi2l�nbsp;0,4342945, and 26057,675 ; and of courfe their, quotient Bnbsp;likewife conftantly the fame,' namely, the very couvenien*^nbsp;number 60000; therefore the .operation of deterrnjning thenbsp;altitudes, amp;c. may be rendered veryfoort; for the whol�nbsp;confifts in multiplying the-difference of the logarithms nfnbsp;the mercurial altitudes, by 6.�000, and the p!'odn4t gives tb�nbsp;altitude fought, :in feet. And if we want the .apfwer in fe'nbsp;thorns, the operation will be reti(d�red fhorter ftill; for fin��nbsp;�X feet are.equal to one fathom, 60000 feet mull be equalnbsp;to 10000 fathoms. Therefore, in that cafe, we need onlynbsp;multiply the difference of the'logarithms by lOQOO i whi�!'nbsp;is eafily done by removing iftie comma, which faparates th�nbsp;decimal part of the logarithmic remainder, four plafes, nfnbsp;figures tQ.the right, Thus, in the laft example, the 1�'

of the Atmojphere^i^c. nbsp;nbsp;nbsp;2^1

In the 7 th vol. of the Philofoj)hical Magazine, there is a paper of L. Howard, Efq. which con^nbsp;tains feveral curious obfervations relative to thisnbsp;fubjeit. This gentleman found both from his own

E'^nthmic remainder is 0,0262437, which, by removing the ^oiTima four places to the right, becomes 262,437, and ex-Pteffes the diftance BD in fathoms; the fame as before,nbsp;^^^gt;437 fathoms being equal 1574,622 feet.

It is now neceffary to recolledt that this rule has been ^ftabliflied upon the fuppofitions that the fpecific gravitynbsp;mercury is 13,619; that the fpecific gravity of air isnbsp;�50oi 3066208 ; that the temperature of the air, as well asnbsp;''fthe mercury, is 32�. and that the mercurial altitude in thenbsp;^^rometer, fituated on the furface of the earth, is equal tonbsp;30 inches. But if any one of thofe circumftances happensnbsp;to be altered, then the refult of the operation, according tonbsp;�te above-mentioned rule, will deviate more or lefs from thenbsp;^�'oth, for inftance, if the temperature happens to be highernbsp;than then the fpecific gravities of the air, and of thenbsp;t�iercury, will differ from the above-mentioned ftatements,nbsp;i^'id of courfe the module of the atmofpherical logarithmic, �nbsp;'Vhich is the fecond term of the analogy, amp;c, mufl; be alterednbsp;^'^'^ordingly.�The fame thjng may be faid with refpedt tonbsp;tfie other particulars.

I^otwithftanding the intricacy of folution which arifes the concurrence and flu�uation of the above-Pientioned circumftaqces, the particular efFedls of eachnbsp;caufe have been examined, yvith immenfe trouble and afli-^^ity, by various ingenious philofophers; and rules havenbsp;k?en forrned for corrcdling hi a great meafure the errors

which

.2,52 nbsp;nbsp;nbsp;Of the Denjity and Altitude

obfcrvacions, and from an examination of the Meteorological Journal of the Royal Society, which is publillied annually in the Phil. Tranfaftions, thatnbsp;the moon had a manifeft aftion upon the baro-

which arife therefrom. We lhall now proceed to examine thofe rules, and the facb upon which they arc eftablilhed.

Since the bulk's of bodies are increafed by the acceflion of heat, and of courfe their fpecific gravities are therebynbsp;diminifliedi and fince different bodies are expanded differentlynbsp;by equal increments of heat; it follows that, under the famenbsp;atmofpherical preffure, the mercury in the barometer mullnbsp;Hand higher or lower, according as it is hotter or colder.nbsp;Alio the ratio of the gravity of mercury to that of air, will,nbsp;Ccstcrh paribus, vary with the increafe or decreafe of temperature ; but this variation has been found to be not exadllynbsp;proportional to the degrees of heat. ' Hence in mcafurlngnbsp;altitudes by the barometer, either the fubtangent of the at-mofph'erical logarithmic muff be derived from the adtualnbsp;temperature of the mercury and of the air at the time ofnbsp;making the obfervations j or' both the adtual denfity of thenbsp;air, and the obferved altitude'of the mercury in the barometer, mull be reduced to-what they would be if the degreenbsp;of temperature were 32�.�The latter niethod is'thc nioftnbsp;expeditious. '......1 nbsp;nbsp;nbsp;. .�

Mercury has been found t�''expaad nearly in the ^proportion of the degrees orh�at j its expanfion for everynbsp;degree of heat, from'32�. 'upwards, or the cOntradlidonbsp;��r every degree of heat from 32'�. downwards is equal

of the Atmojfbere-, amp;c, nbsp;nbsp;nbsp;253

� It appears, he Jays, to me evident, that the atmofphere is fubjedl to a periodical changenbsp;quot; of gravity, whereby the barometer, on a mean ofnbsp;ten years, is depreffed at lead: one-tenth of an

unity; fo that if a quantity of quickfilver, which at the temperature of 32�. meafures one cubic inch, at the temperature of 33�. meafure I,oooio2 inches; it will, atnbsp;the temperature of 34�. meafure 1,000204 inches, amp;c.nbsp;But though quickfilver .in itfelf be expanded regularly by thenbsp;3Cceflion of beat; yet in the tube of the barometer, the perpendicular pillar of it is not expanded with the fame regularity ; and this deviation from that regularity is owing tonbsp;two caufes, viz. to the expanfion of the glafs tube, and to thenbsp;probable generation of fome elaftic fluid, which being extricated from the mercury by the heat, occupies the emptynbsp;part of the barometrical tube above the quickfilver.

The a�tual increafe of altitude in a barometrical pillar of �ttcrcury, arifing from an increafe of temperature, was determined from a�tual experiments on tfae barometer itfelf, bynbsp;the late very ingenious General Roy. When the barome-ter flood at 30 inches, this gentleman expofed a barometernbsp;to different degrees of heat in a very proper apparatus,nbsp;quot;therein the whole column could be rendered of the famenbsp;quot;oiform temperature; and meafured the increafe or decreafenbsp;altitude, which was occafioned by the various degrees ofnbsp;heat. (See bis valuable paper in the 67th vol. of thenbsp;Bhilofophlcal Traniaiflions.) The refulc of his experimentsnbsp;�s contained in the annexed table, where the firft column ex-prefles the degrees of heat, to which the barometer was ex-fiofed ; the fecond column (hews the altitudes of the mercurial

^54 nbsp;nbsp;nbsp;Denfity and Altitude

� inch while the moon is paffing from the quat* ters to the full and new and elevated, in thenbsp;� fame proportion, during the return to the quar-ter.� A great fall of the barometer generallynbsp;'nbsp;nbsp;nbsp;nbsp;takes

rial column, correfpondent with the different degrees of heat; and the third column expreffbs the differences of thofe

cxpan lions.
212�.	30,5117
2�2.	30,4888 � nbsp;nbsp;nbsp;�
192.	30,4652
182.	30,4409
172.	30,4159
' nbsp;nbsp;nbsp;i6a.	30,3902
152.	.30,3638
I42.	30,3367
132*	30,3090
122.	30,2807 � � �
112.	30,2518
102.	30,2223 nbsp;nbsp;nbsp;�
92.	30,1922 ' ' '
82.	30,1615
72.	30,1302
62.	30,0984
52.	30,0661
42.	30,0333
32-	30,0000
22.	29,9662
12.	29,9319
2.	29,8971
0.	29,8901

i 0,�22g

, 0,0236 0,0243nbsp;0,0250nbsp;0,0257nbsp;. 0,0264nbsp;0,0271nbsp;0,0277nbsp;- 0,0283nbsp;. 0,0289nbsp;. 0,0295nbsp;0,0301nbsp;0,0307

of the Atmofpherei nbsp;nbsp;nbsp;255

In the year 1794, a regular rife and fall of the ntercury in the barometer was obferved at Calcutta

quot; From the experiments,� CoL Roy fays, � it appears, that a column of quickfilver, of the temperature of 32��nbsp;fuftained, by the weight of the atmofphere, to the heightnbsp;of 30 inches in the barometer, when gradually affedfed bynbsp;'iilFercnt degrees of heat, fuffers a progrelSvc expanfion ;nbsp;and that having acquired the heat of boiling water, it isnbsp;lengthened toW�- parts of an inch: alfo, that the famenbsp;Column, fuffering a condenfatlon by 32�. of cold, extending to the zero of Fahrenheit, is fliortenednbsp;nbsp;nbsp;nbsp;parts.

the weight of the atmofphere remaining in both cafes un-� altered 5 but that in the application of the barometer to � the meafurement of altitudes, fince the preflure andnbsp;quot; length of the column change with every alteration ofnbsp;^ Vertical height, the correiStion, depending on the difference of temperature of the quickfilver, will neceffarilynbsp;augment or diminifli by a proportionable part of thenbsp;' whole. Thus, if the weight of the atmofphere (hould atnbsp;^ny time be fo great as to fuftain 31 inches of quickfilver,nbsp;the corredtion for the difference of temperature will bejuftnbsp;3 oth part more than that for 30 inches; at 25 inches itnbsp;'vill be 'ths; at 20 inches |ds; at 15 inches f; and atnbsp;*0 inches only |d of that deduced from experiment,�nbsp;This reafoning, however,'is not quite corredt; for whennbsp;^lie original column of quickfilver is lefs than 30 inches, anbsp;gteater vacuum will remain in the upper part of the tube,nbsp;a fmaller quantity of quickfilver remains in the lower

2^6 nbsp;nbsp;nbsp;Of the T)�nftty and Altitude

by F. Balfourgt; Efq. During the month of ApH^# beginning from fix o�clock in the morning, the barometer role a little during four hours, then fellnbsp;during eight hours j after which it rofe again duringnbsp;part of it, in which cafe the fuppofed vapour, which is extricated from the mercury by the heat, is lefs in quantity,nbsp;and finds a greater fpace to expand itfelf in; therefore thenbsp;irregularity of apparent expanfic-n, which is occafioned bynbsp;this vapour, is not fo great as when the column of quick-filver in the barometer is 30 inches ;fo that if the experimentsnbsp;were performed with a column of 15 inches,-the expanflonsnbsp;would not come out exadtiy the halves of thofe which arenbsp;ftated in the table, which are the refults of experiments performed with a colum of twice 15, viz. 30 Inches the dif--ference however, would not be very confiderable.

In order to apply the correiSlion for the expanlion, we muft find, by means of the preceding table, what the columnnbsp;of mercury would be- if the quickfilver of the barometernbsp;had been at the temperature of 32�. iiiftead of its actualnbsp;temperature. For this purpofe the adtual temperature ofnbsp;the mercury, which is afeertained by means of the thermometer, muft be found out in the firft column of the table,nbsp;and oppofite to it is the expanfion for a column of 3�nbsp;inches, or its bulk at that temperature. Then fay, as thisnbsp;bulk is to 30 inches, fo is the obferved altitude of the met'nbsp;cury in the barometer, to a fourth proportional, which is thenbsp;correfled altitude. 1'hus, if the obferved altitude be 2^nbsp;inches, and the temperature of the mercury be 72�. you wiHnbsp;' find 30,1302 againft 72�. in the table; therefore fay,nbsp;30,1302 ; 30 ;; 28 ; to a fourth proportional, which

ing four hours, and then fell during the laft 8 hours of the 24, And this took place every day regularly,nbsp;With very few exceptions.

But it feems, that ihofe regular fluftuafions of the Barometer at Calcutta could not be owing to thenbsp;inamediate adion of the moon, fince the moonnbsp;oould not crofs the meridian every day at the famenbsp;BtUe. So that upon the whole it appears that wenbsp;have very little, if any, proof of the exiftence of anbsp;�^hirnal Bux and reflux of the atmofphere, fimilarnbsp;*�0 the tides of the fea; yet the caufes which rendernbsp;fhe diurnal tide of the atmofphere infenfible to us,nbsp;^3y be the elafticity of the air, and the interferencenbsp;the much more powerful eft'eds of heat, cold,nbsp;Vapours, amp;c.

Having thus given a fufficient idea of the nature 3nd extent of the atmofphere, and of the ufe of the ba-forneter, 1 fliall conclude this chapter with a lift of thenbsp;^hitudes of fcveral remarkable mountains, hills, andnbsp;^ther places, which have been afcertained by variousnbsp;*^genious perfons, either geometrically or by means

� 'gt;^79 inches j fo that had the temperature of the mercury barometer been 32�. the obferved barometrical alti-^�Jde Would have been not 28, buf 27,879 inches.�If thenbsp;gree of temperature be not mentioned in the table, thennbsp;take a proportional part of the difference of thenbsp;'^^tiguous expanfions in the third column of the table, andnbsp;add it to the expanfion next below} for the funi willnbsp;'nbsp;nbsp;nbsp;nbsp;snbsp;nbsp;nbsp;nbsp;b?

of barometrical obfervations. I have, howeV�flt; preferred the refuk of the geometrical meafurc'nbsp;ment to that of the barometrical* for all thofenbsp;places which have been meafured by both means.

Table of Heights, exprejfed in Englijh Feet, as dc' ter mined by M. De Luc, Sir George Shuckburgb�nbsp;Col. Roy, Mr. Eouguer, and other Jcientific Perjons-

Thus if the obferv�d altitude be 28 inches, and the tehi perature 47�. then 47�. is not to be found in the table;nbsp;47�. is equally didant from 42�. and 52�. which are m

The fumrait of Mont Blanc, the higheft of the Alps, and, as Sirnbsp;George Shuckburgh Itippoles, thenbsp;moft elevated point in Europe, Afia,nbsp;and Africa. G. �nbsp;nbsp;nbsp;nbsp;�nbsp;nbsp;nbsp;nbsp;. �

The deepeft part of the lake of Geneva The greateft depth of the lake beingnbsp;393

table; therefore we take the half of the difference of the cxpanfions for thofe degrees, viz. the half of 0,0328,nbsp;'vhich is 0,0164, and add it to 30,0333 ; the fum 30,0497nbsp;is the bulk anfwering to 47�. Then we proceed as before,nbsp;viz, fay as 30,0497 ; 30 : : 28 : to a fourth proportional, amp;c.

Notwithftanding the great accuracy of Col. Roy�s experiments, it is believed that his (latements of the expanhons

St. Joire, in a field at the foot of the Mole, G. �nbsp;nbsp;nbsp;nbsp;��nbsp;nbsp;nbsp;nbsp;�

The fource of the river Arviron, at the bottom of the Vall�e de Glace �nbsp;The ballon the higheft, or fouth-weft,nbsp;tower of St. Peter�s church in Geneva (249 f�et above the lake) G.nbsp;Frangy, at the inn, firft-floor, belownbsp;the lake of Genevanbsp;nbsp;nbsp;nbsp;�nbsp;nbsp;nbsp;nbsp;166

Aixj a la ville de Geneve, firft-floor, below the lake of Geneva 378 Chambery, au St. Jean Baptifte,nbsp;firft-floor, below the lake of G. 352nbsp;Aiguebelle, at the inn, firft-floor,nbsp;below the lake of Geneva � 190nbsp;La Chambre, at the inn, firft-floor,nbsp;above the lake of Geneva � 337nbsp;St. Michael, at the inn,firft-floor,nbsp;above the lake of Geneva � 1113nbsp;Modane, at the inn, firft-floor,nbsp;above the lake of Geneva 2220

are rather too great, and that the mean expaniiori of an ind* of mercury for each degree of Fahrenheit�s thermometerjnbsp;betv/een 20�. and 70�. (within which extremes moft bare-*nbsp;mstrical obfervations are made) is 0,o0blo2 of an inch-But it is highly probable that different fpecimens of mercurynbsp;follow different rates of expanfion. Admitting then thenbsp;mentioned expanfion, we derive therefrom an eafier method

quot;The fummit of Mont Cenis � �� ^ovalefe, at the foot of Mont Cenis,nbsp;on the fide of Italy, at the inn,nbsp;firft-floor �nbsp;nbsp;nbsp;nbsp;�nbsp;nbsp;nbsp;nbsp;�

dc los Reyes, one of the Pyrenn�es I*ic du Medi, one of the Pyrenn�es -�ic d�Oflano, one of the Pyrenn�es -

Tiacenza, St. Marco, firft-floor � -Tarma, au Paon, firft-floor � � Bologna, au Pelerin, firft-floor � -Loiano, a little village on the Appe-nines, between Bologna and Florencenbsp;quot;The mountain Raticofa �nbsp;nbsp;nbsp;nbsp;�

The fummit of Monte Velino, one of the Appenines, covered with fnownbsp;in June j about 46 geographicalnbsp;miles, N.W. of Kome, and whichnbsp;is probably the higheft of the Appenines. G.nbsp;nbsp;nbsp;nbsp;�nbsp;nbsp;nbsp;nbsp;�nbsp;nbsp;nbsp;nbsp;�

Florence, nel Corfo dei Tintori, 50 feet above the Arno, which was 18 feetnbsp;below the wall of the quay �nbsp;nbsp;nbsp;nbsp;�

Pifa, aux Trois Bemoijelles, fecond-floor Siena, aux Trois Rois, fecond-floor -Redicoflfani, at the Poft, firft-floor -Kedicoffani, the top of the tower ofnbsp;the old fortification on the fummitnbsp;of the rocknbsp;nbsp;nbsp;nbsp;�nbsp;nbsp;nbsp;nbsp;�nbsp;nbsp;nbsp;nbsp;�

Thus, ufing the fuppofitions of the preceding exampk� the temperature 72�. exceeds 32�. by 40�; thereforenbsp;multiply 28 (which is the obferved barometrical altitude)nbsp;by o,0OCi02, and multiply the produdf 0,002856 by 4��nbsp;which produces 0,11424; then fubtraft this laft produiftnbsp;from 28, and the remainder 27,88576 inches, is the cor-redled barometrical altitude; which differs from the refaknbsp;of the other method by about one 5oodth part of an inch.

quot;The union of the Viminal and Quirinal Hills, in the Carthu-fian�s church; Dioclef. Baths 141'

by far the moft intricate and perplexing particulars of the fubjeft; for the air doss not only expand irregularly throughnbsp;^ progrefiive increafe of heat; but its expantdiility is dif-^�rerit according both to its deniity andto its purity.

The beft contrived, the moft extenfive, and the moft COnclufive experiments relative to this expanfibility, were

^^tis, mean height of the Seine, viz-quand les eaux Je trouvent a i 3 pieds 9 fauces fur Vechelle du Pont Royal,nbsp;Lion M. de Lalande �nbsp;nbsp;nbsp;nbsp;�

correfting the efte�ls of aerial expanllon. How-the pra�ficability of afeertaining the various but contemporaneous temperature and moifiure of a confiderable ^ratum of air, feems, at lead for the prefent, to be utterlynbsp;�ut of our power

M. de Lalande's obfervatory, at the College Royal, firft-floor,nbsp;above the Seine, at Paris � loinbsp;Stone gallery of the church onnbsp;Mount Valerien, above thenbsp;Seine, Parisnbsp;nbsp;nbsp;nbsp;�nbsp;nbsp;nbsp;nbsp;� 47 j

Depth of the cave of the Royal Obfervatory at Paris, belownbsp;the pavement �nbsp;nbsp;nbsp;nbsp;� gg

Height of the North Tower of , tne church of Notre Dame atnbsp;Paris, above the floor. G. � ai8|nbsp;Chantilly �nbsp;nbsp;nbsp;nbsp;.�nbsp;nbsp;nbsp;nbsp;�

Amiens, Rice de Noyon, firft-floor .Abbeville, firft-floor �nbsp;nbsp;nbsp;nbsp;�

Mean height of the river Thames at London (viz, when the waternbsp;is 151 feet below the pavement in the left-hand arcade atnbsp;Buckingham-ftairs) which isnbsp;above the mean height of thenbsp;river Seine at Paris 6,8nbsp;nbsp;nbsp;nbsp;�

In the prefent ftate of knowledge, the only correction W� can apply is founded upon the fuppofition that the temperature of the whole flratum of air, which lies between tw�nbsp;ftations, is the mean of the temperatures Vif the air at thenbsp;two Ifations ; and that air of the more common degree ofnbsp;moiflure is expanded, at a mean 0,00245 of its bulk, which

cf the Atmojphere^

Iron gallery over the Dome of Sc. Paul�s church, in Londonnbsp;above the church-yard. Northnbsp;fide. G. �nbsp;nbsp;nbsp;nbsp;�

J Called of3�, by each degree of Fahrenheit�s thermometer� Ween 20�. and 70�. which is the range of temperaturenbsp;^ fough which moft barometrical obfervations are likely tonbsp;� triade�, Pbe rule then, which is efiablifhed upon thofenbsp;��'Ppofitions, is as follows:

l^ultipiy the difference between 32�. and the mean tem-Pctatureof the air, (viz. the mean between the temperatures

Safe of Hawk-hill Obfervatory, above the bottom of the fmallnbsp;rock on Arthur�s feat, Scotland. G. �nbsp;nbsp;nbsp;nbsp;�nbsp;nbsp;nbsp;nbsp;� 684

multiply the product by the approximated perpendicular dif' tance, already found, between the two ftations, and the laftnbsp;product muft be added to, or fubtradted from (accordingnbsp;the mean ternperature of the air is above or below 32�.) th�nbsp;approximated altitude j and the fum or difference is the.nbsp;correiff altitude.

For if what we have called the approximated elevation* gives the real diftance between the two ftations whennbsp;mean temperature of the air is 7^.�. it is evident that whennbsp;the air is one degree hotter, its bulk is 0,00245nbsp;nbsp;nbsp;nbsp;�

hence in this cafe the fame weight, or the fame preffure oH tire mercury of the barometer, is produced by a ftratum

of the Aimojphere, amp;Ci nbsp;nbsp;nbsp;269

The Cafpian fca is faid (hj Lacre) to be 306 feet below the ocean.

The

thicker than the former by 0,00245 of the whole, viz. of whole number of feet, or fathoms, by which tliat thick-is expreffed; hence the quantity 0,00245 mull benbsp;�^'tiltiplied by the number of feet or fathoms, which wouldnbsp;�^^prefs the real thicknefs of the ffratum if its temperaturenbsp;Were 32�.�It is alfo evident, that if one degree of heat in-'^feafes the ftratum 0,00245 of the whole, two degrees niuftnbsp;'ncreafe it of twice that quantity ; three degrees, of threenbsp;that quantity, amp;c. Therefore the above-mentionednbsp;{�quot;oduft mufl; be alfo multiplied by the number of the degreesnbsp;'�fbeat, amp;c.

Having thus fhewn the foundation of the method of ap-Plying the barometer to the meafuremenc of altitudes, in fe-P^i'ate parts, for the fake of perfpicuity, I fhall now colledt the neceffary rules under one point of view; which maynbsp;confidered as the ultimate refult of the invelf igation.nbsp;b For this purpofe two accurate barometers, as nearlynbsp;Poflible of the fame conftrudfion, mull: be had j and eachnbsp;*^arometer muft be furnifhed with a thermometer, whichnbsp;be attached to it in fuch a manner as to have its bulbnbsp;contadf, or nearly in contadf, with the mercury of thenbsp;^�ftern of the barometer. Two other feparate thermometersnbsp;likewife be provided.

One barometer and a detached thermometer muft be fi-^'^^��ed at each of the two places, between which the per-P^ndicular diftance is required to be meafured; and the ob-^^��vations at both places muft be made by two obfervers, at Very fame time; obferving the altitude of the mercurynbsp;the barometer, the temperature of its mercury, which isnbsp;^ttJicated by the attached thermometer, and the temperature

ayo nbsp;nbsp;nbsp;Of the 'Denfity and Altitude

The heights of the Afiatic mountains have not� as far as I know, been meafured with any tolerablenbsp;degree of accuracy.

of the ambient air, by means of the detached thermometer? which for this purpofe muft be fituated in fome expofeJnbsp;place, out of the influence of a fire, of the fun, icc.�Thol�nbsp;two fets of obfervations muft be written one under thenbsp;other, after the manner of the fubjoihed example.

II. nbsp;nbsp;nbsp;Each barometrical altitude mull be reduced to wh^tnbsp;it would be, if the temperature were 32�. which may bsnbsp;done two ways, viz. Find in the table of mercurial expar.'nbsp;fions, in page 254, the bulk of mercury anfwering to thrnbsp;obferved temperature of the mercury; then fay, as tba^nbsp;bulk is to 30 inches, fo is the obferved barometrical altitudenbsp;to a fourth proportional, which is to be found by the com'nbsp;mon rule of three, and is. the reduced barometrical altitudenbsp;in queftion. Otherwife, multiply the conftant quantitynbsp;0,COOiC2, by the inches and decimals of obferved baromfi'nbsp;trical altitude, and multiply the produfl by that number 0^nbsp;degrees of heat by which the temperature of the mercury h'nbsp;the barometer differs from 32�. Then-add'this laft produ^:nbsp;to the obferved barometrical altitude, if the temperaturenbsp;the mercury exceed 32�.; or fubtrad it from that altitude?nbsp;if that temperature be lefs than 32�.; and the fum or diffe'''nbsp;ence is the reduced barometrical altitude.�It is evident ths*-when the temperature of the mercury is 32�. no redudk�nbsp;will be wanted.

III. nbsp;nbsp;nbsp;In a table of the logarithms of numbers, whem'��nbsp;the logarithms confifl: of feven places of figures, find tbquot;nbsp;logarithms anfwering to both reduced barometrical altitudes gt;nbsp;lubtrad the leffer from the greater; then the rerr.aiu*^'^''

of the Atmofphcre, ^c. nbsp;nbsp;nbsp;271

M^otwithftanding the ftupendous altitude of fame the abovein�ntioned mountains; it is fhewn bynbsp;an eafy calculation, that the higheft mountain onnbsp;the furface of the earth docs not make fo great annbsp;appearance, with rel'peft to the globe of the earth,

multiplied by 6000c, will give the approximated ele-''ation in feet; or.if multiplied by JOOOO, will give it ia fathoms. Both methods come to the fame thing; but thenbsp;is more expeditious, becaufe the multiplication of thenbsp;^^garithmic remainder by loooo is done by removing thenbsp;four figures to the right.

� V. Take the mean between the temperatures of the air both ftatlons, which are indicated by the detached-ther-�^onieters fviz. the half of their fum) ; take the differencenbsp;ftween this mean, and 32�.; multiply this difference bynbsp;and multiply the produdl by the approximatednbsp;^^�yation already found. Then add this laft produdf to, ornbsp;it from, the approximated elevation, aexording a$nbsp;mean temperature of the air is above or below 32�.;nbsp;the fum or difference is thecorredl perpendicular diftancenbsp;stvveen the two ftations.

^�it this corredfion for the expanfion of the air may be ^'�dered more exadf by the ufe of the following table; viz.nbsp;he the mean of the correEfed barometrical altitudes, andnbsp;the

tnean temperature of the air; find out tliofe .quanti-gt; or the nearefl: to them, in the upper and in the left-t;olumns of the table, and in the place which flands under the one, and level with the other, you will findnbsp;� e.xpaivfion which mufi be ufed iiiftead of the above-

272 nbsp;nbsp;nbsp;Of the Denfity and Altitude

Would make upon a globe of two feet in diameter. This calculation is made by faying, as the diameternbsp;of the earth is to the altitude of the higheftnbsp;mountain, fo is a diameter of two feet to a fourthnbsp;proportional, which being found by the rule .o^*nbsp;three, is the height of a firailar mountain on a glob^nbsp;of two feet in diameter.

mentioned conftant quantity 0,00245, viz. it muft be multiplied by the difference of degrees between 32�. and thS mean temperature of the air, as alfo by the approximatednbsp;elevation^ amp;c. as mentioned in the preceding paragraph.

N. B. There are fome other ways of performing this probleni, and of applying the correflions ; but I have preferred the above as being the moft accurate 5 and more evidently deduced from the foregoing principles.

of the Atmofphere, ^c.

Expanfm of common air for each degree of .Fahrenheit's ^her~ ^mteur between I2�. and 92�. and under different prejjures.t as indicatednbsp;^ ^he height of the mercury in the barometer.^ from 19nbsp;nbsp;nbsp;nbsp;3� � inches.

22�. nbsp;nbsp;nbsp;32�.

52�. nbsp;nbsp;nbsp;62�.nbsp;nbsp;nbsp;nbsp;72�.nbsp;nbsp;nbsp;nbsp;82�.nbsp;nbsp;nbsp;nbsp;92�

000133	ogt;ooi39	0,00x44	0,00149	0,00155	0,00152	0,00149	0,00144
_ II*,							..
0,0016	0,00167	0,00173	0,0018	0,00187	0,00183	0.0018	0,00173
0,0016	0,00167	0,00173	0,0018	0,00187	0,00183	o,coi8	0,00173
�gt;ooi6	0,00267	�cgt;jCoi73	0,0018	0,00187	0,00183	0,0018	0,00173

o,ooig8	0,00195	0,00203	0,0021	0,0021 8	0,00214	0,002 I	0,00203
_
0,00,88	0,00195	0,00203	0,C02I	0,002iS	0,00214	0,0021	0,00203
�
0,00188	0,00195	0,00203	0,0021	0,00218	0,00214	0,0021	0,00203

�}OOip^	0,00205	0,00213	0,00221	0,00229	0,00225	0,00221	0,00213
�'0020�	0,00209	0,002X8	0,00226	0,00234	0,0023	0,00226	0,002 T 8
0,00206	C,C02I�:r	0,00222	0,00231	0,00239	0,00235	0,00231	0,00222

�gt;002 1	0,00219	0,00227	0,00236	0,00245	0,0024	0,00236	0,00227
	0,00224	0,00232	0,00241	0,0025	0,00245	0,00241	0,00232
0,002 ip	0,00228	0,00237	0,00246	0,00255	0,00251	o,'-'0246	0,0023
0,00224	0,00133'	0,00242	0,00251	0,0026	0,00256	' 0,0025 J	0,00242
0,00228	0,00238	0,00247	0,00256	0,00266	0,00261	0,00256	oJo024'
;,002;..	0,00242	0,00252	0,00261	0,00271	0,00266	0,0026 �	0,0025-'
^gt;0c227	*^gt;00247	0,00257	0,00266	0,00276	0,00271	0,0C266	0,00257

Example

Of the Benfily and Altitude

Example 1. It is required to determine the perpendicular diftance between the fummit and the foot of a hill, frotu

At the foot of the hill � 29,561 inches � 63� � 56� At the furnmitof the hill 28,272 inches � 54� � 48�

From the table in page 254, we find the bulk of mercury for 63�. equal to 30,1; therefore 30,1 : 30 ; ; 29,561 ; ^nbsp;the reduced barometrical altitude, 29,462.

The bulk of mercury for 54�. is, fron^the table, 30,0726 i therefore 30,0726 : 30 : : 28,272 : to the reduced barometrical altitude, 28,204.

Now if the comma be removed four places towards the right hand, this reinainder will exprefs the approximate*!nbsp;elevation in fathoms ; viz. 189,515 fathoms. Or if it h�nbsp;multiplied by 60000, it will exprefs the fame approximate*!nbsp;elevation in feet, viz. (0,0189515 x 60000=) ii37,�9'nbsp;feet.

which exceeds 32� by 20�; therefore (0,00245 X 20 i*375�9nbsp;nbsp;nbsp;nbsp;55gt;7i74i, which, fmee the mean temperatur�

of the air is above 32�, muft be added to the approximated elevation, and their fum, viz. (1137509 5557 ^74*nbsp;1192,80741 feet, is the corre�l elevation,' or the perpendi'nbsp;cular altitude of the hill.

Forthe' fake of greater accuracy, the expanfion of the may Oe taken from the preceding table, according to the l^�nbsp;part of the rulej viz. the mean between the reduced batOquot;

metrical altitudes is ( nbsp;nbsp;nbsp;) 28,833 5

^ nbsp;nbsp;nbsp;^nbsp;nbsp;nbsp;nbsp;^nbsp;nbsp;nbsp;nbsp;tn�

cf the Atmofphere, nbsp;nbsp;nbsp;275

mean temperature of the air is 52�. Then in the table '''e find facing 28,5, which is the neareft to 28,833; andnbsp;'inder ^2�, or properly under the degrees of heat betweennbsp;S2�. and 62�. the quantity 0,00255, which quantity diuftnbsp;ufed inftead of 0,00245; therefore (0,00255 X 20� Xnbsp;^*37i09 =) 575*59159gt; which being added to the approxi-*^ated elevation, gives (i 137509 S7gt;99�^�'�nbsp;nbsp;nbsp;nbsp;1195,08

^^et for the altitude of the hill, which is a nearer approximation to the truth.

Example 11. It is required to determine the perpendi-'^olar altitude between two fituations, where the following *^fiorvations were made.

�'tom the table in page 254, we have the bulk of mer-'^Ory for 28�. equal to 29,9865; therefore fay, 29,9865 :

�^Ifo the bulk of mercury for 26�. is 29,98; therefore-^^75 29,98 : 30 ; : 29,032 : to the reduced barometrical al-*gt;tude 29,051.

quot;The logarithm of 29,897 is 1,4756276 *I'he logarithm of 29,051 is 1,4631611

Of the Oenfity and Altitude

which is lefs than 32�. by 7�. therefore (0,00245 X 7� 747,99 =) 12,828 muft be fubtracled from the approximated elevation, and the remainder 735,161 feet, is thenbsp;corredl perpendicular altitude in queftion.

Otherwife, inftead of the quantity 0,00245, the expanfioit of the air may be taken from the table in page 273. Thusnbsp;the mean between the reduced barometrical altitudes

of the air is 25�. Then in the table we find, facing 29,5* which is the neareft to 29,474, and under 25�. the quantitynbsp;0,00238. Therefore (0,00238 X7�X 748=) 12,46168nbsp;muft be fubtradled from the approximated elevation; finccnbsp;the mean temperature of the air is below 32�. And thenbsp;remainder, viz. (747,99 � 12,46168 = ) 735,53 is thenbsp;correct perpendicular altitude between the two fituations.

Example III. Let the barometrical obfervations made at two places, be 28,65, ^^nd 29,9. Allb let the temperaturenbsp;of the mercury and of the air at both places, be 32.

The perpendicular diftance between thofe two places, i* thereby eafily determined, fince in this cafe no corredtiounbsp;needs be made for temperature.

The difference of thofe log�, is o,Oi 85466, which flieWSj that the perpendicular diftance in queftion is 185,466nbsp;thorns, or 1112,796 feet.

After all, it muft be acknowledged, that notwithftanding the greateft exertions of feveral ingenious perfons, the method of meafuring altitudes by means of barometricalnbsp;thermometrical obfervations, has not yet attained a degt^�nbsp;of perfection fufficient to fuperfede the geometiica!, or tr*'nbsp;gonometrical, meafurements.

The

ef the Atmo/phere^ amp;c. nbsp;nbsp;nbsp;277

The facility and expedition with which the former is Performed, renders it ufeful whenever no very great degreenbsp;accuracy is required; for in general the barometricalnbsp;�Method gives the perpendicular diftance within about onenbsp;^'ghtieth part of the truth ; for inftance, if the altitude givennbsp;y the batometer be 560 feet, the error or deviation fromnbsp;true altitude, may amount to about 7 feet.

^fiveral altitudes, which had been purpofely and accurately *^2afured by geometrical means, were afterwards repeatedlynbsp;**'^afured by means �f barometrical obfervatlons; but the re-^^Its of the latter were found to difagree more or lefs fromnbsp;of {-jjg former method. The following is an examplenbsp;this fort, which I have taken from Col. Roy�s paper in thenbsp;7th vol. of the Philofophical Tranfadlions.

^ The perpendicular diftance between two 'quot;places, having meafured geometrically, was found equal to 730,8nbsp;^et. The fame was afterwards meafured with all pofliblenbsp;^^curacy, and at different times, by means of barometersnbsp;and the refult was, at one time 721,8 feet; at a fecondnbsp;it was 734,6 feet; a third time it was 733,9 feet; andnbsp;* hjurth time it was 748,4 feet; the mean of which refultsnbsp;** 734,7 feet.�-It is evident that the true or geometricalnbsp;'^^afurement differs from every one of thofe refults, as wellnbsp;^ fforn their mean.

. quot;^his difagreement, undoubtedly, depends upon the vary-'�S gravity, and the varying expanfibility, of air; whence the difnculty of afeertaining the real mean expanfibilitynbsp;obf ffi'atum of air which lies between the two places ofnbsp;� ^�^^^tion. The air at different altitudes is loaded withnbsp;^'�ent quantities of moifture; hence its expanfibdity isnbsp;^�tacfly the fame in any two placesi Befides, both thenbsp;and the fpecific gravity of the air differ at differentnbsp;do we know how to afeertain thofe quantities atnbsp;�'^^'-ent altitudes.

278 nbsp;nbsp;nbsp;Of the Benfity and Altitude

It is alfo neceflary to obferve, that in different latitude* neither the gravity nor the expanfibility of air is the fame-Hence the ratio of the gravity of air to that of mercurynbsp;by no means conftant; nor is it eafily afcertained for affnbsp;particular place and time. In the province of Quitonbsp;Peru, which Hands conllderably above the level of thenbsp;ocean, the altitudes which are deduced from barometricalnbsp;obfervations, fall greatly fhort of the real or geometricalnbsp;menfurations; whereas at Spitzbergen, they greatly ex'-ceed the truth. � It feems,� as Col. Roy jufly objerve^fnbsp;� that the atmofphere furrounding our globe might poffibl/

be compofed of particles, whole fpecihe gravities wete � really different; that the lighteft were placed at thenbsp;� equator, and that the denfity of the others gradually ia-� creafed from thence towards the poles, where the heavieH-� of all had their pofition.�

This fuppofition is corroborated by two obvious confi' derations, namely, that on account of the cold thenbsp;about the poles of the earth is much dryer than in othefnbsp;places, and tha: on account of the polar diameter bei^Snbsp;fhorter than the equatorial diameter, the air which lies **�nbsp;equal diftances frerm the furface of the earth, is adtuallynbsp;nearer to the centre of attra�ion about the poles thannbsp;about the equator. We may therefore conclude, upo*�nbsp;the whole, that in order to render the barometrical mc�'nbsp;furement capable of greater accuracy than it is at prefer**^�nbsp;farther experiments and obfervations muft be made with aHnbsp;pohible attention, in different latitudes, and in differeu*-ftates of the atmofphere. It is alfo probable that it will b�nbsp;found lifeful to accompany with the barometer and thermO'nbsp;meter, the ufe of other inftruments, fuch as the hygromctetjnbsp;the eloflrcrpeter, and the manometer.

particular manner, may confult the following valuable publications ; M. de Luc�s Recherches fur les Modifications de * -^tmofphere. Dr. Horfley�s Paper in the Philofophicalnbsp;^ranfadtions, vol. 64th. Sir George Shuckburgh�s Paper,nbsp;de Luc�s Paper, and Col. Roy�s Paper, all three in thenbsp;vol. of the Philofophical Tranfadtions. Alfo thenbsp;article Pneumatics in the Encyclopedia Britannica.

weight and preffurc of the atmofpherical air have been explained in the precedingnbsp;chapters. It is now necelTary to examine the par-^'culars which relate to the motion of the famenbsp;and thofe particulars may be arranged undernbsp;*�'^0 principal denominations, viz. of wind, and ofnbsp;S�und.

Wind, or a current of air, is the progreffive mo-of air from one place to another. Sound, or ��he fenfation which we perceive through our ears isnbsp;produced by a vibratory motion of the foundingnbsp;^^dy, and is conveyed to the ear by a vibratorynbsp;l^ocion of the particles of air, or other body whichnbsp;��^tervenes between the founding body and the ear.

The particles of air in that cafe move a fhort way backwards or forwards from their rcfpedtive ftua-tions, and at the end of every other vibration, arenbsp;to be found precifely at their original fituations.�nbsp;What relates to found will be treated of in the nex*^nbsp;chapters; hut the progreffive movements of airnbsp;will be examined in the prefent.

The theory of thofe iTtovemcnts may be comprized into four principal propofitions j the firfl of which is to determine the velocity with wdiich airnbsp;of the ufual denfity on the furface of the earth, or ofnbsp;any denfity, will rtifh into a vacuum through a givennbsp;aperture; the fecond is to determine the velocitynbsp;With which air of a certain denfity will rufh into anbsp;velTel containing air of lefs denfity; the third is tonbsp;determine the velocities of the natural currents ofnbsp;air, or of the winds; and the fourth is to determine the refiftance which the air in motion offers tonbsp;folids of a given fize, or the refiftance which the latternbsp;meet with in moving through the air.

Both the theoretical propofitions, and the caufes which render the refults of the experiments dif'nbsp;ferent from thofe of the theoretical propofitions'in

the movements of water, and other non-elafti*^ fluids, bear a great degree of analogy to what maynbsp;be faid with refpeft to the movements of air andnbsp;other permanently elaftic fluids, excepting whennbsp;clafticity is concerned ; hence, having been rather

h If we confider air in its natural ftate, viz. P'effed by the weight of the atmofphere, we maynbsp;Calculate the velocity with which it will rulli into anbsp;'^acuum through any aperture, by confidering it asnbsp;^ non-elaftic fluid; but then we muft take for itsnbsp;^I'^hude, the altitude of an homogeneous at-�^ofphere, viz. fuch an altitude as is equivalentnbsp;^0 the natural decreafing altitude of the whole at-^ofphere (fee the note in page 246). Thus, whennbsp;'^he fperific g'-avity of air is 0,0013, the altitude ofnbsp;homogeneous atmofphere may be reckoned equalnbsp;2^038 feet. Then fince the velocities, whichnbsp;acquired by falling bodies, are as the fquarcnbsp;*'oots of the fpaces; therefore (agreeably to whatnbsp;been faid in page 160, and following, of thisnbsp;^^cond Part) the velocity with which air of thenbsp;^naal denfity will ruth into a vacuum near the fur-of the earth, is that which a body would ac-'luire by falling from the height of 13029 feet,nbsp;is the half of 2605 8 ; namely, the velocitynbsp;1292 feet per fecond. But this velocity is alterednbsp;heat and cold, fince the altitude of an homoge-atmofphere is thereby increafed or diminifh-It is to be obferved, however, that the varia-which arifes not from a change of tempera-but that which is indicated by the barometernbsp;^lone, will not alter the height of an homogeneousnbsp;atmofphere, and of courfc neither will it alter the

above-mentioned velociry; becaufe that variation is attended with a proportionate denfity of the at-niofphere.

II. The velocity with which air of the ufual den-fity will rufh into a veffel containing air lefs denfo may alfo be cafily calculated; for in this cafe, wenbsp;muft confider the air as prefled not by the wholenbsp;atmcfphere, but by the difference between thenbsp;whole atmofphere, and that part of it which produces the denfity of the air in the veffel. Or, innbsp;other words, the altitude of an homogeneous at-mofphere muft be reduced in the proportion of thenbsp;ufual denfty of the air at the furface of the earth,nbsp;to the denfity of the air in the veffel; the reft ofnbsp;the calculation proceeds exadly as in the precedingnbsp;cafe. The velocity, however, which is obtainednbsp;by this means, will be gradually checked and dimi-nifhed, becaufe by the entrance of the external airgt;nbsp;the quantity, and, of courfe, the denfity of the air innbsp;the veffel, is gradually increafed.

The like calculations may be eafily and evidently applied to the entrance of air, which is preffed bynbsp;any given preffure greater or lefs than that of thenbsp;whole atmofphere; as alfo to the efflux through ^nbsp;given aperture, of air, which has been confined in anbsp;given veffel by a given weight. But in pradlicCjnbsp;both the influx and the efflux of air into, or out ofnbsp;a given veflel through a given aperture, turn outnbsp;by much different from the determinations of thenbsp;theoretical calculations; which is owing to the

fame concurring and fluftuating caufes, as have in ^hap. VII. of this Part, been fliown to afFeft thenbsp;��'ovements of non-elaftic fluids, viz. the attradlionnbsp;aggregation, the attraction of cohefion, the formation of the vsna contraSta, in certain cafes, thenbsp;quot;'ant, or the affiftance, of an ajutage or fhort pipenbsp;m the aperture, the different directions which different parts or filaments of fluid acquire in tHeirnbsp;motion, the friCtion, amp;c. And in elaflic fluids fuchnbsp;quot;^�I�iations mud evidently be greater than in water,nbsp;*nd other non-elaftic fluids.

The fame obfervations may be made with refpeCl m the paffage of air, and other elaftic fluids,nbsp;through long pipes, channels, amp;c. which retard itsnbsp;'velocity in a very great degree, and the irregularitynbsp;ts fo great, that no known theory is fuflicient to de-t^rrnine the effeCt in moll cafes.

The quantity of air difcharged into the atmod' phere, through a given aperture in a veffel, whereinnbsp;��he air is prefled by a given weight, as appears fromnbsp;Young�s Experiments, feems to be nearly asnbsp;fquare-root of the pr�lTure; and that the ratio ofnbsp;��he expenditures by different apertures, with thenbsp;ftme preflure, lay between the ratio of their diame-and that of their areas *.

III. The velocity and the force of the wind, or a natural current of air, deferve to be examined

with all poffible attention ; it being owing to that current that we are enabled to navigate the ocean�nbsp;to make ufe of windmills, amp;c. But the obftruc-tion which the motion of air receives from the various caufes that have been mentioned in /peakingnbsp;of non-elaftic as well as of elaflic fluids, in the iV^thnbsp;and in the prefent Chapter of this Second Part ofnbsp;thele Elements, invalidates the application of everynbsp;theory, and renders the refults of a�lual experiments the only guides which can dired us in thenbsp;ufe and application of the winds.

The velocity of air in natural currents of certain denominations, has been attempted to be mea-fbred by various means. It has been attempted by meafuring the velocities of the lhadows of cloudsnbsp;upon the furface of the earth ; but this method isnbsp;very fallacious: firft, becaufe it is not known whether the clouds do or do not move exadly with thenbsp;air in which they float; and fecondly, becaufe thenbsp;velocity of the air at the region where the cloudsnbsp;are, is by no means the fame as that of the airnbsp;which is nearer to the furface of the earth, andnbsp;fometimes is quite contrary to it, which is indicatednbsp;by the motion of the clouds themf�lves.

The beft method of meafuring the velocity of the wind is by obferving rhe velocity of the fmoke of anbsp;low chimney, or to eftimate it by the effed it produces upon certain bodies.

IV. Whatever has been faid in Chap. IV. of the prelent Second Part of thefe Elements, is fo evidently

applicable to the impulfe which air in motion gives to folids, or to the obftru�dion which folidsnbsp;�quot;^ceive in their movements through air; that itnbsp;quot;'ould be needlefs in this place to dwell any longernbsp;the theoretical part of the fubjelt;5t.

The beft method of eftimating the force as well the velocity of the wind, is from the effeftsnbsp;'^hich it produces upon certain bodies. The in-^��urnents which have been found to anfwer thefenbsp;PUrpofes in the beft manner, will be defcribednbsp;hereafter; but for the prefent we fliall obferve, thatnbsp;^''orn the concurrence of the experiments whichnbsp;^ave been made with various inftruments and dlf-^^tent methods, the following eftimate has btcinbsp;^^duced; namely, that in currents of air of Jienbsp;'^^nominations which are expreflfed in the fourthnbsp;'Column of the following table, the air moves at thenbsp;fate of fo many feet per fecond as are exprefled innbsp;fhe fecond column, or of fo many miles per hournbsp;are exprefled in the firft column. The thirdnbsp;'�'^himn expreffes in avoirdupoife pounds, the forcenbsp;die wind on an area of one foot fquare, which isnbsp;Pi'efented in a diredtion perpendicular to it.

This table was firft publilhed in the 51ft volume the Philofophical Tranfaftions, by Mr. J. Smea-the celebrated engineer, who, in his valuablenbsp;. on the natural pow'ers of water and wind,nbsp;''^^foduces it with the annexed paragraph.

The following table, which was communicated fo me by my friend Mr. Roufe, and which ap-

pears to have been conftrufted with great care� � from'a confiderable number of fadts and expert'nbsp;ments, and which having relation to the llibjcdtnbsp;*' of'this article, I here infert it as he fent itnbsp;� me j but at the fame time muft obferve, tha^^nbsp;the evidence for thofe numbers, where the velo'nbsp;� city of the wind exceeds 50 miles an hour,

� not feem of equal authority with thofe of 5� miles an hour and under. It is alfo to be ob-� ferved, that the numbers in the third column arenbsp;� calculated according to the fquare of the velocitynbsp;of the wind, which- in moderate velocities�nbsp;� from what has been before obferved, will holiJnbsp;� very nearly¹.�

The propofition upon which the third column has beo^ calculated, feems to be, that the impulfe of a current ofnbsp;ftriking perpendicularly upon a given furface, with a certah¹nbsp;velocity, is equal to the weight of a column of air which hasnbsp;that furface for its bafe, and for its height the fpace throughnbsp;which a body muft fall, in order to acquire that velocitynbsp;the air.

Veiocjty of the Wind.		Perpendi cular
		one foot
^iles	Feet	area, in pounds
one	in one	area, in pounds
hour.	fecond.	avoirdu- poife.
I	Ij47	0,005
2	2j93	0,020
3	454^	0,044
4	Sgt;87	0,079
S	7.33	0, I 23
10	14,67	0,492
	22,00	1,107
20	^^9�34	1,968
25	36,67	3.075
3tgt;	44,01	4.429
3S	5 ¹.34	6,027
40	58,68	7.873
4S	66,01	9.963
50	73.35	12,300
60	88,02	17.715
ifo	*17.36	31.490
too	146,7c	49,200

When the direction of the wind is not perpen-^�Cular, but oblique to the furface of the folid, then force of the former upon the latter will not benbsp;�reat as when the impulfe is diredt, and that for

7 uncertain, that the eftimates given by different perfons very far from agreeing with each other. Mariottenbsp;ckoned it at 34 feet per fecond 5 Derham at 66 feet pernbsp;j and de la Condamine at 90 f feet per fecond.

reafoRS which are eafily derived from the theory of the reiblution and compofition of forces, and fromnbsp;the theory of diredl and oblique impulfes which havenbsp;been delivered in the Firft Part of thele Elements gt;.nbsp;alfo from what has been faid in the IVth Chapternbsp;of this Second Part. In Ihort, the general pro-pofition for compound impulfes is, that � I'htnbsp;effeSiivs impilfe is as the Jnrface, as the /quartnbsp;of the air's velocity, as the fquare of the fine of thtnbsp;angle of incidence, and as the fine of the obliqudynbsp;of the folid�s motion to the direblion of the impulfi)nbsp;jointly ; for the alteration of every one of thofenbsp;quantities will alter the effedl in the fame propof'nbsp;tion. But thofe general rules, as we have alreadynbsp;more than once obferved, are fubjed to great varia-tionsj fo that their refults feldom coincide withnbsp;thofe of adual experiments. In the motion ofnbsp;folids through air, a great retardation ariies (be-fides other caufes) from the condenfation of thonbsp;air before the folid, and from the rarefadion, and�nbsp;with fome velocities, the vacuum, which is formo^^nbsp;behind the folid ; hence nothing but adual experiments can poffibly illuftrate this fubjed*. Winds

? See Derham�s Paper on the Velocity of Souii^i' Philofophical Tranfadions Abridged, vol. IV. Robins Snbsp;Treatife on Gunnery. De Borda�s Experiments, in t'��nbsp;Memoirs of the Academy of Sciences for 1763. Smeaton snbsp;Paper in the Philofophical Tranfadion?, vol. 51 ft. But �nbsp;great many more experiments muft be inftitutcd by fcic�'nbsp;tific perfons before the fubjed can be fufficicnvlynbsp;cidated.

^re of great ufe to us; but in the application of the '^inds to navigation, to wind-mills, and to othernbsp;�Machines, fome other circumftances muft likewifenbsp;had m view; namely, the probable force, dura-and direftion, of the wind which is likely tonbsp;blow in any giv�n place. Thefe particulars muftnbsp;derived from the hiftory of countries, or frornnbsp;Meteorological journals, viz. from long and accuratenbsp;experience.

It appears that almoft in all expofed fituationSi ftich as the open fea, extenfive plains, tops of hills,nbsp;^e. the wind almoft always prevails j and few intreed are the days, or the hours, throughout thenbsp;^quot;ear, in which a real, or what is called a dead, calmnbsp;ts to be obferved.

Iti thofe places for more than three 'quarters of the year (I do not mean without interruption) thenbsp;�Orce of the wind is fufficient to work a nicelynbsp;Made wind-mill, or at leaft to impel the fails of anbsp;Ihip.

The wind machines of larger fize and greater Ptgt;\ver, which are applied to pumps for extradtingnbsp;^'''ater from deep pits, which are applied to thenbsp;�''inding of hard materials, amp;c. require a highernbsp;to put them in motion. Dr. Stedman wasnbsp;Mformed by a gentleman of experience, who hadnbsp;^Mfted a wind-machine to drain his coal-pit, thatnbsp;never could depend upon more than 53 or 54nbsp;of wind fufficient for moving that machine in

fdf, from a careful infpeclion of a column for th^ wind in a meteorological journal, endeavourednbsp;form a proportion between the duration of wind ofnbsp;a certain degree, and that of another degree.

� From this computation,� he Jays, �we hav^ � 2,592 days in a week, or 19,307 weeks in ^nbsp;� year, in which wind machines of the heaviernbsp;� kind, and of confiderable friflion, may be fup'nbsp;� pofed to be kept in motion j which, to the timesnbsp;� wherein they cannot go, is as 10 to 17.�

But the journal upon which he grounded his pro-' portion, was the journal of a fingle place ; the pe*nbsp;riod of years, as he juftly obfcrves, was too fliortjnbsp;the proportion for the different months of the famenbsp;name in different years, as alfo the pi�oportion fornbsp;the different years, as appears from the tables be hasnbsp;given, are too fiudliiating and irregular ; to whiohnbsp;we may add, that the meteorological journals it*nbsp;general, wliereia one or two obfervations are {fatednbsp;for every 24 hours, do not afford materials fufficientnbsp;for an accurate eftimate*.

The direftion of the wind, which is various moft countries, and varies in the fame country, acquires its diitcrent denominations from the foornbsp;principal quarters, or cardinal points of the world-Thus it is czWnA North wind, when it blow's fromnbsp;north towards the fouth ; it is called Eaft �

See Dr. Stcdm.�.n�s Paper in the 6;th volume of the Philofophicai Tranfadions,

when

it blows from the eafi: towards the weft; it is South wind, when it blows from the fouth to-'''S'ds the north, and Wefi windi when it blows fromnbsp;*^iie Weft towards the eaft.

The winds which deviate a little from the cardi-points, are commonly called northerly, eajlerly, S�^utherly^ and weJleHy, winds. But for the fake ofnbsp;cgt;feater diftinftion, the fpace or arch which lies be-^-'''een any two contiguous cardinal points, is fup-P^ftd, by the mariners, to be divided into eight equalnbsp;P^tts, or points, and each point into four equal parts,nbsp;^^lled quarter-points. So that the horizon is Rip-P^fed to be divided into 32 principal points, whichnbsp;called rhumbs, or winds, to each of which anbsp;Particular name is affigned; and thofe names arenbsp;'^^rived from the names of the adjacent, cardinalnbsp;Points, as is Ihewn by the following table, wherein

the north, eaft ward, amp;c. but thofe names generally exprefled fimply by their initials.

Eaft by South Eaft South Eaftnbsp;South Eaft by Eaftnbsp;South Eaftnbsp;South Eaft by Southnbsp;South South Eaftnbsp;South by Eaft

Weft by North Weft North Weftnbsp;North Weft by We^^nbsp;North Weftnbsp;North Weft by Northnbsp;North North Weftnbsp;North by Weft.

Aimoft in every country, the wind is more ot lefs predominant in a particular diredtion j but be^nbsp;fore we begin to enumerate the obfervations whichnbsp;Irave been made relatively to thofe diredlibns,nbsp;will be proper to mention the caufes, which, asnbsp;as we know, produce the wind, in order that thenbsp;reader may be enabled in fome meafure to comptC'nbsp;hend the reafons of the particular diredlions, whichnbsp;will be mentioned in'the fequel.

Heat, which rarefies, and cold which condenft^� the air, are by far the principal, and more generalnbsp;caufes which are prodinftive of a current of air;

� the greateft general heat or cold is derived from th^ prefence or abfence of the fun.

The next caufe has been juftly attributed to th'^ attraftion of the fun and moon, whofe influencenbsp;fuppofed, with great probability, to �ccafion a tid^�nbsp;or flux and reflux, of the atmofpherical fluid, fimh^'quot;nbsp;to that of the fea, but greater, becaufe thenbsp;lies nearer to thofe celeftial bodies, and becaonbsp;air is incomparably more expanfible than water.

It has been calculated by D�Alembert from the S^rieral theory of gravitation, that the influence ofnbsp;fun and moon in their daily motions, is fuffl-^'^tit to produce a continual eaft wind about thenbsp;^fluator. So that upon the whole we may reckonnbsp;*^tee principal daily tides, viz. two arifing from thenbsp;^�^'^racbons of the fun and moon, and the third fromnbsp;heat of the fun alone: all w'hich fometimesnbsp;Combine together, and form a prodigious tide.

I'l corroboration of the opinion of the influence the fun, and principally of the moon, in the pro-^tiftion of wind, we muft likewife mention the ob-^^tvations of Bacon, GalTendi, Dampier, Halley,nbsp;namely, that the periods of the year moftnbsp;likely to have high winds, are the two equinoxesnbsp;that fcorms are more frequent at the time of newnbsp;^tgt;d full moon, efpecially thofe new and fullnbsp;*^0008 which happen about the equinoxes; that,nbsp;^t periods otherwife calm, a fmall breeze takesnbsp;at the time of high water; and that a fmallnbsp;�Movement in the atmofphere is generally perceivednbsp;^ fhort time after the noon and th� midnight ofnbsp;day.

^ Some action in the produdion of wind may alfo ^ derived from volcanoes, fermentations, evapora^nbsp;and efpecially from the condenfation of va-P'^eirs :_for vve find that, in rainy v/cather, a confi-^^�quot;able wind frequently precedes the approach ofnbsp;Angle cloud, and that the wind fubfides asnbsp;as die cloud has pafled over our zenith.nbsp;Wherever any of the above-mentioned caufes isnbsp;V 3nbsp;nbsp;nbsp;nbsp;conftantly

conftantly more predominant, as the heat of fun within the tropics, there a certain direftionnbsp;the wind is more conftant; and where difFeref¹-caiifes interfere at different and irregular period?�nbsp;as in thofe places which are confiderably difta�^²'nbsp;from the torrid zone, there the winds are mot^nbsp;changeable and uncertain.

In flrort, whatever difturbs the equilibrium of atmofphere, viz. the equal denfity or quantity of aifnbsp;at equal diftances from the furface of the earth�nbsp;whatever accumulates the air in one place, anonbsp;diminifhes it in other places, muft occafion ^nbsp;wind both in difturbing and in reftoring that eqoiquot;nbsp;librium¹.

Thofe general obfervatlons feem to agree toler^' bly well with the following fafts, which have beeflnbsp;.afcertained by the concurring teftimony of fkilf^^nbsp;feamen, and other obfervers.

I. Between the limits of 30�. north and fouth latitude, there is a conftant, or almoft coO'nbsp;ftant, eafterly wind, blowing, but not violently,nbsp;all times of the year, in the Atlantic and Pacih^'nbsp;oceans. This is called the trade wind,

Mr, Briflbn is of opinion that eleflricity is the pr³' cipal and more general caufe which produces wind? �

famerois mieux� he fays, � donner pour caufe prunin'''^ � et generale des vents, P�leStrich�, qu�on fait qui regne connbsp;� iimellement dans Patmofphere, et a la furface de

Towards the middle of the above-mentioned of about 60�. viz. about the equator, the windnbsp;blows either exaftly from the eaft, or very littlenbsp;from that point 5 but on the borders of thenbsp;above-mentioned fpace, the wind deviates fromnbsp;^bat point, viz. near the northern limit the trade-blows from between the north and the eaft,nbsp;and near the fouthern limit, it blows from betweennbsp;^be fouth and the eaft.

The trade-wind feems to depend principally '^pon the rarefaftion of the air, which is occafionednbsp;by the heat of the fun progrefiively from the eaftnbsp;towards the weft. The air which is rarefied, and, ofnbsp;courfcj elevated by the heat of the fun immediatelynbsp;it, is condenfed and defeends, as foon as thenbsp;is gone over another place to the weft of thenbsp;bottner; then the air of the latter place is rarefied,nbsp;^*id the condenfed air of the former rulhes towardsnbsp;�b amp;c. From the northern and fouthern parts ofnbsp;^he world, the air likewife runs to the place which isnbsp;^�^mediately under the fun j but thofe direftions,nbsp;^'^mbining with the eafterly wind, which blowsnbsp;bearer to the equator, form the above-mentionednbsp;eafterly and fouth-eafterly winds on the bor-of the trade-wind.

In places that are farther from the equator, rarefa�lion which atifes from the heat of thenbsp;and from the attradlion of the fun and moon,nbsp;lefs aftivei and is befides influenced by a varietynbsp;bf local and accidental circumftances, fuch as cx-

tenfive continents, mountains, rains, iflands, which difturb, interrupt, or totally change the di-re�tion of the wind. Hence, in thofe latitudes northnbsp;and fouth, which are beyond the limits of thenbsp;trade-wind, or near the coafts, the winds, are verynbsp;uncertain j nor has any good theory been as yetnbsp;formed refpedting them : I fnall, however, proceednbsp;to enumerate the fadls which have been afcertain-ed, and to mention the moft plaufible elucidation^nbsp;of the caufes upon which they mav depend*.

3. In fome parts of the Indian ocean there art-winds which blow one way during one half of the year, and then blow the contrary way during thenbsp;other half of the year. Thofe winds are called

It is faid, that as the air which is cool and denfegt; will force the warm rarefied air in a continual flreatnnbsp;upwards, there it mufc fpread itfdf to preferve thenbsp;equilibrium. Therefore the upper courfe or current of air rauft be contrary to the under current*nbsp;for the upper air mull move from thofe part*nbsp;where the greateft heat is; and fo, by a kind 0^nbsp;circulation, the N.E. trade-wind below will be at'nbsp;tended with a S.W. above �, and a S.E. beloV'^�nbsp;vrith a N.W. above.

* Thofe particulars have been colledled principally Mr. Robertfon. See his Elements of Navigation, B.nbsp;Sect. VI.

4* In the Atlantic ocean, near the coafts of Africa, at about 300 miles from the Paore, betweennbsp;north latitudes of 10�. and 28�. feamen con- 'nbsp;ftantly meet with a frefii gale of N.E. wind.

5- Acrofs the Atlantic ocean, on the American of the Caribbee hlands, it has been obferved,nbsp;^^^t the above-mentioned N. E. wind becomesnbsp;^afterly, or fekiom blows more than a point fromnbsp;eaft on either fide of it,

6. Thefe trade winds on the American fide arc extended as far as the 3a^ degree of N.nbsp;^^titude, which is about 4� farther than their ex-*^nfion on the African fide. Alfo, on the fouth-fidcnbsp;the equator the trade winds extend 3�, or 4��nbsp;farther towards the coaft of Brafil on the Americannbsp;fide, than they do near the Cape of Good Hope, ornbsp;Arrican fide.

7- Between the latitudes of 4% N. and 4�. S. wind always blows between the fouth and eaPr,nbsp;the African fide the winds are neareft to thenbsp;fi^uth; and on the American fide, neareft to thenbsp;^aft. In thefe feas Dr. Halley obfervcd, that whennbsp;wind was' eaftward, the weather was gloomy,nbsp;^arlv, and rainy, with hard gales of wind j but whennbsp;wind turned to the fouchward, the weathernbsp;generally became ferene, with gentle breezes ap-Ptoachinlt;gt;- to a calm. Thefe winds are fomewhat

changed by the feafons of the year; for when thi; fi^n is far northward, the Brafil S�.E. wind get^^nbsp;^0 the fouth, and the N.E. wind to the E. ; and

�when the fun is far .fouth, the S. E. �wind gets to the E. and the N.E. wind on this fide of the equatornbsp;goes more towards the north.

8. Along the coaft of Guinea, from Sierra Leoir to the ifiand of St. Thomas (under the equator)nbsp;�which is above 1500 miles, the foutheriy and fouth-weft winds blow perpetually. It is fuppofed thatnbsp;theS.E. trade-wind, having pafled the equator, andnbsp;approaching the guinea coaft within 240 or 30Onbsp;miles, inclines towards the (hore, and becomes S. gt;nbsp;then S.E., and gradually, as it comes near the land�nbsp;it inclines to fouch, S.S.W. and clofe to the land ftnbsp;is S. W. and fometimes W. S. W.�This traeft ftnbsp;fubjedt to frequent calms, and to hidden gufts ofnbsp;wind called tc/nadoes, which blow from all points ofnbsp;the horizon.

The wefterly wind on the coaft of Guinea is probably owing to the nature and fituation of the landj which being greatly heated by the fun, rarefies th^nbsp;air exceedingly; Iience the cooler and heavier airnbsp;from over the fea will keep rufhing in to reftore thonbsp;equilibrium.

9,. Between the ;latitudes of 4� and 10� north� and between the longitudes of Cape Verd, and thenbsp;eaftermoft of the Cape Verd Ifles, there is a tradt ofnbsp;lea, which feems to be condemned to perpetualnbsp;calms, attended with terrible thunder and lightning^�nbsp;and luch frequent rains, that this part of tne feanbsp;called the Rains. It is faid that ihips have foua^'nbsp;Inbsp;nbsp;nbsp;nbsp;,nbsp;nbsp;nbsp;nbsp;tiita^�

The caufe of this feenis to be, that the wefterly quot;'�nds fetting in on this coaft, and meeting thenbsp;general eafterly wind in this trafl:, balance eachnbsp;�ther, and caufe the calms; and the vapour carriednbsp;thither by the hotteft wind, meeting the cooleft,

to. Between the fouthern latitudes of io�. and 30�. in the Indian ocean, the general trade-windnbsp;^boiit the S.E. by S. is found to blow all the yearnbsp;In the fame manner as in the like latitude innbsp;Ethiopic ocean: and during the fix monthsnbsp;from May to December, thefe winds reach tonbsp;'''�thin two degrees of the equator ; but during thenbsp;�'^her fix months, from November to June, a N.W.nbsp;''^gt;nd blows in the trafl: lying between the latitudesnbsp;�f3�. and 10�. fouth, in the meridian of the northnbsp;^tid of Madagafcar; and between the latitudes ofnbsp;^ � and 12�. fouth, near the longitude of Sumatranbsp;^ad Java.

ti. In the tradb between Sumatra and the �African coaft, and from 3� of fouth latitude quitenbsp;*^orthward to the Afiaftic coafts, including thenbsp;�Arabian fea and the gulf of Bengal, the Monfoonsnbsp;i^low from September to April on the N. E. andnbsp;from March to Odlober, on the S.W.^ In thenbsp;former half-year the wind is more fteady and gentle,nbsp;�tid the weather clearer than in the latter half-year.

Alfo the wind is ftronger and fteadier in the Arabia� fea than in the gulf of Bengal.

12. nbsp;nbsp;nbsp;Between the ifland of Madagafcar and thenbsp;coaft of Africa, and thence northward as frr as thenbsp;equator, there is a traft, in which, from April tlt;gt;nbsp;OS ober, there is a conftant frefh S.S.\�. win^hnbsp;which to the northward changes into the W.S.VV.nbsp;wind, blowing at the fame time in the Arabiai^nbsp;lea.

13. nbsp;nbsp;nbsp;To the eaftv/ard of .Sumatra and Malaccanbsp;on the north fide of the equator, and along thenbsp;eoafts of Gambodia and China, quire through th^nbsp;Philippines as far as Japan, the Monfoons blo'^tnbsp;northerly and foutherly; the northern fetting i�^nbsp;about Oftober or November, and the fouthernnbsp;about May. Th�fe winds are not quite fo certaitanbsp;as thofe in the Arabian fea.

14. nbsp;nbsp;nbsp;Between Sumatra and Java to the weft, an^lnbsp;New Guinea to the eaft, the fame northerly andnbsp;foutherly winds are obferved ; but the firft half-year Monfoon inclines to the N.VV, and the latternbsp;to the S.E.�Thefe winds begin a month ornbsp;weeks after thofe in the Chinefe feas fet in, and arenbsp;quite as variable.

15. nbsp;nbsp;nbsp;Thefe contrary winds do not fhift from on�nbsp;point to its oppofitc all at once. In fume places thenbsp;time of the change is attended with calms, in otneinbsp;with variable winds. And it often happens on t^enbsp;fliores of Coromandel and China, towards the end

of the Monfoons, that there are moft violent ftorms� ,nbsp;nbsp;nbsp;nbsp;greatly

greatly relemblins the htirricanes in the Weft Indies, '''hen the wind is fo vaftiy ftrong, that hardly anynbsp;*^hing can 'refift its force.

'6, The irregularities of the wind in countries ^hich are farther from the equator than tholenbsp;^hich have been mentioned above, or nearer to thenbsp;poles of the earth, are fo great that no particularnbsp;P^tlod has as yet been difeovered, excepting that innbsp;Particular places certain v.finds are more lik�ly tonbsp;blow than others. Thus at Liverpool the windsnbsp;^re Paid to be wefterly for near two thirds of thenbsp;in the fouthern part of Italy a S. E. windnbsp;(called the Jchirccco') blows more frequently thannbsp;^oy other wind, amp;c.

17. The temperature of a country with refpeft � ^0 heat or cold, is increafed or diminiflred bynbsp;quot; mds, according as they come from a hotter ornbsp;'bolder part of the world. The north and north-cafterly winds, in this country and all the wefternnbsp;P^rts of Europe, are reckoned cold and dryingnbsp;quot;'tnds. They are cold becaufe they come from' thenbsp;b'ozen region of the north pole, or over a greatnbsp;of cold land. Their drying quality is derivednbsp;frorn their coming principally over land, and fromnbsp;3 Well known property of the air, namely,, thatnbsp;quot;'arm air can diflblve, and keep diflblved, a greatei;nbsp;fttiantity of water- than colder air : hence the airnbsp;'vhich comes from colder regions being heated overnbsp;quot;'armer countries, becomes a better folvent ofnbsp;*^oifture, and dries up with greater energy the

302 nbsp;nbsp;nbsp;of- Air in Motion,

moift bodies it comes in conta�l with ; aiid, on th^ other hand, warm air coming into a colder regio^^nbsp;depofits a quantity of the water it kept in Iblution�nbsp;and occafions mifts, fogs, clouds, rains, amp;c.nbsp;nbsp;nbsp;nbsp;�

� fhort,� fajs Col. Roy, � the winds feem to be � drier, denfer, and colder, in proportion to thenbsp;� extent of land they pafs over from the poles to-� wards the equator; but they appear to be morenbsp;� moift, warm, and light, in proportion to the eX-tent of ocean they pafs over from the equatornbsp;� towards the poles. Hence the humidity, warmth/nbsp;� and lightnefs, of the Atlantic winds to the inha-*- bitants of Europe. On the eaft coafts of Northnbsp;� America the feverity of the N. W. wind is uniquot;nbsp;� verfally remarked 5 and there can fcarcely be anbsp;doubt, that the inhabitants of California, and othernbsp;� parts on the weft fide of that great continent)nbsp;will, like thofe on the weft of Europe, feel thenbsp;� ftrong effefts of a N. E. wind.�

18. In warm countries fometimes the winds� which blow over a great tralt;fl of highly heatednbsp;land, become fo very drying, fcorching and fuffoquot;nbsp;eating, as to produce dreadful elfe�ls. Thefenbsp;winds under the name of Solanos, are often felt ionbsp;the deferts of Arabia, in the neighbourhood of thenbsp;Perfian gulph, in the interior of Africa, and in fonienbsp;other places*. There are likewife in India, part

China, part of Africa, and elfewhere, other ''^inds, which depolit fo much warm moifture as tonbsp;Soften, and adlually to diflblve glue, falts, and almofl:nbsp;^very article which is foluble in water.

' 9' It is impoffible to give any adequate account ^f irregular winds, efpecially of thofe fudden andnbsp;'violent gufts as come on at very irregular periods,nbsp;^nd generally continue for a fliort time. Theynbsp;^^rnetimes fpread over an extenfive traft of country,nbsp;at other times are confined within a remarkablynbsp;�harrow fpace. Their caufes are by no meansnbsp;*'^ghtly underftcod, though they have been vaguelynbsp;^^fributed to peculiar rarefactions, to the combinednbsp;^�^'^taftions of the fun and moon, to earthquakes, tonbsp;^^^ftricity, amp;c. They are called in general hurri-or they are the principal phenomenon of anbsp;^�Jiricane, that is, of a violent ftorm.

Ahnoft every one of thofe violent winds is at-^^nded with particular phenomena, fuch as droughts, heavy rains, or hail, or fnow, or thunder andnbsp;%htning, or feveral of thofe phenomena at once.nbsp;They frequently fhift fuddenly from one quarternbsp;the horizon to another, and then come again tonbsp;*-he foriner point. In this cafe they are callednbsp;^�^nadoes.

' Several years ago fome general charafters or Ptognoftics of hurricanes were collefled by Capt.nbsp;Tangford, which feem not to have been materiallynbsp;t^ontradifted by fubfequent obfervations. See hisnbsp;Taper in the Philofophical Tranfadions Abridged,

� All hurricanes come either on the. day of � full, change, or quarter of the moon.�

� If it will come on the full-moon, you being *' the change, then obferve thofe figns,�

� That day you will fee the fkies very turbU' ** lent, the fun more red than at other times, ^nbsp;� o-reat calm, and the hills clear of clouds,

� It is to be obferved, that all hurricanes beg'-quot;' ** from the north to the weftward, and on tho^quot;nbsp;� points that the eafterly wind doth moft violentlynbsp;blow, doth the hurricane blow moft fitrccfnbsp;� againft it; for from the N. N.E. to the E.S-�l*nbsp;quot; the eafterly wind bloweth freftieft; fo doth th*^nbsp;� W.N.W. to theS.S.W. in the hurricane blo'^nbsp;� moft violent; and, when it comes back to th'^nbsp;S.E. which is'the common courfe of the trade'nbsp;wind, then it ceafeth of its violence, andnbsp;breaks up.�

f� In a tornado, the winds come on ftvcr^^ � points. But before it comes it calms the coU'nbsp;ttant eafterly winds; and when they are paft,

� eafterly wind gathers force again, and the weath^�quot; � clears up fair.�

Thofe obfervations were intended for pl^^^* within, or not far from the torrid zone, andnbsp;cipally for the Weft-India iflands, which arenbsp;q^uently vifited by hurricanes.

go. Whef�

�0. When the giifts of wind come from different quarters at the fame timcj and meet in a certain P^ace, there the air acquires a circular, or rotatory,nbsp;fcrcw-like motion, either afcending or defcerid-*ng, as it were, round an axis, and this axis fome-times is ftationary, and at other times moves onnbsp;a particular diredion. This phenomenon, whichnbsp;called a whirlwind, gives a whirling motion tonbsp;^nfl, fand, water, part of a cloud, and fometiraesnbsp;^'^en to bodies of great weight and bulk �, carryingnbsp;either upwards or downwards, and laftly fcat-them about in different diredions.

The water Jpout has been attributed principally, not entirely, to the meeting of different winds.nbsp;In that cafe the air io its rotation acquires a centrical motion (fee p. 138 of part L); whence it en-�^eavours to recede from the axis of the whirl, innbsp;^nnfequence of which a vacuum, or, at leaft, a considerable rarefadion of air, takes place about thenbsp;and, when the whirl takes place at fea, ornbsp;^Pon water, the water rifes into that rarefied place;nbsp;Sdr the fame reafon which caufes it to afeend intonbsp;exhaufled tube (fee page 205 of this part), andnbsp;forms the water-fpout or pillar of water in the air :nbsp;y^t the various appearances of water fpouts do notnbsp;Poem to be quite reconcilable to the above men-^oned theory.�Some ingenious perfons have con-Pidered the water fpout as an eledrical phenorne-*ion; having obferved, that thunder clouds andnbsp;II.nbsp;nbsp;nbsp;nbsp;Xnbsp;nbsp;nbsp;nbsp;lightnings

lightnings have been frequently feen about the places where water fpouts appear, and iikewife tha^tnbsp;by means of artificial eleftricity, a w�ater fpout maynbsp;in fome meafiire be imitated. But it muft be ob-ferved, that the lightning and other eleftrical phe- _nbsp;nomena appear to be rather the neceflary confe-quence than the caufe, of the water fpout j it beingnbsp;well known that eleiSricity is produced whenevernbsp;water is reduced into vapour, or vapour is con-denfed into water. We fhall, however, examinenbsp;-this particular in another part of thefe elements.

Two, or three, or more, water fpouts are frequently feen within the fpace of a few miles, and they are mofily feen at fea.

Their fize is various, not exceeding, however, a few feet in diameter; and the fame water fpoutnbsp;fome;times increafes -and decreafes alternately; i^^nbsp;alfo appears, difappears, and reappears, in the famenbsp;place. �

The water fpout fometimes proceeds a little way from a cloud, or a little way from the lea; andnbsp;often thofe two ftiort and oppofite {pouts are notnbsp;only direfted towards each other, but they are extended and meet each other.

Wh -n it proceeds from the fea, the water abou*^-the place appears to be much agitated, and rifes a *nbsp;nbsp;nbsp;nbsp;{hoif

or of the UTind� nbsp;nbsp;nbsp;J�7

ftiort Way in the form of a jet or fpray, or fteamj in the middle of which a thick, well defined, andnbsp;generally opaque, body of water rifes, and proceedsnbsp;a confiderable height into the atmofphere, wherenbsp;IS diffipated into a vapour, �r it feeiiis to form a

'^loud.

^hen it proceeds from a cloudj the clouds shout the fpot frequently appear much agitat.d,nbsp;an agitation of the water immediately undernbsp;*ne fpot is generally feen at the fame time.

The water fpout is frequently feen to have a fpl-^al or fcrew-like motion, and fometimes is attended quot;'ith confiderable noifci

Some of them ftand in a perpendicular dire(5tion, Others are inclined, and fome water fpouts form anbsp;'^Utve, or even an angle.

The water fpouts generally break about their '�diddle, and the falling waters occafion greatnbsp;'^st�iage, either to Ibips that have the misfortunenbsp;�f being under them, or to the adjoining landjnbsp;fuch fpouts are fometimes formed on a lake,nbsp;river, or on the fea clofe to the land.

Sometimes the water fpouts are feen Where *here is no appearance'of whirlwind, or where thenbsp;quot;^ind (at leaft to a fpeftator at fome diftance) appears to blow' regularly one way.

The oblique fpouts almoft always point from �^he windj for inftance, when the wind'is N.E.nbsp;fpout will point to the S. W. fig. 20. ofnbsp;X 2nbsp;nbsp;nbsp;nbsp;Plate

Plate XIII. reprefents a water Ipout of the tnoft complete form*.

* Several particular accounts of water fpouts may be feel' in various volumes of the Philolbphical Tranfa�lions, efp^'nbsp;daily in the 4th volume of Jones�s Abridgment. Alfo i''nbsp;Franklin�s Mlfcellaneous Papers; in almofl all the accountsnbsp;of voyages; and in moft works upon Fleflricity.

[ 3�9 ]

|~^HE fenfation, which we perceive through the organ of hearing, is called found fuchnbsp;the found of a human voice, or of the voices ofnbsp;tether animals s as the found of a bell, or of the ftrokenbsp;a hammer, of the wind amongft trees, or ofnbsp;falling water, of an organ, amp;c.

The Icience which treats of Ibund in general is Called acoufiics (from the Greek verb for hearing)nbsp;phonics (from the Greek word which means anbsp;''^tgt;ice or found). And moft of the other termsnbsp;'^hich are ufed in treating of found, are derivednbsp;ftom tlie above-mentioned words; fuch as diacou-viz. of refrafted found; catacoujlics, viz. ofnbsp;found, or of the echo j otacoujlics, viz. ofnbsp;means of improving the fenfe of hearing, as bynbsp;^eans of the hearing trumpet, amp;c.

The body which produces the found is called the �^�^^rous body^ or founding body ; and whilft found-the fonorous body is evidently, and unquefti-�t*ablyj in a ftate of vibration.

�^ir is the only fubftance which, in cornmon, ms to exift between fonorous bodies and ournbsp;s ; and it has been obferved that, cateris paribuSynbsp;^ found of the very fame fonorous body, fuch

X3 nbsp;nbsp;nbsp;as

as a bell, a drum, amp;c. is louder or more power' fuJ, and may be heard farther, where the air i�nbsp;denfer, as in vallies, than where the air is le^�nbsp;denfe, as on the tops of high mountains. There-,nbsp;fore we are led to conclude that air is the vehiclenbsp;of found, viz, that the fonorous body communi'nbsp;cates a vibratory motion to the furrounding air�nbsp;which motion is gradually communicated from thenbsp;amp;ir next to the founding body, to that which, j�nbsp;more diftant from it, fomewhat like the wavesnbsp;upon the furface of water; until that vibratorfnbsp;motion is communicated to the fenfible part of thenbsp;car. But found is likewife conveyed b,y other bodies, both folid and fluid j as will be fhewn in tht^nbsp;fequel.

Infinite is the variety of founds j for a manifeft difference is to be perceived between the voices ofnbsp;any two human beings, or between the voices ofnbsp;other animals j and perfons who have accuftom^^nbsp;their ears to nice difcriminations, can diftinguifh ^nbsp;difference between the founds of very fimilar mO'nbsp;fical iriftruments, viz. fuch as are conflrudlet^�nbsp;tuned and ftruck, to all appearance, perfeiflffnbsp;alike.

The variety of founds arifes from three caufesprit^' eipally, viz. iff, from the greater or lefs frequeflofnbsp;of the vibrations of the fonorous bodies;nbsp;from the quantity, force, or momentum ofnbsp;vibrating particles which flrike the ear; and 2^^^*.nbsp;fpom the greater or lefs flmplicjty of die fouAlt;^�'

If you ftrike the firing of a mufical inftra-then ftop that firing in the middle, and ^tike one half of it only, or flop any part of it,nbsp;^tid flrike the other part, the flaort part will per-�nbsp;quicker vibrations, or what is called a highernbsp;than the whole firing; fo that the frequencynbsp;^f the vibrations produces high or low, acute ornbsp;S�^^ve, foarp or flat, founds; for the more frequentnbsp;the vibrations are, the higher, or more acute, ornbsp;^3tper, is the found faid to be, and vice verja.

The ftrength of found arifes from the Ipace through which the vibrating parts mow?, or fromnbsp;^he lengtir of the vibrations; it is alfo owing tonbsp;��^fledlion. The vibratory motion of a foundingnbsp;body is communicated fpherically all rpund thenbsp;^�dy, and of courfe, like other emanations from anbsp;Centre, is gradually diminifhed in intenfity, ac-�nbsp;Cording to the diftance (fee page 62. Part I.)*,

* The decay of found, or the diminution of its intenfity, been fuppofed by D. Bernoulli, De la Grange, and others,nbsp;he nearly in the diredl ratio of the diflances. But otliernbsp;��genlous peifons have fuppofed it to be nearly as the fquaresnbsp;the diftances. Their reafonings and calculations arenbsp;�ftablifhed on dilFerent principles; but all the particularsnbsp;quot;'hich fhould be taken notice of in this calculation, are bynbsp;�^0 means known; nor do we know of any pradlical methodnbsp;meafuring the intenfity of found.

X 4 nbsp;nbsp;nbsp;But

312 nbsp;nbsp;nbsp;Of Sound, or of Jcouftks,

But if that communication be prevented on certain fidesj and be permitted to take place on a particular fide only ; or if the vibrations which are com'nbsp;municated by the fame fonorous body to differentnbsp;bodies, be reflefted from the latter to a particularnbsp;place; the found will be heard in that placenbsp;much louder than otherwife. Hence arifes the effectnbsp;of the fpeaking trumpet, or fentorophonic tube ¹ gt;

In a fjjeaking trumpet the found in one diredlion is fup-pofed to be increafed, not fo much by its being preventelt;l to fpread all round, as by the refieftion from the fides of thenbsp;trumpet. But as the real action of the inftrument, or thenbsp;true motion bf the air through it, is not clearly underftood�nbsp;different perfons, according to their particular conception¹nbsp;of the cafe, have recommended peculiar fliapes for the con-ftrudtion of fuch trumpets; fome having recommended anbsp;conical fhape, others that which is formed by the rotation ofnbsp;certain curves round their axes ; others again have recommended an enlargement or two of the cavity in the lengthnbsp;of the trumpet, amp;c. That which has been more commonlynbsp;recommended as the bell: figure for fuch trumpets, is generated by the rotation of a parabola about a line parallel tonbsp;the axis.

A fpeaking trumpet of the fhape moftly ufed by navig¹' tors, js reprefented at fig. 15. Plate XIII. It is an hallovitnbsp;inftrument of copper or of tinned iron-plates. It is open a¹-both ends; and the narrow end, A, is fhaped fo as to gonbsp;round the fpeaker�s mouth, and to leave the lips at libertynbsp;within it. The edge of this nafrow epd is generally covered with leather or cloth, in order that it may more ef-

Of Soundy or of Acouftics. nbsp;nbsp;nbsp;313

^cnce the effeft of what are called whifpering ZAlerieSy or whifpering domes-, hence the found ofnbsp;a bell, or the report of a piftol in a room, producesnbsp;a much ftronger effefl: upon our ears than in thenbsp;^pcn air, amp;c.

3- A founding body vibrates in more directions ^han one j for inftance, if a body of irregular fhapenbsp;fize be ftruck, the thin parts of it will performnbsp;their vibrations in different times from thofe in

factually prevent the paflage of any air between the trumpet aad the face of the fpeaker. When a perfon applies hisnbsp;'^'outh to the narrow end, and, direfling the tube to a par-t'^^ular place, fpeaks in it; the words may be heard muchnbsp;farther and much louder in the direflion of the trumpet, bynbsp;Potions who are before it, than they would without thenbsp;^funipet. A perfon who is not in the direflion of thenbsp;^'quot;^nipet will hear the found of it both weaker and lefs dif-in proportion as he is more or lefs diftant from the di-*^^flion of the found ; which is the direflion ftraight beforenbsp;trumpet.

quot;^he words which are fpoken through a fpeaking trumpet *aay be heard much farther and louder, but not fo diftinflly,nbsp;as without the trumpet.

fpeaking trumpet has alfo been applied to the mouth of a gun or piftol, by which means the explofion has been ren-^^i^ed audible at a vaft diftance.�Such contrivai^ces may benbsp;'*fed as fignals in certain cafes.

^ee the defcription of fome particular fhapes of fpeaking b'Umpets in the Philofophical Tranfaflions, N� 141, ornbsp;. owthorp�s Abridgment, vol. I. page 505.

number and quality, ;tccording to the irregularities of the founding body. The more uniform the foundingnbsp;body is in fhape and quality^ the fimpler, mlt;gt;icnbsp;uniform, and more pleafing its found i ; but pt^'nbsp;bably there is no founding body in nature, whic^^nbsp;emits a fingle found. However, when the fount^rnbsp;jng body emits one predominant found, and thenbsp;concomitant founds are barely diftinguiflied, ther-that predomdpant found rtiay be confidered as ^nbsp;fimpk found.

From the combination of the above-mentionelt;^ three caufes, die various founds derive their denOquot;nbsp;piinations of high, low, weak, harjh, clear, rougb)nbsp;fmsoth, fleafant, unpleafant, confujed, amp;c.

The vibratory motion of a founding body continue for a longer or fhorter time after thenbsp;ftroke which caufes it to vibrate, according as tha*^nbsp;body is more or lefs elaftic j as it is thickernbsp;thinner, amp;c.

/ - nbsp;nbsp;nbsp;-When

Of Sotifid, or of Acoujlics. nbsp;nbsp;nbsp;3^5

When a ftring of unifor;n fhape and quality is ft^etched between, and is fixed to, tv/o fteady pins,

A, B, fig. i6, of ?Ute XIII. if it be drawn out ^Hts natural, or quiefcent, pofition AB, into thenbsp;fitiiation ACB, and if then it be let go, it will, innbsp;confequence of its elafticity, not only come back tonbsp;pofition AB ; but it v/ill go beyond it, to thenbsp;fituation ADB, which is nearly as far frorti AB, asnbsp;acb was on the other fide, and all this motionnbsp;�ne way is called one vibration; after this, thenbsp;ftring will go again nearly as far as C, making anbsp;ftcond vibration; then nearly as far as D, makingnbsp;^ third vibration, and fo on; diminifhing the extentnbsp;its vibrations gradually, until it fettles in its ori-B�nal pofition AB.

It feems natural that the air, which is contiguous the founding body, muft receive the like vibra-^tgt;ry motion, viz. it muft be caufed to perform vt-*^tations of equal duration with thofe of ,the found-body; and thofe vibrations, being fpread fuc-^eflively through the air, in their courle, reach ournbsp;and communicate to them the like vibrations,nbsp;'^bich excite in us the fenfation of a particular

Ibund.

quot;The air communicates the above-mentioned vibrations not only to the organs of hearing; but like-^ife to other folids in certain circumftances, viz. to ftuch folids as, if ftruck, would emit a found whichnbsp;either exadtly like, or bears fome analogy to, thatnbsp;of the original founding body. Thus let the ftring

516 nbsp;nbsp;nbsp;0/ Seund, or of Acouftics.

of a violin be tuned exaftly like a fimilar firing another violin ; fo that if either of them be flruck�nbsp;the fame found may be heard. Place a little bi^nbsp;of paper upon the firing of one of the violins, aboutnbsp;the middle of it, and place that inflrument upon ^nbsp;table 5 let the other violin be held near it, for iu'nbsp;fiance, within a foot or two, and in that fituationnbsp;flrike the above-mentioned firing of the latte?nbsp;violin. It will be found that whilfl this is founding, the correfponding firing of the other violinnbsp;upon the table, will evidently vibrate, as is man!'nbsp;fefted by the bit of paper upon it.

In fhort, it has been generally obfcrved, that i^ of two firings, or of two other fonorous bodies 1nbsp;which are capable of performing their vibrationsnbsp;in equal times, one only be caul�d to found, thenbsp;other firing or other fonorous body will alfo benbsp;found to vibrate, provided it be not too far froO?nbsp;the firfl mentioped fonorous body.

The fame thing, though not in an equal degree� will take place if one of the fonorous bodies be capable of performing two, or three, or four completenbsp;vibrations, whilft the other is capable of performiuSnbsp;one vibration only, and either of them is caufed tonbsp;found.

If one of the firings which is put in rnotion, pe?' forrns three vibrations, whilfl another firing, whichnbsp;is to be fet a vibrating by the found of the firfl, cannbsp;perform only one vibration with its whole length jnbsp;then this laft firing will divide itfelf into three vi'

Of Sound, or of Acoujlics, nbsp;nbsp;nbsp;317

brating parts, and there will be two points at reft, as be feen by placing bits of paper or other lightnbsp;tgt;odies upon different parts of the latter ftring.

This fhews that the vibrations of the founding body are communicated to the air, and by the airnbsp;the other fonorous body. It (hews likewife, thatnbsp;^be vibrations of the air muft be performed in thenbsp;farne time as thofe of the founding body¹.

The

A firing, or a body capable of being put in a fiate of ''�^ration, as a pendulum at reft, may be caufed to vibrate bynbsp;'be repeated application of the ieaft impulfe, provided thofenbsp;^ftipulfes be repeated at the expiration of fuch portions ofnbsp;brne as the pendulum, or other body, would perform everynbsp;'quot;'0 of its vibrations ; for inftance, if a pendulum, whennbsp;in motion, would perform each vibration in one fe-and of courfe it would come to the fame fide everynbsp;b^ber fecond ; then if, when fuch' a pendulum is at reft, younbsp;it an impulfe ever fo little (even a puff of air fromnbsp;mouth) at the end of every two feconds ; the pendu-vibrate. The reafon of which is,nbsp;'bat from the law of collifion, (fee page 42 of Plate i.)nbsp;l^^tidulutn would by itfelf (fee page �74 of P. 1.) performnbsp;^¹iother vibration ftiorter than the firft, then another ftiftnbsp;end of the proper time, the effclt;ft of that impulfe, con-*Pir,ng with the natural motion of the pendulum, will enable

jt8 nbsp;nbsp;nbsp;Of Sound-, or of Acoufiics.

The furface of water is agitated a little by found of a large bell, or the report of canon*nbsp;�Windows, wainfcots, amp;;c, are frequently caufd wnbsp;vibrate by the found of organs, and other larg^nbsp;inilruments*

The communication of the vibrations to the air is ufuaily explained in the following manner.�nbsp;the fonorous body be a firing fattened to, andnbsp;ftretched between, two fixed pins j (for whatevernbsp;is faid with refped; to the vibrations of the ftriHo*

it to perform a longer vibration than it could perform wid�' out it. By the fame way of reafoning it will appear tha^nbsp;the third impulfe will increafe the length of the vibration^nbsp;ttill more, and fo on.

If the impulfe be repeated at the end of every 4, or eveif 6, amp;c. vibrations; the vibration of the pendulum willnbsp;be increafed, and will at laft become vifible, but not fonbsp;fedtually as by the repetition of the impulfe at every oth^rnbsp;vibration ; which is fo evident as not to require any fartb^^nbsp;illuftration.

If the impulfes be repeated not at the proper interval� of time, then their action, inftead of conlpifing withnbsp;motion of the pendulum, will check the little moti�*^nbsp;which was communicated to it by the firft impulfe, andnbsp;cdurfe the vibration of the pendulum cahnot be render^nbsp;vifible.

Therefore, whenever we find that a certain body caufed to vibrate by the reiteration of a certaiii weak nn^nbsp;pulfe, we may conclude that fuch impulfe hi'S bt ennbsp;at fuch intervals of time as the body is capable of periornnno

be applied to the vibration of other founding bodies) and c, amp;c. be a row of aerial pat-^'cles on one fide, and in the direftion of the vibra-^�Ons of the firing. When this firing is caufed tonbsp;'^*firate, the firfl vibration will drive the particle a,nbsp;^'^'vards b, and of courfe b muft impel c towardsnbsp;amp;c. but whilfl: the motion is thus communicated

��Onn one particle to the next, the firing goes back '�'^Wards the axis, or performs its fecomd vibration,nbsp;quot;^his removes the preffure from a, amp;c. and befidesnbsp;fifing, by its quick motion, occafions a rarefaflionnbsp;he place where a little before it had cauferi anbsp;'^'^f'denfation, in confequence of which the particlesnbsp;� ^tid b will recede a little way from each other, andnbsp;expanfion will gradually proceed through thenbsp;^^joining particles; then again another condenfa-on that fide takes place, amp;c. Thus the fuc-^^Tive waves or fhells of condenfed and rarefied\irnbsp;ollow each other.

ceived, except in an imperfeft manner by the very fmall motion of the particles of duft, fmoke,nbsp;which are feen to float in the air in certain lights�nbsp;and which are made to vibrate in a fmall degree bynbsp;the powerful found of a large fonorous body.

But the explanation of the vibration of a ftretch' ed ftring, which we have given above in anbsp;manner for the fake of perfpicuity, is far fro^tnbsp;being accurate and complete. In the firft place Jtnbsp;is eafy to perceive that the ftring, AB, fig.nbsp;Plate XIII. muft be longer when it ftands in th�nbsp;fituation A C B, or A D B, than when it ftaflC^nbsp;ftraight between A and B j therefore it appeal's�nbsp;that befides the lateral, there is alfo a longitudin^^�nbsp;vibration, which is capable of producing anoth^'-found, though not fo powerful as that of the lateralnbsp;vibration.

Secondly, the ftrings of mufical inftruments i¹� their vibrations, efpecially at firft, form curv^�nbsp;fomewhat different from each other, accordingnbsp;the different methods by which they are caufednbsp;vibrate, viz. whether they be ftruck in the middl^'nbsp;or clofe to one end �, whether by the application ^

Thirdly^ the firing fometimes feems to divide itfelf into parts, vi2. fome parts of the firingnbsp;perform vibrations peculiar to their lengths at thenbsp;fame time that they partake of the general vibra-*nbsp;tions.

And, fourthly, a firing feldom continues long to vibrate in one and the fame plane; but thenbsp;plane of its vibrations moves in different direftions,nbsp;'''hich are far from being regular. This deviationnbsp;of the plane of vibration from its original fituation,nbsp;ttiay probably be owing to the obliquity of the im^nbsp;pulfe, or to the inequalities in the figure of thenbsp;ftring, or to the refifianCe of the air, amp;c. Thisnbsp;tuovement of the plane of vibration may be difi -oerned by viewing a founding firing in the diredionnbsp;of its length.

If the movements of a firetcheff firing be fo oomplicated and uncertain, one may eafily conceivenbsp;difficulty of comprehending, or of invefiigating.

quot; which a fine filvered wire is wound in a fpiral form; con-quot; traiSt the light of a window} fo that, when the eye is placed in a proper pofition, the image of the light maynbsp;appear final], bright, and well defined on each of the con-''olutions of the wire. Let the chord be now made tonbsp;''ihrate, and th� luminous point will delineate its path,nbsp;like a burning coal whirled round, and will pfefent to thenbsp;�yc a line of light, which, by the affiftance of a microfeope,

the movements of ocher founding bodies, the greatef^ part of which are vaftly more irregulat in fiiape andnbsp;quahty than the ftretched ftring.

The vibrations of the air, wh�ch are produced by the above-mentioned movements of the f^menbsp;founding body, muft evidently be very compile: tednbsp;and uncertain. Befides, even in the fimplefl: modenbsp;of vibration, as that of the ftring; it is evidentnbsp;that the collapfing of the air behind it muft occafionnbsp;another fort of vibration, befides that which isnbsp;produced on the fore part of the ftring. In fhort,nbsp;it muft be confefled, that the real motion - of diCnbsp;air, or its various movements, in its conveyance ofnbsp;found, are far from being rightly under bood.

Moft fonorous bodies not only perform different vibrations at the fame time, but they may benbsp;caufed to perform certain vibrations and not others�nbsp;or they may be caufed to vibrate at pleafure ihnbsp;certain direftions more powerfully than in othefnbsp;dire'dions; and that by the different manner ofnbsp;holding or ftriking them. Thus, if a glafs, partiallynbsp;filled with water, be ftruck on the fide, it will eminnbsp;one found, and if, inftead of that, you rub yournbsp;wet finger over the edge of it, you will perceive anbsp;different found.

Moft oblong and elaftic bodies may be caufed to vibrate longit�dinally by means,of proper fridiotinbsp;in the diredion of their length. They maynbsp;rubbed with the finger, or with any folt fubftance

*^ver which fome pounded rofin is fpread. The t'eft way of rubbing glafs rods, is by means of a-rag beftrewed wirh fine fand*.

The founds which arife from the longitudinal Vibrations of fonorous bodies, are confiderablynbsp;higher than thofe which are produced by, the k-^eral vibrations of the fame bodies. The formernbsp;^gi^ee with the latter in this, viz. that they arenbsp;^'gher or lower inverfely as the lengths of the fo-*iorous body ; but otherwife a very ftriking dif-^^I'ence is to be remarked between the produdlionnbsp;ihe former and that of the latter; namely, thatnbsp;production of the latter depends upon thenbsp;'^'igth, weight, and tenfion of the firing or othernbsp;'^horous body : whereas the former depend morenbsp;^Pon the quality or nature of the fonorous body,nbsp;upon its thjcknefs and weight. quot; I have ex-^ atnined,�- fays Dr. Chladni, � every fubftancenbsp;V'hich I could obtain in a fufficiently lone rod-like form, in regard to longitudinal vibration ;nbsp;example, many kinds of wood and metal,nbsp;glafs, whalebone, amp;c. The fpecific gravity

Chladni of Wittemberg, who has made a very great dnbsp;nbsp;nbsp;nbsp;experiments on the longitudinal vibrations ef

bodies, lately contrived a mufical inftrument, which jjj Ibe euphony and which confifts of glafs rods difpnfcdnbsp;which exprcfs their founds by .bciVignbsp;ed longitudinally. A Ihort account of this inftrumentnbsp;be feen in the Phil. Mag. vol. II. p. 391.

324 nbsp;nbsp;nbsp;0/ Somdy or of Acoufus.

Different bodies are more or lefs fonorous; that property does not feem to be entirely dep^��nbsp;dent, either upon their fpecific gravity, or theirnbsp;nacity, or even their elafticity. Copper feems to ^nbsp;the moft fonorous of the fimple metals, thennbsp;filver, then iron, tin, platina, gold, and, lafti/�nbsp;lead, which feems to be the.leaft fonorous metsi^�*'nbsp;fubflance.

different forts of vibration, or rather the different flat fonorous bodies, which are caufed to vibrate by pecU'nbsp;managements.�His method is briefly as follows;

piece of board, amp;c. and ftrew very light bodies, fucb a* fand, over it. Then, holding it horizontally between y�'�^nbsp;finger and thumb, you rub a violin bow acrofs thenbsp;the plate; you will find that part of the plate isnbsp;caufed to vibrate, as will be (hewn by the motion ofnbsp;fand ; and by continuing the^fri�lion of the bow, yo'*nbsp;perceive that the fand will be gradually removed fromnbsp;vibrating parts, to thofe parts which do not vibrate. . ^nbsp;By holding the plate in different places, and by ^nbsp;two or more fingers to it, and then rubbing the boWnbsp;one part or another of the edge, the fand may be cao ^nbsp;affume different forms (called vibration figures)nbsp;circle, an ellipfis, a quadrangle, Sec. Sec the Bhil- ^ �nbsp;vol. III. p. 389.nbsp;nbsp;nbsp;nbsp;r^i^c

The communication of the vibrations from the ''ibrating part of a ftretched firing to fome othernbsp;part of it, which, at firft fight, migr'.t be fuppofednbsp;be at refl, is likewife attended with remarkable

^Pyou divide a firing, as AD, fig. 17. Plate XIII. jrito three equal parts AB, BC, CD, by placingnbsp;at C and B j place a bridge, like a violinnbsp;bridge at B, alfo place light bodies, fuch as fmallnbsp;of paper, at C, and at other places of the partnbsp;i then draw a violin bow over the part AB ;nbsp;will find that all the bits of paper will be thrownnbsp;from the part BD, excepting the one at C;nbsp;^'cwing that the point C remains at refl, whilfl thenbsp;*^^hnainder of the firing is vibrating.�This point,nbsp;^^'rl all other points whereon, in fuch experiments,nbsp;bits of paper remain at refl, as alfo the

Thus, by a proper divifion of the firing, and b/ intercepting one or more aliquot parts of it,nbsp;any moderate number of vibration nodes may bsnbsp;exhibited¹. But it muft be obferved, that 1�^nbsp;thofe experiments, the communication of motionnbsp;from the founding part of the firing, to the othe¹'¹nbsp;may be effedled not fo much through the fubftanconbsp;of the firing, as through the air. See p. 315-

In an organ pipe, and other wind inflruments, is not the inflrument itfelf that principally vibrates)nbsp;or rather the found is produced by the vibrationnbsp;the column of air within the pipe. In a large org^fnbsp;pipe this vibration of the column of air, whichnbsp;fomewhat longer than the pipe, may be felt bynbsp;applying'the open hand to the aperture of thonbsp;pipe. But the particular manner in which thisnbsp;vibration is performed, is by no means rightly

The general rule for finding out the number of vibrS' don nodes, according to any divifion of the firing, isnbsp;follows ;

^nderftood.�The found of the lame pipe may be ^^cre fed or diminifoed in quantity, or in acutenefs,nbsp;fupplying the pipe with different quantities ofnbsp;and by particular modes of blowing¹.

Upon the whole it appears, that, by certain ma-^'^gements, the height of a found may be increaftd diminifoed and, by other managements, thenbsp;^�quot;'^ngth and quality of the found may be altered,nbsp;quot;�'hus expert violin players pals the bow over thenbsp;fttings fometimes very clofe to the bridges of theirnbsp;^'olins; and, at other times, at a greater diftance,nbsp;nearer to the middle of the firings: by whichnbsp;�^eans, cateris parihus, they actually produce dif-^^fent effeds.

It alfo appears that every found, even thofe of fimplefi mufical inftruments, is accompaniednbsp;'''ifo other inferior, fecondary, or iefs audible,nbsp;lonnds; and thofe fecondary founds are heard morenbsp;^'ftindly when the founding bodies are large ornbsp;Powerful, and when the principal found is gravenbsp;^'id continuate, than otherwife. �Hereafter, innbsp;%¹saking of the founds, or of th� vibrations, ofnbsp;^�^Unding bodies, we mean only the vibrationsnbsp;^bich produce the principal or predominant found,nbsp;'^olefs the contrary be mentioned.

fliall now ftate the moft ufeful fads and ob¹ '''^tions which have Deen eftabiifoed and made

by various ingenious perfons, concerning the velocity� inrenfity, communication, refledion, and othernbsp;perties of founds in general.

Sound is propagated fucceffively from the founding body, to the places which are nearer to it, the^^ to thofe that are farther from it, amp;c.

A great many long and laborious calculation� have been made by divers able philofophcrs andnbsp;mathematicians, for the purpofe of deducing thenbsp;velocity of found through the air, from the kno'�'t^nbsp;�weight, elafticity, and other properties of air;nbsp;the refults of fuch calculations differ confiderablfnbsp;from each other, as alfo from the refults of afluainbsp;experiments, which fliews ekher that the calcula'nbsp;tions have been eftablifhed upon defedive principles, or that not all the concurring circumftancc�nbsp;have been taken into the account. Therefor*^�nbsp;without mentioning any thing farther withnbsp;fped to thofe calculations, I ihall immediatelynbsp;date the refuk of authentic and ufefui expet^*�nbsp;ments.

Alnioft every body knows, that when a gun fired at a confiderable diftance from him, henbsp;ceives the flafh a certain time before he heatsnbsp;the report j and the fame thing is true with rc-fped to the ftroke of a.n hammer, of an hatch^bnbsp;with the fall of a ftone, or, in fliort, with an/nbsp;vifible adion which produces a found or found�*nbsp;This lime which Ibund employs in its motiu^

t^^rough th� common air, has been meafured by 'various ingenious pcrfons. The principal and morenbsp;general method has been to meafure (by meansnbsp;a ftop watch or a pendulum) the time whichnbsp;^�apfes between the appearance of the flafh, andnbsp;hearing of the report of a gun fired at a certainnbsp;��Meafured diftance from the obferver; for lightnbsp;travels fo fall through the diftance of 1000, ornbsp;^�000 rniles, that we cannot poffibly perceive thenbsp;htrie�; therefore we may conclude that the explo-of a gun takes place at the very fame momentnbsp;tn which we perceive the flafh.

�In the firft place it has been unanimoufly ob-^^rved, that found travels at a uniform rate, viz. that it will go as far again in two feconds, as itnbsp;'''hi in one fecond; that it will go three times asnbsp;in three feconds, or four times as far in four fe-^�nds, as it will in one, and fo on. Therefore, innbsp;^he above-mentioned manner of performing thenbsp;Experiment, if the diftance fin feet) between thenbsp;Eannon, and the obferver, be divided by the num-^Er of feconds elapfed between the perceptionsnbsp;' Ef the fiafn and of the report, the quotient will Ihewnbsp;*he rate of travelling, or how many feet per fecondnbsp;Ihund runs through.

This rate has been eftimated differently by different perfons, whofe experiments have beennbsp;performed at different times, in different places,nbsp;��nd with inftruments more or lefs accurate, viz.

By Sir Ifaac Newton, at the rate of 968 By the Hon. Mr. Robarts, at -nbsp;nbsp;nbsp;nbsp;13�*^

By the Florentine Academicians -By the French Academicians De Thury, Maraldi, and de lanbsp;Caille -nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;--nbsp;nbsp;nbsp;nbsp;--nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;1107

By Flamftead, Flalley, and Der-ham, at nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;114'^

Dr. Derham, as it appears from the account the Philofophical Tranfaclions, feems to havenbsp;the greateft number of accurate and more divterfi-fied experiments j therefore we may take his cofi'nbsp;clufion, which coincides with thofe of Flamfteadnbsp;and Flalley, as the neareft to the truth, viz. that�

They reckoned it equal to 173 toifes, which ar? nearly = 1107 feet Englifti. See Alem. de I�Acad-for 1738, p. 128, See.

genera], found travels uniformly through the ^tniofpherical air at the rate of i r 42 feet per fe-or one mile in little lefs than 5 feconds; atnbsp;this refult cannot differ from the truth bynbsp;than 15 or 20 feet*. But it will appear fromnbsp;following paragraphs, and from the difficulty ofnbsp;^^afurins: time to a fraflion of a fecond, that nonbsp;'^ery great degree of accuracy can be expe6led innbsp;�^�tafurements of this fort.

Derham obferved, that the report of a cannon ^*'^d at the diftance of 13 miles from him, did notnbsp;^fike his ear with a fingle found, but that it wasnbsp;�^^peated five or fix times clofe to each other.nbsp;quot; The two firft cracks,� he fays, � were loudernbsp;quot; than the third, but the laft cracks were louder

quot; fome of my ftations, befides the multiplied found, I plainly heard a faint echo, which wasnbsp;quot; tefledled by my church, and the houfes adja-quot; cent.^� �

This repetition of the found probably originated the refledion of a fingle found from hills,nbsp;^tiufes, or other objeds, not much diftant froirinbsp;cannon. But it appears from general obferva-^^�0, and where no echo can be fufpeded, thatnbsp;found of a cannon, at the diftance of 10 or 20nbsp;is different from the found when near. In

According to Mr. Hales, the undulation of water is to motion of found .as i to 865.

the latter cafe the crack is loud and inftantancOUS, of which we cannot appreciate the height. Whereasnbsp;in the former cafe, viz. at a diftance, it is a gravenbsp;found, which may be compared to a determinatenbsp;mufical found ; and, inftead of being initantaneous�nbsp;it begins foftly, fwells to its greateft loudnefs, an^inbsp;then dies away growling.� Nearly the fame thingnbsp;may be obferved with refpeft to a clap of thunder*nbsp;Other founds are likewife altered in quality by thenbsp;diftance.

Upon the whole, it appears that the velocity found is exactly the fame, whether the found benbsp;high or low, ftrong or feeble, whether it be thenbsp;found of a human voice, or the report of a cannon*nbsp;But its velocity is fenfibly altered by winds.nbsp;the wind confpires with the found, viz. if it bloW*nbsp;in the direction from the founding body to thenbsp;hearer, the found will be heard, fooner; and if thenbsp;wind blows the contrary way, the found will benbsp;heard later, than according to the rate of 1142 feetnbsp;per fecond. In Ihort, the velocity of the wind,nbsp;the former cafe, muft be added to, and in the latternbsp;it muft be fubtrafted from, that of the found*. Bnt

the velocity of the air in the ftrongeft wind is, perhaps, not equal to the twentieth part of thenbsp;�''^elocity of found.

Heat and cold feem to make a very finall al-*^eration in the velocity of found; for found appears to travel a little fafter in fummer then in winter.

Different altitudes of the barometer, as alfo ^'fferent quantities of moifture in the air, feem tonbsp;�^cafion a fmall alteration in the velocity of found,nbsp;^ut it is not in our power to determine what flaarenbsp;�f the effe�t is due to each of thofe caufes.

Upon the whole it appears, that whatever in-creafes the elafticity of the air, accelerates therhotion, alfo the intenfity of found, through it, and vicenbsp;'^erfa. Or in fluids of a determinate elafticity,nbsp;'quot;'hatever increafes the denfity, diminilhes the velocity of found through them. Probably the velocities of found through fuch fluids, are as thenbsp;%uare roots of the denfities.�Experience feems tonbsp;ptove, that at different times of the year (the influence of winds being excluded) the velocity of foundnbsp;be faft�r or flower, not exceeding 30 feet, thannbsp;the above-mentioned mean rate of 1142 feet per

Second.

Calm weather; therefore, knowing in what time it ought to reach us in calm weather, the difference between that'nbsp;time and the time obferved in the above-mentioned cafes ofnbsp;'''indy weather, is the time which the wind employs in paflingnbsp;through that diftance.

The knowledge of the velocity of found through the air, may be applied to a very ufeful piirpofenbsp;viz. to the meafurement of diftances, efpeciallynbsp;when no better method can be ufed with convent'nbsp;ency. Thus we may meafure the diftance of ^nbsp;thunder cloud by meafuring the time which elapft�nbsp;between the appearance of the flafli of lightning?nbsp;and the report of the explofioa or thunder j fornbsp;by looking upon a clock or a v/atch with a fecond�snbsp;hand, we find that the time elapfed is one fecond?nbsp;we may conclude that the explofion took placenbsp;the diftahce of 1142 feet from us j if the elapfctinbsp;time be two, or three, or any otlier number ofnbsp;feconds, we may conclude that the diflance is thenbsp;produft of 1142 multiplied by two, or by three, ornbsp;by the other number of feconds. After the fanronbsp;manner by obferving the flafh and the report of ^nbsp;gun, or the motion of the hand which moves an hatU'nbsp;mer, and the perception of the found. See. we maynbsp;determine, pretty nearly, the diftance of a fliip, ornbsp;of an ifland, or of a workman, amp;c.

Air is always around us, and therefore is the moft common medium through which founds arenbsp;tranfmitted : but founds may alfo be conveyed bynbsp;other bodies, both foiid and fluid, viz. by water, bynbsp;metals, by wood, by ftones, by ropes, amp;c. and tonbsp;moft cafes more readily and perfedlly than by th^nbsp;air. Probably there is no fubftance which is not lUnbsp;fome meafure a condu�lor of found; but foundnbsp;much enfeebled by palling from one mediumnbsp;another.

a man flops one of his ears with his finger, ��*^ps the other ear by prei�ing it againft the end ofnbsp;^ iong flick, and a watcii be applied to the oppofitenbsp;of tke flick, or of a piece of timber, be it evernbsp;^ the man will hear the beating of the watchnbsp;diflinclly ; whereas in the ufual way throughnbsp;air, he can hardly hear it from a greater diftancenbsp;about 13 feet.

^ quot;file fame efFeft will take place if he flops both fars with ins hands, and refls his teeth, hisnbsp;'^pip, or the cartilaginous part of one of his carsnbsp;^S^'nfl the end of the flick.�Inflead of a flick henbsp;ufe a rod of iron or other metal, a block ornbsp;^'iiar of marble, amp;c.

^riflead of applying the watch, a very gentle ''^��atch may be made at one end of a pole, or rod,nbsp;the perfon who keeps the ear in clofe contaftnbsp;the other end of the pole, after the above-men-manner, will hear it with great accuracy.

'fhus perfons who are not quick of hearing, by ^I^Piying their teeth to fome part of an harpfi-or other founding body, will, by that means,nbsp;Enabled to hear the found much better than

againft any thing, he will hear a found- not different from that of a large bell.�Such expc^i'nbsp;ments are capable of great variety ¹.

at Toulon may be heard at Monoco, viz. 3t diftance of about 76 miles, by a perfon lyingnbsp;the ground; but not otherwife. But thenbsp;of placing one's ear clofe to the ground, in o¹� _nbsp;to perceive the approach of horfes or men ; orgt;nbsp;fhort, for the purpofe of hearing diftant fo^n'nbsp;has been obferved even amongft uncivilizednbsp;tions.

Articulate founds may alfo be tranfmitted throng folids; but I muft own, they are not perc^¹'^nbsp;ed very diftinftly by my ear. However,nbsp;Chladni, who has made a vaft number of exp^¹^'nbsp;ments relative to this fubjedt, expreffes himfc^^ ¹nbsp;the following manner :

� Articulated tones alfo are conduced ceedingly well through hard bodies, as Inbsp;by experiments which I made withnbsp;my friends. Two perfons who had ftopP^nbsp;their ears, could converfe with each other ^

� they held a long Hick, or a feries of Hicks� � tween their teeth, or refled their teethnbsp;� them. It is ail the fame whether the P^¹^

Of Sound, or of Acouftm. nbsp;nbsp;nbsp;337

his breaft, or when one refts the ftick which he holds in his teeth againft fome vefl�l into whichnbsp;^he other ipeaks. The efFeft will be greaternbsp;*^he more the veflel is capable of a tremulousnbsp;niovement. It appeared to be ftrongeft withnbsp;Slafs and porcelain velTcls; with copper kettles,nbsp;Wooden boxes, and earthen pots, it was weaker,nbsp;Sticks of glafs, and next fir-wood, conduced thenbsp;lound beft. The found could alfo be heardnbsp;'''hen a thread was held between the teeth bynbsp;both, fo as to be fome what ftretched. Throughnbsp;^ach fubftance, the found was modified in anbsp;Planner a little different. By refting a flick ornbsp;other body againft the temples, the forehead, andnbsp;the external cartilaginous part of the ear, foundnbsp;is conveyed to the interior organs of hearing, asnbsp;quot;'ill readily appear if you hold your watch tonbsp;thofe parts of another perfon who has ftopped upnbsp;his ears. From this it appears, as well as fromnbsp;the experiments relative to the hearing undernbsp;quot;'ater, that hearing is nothing elfe than, bynbsp;tneans of the organs - of hearing, to be fenfibienbsp;tgt;f the tremulous movement of an elaftic body,nbsp;quot;'hether this tremulous movement be conveyednbsp;through the air, or any other fluid or hard body,nbsp;to the auricular nerves. It is alfo �flentially thenbsp;fame whethef, as is ufually the cafe, the founflnbsp;he conveyed through the internal part of thenbsp;ear, or whether it be communicated throughnbsp;atiy other part of tfle bpdy. It certainly woplfl

g nbsp;nbsp;nbsp;f�|3g

be worth the trouble to make experiments try whether it might not be poffible that deaf.nbsp;dumb people, when the deficiency lies onlynbsp;� the external organs of the ear, the auricul^^nbsp;� nerve being perfedl, could not, by the abo''^nbsp;method of conducing found, be made to he^ttnbsp;diftinftly, words articulated, as well as othetnbsp;founds*.�

The velocity with which found moves throng'* folids, is by no means known, nor does it fe^quot;^nbsp;likely to be determined experimentally; for fn*^^nbsp;experiments can only be performed with fevet^^nbsp;hundred feet length of each particular fubftant^'nbsp;The only thing which has been tried relativenbsp;this fubje�l, is to tranfmit a found through a fet*^^nbsp;of pieces of' wood placed in clofe contafb thenbsp;with the fecond, the fecond with the third, and

on. It was found that found is tranfmitted throng** wood fafter than through air ; but it could notnbsp;determined how much fafter f.

f By reafoning and calculation it has been deduced, t** a column of air in a pipe of a certain length, open at bothnbsp;��ends, makes one longitudirtal vibration in the fame tin*�nbsp;that found would employ to percur the lame length

9 nbsp;nbsp;nbsp;.irl

Whether found be tranfmitted at all through ''^cuum, or not, is by no means determined. Anbsp;^^11 inch fed in a glafs receiver, and caufed to found,nbsp;be heard lefs and lefs, according as the glafs isnbsp;^ore and more exhaufted of air : but though Inbsp;nave ufed one of the beft air-pumps that was evernbsp;^onftrufted, and the apparatus which fupported thenbsp;^ell Was laid upon fuch foft fubftances as feemednbsp;likely to tranfmit the found through them ; yetnbsp;^ould never render the found of the bell quite un-^'idible. Befides, it may be fufpeftcd, that whennbsp;glafs receiver is exhaufted of air, the preffure ofnbsp;atmofphere, on its outfide only, may check innbsp;^*'^at meafure the tranfmiffion of the found. If itnbsp;^ afked what can tranfmit the found, or the vibra-of the bell, when the air between it and thenbsp;S^afs has been removed, fuppofing that it might benbsp;Entirely removed ? We muft undoubtedly affertnbsp;ignorance of it. But our ignorance of what maynbsp;^^tifmit the found in that cafe, does not prove that

{Riccatl delle fibre elajliche. Newton�s Frinc, L, 2. .nbsp;nbsp;nbsp;nbsp;50.} hence it maybe prefumed, by analogy, that found

. '^'quot;^nfmitted by folids of a certain length in the fame time �which thofe folids would perform each of their longitudi-

^ Certain length, will perform its longitudinal vibrations I^Uch fafter than an equal pillar of airj therefore it isnbsp;cly that found will move through iron much fafternbsp;through air, and the fame thing may be faid of othernbsp;. ^�lids.

Sounds diminifh in intenfity, or they are lefs dible, according as the hearers are farther fromnbsp;founding body j but there is no accurate methodnbsp;determining this decreafe *. ,

The fame found is ftronger in denfe than thinner air. The aftual fall of rain, fnow, amp;c. ^nbsp;a good deal of moifture in the air, diminilh thenbsp;tenfity of found. In calm, ferene weather, wh^^nbsp;every thing is quiet, a found is heardnbsp;ftronger, and of courfe much farther than othel'nbsp;wife. When a fmooth furface of ground, ^nbsp;elpecially of water, is interpofed betweennbsp;founding body and the hearer, then foundsnbsp;be heard much farther than when water muchnbsp;tated, or ground covered with houfes, trees,nbsp;interpofed-

In favourable circumftances the ftriking of^^^ clock on the bell of St. Paul�s church, in Londo'^�nbsp;has been heard at Windfor, It has been faidnbsp;with a particular concurrence of favourablenbsp;cumftances, the human voice has been heard atnbsp;diftance of more than ten miles, viz. from Onbsp;Gibraltar to New Gibraltar f. The difchargc �nbsp;an ordinary mufket can hardly ever be heard farth^^

Derham�s Phyfico-Theology, B. IV. chap, 3' alfo the Phil. Trauf. N. 300, for more facts of this

tJian

feven or eight miles; but the difcharge of fuch muOcets at the fame time may be heardnbsp;*�0(0 a greater diftance. The quick repetition ofnbsp;found may alfo be heard fomewhat farthernbsp;^^0 tlie fame fingly. In the Dutch war of thenbsp;year i5y 2, it has been faid, that the reports of can-**ons Tvere heard at the diftance of aoo miles, andnbsp;^P'vards.

is commonly faid, that the vibrations, which e i-nmunicated to the air by a founding body,nbsp;f^Pand fpherici ily all round that body ; and in fadtnbsp;found may be heard on any fide of it; yet cer-*�^¹1 it is, that the found will not be heard withnbsp;force and diftindlion in every diredtion; andnbsp;difference is much greater with certain found-bodies, (viz. when a ftrong impuife is givennbsp;the air in a particular diredlion) than withnbsp;Others. The report of a cannon appears loudernbsp;� perfon towards whom it is fired, than to onenbsp;foated in a contrary direction². The fpeakingnbsp;'^t�mpet throws the found diredtly before its aper-^^²�^1 and very little of it can be heard by perfonsnbsp;''^^0 are out of that diredtionf. In windy weather

^ t Upon this principle feveral curious contrivances may ^niadei and the fpeaking of the inanimate figure, fuf-P^nded in the air, which was exhibited in London fome

54^ nbsp;nbsp;nbsp;Of Sound, or of Acoujiics.

the found of a diftant bell is perceived to increaf� or decreafe in loudnefs, according as the wind alters

years ago, depends upon the fame principle. The mecha^' nifm was as follows; A wooden figure was fufpended in th�nbsp;air by means of ribbands, in an opening between two rooms-There was a perforation about an inch and a half in diame'nbsp;ter, from the mouth to the upper part of the head. Tbi*nbsp;aperture had an enlarged termination on the top of thenbsp;and with the other extremity communicated with a fortnbsp;fpeaking-trumpet, which w,as faftened to the mouth of tb�nbsp;figure. Behind the partition the enlarged or funnel-1-^�nbsp;opening of a tube was fituated directly oppofite to, andnbsp;about two feet diftance of, the aperture on the head of tb�nbsp;figure. The tube behind the partition was bent in a c��'nbsp;Venient form, and a concealed performer applied either h'*nbsp;mouth or his ear to the other end of the tube. Now,nbsp;perfon applied his mouth to the opening of the trumpet, 3^*^nbsp;Jpoke into it, the found paffed from the opening on the hc�^nbsp;of the figure through the air, to the opening of the t�*��nbsp;which flood facing it behind the partition of the rooms,nbsp;the perfon, who applied his ear to the farther opening ofnbsp;tube, would hear it diftinflly ; but other perfons in thenbsp;heard very little, if at all, of the faid articulated found;nbsp;the fame thing took place, when the concealed perfon fpo^�nbsp;with his mouth clofe to the farthefl end of the tube,nbsp;another perfon placed his ear clofe to the openmg ofnbsp;trumpet 5 which (hews that th^ found pafied almofl entif�'/nbsp;in a ftraight diredtion, from the opening on the head,nbsp;the oppofite -aperture of the tube, and vice verfa,nbsp;made it appear as if the wooden figure itfelf Gomprehso�nbsp;words, and returned an adeduate anfwer.

Its

ftrength or its diredion. An obftruftion to the of founds, is evidently made by /hills,nbsp;large trees, and ocher bodies of a Certainnbsp;Extent j for the found of a diftant bell, of a mill, ofnbsp;Waves of the fea on the fliore, amp;c. may benbsp;much better when nothing folid is interpofednbsp;'between the hearer and the founding body, thannbsp;^^herwife. This may be eafily obferved by a per-Walking through a town, when a noife'proceedsnbsp;any of the above-mentioned caufes �, for henbsp;quot;'dl hear the noife much better when he comes tonbsp;opening of a ftreet which leads to the foundingnbsp;than when the houfes intervene 5 fo that thenbsp;^�^nd which comes out of an aperture, does notnbsp;^^pand fpherically round that aperture, as round anbsp;^'ntre; and this is analogous to what has beerinbsp;^aid with refpedl to the diredion of a ftream ofnbsp;^3ter, which comes out of an aperture (fee p. 178.)}nbsp;it mull be confefled, that we are lefs able tonbsp;Comprehend the real motion of the air, thannbsp;^^at of the waves on the furface of water, or thatnbsp;ftream.

Sounds are alfo refleded by hard bodies, and this *'^fledion produces the well-known phenomenon.nbsp;Called the echo j and others analogous to it.

if a perfon ftanding at a certain diflance before a ^oh Wall, a bank, a rock, amp;c. utters a word ornbsp;ll^akes a noife, either with his voice or with annbsp;attitner, amp;c. he will frequently hear a repetitionnbsp;quot;^f the word or other noife ; and the time which

eiapfes between the exprefiion of the found aftd hearing of the fame again, is the fame as foundnbsp;general would employ in going twice throughnbsp;diftance between the man and the wall, or thenbsp;tock, Jrc. for the vibrations �f the air muftnbsp;from the man to the wall, and back again j fo thatnbsp;if the wall be 1142 feet diftanc, the time elapfe*^nbsp;b�tw'e�n the expreffion of the found, and the feco-adnbsp;arrival of it to the ear, will be two feconds j andnbsp;fo forth.

But the fame original fouAd, and the repetititnt or it, which is called the echo, may be heard hfnbsp;Other perfons fituated at different diftances both froifnbsp;the original founding place, and from the refleftif^nbsp;Wall, or other Objedl. The effedl, however,nbsp;hot be exadlly alike ; for inftance, thofe who af^nbsp;hearer to the wall, will hear the echo fooner thannbsp;Other perfons ; thofe who are as far again fromnbsp;man who expreffes the found as they are fromnbsp;fefledling obftacle, when the refledtmg objedt isnbsp;amp;n equal diftance from both, will hear bothnbsp;original found and the echo at the fame time gt; n�nbsp;Which cafe they will perdeive, as it were,nbsp;found louder than they would without the rep^nbsp;tition.

But though feveral perfons in different fituation� will hear the echo or reperition of the fame foundjnbsp;yet in a partitular direftion, the echo may be heat

refle�ing furfaccj one to the place whence the ^��'ginal found proceeds, and another in the above-^�^ntioned beft direction ; thofe lines will be foundnbsp;make equal angles with, or to be equally in-^^ined to, that furface. Plence it is faid, that foundnbsp;^fieSled by certain bodies., and that the angle of re^nbsp;fi^biion is equal to the angle of incidence.

This fhews, that though found proceeds from an ^��iginal founding body, or from a refledting fur ace,nbsp;every diredlion ; yet a greater quantity of it pro-^^eds in fome particular diredtion than in any other;

this is probably owing to the original impulfe ^ing given to the air in one direction more forciblynbsp;in others, as alfo to the want of perfedl freedomnbsp;motiop in the aerial fluid.

The furface of various bodiesgt; follds as well as ^^ids, have been found capable of refledling founds,nbsp;'^�2* the fides of hills, houles, rocks, banks of earth,nbsp;large trunks of trees, the furface of water, efpe-�Cially at the bottom of a well, and fometimes evennbsp;clouds. It is therefore evident, that in an ex-tenfive plain, or at fea, where there is no elevatednbsp;^^dy capable of refledling founds, no echo can benbsp;^eard.

The configuration of the furface of thole bodies ^^crris to be much more concerned in the production of the echo, than the fubftance itfeif. Anbsp;^l�iooth furiace refleds founds much better than anbsp;tough one. A convex furface is a very bad re-fledor of found; a flat furface refleds it very well;

but a fmall degree of concavity, and efpecially when the founding body is in the centre, or focus�nbsp;of the concavity, renders that furface a much bettednbsp;refleftor.

Thus in an elliptical chamber, if the founding body be placed in a focus of the ellipfis, that foundnbsp;will be heard much louder by a perfon fituatednbsp;the other focus, than in any other part ofnbsp;chamber. In this cafe the effedl: is fo powerful�nbsp;that even when the middle part of the chamber tsnbsp;wanting, viz. when the two oppohte elliptical Ihell�nbsp;only exift, the found expreffed in one focus will b^nbsp;heard by a perfon fituated in the other focus, butnbsp;hardly at all by other perfons¹.

This in fome meafure explains the effcdt of what are called whifpering domes, and whifpering galleries gt;nbsp;wherein, if a perfon fpeaks pretty near the wall 0¹^nbsp;one fide of it, another perfon will hear him diftintft'nbsp;Jy when he places his ear pretry near the wall ounbsp;the oppofite fide. The dome in St. Paul�s cathedral, in London, has this curious property�

If from any point in the circumference of an eliip�� two lines be drawn to the foci, thofe lines make equal angllt;^nbsp;with the curve at that point. Tais is demonflrated by aanbsp;the writers on conics. 'Fherefore, the found which is pt�'nbsp;duced in one focus of an elliptical chamber, and isnbsp;from the wall to the other focus, makes all the angles of iac¹'nbsp;dence equal to the angles of refletSion refpedively. Henc^�nbsp;that focus is the place where the found is heard beft.

tors.

Several phenomena thay be explained fo eafily ^�pon ;he above-mentioned theory of the refledlionnbsp;^ound, th �t they need be merely mentioned tonbsp;intelligent reader.

Several receding furfaces frequently are fo pro-Periy fituated with refped to diftance, and direc-that a found proceeding from a certain pointy fefle�ted by one furface firfl, then by anothernbsp;^hich is a little farther off, after which it is refledednbsp;� third furface, and fo on ; or it is refleded fromnbsp;furface to a fecond, from the fecond to a third,nbsp;the third to a fourth, amp;c. Hence, echos,nbsp;^i^'ch repea the fame found, or the fame word, twonbsp;three, or feveral times over, are frequently metnbsp;^ich.

�According to the greater or lefs diftance from fpeaker, a refleding objed will return the echonbsp;feveral, or of fewer fyilables; for all the, fyllablesnbsp;bg uttered before the echo of the firft fyllablenbsp;�^^ches the ar, otherwife it will make a confufion.nbsp;^ ^ moderate way of fpeaking, about j| fyllablesnbsp;^ pronounced in one fecond, or feven fyllables innbsp;1'econds*. Therefore, when an echo repeats

�from the computation of fliort-hand writers it appears a ready and rapid orator in the Englifh language, pro-*��utices from yooo to 7500 words in an hour, viz. aboutnbsp;Words in a minute, or two words in each fecond.nbsp;Memoirs of Gibbon�s Life.

feven

feven fyl'ables, the refle�ling obje�l is 1142 dilt-nt; lor found travels at the rate of 1142nbsp;prr 1�econd, and the diftance from the fpeaker tonbsp;the refieding objed, and again from the latter tonbsp;the former, is twice 1142 feet. When the eCttOnbsp;returns 14 lyllables, the refieding objed muftnbsp;2282 feet diftant) and fo on. A famous echo isnbsp;faid to be in Woodfiock Park, near Oxford.nbsp;repeats 17 fyllables in the day, and 20 at night¹nbsp;Another remarkable echo is faid to be on the northnbsp;fide of Shipley church, in Suflex. It repeatsnbsp;difiindly, in favourable circumftances, 21 fyll^'nbsp;bles f.

Therefore the farther the refieding furface the greater number of fyllables the echo will re²-peat; but the found will be enfeebled nearly in thenbsp;fame proportion, and at laft the fyllables cannot henbsp;heard diftindly.

W hen the refieding objed is too near, the repCquot; tition of the found arrives at the ear, whilft thenbsp;perception of the original found ftill continues, rhnbsp;�which caie an indiftind refounding is heard. Thgt;²nbsp;efie rt may be trequently obferved in empty rooms,nbsp;paflages, dc. efpecially becaufe in fiich places fequot;nbsp;ve.al refledions f om the walls to the hearer,nbsp;alfo from one wall to the other, and then to the

If each of the vibrations of the air, which are oc-Cafioned by a certain found, be performed in the fame time that found employs in going from thenbsp;founding body to the walls of a room, and thencenbsp;^0 the hearer, then the found will be heard withnbsp;Sweater force. � In (hort, by altering our fituationnbsp;^0 a room and exprefling a found, or hearing thenbsp;found of another perfon, in different fituations, ornbsp;^hen different objefts are alternately placed in thenbsp;^oom, that found may be heard louder or weaker,nbsp;more or lefs dlftinft. Hence it is, that blindnbsp;P^rfons, who are under the neceflity of paying greatnbsp;attention to the perceptions of their fenfe of hearing,nbsp;Acquire the habit of diftinguilhing, from the foundnbsp;^'^en of their own voices, whether a room isnbsp;^oipty or furnifhed, whether the windows are opennbsp;ffiut, and fometimes they can even diftinguifh.nbsp;'whether any perfon be in the room or not¹ ².

* The famous Dr. N. Saunderfon, Profellbr of the Ma-�fnatics in the univerfity of Cambridge, who had been

nd finpe he was one year old, poffefled fuch acutenefs of ^earing, that, as is related in the account of his life, � Bynbsp;his quiclcnefs in this fenfe, he not only diffinguilhed per-fons, with whom he had ever once converfed, fo long asnbsp;fix in his memory the found of their voice, but in fomenbsp;nieafure places alfo. He could judge of the ffze of a room

A great deal of furniture in a room, efpecially of a foft kind, fuch as curtains, carpets, amp;c. check lOnbsp;.great meafure the founds thar are produced in '*nbsp;for they hinder the free communication of the vibra*nbsp;tions of the air, from one part of the room, to thenbsp;other.

The fitteft rooms for declamation, or for mufiegt; arc fuch as contain few ornaments thatobftru�l thenbsp;found, and at the fame time have the leaf: echonbsp;poffible; for when they have one or more echos�nbsp;which arife from cupolas, alcoves, vaulted ceiling*�nbsp;amp;c. the repetition of one or more founds comes tonbsp;the ear at the fame time that another diredt foundnbsp;reaches it, which not only fpoils the former, but nin�nbsp;times out of ten forms a difeord.

A pretty ftrong and continued found fatigues the car. The flrokcs of heavy hammers, of artillery�nbsp;6tc. are apt to render people deaf, at leaf: for ^nbsp;certain time. And it has been obferved, that font^nbsp;perfons vgt;?ho have been long expofed to the conU'nbsp;nued and confufed noife of certain manuftdtoric*�nbsp;or of water-falls, or of other noify places, can he^'�

Of Soundy or of Acoujitcs. nbsp;nbsp;nbsp;35E

'''hat is fpoken to them, much better in the midft of ^hat noife than elfewhere.

The attentive reader may naturally enquire in ''hat manner are founds communicated to our fen-borium, and in what manner does the ear receivenbsp;^nd tranfmit them to the auditory nerve ; but tO'nbsp;thofe queftions I am unable to give any fatisfadorynbsp;anfwef^nbsp;nbsp;nbsp;nbsp;particular defeription of the int', rnal, as

quot;^11 as external, parts of the ear, may be found in a Variety of anatomical books ; but the knowledge ofnbsp;*he conftrudion does not inform us of the real ufenbsp;'�f thofe parts. The form of the external part ofnbsp;^he ear is evidently intended for receiving in great

Some very remarkable obfervations lately made, ��elative to the organ of hearing, fliew, in a verynbsp;Pointed manner, that the various fundions of thatnbsp;'^'�gan are far from being rightly underftood*. Anbsp;proper inveftigation of the fubjedt is highly re-^otnmendable to every able philofopher.�It mightnbsp;doubtlefs improve the general fubjefl of acouftics,nbsp;in particular it might furnilh means of remedy-Or of fupplying, the defeds incident to the hu-ear.

*1 he only known mechanical method of improv-that organ, when it is in a certain manner de-

This trumpet is an hollow conical tube, fro'^ about 8 to i6 inches in length. It is often bent no?nbsp;much unlike the letter C, excepting that in genera^nbsp;the fmall end is bent much lefs than the other. Th^nbsp;fmall end (whofe aperture is not above a quarternbsp;an inch in diameter) is applied to the ear, whilftnbsp;large aperture (which is from about a to 4 inchesnbsp;in diameter) is direfted towards a fpeaker, or in'nbsp;wards the founding body. By this means the foun^nbsp;is heard confiderably louder, but lefs diftindt.

Hearing trumpets have been made of vario^� fhapes, though the above feems upon the wholenbsp;be the beft; but no theory can at prefent determi'��nbsp;their moft advantageous conftrudtion.

Their office is to increafe, not the frequency, b^*' the momentum of the aerial vibrations; and this ins/nbsp;probably arife fromthofe vibrations paffing gradual!/nbsp;from the larger to the narrower part of the inftfU'nbsp;ment. Perhaps the vibrations of the air refletft^'^nbsp;from different points of the inftrument, like differed�*'nbsp;echos, reach the ear not all precifely at the fagt;^^nbsp;time ; hence the found is rendered louder, butnbsp;diftindt, I fball not however proceed to expl^'1^nbsp;wlrat I myfelf do not clearly urjderftand..

[ 3^3 ]

The compound effedt which arifes from two ^^unds, exprefled at the fame time, is called Con-.nbsp;Sotiance, or Dijfonance, according as it , produces anbsp;P^^afing or unpleafing effedl;.

An Accord is the eifed which arifes froiTi, or a Combination: of, more than two founds exprefled atnbsp;fame time.

The art which examines, difpofes, and expreflTes ^rgt;ds, fo as to produce melody, or harmony,nbsp;1^'^afing upon the whole, is called Mufic, oir thenbsp;^Mfical Art. And; the founds, which are fo farnbsp;^mipie^ determinate, and pleafing, as to be ufed innbsp;are called Mufical Sounds,nbsp;has been faid, at the beginning of the pre-r;nbsp;^^ding chapter, that the variety of founds arifes frorpnbsp;caufes principally, viz. ift, from the' greaternbsp;lefs frequency of the vibrations ; adly, from thenbsp;�l^'^ntity, force or momentum pf the vibratingnbsp;j and 3dly, from the greater or lefs fipaplicj'tynbsp;each found.

A clear idea of thofe differences may be conceit' ed by comparing the found of a pretty large belbnbsp;with that of a firing of a bafe viol. Thofenbsp;fonorous bodies may be adjufted fo, that eachnbsp;them may perform the fame number of vibratiof¹�nbsp;in the fame time. In that cafe the founds of thof^Jnbsp;inftruments are faid to be of the fame pitch jnbsp;the pitch of a certain found, or of the inftrum^'^¹'nbsp;which expreffes that certain found, is faid to benbsp;equal to, lower, or higher than the pitch of anothe¹quot;nbsp;found, or other fonorous body that emits th^¹nbsp;found, when the firft fonprous body performsnbsp;equal, a fmaller, or a greater number of vibr^^'nbsp;tions than the other fonorous body in the fail��nbsp;time.

But though thofe inftruments exprefs the fa^'^¹^ found with refpefl to the pitch ; yet the foundnbsp;the bell is much louder than that of the bafe viol gt;nbsp;and, in faft, the former may be heard from a mu^bnbsp;greater diftance than the latter. This fhewsnbsp;fecond diftindion ¹,

The greater or lefs ftrength of a found of the feta� pitch is called by muficians, the forte and piano ofnbsp;found. The well known inftrument, called the fortenbsp;derives its name from its being capable of expreffingnbsp;fame tones more or lefs loud; whereas the harpficho^ tnbsp;which is like the forte piano in every other refped, expf�'nbsp;its tones always of the fame ftrength.

The third ftrifes from the inequality, harfhnefs, of the found of the bell in comparifon withnbsp;that of the bafe viol; for a perfon, who is fuffici-cntly Hear, and liftens with attention, will perceivenbsp;that the foundquot; of the bell is attended with a fort ofnbsp;t^tidulation, both in pitch and ftrength} and is, bendes, accompanied with one or more fecondarynbsp;bounds i whereas the found of the bafe viol is muchnbsp;Ample and uniform.

There is no method of meafuring the quantity of the above-mentioned fecond and third diftinftions jnbsp;t^cepting by the judgment of the ear, whicii is va-t'otis and partial. One perfon, for inftance, pre-the found of a powerful organ to that of anbsp;''iolin; another prefers the latter to the former,nbsp;^ne likes the found of a French horn above thatnbsp;all other inftruments, and another prefers anbsp;^nte.

In general it is not from a proper difcriminatlon, ^^t from the various acutenefs of the ear, fromnbsp;P'�ejudfce, from falhion, from want of difeernment,nbsp;from miftaken ideas, that moft people exprefsnbsp;dieir likings and didikings. Various and difeordantnbsp;the opinions of men relatively to thofe thingsnbsp;'�^hich have no fixed ftandard of perfedion or de-'^onftration j yet it may be prefumed, efpeciallynbsp;'''nh refpeft to mufical founds, that whatevernbsp;Pleafes the majority, and w'hatever. can be endurednbsp;a longer time without difguft, is the beft andnbsp;��hs moft eligible, And there are fome perfons

After a long and diverfified experience, through a confiderable leries of years, it has been.found�nbsp;that certain founds, exprefled in certain fucceffions�nbsp;and in certain combinations, are pleafing to nrioftnbsp;huipan ears. They are of the fimpleft andnbsp;uniform kind, neither too loud, nor too feeble j bul^nbsp;differing from each other in pitch, by certainnbsp;and determinate intervals.�They are callednbsp;founds, or tones,

Befides the human voice, feveral inftruments� which have been invented at various times, and atCnbsp;now in ufe, are capable of exprefling thofe muficalnbsp;founds j hence they are called mufic-al injlrumentt�nbsp;and the beft of them are fuch as are capable of eS'nbsp;preffing the greateft variety of fuch founds, efpC'nbsp;cially with refpefl; to the. pitch, and of the fimpleft�nbsp;as well as of the moft pleafing fort.

Upon fome of thofe inftruments, ,fuch as th� harpfichord, forte piano, the organ, the guitar,nbsp;the pitch of each tone is fixt and immutable,nbsp;others, fuch as the human voice, French horn�nbsp;violin, violoncello, amp;c. the pitch proper for eachnbsp;tone, muft be determined by the performer. Th�nbsp;accompliihment of this tafk is very difficult

What has been faid above may fufEce with re-to the lefs definite qualities of founds; viz. length and fimplicity. It is now neceflary tonbsp;^I'eat of the more difficult, but more determinate,nbsp;Quality, called the ptchy which has already beennbsp;^^id to depend upon the frequency of the vibra-^ons.

The human voice, in its ordinary way of fpeak-generally changes its pitch by imperceptible intervals, or rather by Aiding a little way up ornbsp;'^own. But there are different and confiderable in-^^rvals between the mufical tones. Thofe muficalnbsp;tones were perhaps in great meafure found out experimentally ; but they have afterwards been reduced to, and may be expreffed by means of, ac-t^tirate mathematical meafurements.�The order, ornbsp;the arrangement, of thofe founds is called the jeale

A voice or an inftrument, which expreffes thofo Pounds in a particular order under certain reAric-t^ons, produces mufic; otherwife the effedt is notnbsp;Pleafing, nor is it called mufic. The naturalnbsp;fioging of birds may exhibit a fine voice in certainnbsp;t-^fos j but it is not mufical, their founds havingnbsp;tiothing to do with the mufical intervals; and, innbsp;the arrangement of their various founds is bynbsp;tto means pleafing.nbsp;nbsp;nbsp;nbsp;,

� formed by a ftretched ftring, when its tenfiori� length, and weight are known, may be afcertainet^nbsp;with tolerable accuracy.

The number of vibrations of moft other found' ing bodies, cannot be afcertained otherwife than b/nbsp;comparing their founds with thof� of ftringed i'�'nbsp;ftruments} for the human ear can judge with con'nbsp;fiderable accuracy when the two inftrumehts are ii�nbsp;iiniron, or perform contemporaneous vibrations, ^nbsp;which cafe they are faid to be of the fame ^nbsp;and indeed fome expert muficians can determine b/nbsp;the judgment of their ear, not only wjien two found*nbsp;are of the fame pitch, but alfo when they are at ^nbsp;certain diftanqe of each other! Therefore, in odnbsp;inveftigatlon and expreffions of mufical founds,nbsp;will be fufficient to fpeak of ftretched firings dnbsp;chords only; as the founds of all the other inftt^^nbsp;ments may be referred to thofe of ftrings.

The following particulars relative to ftretched firings have been demonftrated mathematically,nbsp;the demonftration will be found in the followingnbsp;note, for the ufe of thofe readers who are fufficiendynbsp;{killed in mathematics.

I. If a ftretched cylindrical chord be ftruck, then be left to vibrate by itfelf, it will performnbsp;vibrations, whether large or narrow, in equal time��nbsp;and, of courfe, the found, though decaying grad^^nbsp;ally, yet continues in the fame pitch ; exceptm�nbsp;Jtowever, when the ftring is ftruck violently i

2. If various firings be equally flretched, and of the fame fubftance 5 or, in ftiort, if they benbsp;^^Hal in every refpedt, excepting in their lengths ;nbsp;^hen the duration of a fingle vibration of each ftringnbsp;'''ill be as the length of the ftring ; or (which is thenbsp;thing) the number of vibrations performed bynbsp;^acli firing in a given time, will be inweffely as thenbsp;^^iigth ; for inftance, if a ftring be four feet long,nbsp;another firing, cjeteris paribus, be one footnbsp;; then the latter will vibrate four times whilftnbsp;former vibrates once. Or if the length of thenbsp;former be to that of the latter, as 10 to 3; thennbsp;vibrations performed by the latter will be tonbsp;��^lofethat are performed by the former, as 3 to 10 ;

fo on. Alfo, the fame thing mull be under-ftood of the parts of the fame ftring; for inftance, ^f certain ftring perform 8 vibrations in a fe-; then, if that ft ring be flopped in the middle,nbsp;^nd one half of it only be cauied to found, thennbsp;'�^^t half will perform i6 vibrations in a fecond.�nbsp;third part of the fame ftring will perform 24nbsp;''i^tations in a fecond; and fo on.

'I'he length of the ftring is reckoned from one bridge to the other, or from one refting place tonbsp;other; thus, in fig. 19. Plate XIH. thenbsp;^^'^gth of the ftring is reckoned from R to S.nbsp;tenfion of the ftring is meafured by the

360 nbsp;nbsp;nbsp;�f Mufical Sound's.

�weight 'w, �which is fufpeiidcd to one end of If inftead of ftretching a ftring by fufpending ^nbsp;weight to it, as indicated by the above-rhentionc^^nbsp;figure, the ftring be twifted round a peg,nbsp;the manner commonly ufed in mufical inftr^'nbsp;m�nts, then the tenfion ftill muft be exprelf*^^^nbsp;by a weight; meaning a weight which itiaynbsp;capable of ftretching the ftring as much as igt;^nbsp;ftretched by turning the peg.

the number of vibrations which each of thei^ performs in a given time, is as the fquare root 0nbsp;the ftretching weight. Thus, if a chord be ftretd^'nbsp;cd by a weight of 16 pounds, ^nd another chotnbsp;be ftretched by a weight of 9 pounds; thennbsp;former will perform 4 vibrations in the famenbsp;that the latter performs 3 vibrationsi

4. nbsp;nbsp;nbsp;If cylindrical chords differ in thicknefs onl/^nbsp;then the number of vibrations which they perfot^nbsp;will be inverfely as the diameters, viz. if thediato^'nbsp;ter of a chord be equal to twice the diameter 0nbsp;�another chord ; then the former will perform o�^^nbsp;vibration in the fame time that the latter perfot''*''*nbsp;two vibrations.

By a proper adjuftment of the lengthsj thi^^ iieffes, and ftretching weights, diffimilar chot^�nbsp;may be caufed to perform any required numbernbsp;Vibrations j which is evidently derived fromnbsp;preceding paragraphs.

6. The aftual number of vibrations, which are performed by a given ftretched chord, may be determined, without any great error, by ufing the fol'-lowing rule; provided the lengrh and weigiit of thenbsp;t^'brating part of the chord, as RS, fig. icj, andnbsp;likewife the ftretching weigat w, be known,�nbsp;^ule. Multiply the ftretching weight by 39, t 2 inchesnbsp;('^hich is nearly the length of the pendulum thatnbsp;Vibrates feconds). Alfo multiply the weight of thenbsp;'-kord by its length in inches ; divide the firft pro-by the fecond ; extradt the fquare root of thenbsp;Quotient; multiply this fquare root by 3,1416,nbsp;h and this laft produft is the number of vibrationsnbsp;that are performed in one fecond of time by thenbsp;�iven chord.�The refiftance of the air, as alfonbsp;^ome other fluftuating caufes of obftruftion, not be-noticed in this rule; it is moft probable that thenbsp;teal vibrations are not quite fo numerous as they arenbsp;Biven by the rule.

example of the above-mentioned rule.�A, copper of 35,5 s inches in length, weighing 31nbsp;E^ains troy, was ftretched by a weight of fevennbsp;Pounds avoirdupois, which is nearly equal tonbsp;49000 grains. How many vibrations did it per-^�rna in each fecond?�The produdt of 49000nbsp;ttiultiplied by 39,12 is 1916880. The produftnbsp;dijSS hy 31, is 1102,05. If 1916880nbsp;^0 divided by 1102,05, the quotient will benbsp;*739gt;37, the fquare root of which is 41,7;

3^2 nbsp;nbsp;nbsp;Of Mufical Sounds.

and this fquare root being multiplied by3,i4*^^ gives 131 for the required number of vibrations. fi.)

(l.) It is evident from what has been faid above, that b/ diminishing the tenhon and incrcafmg the length of th^nbsp;chord, the number of vibrations may be diminiftied tonbsp;a degree as to render the imgle vibrations difcerniblenbsp;each other ; hence it feems, that the vibrations of a chof'^nbsp;that^exprefles a certain tone, might be counted; but 1*^nbsp;pradlice the performance of fuch experiments is attend^slnbsp;with very great, and hitherto unfurmounted, difficulti^^�nbsp;Several perfons have tried the experiment; but no decifiv'^nbsp;refults have ever been derived therefromt

I have attempted fuch experiments, both with metallic with catgut firings of various fixes and lengths, as far as *7nbsp;feet; and with various degrees of tenfion, or withnbsp;ilretching weights. I have ufed thofe firings in the manO^^nbsp;of pendulums, with a weight faflened to the lower exf^'nbsp;mity;�I have alfo placed them horizontally, after

Of Mufical Sounds. nbsp;nbsp;nbsp;36J

It is now neceflary to fpecify thofe founds which Experience has fhewn to be fit for mufical composition. And here we fhall only fpeak of the pitch,nbsp;'''hich is denoted by the number of vibrations that

Vmyfelf, and in the prefence,of a very intelligent friend; S�^'tce it may be prefumed to be as accurate as the nature ofnbsp;fubje�l can admit of.

A brafs firing, fuch as is ufed for harpfichords, was fuf-Pfinded like a pendulum, with a weight of 5 pounds, (''iz. ,^0250 grains) at its extremity.

The length of the firing was 100 inches. Its weight ^30 grains; when flruck and fet a vibrating, if a piece ofnbsp;P^per was fet on one fide of it, the firing ftruck the papernbsp;^^out 14 times in a fecund, as nearly as I could polfiblynbsp;*^�ckoii. And as it would have flruck a piece of paper ortnbsp;other fide as often in the fame time, therefore it perform-28 vibrations in a fecond.

But, by calculation, it ought to have performed 34,56 ''�1�rations in a fecond.

^hen,- inflead of 5 pounds and |, one pound only, or 70oo grains, was fufpended to it, the firing performed fromnbsp;to 12 vibrations in a fecond; and in fadl the numbers ofnbsp;''�l^rationr. being as the fquares of the flrctching weights, wenbsp;4025011 ; yoo�]i : : 200,6 : 83,6 ; ; 28 : 11,6 ; whichnbsp;^ pretty good agreement.

Therefore, it feems, that the method of determining the *'�itnber of vibrations that are performed by a firing whichnbsp;^'^unds a certain tone, mufl be derived from the theoreticalnbsp;^Hionflration ; but the refult of fuch demonftration muft

3^4 nbsp;nbsp;nbsp;Of Mufical Sounds.

are performed in a given timei or by the length o( the firing which emits each �f thofe founds �, fotnbsp;has been already fliewh that, when ftretched firing*nbsp;are alike in all other refpe(5ls, excepting in theit

deviate in a certain degree from the truth, principally on count of the reftftance of the air, and of the want of perf^^*^nbsp;pliability in the chord, amp;c.

The ratio which the number of vibrations bears to th� weight, tenfiron, length, amp;c. of the chord, has been dernof'nbsp;ftrated, with fome variation of method, by fevera!nbsp;writers. The conclufion is always the fame. I ha'^^�nbsp;however, preferred Dr. Taylor�s original demonftratio'��nbsp;fuch as is publiflied in the Philofophical Tranfaflions,nbsp;caufe it is lefs dependent upon other extraneous prop^�'nbsp;fitions, and of courfe it may be efteem.ed thenbsp;concife.nbsp;nbsp;nbsp;nbsp;.

It may be objeded, that this demonftration does not ta^ in .all the fnapes which a firing, according to the vario'**nbsp;modes of firiking it, affumes in its vibrations. But itnbsp;be obferved, that as, cateris paribus, the fame chord, bo''''nbsp;ever ftruck, provided it be not ftruck too violently, gi'^* ^nbsp;tone conftantly of the fame pitch ; its vibrations muft honbsp;frequent when it affumes the fimpleft, as when it aflornosnbsp;any other, form.

� Lemma I. Let A D F B, A A ^ B, fig. i. Plate be two curve.s, the relation of which is fuch, that tb^

Of Mufical Sounds, nbsp;nbsp;nbsp;2^^

^^ngths, then the duration of a fingle vibration of each firing, is proportionate to the length , of thenbsp;^*'*ng 5 or, (which amounts to the fame thing)nbsp;that the .number of vibrations performed by each

�'^^inates C A D, E 4gt; F,. being drawn, it may be ,CA ; CD �E^;�P_ Then the. ordinates being diminifhed ainbsp;fo that the �curvos.-nray coincide with the axisnbsp;I fay, that tlie ultimate ratio of the curvature in, A�nbsp;be to the curvature in D,,' as C A to C D.,�'

� l^emonji. Draw the ordinate c ? d very near to CD, at D and A draw the tangents D t and A fl, meetingnbsp;ordinate r r/ in f and 9. Then becaufe oi :.,c d.'. �.nbsp;�* : C D, (by hypothefis) the tangents being producednbsp;meet one another, and the axis in the fame point P,nbsp;hence, be.caufe of fimilat; triangles C D P and r f P,nbsp;^^P and f fiP, it will be r ; rf: : C A : CD ;; r J :nbsp;^ (hy hypoth.) S6: (c6 � c^) : dtnbsp;nbsp;nbsp;nbsp;d) But

is, b

Of Muftcal Sounds.

if you take feveral firings precifely of the farn� fubfiance^ the fame form, and the fame thicknefsgt;

an^

the point 0 ere�t a perpendicular aR, equal to the radii** of the curvature at which let the tangents p f, w r, me�*quot;nbsp;in f, the parallels to them ?r r, �gt; r, in r, the chord �) innbsp;Then by the principles of mechanics, the abfolute force bynbsp;which the two particles f o and om-, are urged towardsnbsp;will be to the force of tenfion of the firing, as st tonbsp;and half this force by which one particle �gt; a is urged,nbsp;be to the tenfion of the firing, as cr to ip\ that is,nbsp;ca�fe of fimilar triangles ctp~, R) as/ygt; or op tonbsp;orirR. Wherefore, becaufe of the force of tenfion bei**�

op,

But the acceleration generated is in a compound ratio the ratios of the abfolute force directly, and of thenbsp;to be moved inverfely ; and the matter to be moved **nbsp;the particle itieif op. Wherefore the acceleration is

�; that is, as the curvature ins. For the curvatuf� is reciprocally as the radius of curvature in that poj**^*

, . .

� In this aitd the following problem, I fuppofe the to move from the axis of motion through an indefin*^^|^nbsp;little fpace ; that the increment of tenfion from the increunbsp;df the'length, alfo the obliquity of the radii of curvature�nbsp;play fafely be negleified,� .nbsp;nbsp;nbsp;nbsp;�

Of Mufical Sounds. nbsp;nbsp;nbsp;367

and ftretch them eqir^lly by fufpending equal weights ^0 their extremities, or otherwile ; then make theirnbsp;^^ngths of the proportions that are ftated in thenbsp;following table j thofe firings, when ftruck, will

� Therefore let the firing be ftretched between the points ^ and B, fig. 3. Elate XIV. and with a bow let the point anbsp;drawn to the diftance C z, from the axis A B, Thennbsp;^king away the bow, becaufe of the flexure in the point Cnbsp;^^one, that will firft begin to move {hy Lem. 2.) But nanbsp;f^ner will the firing be bent in the nearefl points (p andnbsp;thefe points alfo will begin to move ; and. then E andv;nbsp;^^d fo on. Alfo becaufe of the great flexure in C, thatnbsp;f*tgt;int vvill firll move very fwiftly, and thence the curvaturenbsp;increafed in the next points D, E, amp;c. they will im-��ediately be accelerated more fwiftly; and at the fame timenbsp;Curvature in C being diminifned, that point in its turnnbsp;quot;^*'1 be accelerated more flowly. And in general, thofenbsp;which are flower than they fhould be, being accele-^^ted more, and the quicker lefs, it will be brought aboutnbsp;^^11, that the forces being duly attertipered one with an�nbsp;'^�her, all the motions will confpire together, and all thenbsp;P�gt;nts will at the fame time approach to the axis, going andnbsp;alternate!}', ad infiniltm.�'

� No'^v^that this may be done, the firing mufl always on-the form of the curve A C D E B, th� curvature ofnbsp;quot;'kich, ill any point E, is as the diftance of the fame E � fromnbsp;axis ; the velocities of the pednts C, D, E, amp;c. beingnbsp;m the ratio of the di (lances from the axis C z, D .5,

36S nbsp;nbsp;nbsp;0/ Muftcal Sounds.

Wherefore the remaining fpaces k z, JS, sn, amp;c. v/iH to each other in the fame ratio. Alfo (by Lem. a-)nbsp;accelerations will be to one another in the fame ratio,nbsp;which means the ratio of the velocities always continuingnbsp;the fame with the ratio of the fpaces to be defcribed, ^nbsp;the points will arrive at the axis at the fame time,nbsp;always depart.from it at the fame time. And therefore ta�nbsp;curve A C D E B will be rightly determined. Q. E. D-�nbsp;� Moreover the two curves A C D E B andnbsp;being compared together, by Lemma i. the curvatures i**nbsp;P and J will be as the diftanees from the axis D S andnbsp;and therefore, by Lemma 2. the acceleration of any gi''^nbsp;point in the firing will be tts. its diftance from thenbsp;Whence, (by Sect. lO. Prop. 51, of Newton�s Prineihi^)nbsp;all the vibration's, both great and fmall, will be perfortu^'^nbsp;in the fame periodical time, and the motion of any poi*'*�nbsp;W'ill be fimilar to the ofcillation of a body vibrating *nbsp;Cycloid. Q^E.f.�

� Cor, Curvatures are reciprocally as the radii of circle� of the fame degree of curvature. Therefore let be lt;1nbsp;given line, and the radius of curvature in E will be equal

� Prob. ?. The length and weight of a firing beiUo given, together with the weight that flretches the ftnhg�nbsp;tg find the tipie of a fingle vibration.�

If pet

Cf Muf cal Sounds. nbsp;nbsp;nbsp;5'6^

g�od �r bad. The contemporaneous expreillon of two of them is called a conjonance or dijfonance, according as it produces a pleafant or unpleafantnbsp;A Angle firing may be made fucceflively

fhorter . Let the firing be llretched between the points A andnbsp;. � %. 4. Plate XIV. by the force of the weight P, andnbsp;the Weight of the firing itfelf be Nj and its length L.

let the firing be put in the pofition AF/i C B, and at tniddle point Cj let C S, a perpendicular be raifed, equalnbsp;� the radius of the curvature in C, and meeting the axisnbsp;^ ^ in D ; and taking a point p near to C, draw the per-P^rgt;dicular p f and the tangent pt.quot;

^ � Therefore it appears, as in Lemnia 2, that the abfolut� by which the particle pC is accelerated, is to thenbsp;�tce of the weight P, as r r to * t; that is, as � C to

Of Mufical Sounds.

fhorter and fhorcei-; according to the proportions the table; and thus a fingle firing may exprelsnbsp;the various mufical founds; but in this cafe, twOnbsp;founds cannot be expreffed at the fame time*

�To find the line a, let the abfcifs of the curve be z, and the ordinate E F = v, and the curvenbsp;AF � V, and CD = Then (by Cor. Probi !�)

X ~ ^ b'^ X k xquot;^ X nbsp;nbsp;nbsp;, �A

n/ a* nbsp;nbsp;nbsp;x^ � I x^ � � i'�' { b x^

centre C, and radius D C fig. 5- Plate Xl^' quadrant of a circle D P E being defcribed, and mahiflflnbsp;C Q_=: X, and eredling the perpendicular Q_P; then t

i.,r

�4 Whehc�-'

Of Mafic ai Sounds. nbsp;nbsp;nbsp;371

�n fome mftruments, as the forte-piano, harpfi-�^hord, amp;c. eath firing expreflcs a particular tone.

other inftruments, fuch as the violin, violoncello, amp;c. each firing is caufed to cxprefs feveral ^cnes fucceffively, by flopping part of it with the

^ � C D, in which cafe it is alfo y n quadrantal arch ^ �, and zCzADazfL; it will be 5 L =: 0 X

let D be the length, whofe periodical time is r, ~ X -^5 will be the periodical time of the

time

'^he Scale of Mufical Sounds^ or of the proportions^ Lengths of the Strings^ which emit thofe Soundt)nbsp;together with fheir Literal and Numericalnbsp;as alfo the Names of the Intervals between thein gt;nbsp;�where T ftands for Major Tone i t forNldSNnbsp;Tone ; cmd H for Hemi-Tone.

ing given, the time is v' N x L. And the firings made of the fame thread,.!� which cafe it is N asnbsp;time will be as L%�1

This table might be continued to any length, the law of continuation will appear from thenbsp;following paragraphs, which will be found to con-the neceflary explanations.

The fraflions denote the relation of each firing 1^�' Cone to the firll, or to the key, note. Thenbsp;^'^gth of the firft firing may be a foot, or a yard,nbsp;in Ihort of any other dimenfion; but then thenbsp;^cher firings mufl be made in due proportion tonbsp;length, which is called one or unity. For in-_ if the firfl firing be a yard long (viz. 3^nbsp;Z'^hes) then the next firing mufl be 32 inches innbsp;^^^gthj for 32 is equal to iths of 36. Thisnbsp;^'^^ftion likewife fliews, that the fecond firing per-nine vibrations, whilfl the firfl performsnbsp;vibrations. Alfo the length of the fourthnbsp;is marked I, meaning that it mult be three-^cths of the firft and it fliews, that this firing

performs four vibrations whilft the firft perforrfl� only three �, and fo of the reft.

The letters which are annexed to the fractions in the fecond column of the table, are the names by

which muficians diftinguifli the various tones; sn the numerical names of the third column,nbsp;the diftance of each tone from- the firft, whichnbsp;otherwife called the key-note, or principalnbsp;Thus the fifth firing is called G; it is a fifth abo''^nbsp;the firft, and its length is equal to two thirds of bquot;*�nbsp;firft; and fo forth.

Itnuift be remarked, that feven names, or letter^� are given to all the tones; viz. C,D,E,F,GjA^'b^nbsp;B to the firft feven; then the fame names or lettef^nbsp;are repeated in the fame order for the next feven,nbsp;might again be repeated for a thiid fet, a fourthnbsp;fet, amp;c.

By a clofer infpedlion, it may be perceived, the fradtions, which exprefs the lengths ofnbsp;firings, are quite different from each other fornbsp;firft feven notes only; but after that they cocr'^nbsp;the fame order ; excepting only that f^^

uticreafing progreffively; for they only fhew the Pittance of each, tone from the firft; thus c is faidnbsp;*0 be an o�iave to C j ^ is faid to be a melfth- tonbsp;amp;c.

It is therefore evident, that feven are the prin-tones of die mufical fcale. The next feven laid to be the craves of the firft; th� nextnbsp;^^ven to thofe are faid to be the douhle oElaves tonbsp;firft feven, amp;c. Therefore with refpeift to thenbsp;Peculiar nature of each tone, we need only examinenbsp;oiftave, viz. the firft fet of feven tones, togethernbsp;the firft tone of the next fet.

The fradions of the table exprefs the propor-'�^onal lengths of the firings with refped to the ^��ft; but if the length of each firing be comparednbsp;'¹'ith the firing next to it, then it will appear thatnbsp;intervals are not equal throughout the odave jnbsp;that there are three forts of interval. Thus Cnbsp;(always meaning the firing which expreffes C, andnbsp;fame of the reft) is to D as 9 to 8. D is to Enbsp;10 to 9 ¹. E is to F as 16 to 15. F is to Gnbsp;9 to 8. G is to A, as 10 to 9. A is to B asnbsp;9 t:o 8 j and laflly, B is to the C, next to it, as 16

In order to make the above-mentioned comparifon, the ^ tions muft be reduced to a common denominator; thennbsp;ratio of their numerators muft be expreffed in thenbsp;'QvVeft integral terms; thus | and | reduced to a commonnbsp;to

to 15. The intervals farther on are equal to the former, and come in the fame order.

By infpefting the preceding paragraph, it appear that thofe intervals are of three forts,nbsp;the interval of 9 to 8, the interval of 10 to 9,nbsp;the interval of 16 to 15. The firfl: of thofe intervals has been called a major tone; the fecond h^snbsp;been called a minor tone �, and the laft has been call^^nbsp;an hemitone¹.

The intervals which form an ofliave, are dd pofed in the following order, viz, major tonenbsp;minor tone, hemitone, major tone, minor tone�nbsp;major tone, and hemitone; which may be expredquot;^nbsp;by their initials, as in the fourth column ofnbsp;table in p. 37a, viz. T, t, H, T, t, T,nbsp;Whence it appears, that a fifth, or the interv^^nbsp;between C and G, contains two major tones, on-minor tone, and an hemitone j alfo a fourth, or thenbsp;interval between C and F, contains a major tone� ^nbsp;minor tone, and an hemitone, amp;c.

If it be afked why are the intervals difpofed the above-mentioned order, and why is C confiderednbsp;as the firft or fundamental note ? The anfwer 1��nbsp;that repeated experience has fhewn, that this ordernbsp;produces a pleafing mufical melody, and that thenbsp;is called the fundamental, or key-note, or the firft

The difference between a major and a minor tone, between | and which is the interval of 81 to 80,nbsp;been called a comma.

that order of intervals; becaufe the melody generally begins, and almoft always ends with thatnbsp;note j befides, the rules of compofition, and thenbsp;arrangement of the various periods of the melody,nbsp;always have a reference to that key-note.

In the table of page 372, there is, however, another tone, which may be taken for the principalnbsp;nr key note, and that is A ; but the intervals innbsp;oftave, from A to a, are in the following or-^^r, viz. T, H, T, t, H, T, t, which order differsnbsp;I'^'Orn the other, principally in its having the intervalnbsp;nl'the third, and the interval of the fixth, fmallernbsp;than in the other order; hence this order is callednbsp;the flat mood, or the key of A with a flat third;nbsp;'''hereas the other is called the Jharf mood, or thenbsp;hey of C with a fharp third.

Nature feems not to admit of any other order of intervals fit for mu fie; therefore, in the naturalnbsp;hcale, as expreffed in page 372, no other notenbsp;t^ay be taken for the principal or key-note; fonbsp;that no piece of mufic could be written in any othernbsp;hey befides C or A. But the ingenuity of mufi-'^lans has contrived to multiply the key notes, ornbsp;father to render every tone capable of being confi-tiered as the key note of a fharp as well as of a flatnbsp;friood ; and this obje�l has been accompliflied by

e interpofition of certain intermediate tones between thofe of the natural fcale, which are to be Ufed occafionally, and which have no particularnbsp;flame or letter; but derive their appellations from

the neighbouring principal notes ; thus a certain found, interpoied between C and D, is called eithernbsp;C diarp, or D flat: another interpofed 'betweennbsp;D and E, is called either D fliarp, or E flat i nnflnbsp;fo of the reft. It muft be remarl^ed, however, tnatnbsp;between E and F, as alfo between B and C, n�nbsp;other found -is interpofed, becaufe the intervals between thofe notes are already very final!, therenbsp;ing only an hemitone between each pair.

The nature and the ufe of thofe intermedia'^ founds, which are commonly called flats and fljard-gt;nbsp;will appear from the following example and explanation.

If, inftead of C, a perfon wifhed to make F the key note; then the proper order of intervals eithernbsp;for a flat, or for a fliarp mood, muft take its corn'nbsp;mencement from F.�Suppofe it be required to benbsp;a'fharp mood, in which cafe the intervals muft benbsp;T, t, ItI, T, /, T, H. Now, by obferving thenbsp;table in page jya, it will be found that there is,nbsp;it ought to be, a major tone between F and G, ^nbsp;minor tone betw�een G and A; but between A anftnbsp;B there is a major tone; whereas there fhould benbsp;an hemitone ; therefore in order to remedy th'�

B, nbsp;nbsp;nbsp;of fuch a length as may exprefs a proper fourthnbsp;to F ; and this intermediate found is called B

^hen F is to be reckoned the key note, we muft ^hen ufe B flat inftead of B natural.

After the fame' manner it may be eafily fliewn fhat when any o'quot; the ocher notes is taken for thenbsp;note, there needs be interpofed flats or fliarpsnbsp;^ftween fome of the other natural or primitivenbsp;bounds, amp;c.

In fliort, by the interpofition of one found be-^^Ween any two contiguous tones of the natural �ftave, except between E and F, as alfo betweennbsp;^ and C, the whole odtave is caufed to contain 12nbsp;intervals; and by this means every one of thofcnbsp;�2 founds may be taken for the key note of a (harpnbsp;a flat mood, and is called accordingly; for in-^'ance, the key of D with a fharp, or with a flat,nbsp;^hird'; the key of E with a fharp, or wnth a flat,nbsp;^^fird; the key �f P� flat, tvith a fliarp thiiquot;d, ornbsp;key of E flat, with a flat third ; and ib of thenbsp;i-efl.

Yet this difpofition of tones, both principal and ^'ttermediate, is attended with a remarkable imper-^^�ftion, which may be palliated, but cannot benbsp;Entirely removed. � The nature of this imper-I*^ftion will be flrewn in the fequel j but pr�-''^ioufly to it, fomething muft be faid with refpednbsp;*�0 die notation of the various mufical founds.

The whole range of -mufical founds, comprehending all thofe which may be exprefled by hu-tnan voices, as alfo by the mufical inftruments that moftly in ufe, confifls of about feven or eight

oflaves; yet muficians can exprefs every one tbofe Ibunds by placing certain fpots, marks, ofnbsp;notes, upon, and adjoining, five parallel lines;nbsp;in fad, mufic paper is ruled with fuch zones of P^quot;nbsp;rallel lines.

A mark or note, placed upon one of thofe lio^*� denotes a certain tone ; for inftance C, anbsp;placed in the fpace which is between that linenbsp;the next above, denotes the next note tonbsp;viz. D; a mark on the next line above, denotes Enbsp;and fo forth. The intermediate founds, ornbsp;fiats and (harps, are denoted by auxiliary niarks^nbsp;viz. denotes a fnarp, and lgt; denotes a flat; th^*^nbsp;prefixed to the note of D, means the fonr*^nbsp;intermediate between D and E �, and bnbsp;fixed to the note of E, means the fame founAnbsp;viz. the found intermediate between Dnbsp;E, amp;c.

'1 be form of the notes, viz. whether the maf^ is entirely black, or open like an o, or having ^nbsp;tail annexed to it, has nothing to do with re fpednbsp;to the particular found. That diverfity of tof^nbsp;rcidicates the duration only of the founds ; or whatnbsp;�S called the tirae^

By infpefiing any one of the zones in fig-Plate XIV. it will be perceived that, upon the ufi'ai five lines of mufic, no more than eleven differentnbsp;notes can be marked, viz. one upon each line, onenbsp;upon each of the four fpaces between thofe lines.

fh,

: amp;t prefenr, indeed, the notation is extended confiderably above and below the five lines, andnbsp;that by means of auxiliary little lines, as in fig. 7.nbsp;I'hate XIV. ; yet this laft-inent�oned method is bynbsp;tio means fufficient to exprefs the whole range ofnbsp;tttufical founds. Formerly, however, they ufednbsp;the eleven notes of fig. 6 *. Now, in ordernbsp;to eXprefs the higher or lower tones, the namesnbsp;�nd fignification of the notes are altered, and thisnbsp;�^teration is indicated by a certain mark, called cliffnbsp;''�hich is always placed at the beginning of a piecenbsp;tgt;f mufic, and likewife wherever die value of thenbsp;Ootes is required to be altered.

There are feven of thofe cliffs. (See fig. S, ^late XIV.) They are of three different forms,nbsp;of three different fignifications, viz. the firftnbsp;two are called cliffs of F, becaufe where they arenbsp;Placed, (viz. on the fourth line and on the third line)nbsp;there the note of F is fituated, and the other notesnbsp;above and below are named accordingly. Thenbsp;^ur cliff's of the fecond fpecies are called cliffs ofnbsp;becaufe where they are fituated, viz. upon fournbsp;the five lines, there the C is placed. Of the

The ancient matters of mufic reckoned a good voice fin ging, whether bafe, or tenor, or treble, amp;c. that whichnbsp;exprefs eleven good and pleafant tones. In fadl, verynbsp;feldom a finger can go higher or lower, without changingnbsp;the quality of his voice. Hence eleven principal marks werenbsp;^�ckoned fufficient for mufical notation.

third

third Species there is but one cliff, which is callc^^ the cliff of G, becaufe where that cliff is ficuateti�nbsp;viz. on the lecond line, there the note of ^d�nbsp;placed.�Thofe cliffs, befides the fpecific name-�nbsp;have each a peculiar appellation. The pecuh^quot;'nbsp;appellations of thofe cliffs, together with the natn^�nbsp;or fignifications of the notes in each cliff, are clearlynbsp;exhibited in fig. 6. Plate XIV. wherein the notes�nbsp;for brevity fake, are not carried on farther above otnbsp;below the eleven above-mentioned notes¹.�Sho'jl¹^nbsp;the reader be defirous of learning which note 0^nbsp;one cliff correfponds with a certain other note ofnbsp;the ocher cliffs, fig. 9. Plate XIV. willnbsp;him the required information ; for in that figure�nbsp;a note is placed affer every one of the feven cliffy�nbsp;and every one of thofe notes indicates the fairrenbsp;found precifelyj namely, the C, which is expreffe^^nbsp;by placing the cifird finger upon the fourth or largednbsp;firing of a violin.

Hitherto we have only mentioned the depend' ance, or rather the ratio that one found bears tonbsp;another 5 fo that when one found is given, its fifth)nbsp;or third, or o�lave, amp;c. may be eafily found 5 hotnbsp;,jt will be neceffary to define or determine the firff�nbsp;or any one of them, fince from one bei'no- known�nbsp;all the others may be derived. The conveniencynbsp;cf fingers has effabllflisd a certain ftandard, which

At prefent, however, the baritone cliff, and the hal^ fopocano cliff, are feldom, if ever, ufed.

Of Mufical Sounds. adopted by moft muGdans in this country j is ufed innbsp;�Concerts, as allo at the opera houfe, play houfes, amp;c.

is called concert pitch �, and this found is ex-P'^effed by a Gnall inftrumenC,which is conveyed from place to place by thofe perfons who tune organs,nbsp;I�afpfichords, amp;c. It is a fteel inflrument, whichnbsp;^lien ftruck founds a certain note. See Gg. 11. Platenbsp;or elfe a little fort of flute, which founds thatnbsp;P^ftain note. .T\\o(q tuning forks, 'ox tuning pipes,nbsp;(fcr fo they are called) are tuned all alike, after anbsp;1^�^ttern one, which is kept in referveby the makers;nbsp;indeed, notwithftanding the wear and,alterationnbsp;heat and cold, thofe tuning forks are in generalnbsp;Ptetty much of the fame pitch. According to thatnbsp;P^quot;Ch, the C, which follows the cliffs in fig. 9. per-^'^rrns about 513 vibrations in one found.

Fig. 12. of Plate XIV. exhibits in one view all particulars which may be of ufe with refped tonbsp;octave of tones, hemitones, amp;c. ' It confifts ofnbsp;^ horizontal rows. The firfl; row contains the 13nbsp;*^otes of an oftave exprelfed in the bafe cliff. Thenbsp;Ihcond row fnews the ratio of the ftring which ex-P�'ffles each found, with refped to the firft. Thenbsp;third row expreffes the lengths of the variousnbsp;brings, (which mutt be equal in all other re-Ppefts) la numbers of equal parts, of which 3600nbsp;equal to the length of the firft ftring. Tltenbsp;fourth row expreffes the adual number of vibra-tgt;ons performed in one fecond by each found, ac

3 3 -}� nbsp;nbsp;nbsp;Qf Muficul Sounds.

cordiiig to the concert pitch *. The fifth row (i�h' tains the literal names; and the fixth row contain*nbsp;the numerical names of the founds, when C i*nbsp;firft, or key, note*

Hitherto we have only fpoken of the fuccelfio'^ of founds, and have aiTerted that the founds onlfnbsp;the fcaie, wJjich is ftated in page 372, can furnish ^

duced by calculation, according to the rule in page 3*^ wherein the refiftance of the air is not noticed} hencenbsp;probably are a little higher than the truth.

For this purpofe a brafs harpfichord ftring Was like a pendulum, with a weight of 5 lb. and 14 ouncesnbsp;4t 125 grains) at its extremity. The length of the ftrii^Snbsp;Was 62 inches, its weight was 22,25 grains. Its fouf*^^nbsp;according to the concert pitch, was eXaiStly A, viz-o�lave below the A, in fig. j2. By calculation,nbsp;thofe data, it was determined to perform 107 vibrationsnbsp;one fecond.

Heat and cold have a eonfiderable influence on the of all fonorous bodies, which arifes from their beingnbsp;panded or contra�fed in their dirrtenfions, alfo from an alter�'nbsp;tion of their elafticity. A fte�l tuning-fork, heated to th�nbsp;degree of boiling water, will found a note about a hemito*��nbsp;lower than it will when cooled to the decree of freezifSnbsp;water. The pitch of an organ pipe will be higher in fuf^'nbsp;mer than in winter ; for in that pipe it is the columrt ofnbsp;that vibrates ; and in the winter time that column of airnbsp;denfer, heavier, and of courfe vibrates flower, than 'knbsp;fammer. See Smith�s Harmonics, Sedl. IX. Schol-Prop. XVIII.

�'^eafing melody, or rather the moft pleafing melody. But it is neceflary to obferve, that the pro-priety of fuch founds is fhewn likewife by the ^Steement, or pleafing effeft, which arifes fromnbsp;*^^rtain two or more of them being exprefled at thenbsp;^�tne time; and it is remarkable that the like pleaf-effed: cannot be produced by any other fcalc'nbsp;founds. .

When two fonorous bodies, that exprefs the� note precifely (in which cafe they are faid tonbsp;in unijon) are founding at the fame time; thenbsp;Agreement is fo great, that we can feldom perceivenbsp;^�hether it be one found or two. The next bed:nbsp;Agreement is when any note, and its odave, arenbsp;^�unded at the fame time. Next to this is that ofnbsp;note and Its fifth; then that of any note andnbsp;third (harp, and then that of any note and itsnbsp;^^itd flat, or its fixth, either flat or lharp.

perfect accord is that which arifes from four ttotes exprelTed at the fame time, viz. any note, itsnbsp;^^ird (harp, its fifth, and its odave. The othernbsp;^'^cords are imperfe5t} and fome of them are verynbsp;difagreeable j yet with certain reftridions fome ofnbsp;are not only tolerable, but may be intro-^^ced with confiderable effed.

'The rules of mufical compofition, which dired proper arrangement of accords, and likewifenbsp;the neceffary limitations or management of thenbsp;*^elody, have been deduced from long and diversified experience. Upon the whole, they are rathernbsp;II*nbsp;nbsp;nbsp;nbsp;0 cnbsp;nbsp;nbsp;nbsp;intricate

intricate and numerous j buc noxwithftanding theif 'multiplicity� the various cafes and combinationsnbsp;of muficai founds are far from being all reduced�nbsp;and feem not to be all reducible, to certain and determinate rules. In mufical compofition, anbsp;. deal muft depend upon the genius of the compo^^^'nbsp;and this genius, or natural difpolition, to invenlgt;nbsp;pleafing melodies, and plcafing harmony, is wha^nbsp;principally diftinguilhes one compofer from another*nbsp;It isquot; the gift of nature j it may be guided, butnbsp;given, by art.

It has been faid above, that the difpolition of tones and hemi-tones, fucK as is exhibitednbsp;fig. 12. Plate XIV. is attended with a remarkabi^nbsp;imperfedlion, which may be palliated, but ca.n^�^nbsp;be entirely removed.�The nature of thisnbsp;feftion will be eafily manifefted by means of ^nbsp;example.

. The proportional, as well as the proper lengd�� of the firings, which exprefs the ad, jd, 4th,

Sic. of C; viz. when C is taken for the key are exprefled in fig. la. But fuppofe it be sC'nbsp;q.uircd to make, not C, but D, the key note; thennbsp;A, which was the fixth of C, does now becort��nbsp;the 5th of the key note Dj and therefore its leog^

2i3gt;33, amp;c.) i therefore the A in the

^Hich is a proper fixth to C, is an imperfefb 5th to ^ j nor can this deficiency be fupplied by the inter-Pofition of another firing between A and A fbarp ;nbsp;^ecaufe that other firing, though a perfedl fifth tonbsp;would be an imperfeft fourth, when E is takennbsp;the key note, or it would be an improper 3d,nbsp;�When F is taken for the key note, amp;c. And if fonbsp;^any firings were interpofed between A and Anbsp;^arp, as to fupply all thofe deficiencies, the com-PHcation and multiplicity of founds would benbsp;^ndlefs j for what has been faid of A may, with,nbsp;^qual propriety, be faid of every other found of thenbsp;'^ftave.

The only expedient which is at prefent pra�lifed the purpofe of palliating the above-mentionednbsp;fitiperfedlion, is to tune the A not fo high, or tonbsp;^ake the length of that firing not fo long as 2160nbsp;P^tts, nor fo fhort as 213353, by which means thatnbsp;is rendered an imperfect fixth to C, and an im~nbsp;P^tfedl fifth to D } or the imperfecition is divided,nbsp;''^hich renders it tolerable in both cafes, other-it would be very pleafant in one cafe, but intolerable in the other. The fame thing is^donenbsp;'''ith refpedt 'to all the other founds of the ocflave;nbsp;^12. they are made to deviate a little from thofe pro-pitches, or from the lengths, which are expreflednbsp;fig. 12. for the purpofe of rendering them tolera-^ when one note or another is taken for the key

This deviation from the proper lengths, or the proper pitches, is called the temperamentnbsp;c c anbsp;nbsp;nbsp;nbsp;of

(f muftcal inJirumeniSy or of the tnuftcal fcale; and Is ufcd in tuning ail chofe inftruments which havenbsp;fixed notes, as the harpfichord, organ, amp;c. Andnbsp;even with other inftruments, and with the voice mnbsp;finging, a certain temperament is ufed, both ftoi�*nbsp;imitation and from neceffity*.

It muft be obferved, with refpefb to this tempei^' ment, that if the imperfeftions be divided equally^nbsp;viz. in fuch a manner as to render the effeftnbsp;fame, whether one or another of the i a foundsnbsp;the oftave be confidered as the key note; then that-effedt would not be pleafant; therefore the pradti^�nbsp;is to divide the imperfeftions, but to dividenbsp;unequally, viz. fo as to render the fecond,. third�nbsp;fourth, fifth, amp;c. of fome key notes, in which rtiO^nbsp;pieces of mufic are written, lefs imperfedt thannbsp;others.

An equal temperament, therefore, is impradii' cable; and it is impoffible to fix the limits ofnbsp;unequal one, or fuch as may be commonly uftd �nbsp;for almoft every tuner of inftruments ufes a tern'nbsp;perament a little different from the reft, of whit^^nbsp;he judges by his hearing only; and fome capit^jnbsp;performers fometimes have their inftruments tnn^^nbsp;with a peculiar temperament, for the putpo^h �

Cf Muftca� SoundS� nbsp;nbsp;nbsp;3^9

We �iallj laftly, conclude this long chapter with ^Ome remarks concerning the effefts which are at-^�'ibuted to mufical founds. Of thofe effedts there

fome which arc true and acknowledged; whilft ^'^hers are lefs confpiaious, or doubtful, and per-abfolutely chimerical.

Single founds, or a fucceffion of founds, are pleasant cr unpleafant in various degrees. The fingle Sounds, in order to be pleafant, muft: be uniform,nbsp;**^ither too loud nor too foft, and muft be as fimplcnbsp;^ poffible. A regular fwell and decay in thenbsp;^�quot;ength of the ibund is pkaftng in certain cafes;

The various tones of a natural voice, or of an ^^ftrument, ftiould be of one quality j whereas theynbsp;S�'equently feem to belong to different voices, or tpnbsp;^'fferent inftruments f.

^^'6, which were tuned by one of the beft piano-forte *^�kers in town, according to his temperament j but onnbsp;�*^paring them with inftruments recently tuned hy othernbsp;^^flbns, I �nd that they very feldom, if ever, agree perfe�ly

ftrlngs of piano-fortes, harpfichords, Stc. were all of the fame thickhefs, could not conveniently benbsp;^ of the proper lengths ; therefore, by making them ofnbsp;c c 3nbsp;nbsp;nbsp;nbsp;different

It is impoffible to fay,whence arlfes the pleafufc which is communicated by certain fucceOlons o�nbsp;founds. There are certain periods in mufical w�'nbsp;lody which excite peculiar fenfations more or lei�nbsp;pleafing, ' and produce different fenfations of plea*nbsp;fure or difpleafure, upon different perfons. Thofcnbsp;fenfations cannot be exprefled or defined.

The agreement or difagreement of two or tnos^ founds, exprefled at the fame time, feems, uponnbsp;the whole, to arife from the more or lefs frequentnbsp;coincidence of the vibrations. Thus any tone antinbsp;its odtave, agree better than the fame tone andnbsp;fifth, the latter better than the fame tone and itsnbsp;third, amp;c. viz, the compound found is fmoothet�nbsp;and approaches nearer to the nature of a fing^�nbsp;found in the firft cafe; lefs in the fecond j flnll 1^1�nbsp;;n the third, amp;c. And in fadt, in the firft cafsnbsp;there is a coincidence of Vibrations at every fecondnbsp;vibration of the grave tone; the coincidence is notnbsp;fo frequent in' the fecond cafe; ftill lefs in the third�nbsp;and fo on ; yet the more or lefs pleafant or unple^'

different fizes, and by ftretching them differently, lengths are fuited to the commodious llze of the inftri*'nbsp;ment. Now the great objedt in adjufting the fizesnbsp;lengths of Arch firing?, is to contrive that each firingnbsp;lltetched by a force proportionate to its thicknefs and length�nbsp;othervvife the inftrument will not have a uniform voice**^nbsp;Few makers of fuch inflruments pay fufheient attention W ;nbsp;fhis particular,nbsp;nbsp;nbsp;nbsp;^

^3nt effeft, eannot arife entirely from that more or frequent coincidence; for (befides other reafonsnbsp;^hich, to avoid prolixity, fl-iall not be mentionednbsp;in the firfl; place, a fuccelBon of thirds or ofnbsp;fixths is much more pleafant to the ear than a fuo-^eflion of fifths; and, in the fecond place, the in-troduftion of a difcord in certain accords, is notnbsp;tolerable, but very pkafing. The cafes innbsp;'''hich difcords may be introduced, have been foundnbsp;experience, and are fpecified amongft the prac-btal rules of mufical compofition, which do not be-to this treatife.nbsp;nbsp;nbsp;nbsp;;

It has been faid above, that feldonn, if ever, a ^^unding body exprefles a fingle found; and thatnbsp;^^ch founding bodies are ufed in mufic as exprefsnbsp;fimpleft; founds. But even amongft thofe,nbsp;fingula'r produdions of fecondary founds havenbsp;remarked, and the principal fads are asnbsp;follows:

If a large firing of a mufical inftrument be ^�tinded, or, in Ihort, if a pretty deep and rathernbsp;^fong found be continued for a little time, therenbsp;be heard at the fame time two other founds;nbsp;^3rnely, the i2.th and the 17th of the originalnbsp;^^ond. For inftance, if the loweft C in the bafenbsp;be founded, you will hear the fecond G andnbsp;third K of the fcale above.

It Was difcovered by Tartini, at Ancona, in the ^7*3� that if of the three notes which form

jnftance C, E, and G j or G, B, and D, amp;c.) t'''� be founded at the fame time, a third found will benbsp;heard, viz. a fundamental note *.

The various cafes of this fort are fliewn fig. lo. Plate XIV, where the open notes atenbsp;thofe which muft be founded (and here it is to benbsp;obferved, that they muft be founded perfe�ft,nbsp;without temperament), and the black note isnbsp;found which is heard. The firft cafe is evident!/nbsp;the reverfe of that which is mentioned in thenbsp;paragraph laft but one. In the laft cafe, the no*^�nbsp;which is heard is in unifon with one of tholenbsp;which is founded j but it may be diftinguiihed b/nbsp;its being a found of different quality.

The true reafon of thofe phenomena is fO^ ^ known; nor lhall 1 detain my reader with an/nbsp;account of the infufficient hypothefes that haV�nbsp;been offered for their explanation. Certainnbsp;feems, that the third found is not produced by thenbsp;undefigned communication of the vibrations tonbsp;fome other ftring or pipe of the inftrument j 1^**nbsp;if you take a violin, and found at the fame tioaenbsp;C on the largeft firing, and A on the next, yet*nbsp;will alfo hear an F, which is a i2th below thenbsp;C, and which cannot be expreffed upon any ftt�^c�nbsp;of the violin; G being the loweft note of that lO*nbsp;ftrument.

largifh fort of fpider, called tarantula. At tain periods of the year the perfon that has beef*nbsp;once fo bit, alferts to feel a pain about thenbsp;bit, which is accompanied with dejeftion of fp*'nbsp;rits, failownefs, amp;c. If fprightly mufic be play^^nbsp;(and a certain jig, called the tarantella, is generallynbsp;played on fuch occaiions) the patient gets up,nbsp;begins to dance with irregular geftures j the quick'nbsp;nefs of his movements generally increafes to a cet'nbsp;tain degree; and the dance continues fometiiT^^^nbsp;without intermiffion for hours. At laft the paficn*-�nbsp;fatigued and exhaufted, throws himfelf dpwn onnbsp;floor, or on a chair, or a bed, amp;c. to recruitnbsp;ftrength; and the fit is over for that time.�nbsp;remarkable part of the ftory is, that thisnbsp;tion of dancing, amp;c. cannot bp done withf^*'nbsp;mufic.

In the firft place, it is very doubtful whether ^ider is at all poifonous, or whether it has a*;nbsp;fhare at all in tfie produdion of the pretend^nbsp;illnefs.nbsp;nbsp;nbsp;nbsp;_ j

The diforder, probably a nervous or hyftct*^*^ affedion, may arife from other caufe.s, efpct:�^ /nbsp;in a pretty warm climate.' And the violent agnbsp;tation of the patient, accompanied with perfp�^^nbsp;tion. See. may, very likely, relieve him or her tnbsp;the tarantula bites women as well as men).

i 39^ 1

A GENERAL VIEW OF THE PRINCIPAL USES THE ATMOSPHERE; WHEREIN THE NATUREnbsp;RAIN AND EVAPORATION WILL BE NOTICED*

TH E aerial fluid, which furrounds earth, and whatever exifts thereon, isnbsp;noticed by the vulgar, amongfl: whom thenbsp;air and nothing are almoft fynonimous; it isnbsp;fidered as a fuperfluous appendage by the fupcf^nbsp;cial obferver; but the deepefl: refearches ofnbsp;moft enlightened philofophers, acknowledgenbsp;infinite wifdom of nature, in the creation of anbsp;moft indifpenfably neceffary for the maintenance ^nbsp;animal and vegetable lifej for the difperfioD ^nbsp;lightj for the communication of found} fornbsp;abforption of water from certain places, andnbsp;difperfion of the fame fluid over other pl^^-cs gt;nbsp;for giving motion to a variety of ufefulnbsp;chines, amp;c.

There is not one of the properties of the air, oor one of its movements, however trifling or irregol^*quot;nbsp;may at firft fight appear, which, when duly coonbsp;dered, will be found to be ufelefs or defe'ftquot;'^^'nbsp;Were the air either lighter or heavier} had

Poflefs, were its other properties at all altered, the ^tganifm of the terraqueous globe would be de-^ged, and perhaps utterly deftroyed.

The fame incomprehenfible wlfdom that has ^��tanged all the parts of the univerlal frame innbsp;due weights and proportions, may undoubtedly fitnbsp;to a different fort of atmofphere by a fuitablenbsp;^^'^eration of the whole ftate of things; but our verynbsp;W\ted comprehenfion, not being able to conceivenbsp;^ow fuch an alteration could be made for thenbsp;^^ter, only finds ample reafon for fatisfaftion, ad-*^gt;ration, and wonder, in the inveftigation of thenbsp;t^operties of the exifting atmofphere.

After having admired the general order, and the Ptovidentlal wifdom of nature, it will be neceflarynbsp;^ examine, with patient toil, what more immedi-�^^ly concerns us, viz. the particular ufes of thenbsp;^ofphere, at leaft as far as may be inferred innbsp;'^is place j for we muft neceffarily referve the cheinbsp;*^ical properties of air, and its connexion withnbsp;heat, and eledricity, for the fubfequent partsnbsp;this work.

is in confequence of the weight and elafticity the air, that animals refpire with freedom, andnbsp;that the operations of fucking, pumping, amp;c. are

Performed.

The thoraxj or that part of the human body ^hich is lurrounded by the fpine or back bone,nbsp;ribs, the fternum or breaft bone, and the dia-^hragnn, is almoft entirely occupied by the lungs,

'which confifl: of an immenfe number of veficle^^ whofe cavities communicate with certainnbsp;and thofe dufts, with others of a largernbsp;which at laft communicate with a large onCgt;nbsp;called the mnd pipe, the aperture of which is ^nbsp;the mouth, at the back or root of the tongue�nbsp;The air, unlefs we keep both the mouth andnbsp;noftrils clofed, communicates with the infide fu'''nbsp;face of the lungs �, that is, of its innumerable vC'nbsp;ficles, and with the outfide of the thorax or chef^'nbsp;If we enlarge the cheft, the weight of the at'nbsp;mofphere drives a quantity of air in our lung*�nbsp;which is called an injpiration; and if we contr�*^nbsp;our cheft, a quantity of air is expelled from !*��nbsp;which is called an expiration.

The enlargement of the cheft is occafioned by elevation of the ribs, by a fmall motion ofnbsp;fternum, and by a fuitable movement of thenbsp;phragm j but the aftion of each part cannot b�nbsp;underftood without a particular anatomical defcr'Pnbsp;tion, which does not belong to this treatife. jnbsp;The freedom of refpiration in a found anim^nbsp;body, depends on the equal preffure of the atm�nbsp;fphere, both on the infide furface of the lung-�nbsp;and on the outfide of the body. In faift, tfnbsp;keep both mouth and noftrils accurately doled,nbsp;can neither contra�t nor expand our cheft}nbsp;cepting, indeed, in a fmall degree j for thenbsp;tity of air which always remains within the

A man ufually performs about twelve infpira-^'ohs, and as many expirations in a minute j but *'^fpiration may be quickened by various caufes, asnbsp;agitation of the body or mind, by heat, by a rare-fied or vitiated atmofpjiere, and by difeafes. Infantsnbsp;^'�eathe quicker.

In general, a full grown perfon takes in between ^0 and 30 cubic inches of air at every infpiration,nbsp;�fid expels about the fame quantity at every expi-*^^don, but a great deal of air does always remainnbsp;the lungs. In a forced or violent infpiration ornbsp;^^piration, a double quantity of air, viz. about 50nbsp;^�abic inches of air, may be taken in or expelled,nbsp;5nd even then a eonfiderable quantity of air regains in the lungs, befides what is contained innbsp;mouth, wind pipe, amp;c. for the capacity of thenbsp;of a man, may at a mean be reckoned equal-about two cubic feet.

The operation of fucking, in general, confifts in ^^l�ioving the preffure of the atmofphere from anbsp;^^�quot;tain part of the furface of a fluid, whilft thatnbsp;PtefTure is at liberty to a�t on fome other part ofnbsp;furface of the fame fluid, in confe juence ofnbsp;^bich the fluid is forced to afeend where the preffurenbsp;been removed or diminifhed.

If a man apply his mouth to the aperture of a �^tle full of liquor, and ftanding flraight up, henbsp;^'11 not be able to . fuck any liquor out of it �, but

if a hole be opened at the bottom of the bottle, that bottle be fet in a bafon full of liquor, then thenbsp;liquor may be fucked out of it. And the fant�nbsp;cffeft will take place if an open tube be fet withnbsp;one end in water, and a man apply his mouth t^nbsp;the other end, and fucks. The mechanical partnbsp;the operation is as follows;�By enlarging hi�nbsp;cheft, the man rarefies the air, and, of courfe�nbsp;diminifhes its prefiure on the liquor, which is ii^'nbsp;mediately under the tube; in confequence of whichnbsp;the prelTure of the atmofphere on the furface of th�nbsp;furrounding liquor, forces the liquor to afcen*^nbsp;into the tube. (See the experiment, which isnbsp;fcribed in page 105.)

In the operation of fucking, after the manu^*' of children, the rarefaftion is produced in the fut�nbsp;part of the mouth ; viz. the tongue is applied ihnbsp;as to fill up the Ipace between the lips and th^nbsp;nipple, or pipe which conveys the milk or othciquot;nbsp;liquor; then the tongue is drawn backwards, whh^nbsp;the lips are laterally preffed againft it, by whichnbsp;means a little vacuum is formed before it, and th^nbsp;liquor is forced into that vacuum by the preffutc 0nbsp;the atmofphere upon its external furface, or upc^nbsp;the furface of the bag which contains it.

If an empty veffel, having one aperture, be plied with its aperture to the lips, and the abo^cnbsp;mentioned operation of fucking be performed,nbsp;veffel, if not too heavy, will remaio attached to th^nbsp;lipsi and that for the fame reafon.

It is for the fame rcafon, that fnails remain attached to folids, that limpets adhere very firmly tp ^ocksj that the fea polypus holds with great forcenbsp;'''hatevcr it fattens its claws to, and that fome in-^^fts fufpend themfelves to folids; for though notnbsp;Performed with the mouth, the principle of thenbsp;operation is exattly the fame, viz. a foft membranenbsp;applied to the Yolid, then the middle part ofnbsp;t^at furface is withdrawn a little way, fo as to formnbsp;^ Vacuum, or at lead a rarefacttion of the air be-^'veen the centre of the foft membrane and the folid,nbsp;confequence of which the parts of the membranenbsp;'''bich furround that fpot, are by the gravity of thenbsp;^�^niofphere prefled againtt the folid, and the latternbsp;prefied againtt the former j hence the adhefionnbsp;*akes place.

Leather fuckers, which adt prcclfely upon the IbiTie principle, aro not unfrequently feen in thenbsp;^tids of boys about the ftreets of London. Anbsp;Circular piece of thick leather, about two inches innbsp;^'^nneter, has a firing, fattened to its centre. Thenbsp;Lather being previoufly well foaked in water, isnbsp;applied flat and clofe to the fmooth furface of anbsp;Lone. The interpofition of a little water promotesnbsp;adhefion. Then the boy pulls up the ttring,nbsp;the done, if not too heavy, comes up adheringnbsp;the leather. ?

Y be claws of the polypus are furniflred with a ^cat many fuckers of the like nature. The limpetnbsp;^trris one fucker of its whole body, and the famenbsp;11,nbsp;nbsp;nbsp;nbsp;D Dnbsp;nbsp;nbsp;nbsp;thing,

thing, with little variation, is done by various otbei* animals, efpecially of the infedt tribe.

The a�lion of the glafs cup, which is made to adhere to the flefli, for the purpofe of bleeding,nbsp;pends upon the lame principle ; excepting that thenbsp;air, within the glafs cup, is rarefied by means ofnbsp;heat, or by means of a fmall exhaufting engine.

It is hardly needful to add, that the limpet cooh^ not adhere to the rock, nor could the leather fucketnbsp;aft, or, in Ihort, that none of thofe fucking opet^'nbsp;tions could take place, in vacuo.

The principal advantage which is derived froit^ the vibratory movement of the air, is the prop^'nbsp;gation of found, which could not be accomplh^^^nbsp;by other means; for though founds are convey^^nbsp;by feveral other bodies better than by air �, y^*^

fur-

rounding the whole earth, and whatever exifts it, is always ready to convey founds of any for^^�nbsp;jn every direftion.

t^fOGeffes; on the other hand it is purihed by vegetation in certain circumftances, by agitation arnongft aqueous particles, and probably by othernbsp;^eans. Now it is owing to the winds that the impure portions of the atmofphere are mixed withnbsp;^he more purified parts of it; and that a propernbsp;�^ean is preferved. The winds likewife drive awaynbsp;Vapours, clouds, fogs, and rnifts, from thofe partsnbsp;which they are copioufly formed, to others whichnbsp;^��e in want of moifture; and thus the whole furfacenbsp;the w�ofld is fupplied with water. But it will benbsp;^eceflary to take a more particular notice of whatnbsp;^^lates to evaporation and rain.

When water is left expofed to the ambient air, ^he quantity of it will be gradually diminilhed, andnbsp;^fter a certain time, the whole of it will difappear.nbsp;'I^he water in this operation is reduced into an elaf-

If a fmall drop of water be placed in a large glafs, bottle full of pretty dry air, the drop of water willnbsp;difappear after a certain time, efpccially if the bottlenbsp;placed in a warm place. And if afterwards thenbsp;bottle be cooled, the water will thereby be fe-P^rated from the air, and may be feen adhering tonbsp;inlide furface of the bottle.

Heat promotes, and cold retards, evaporation j ^ut even a piece of ice has been found to evaporate,nbsp;i'ud tobediminlflied in weight, whilft the atmofpherenbsp;^ffually in a freezing ftate.

If a quantity of water be placed in vacuo, viz-be placed under the receiver of an air pump, in common temperature of the atmofphere, andnbsp;air be CKhaufted, a very fmall portion of the watefnbsp;will expand itfelf through the receiver, after wbic^nbsp;the quantity of water will remain unaltered. ^nbsp;the pumping be continued, the water will be dinquot;quot;'nbsp;nifhed a little more j for as part of the fleam isnbsp;trailed from the receiver, a little more fleam isnbsp;parated fi'om the water; but, upon the whole,nbsp;water will by this means be diminifhed in quant'�^^nbsp;very little indeed. On re-admitting the airnbsp;the receiver, the above-mentioned vapour is ags'*^nbsp;condenfed almofl entirely into water.�Heatnbsp;motes the evaporation in vacuo.

� �ch\c

Water then may exifl in airj ill, in an invi�^ flate, which is the cafe when the diffolvingnbsp;of air is confiderable j 2dly, in a flate of incipi^'�*�nbsp;reparation, in which cafe it forms clouds,nbsp;fogs; 3dly, and lallly, in a flate of a�lual fep^'quot;�nbsp;tion, in which cafe it forms either rain, properly 1*^nbsp;called, orfnow, or ha�.

Clouds are thofe well known aflemblages of pours that float in the atmofphere; have diffc��^'^*'nbsp;degrees of opacity, which arifes from their exteo^nbsp;and denfity j and generally have pretty well definenbsp;boundaries'. Their height above the lurface ofnbsp;earth (I mean not above the mountains)' is varioo^

�fi hot weather, or hot climates, the clouds, being more �quot;^refied, are lighter, and afeend much higher thannbsp;they do in colder climates, or colder weather: andnbsp;indeed, in cold weather the clouds frequently touchnbsp;the very furface of the earth ; for a fog may withnbsp;propriety be called a cloud clofe to the ground.

A mi/1 is a very indefinite word. It means an tftcipient formation of clouds, or hazinefs; and itnbsp;tiften denotes a very fmall rain, or a depofition ofnbsp;'''^ter in particles fo fmall as not to be vifiblenbsp;fingly.

The /now is formed when the atmofphere is fo ^�ld as to freeze the particles of rain as foon as theynbsp;^'quot;0 formed, and the adherence of feveral of thofenbsp;Particles to each other, which meet and cling tonbsp;^^ch other as they defeend through the air, formsnbsp;^he ufual fleeces of fnow, which are larger, (fincenbsp;they are longer in defeending, and have a greaternbsp;'Opportunity of meeting) when the clouds are highernbsp;than when they are lower.

The hail differs from fnow in its confifting or 'OotJch more folid, and much more defined pieces 01nbsp;'^'ongealed w'ater. It is fuppofed that the water, al-teady formed into confiderable drops, is driven andnbsp;t^^tained a confiderable time through a cold regionnbsp;the atmofphere, by the wind, which almoflnbsp;always accompanies a fall of hail. But thenbsp;globes of ice, or hail-Jlonesy in a fall of hail,nbsp;^^^ftietimes far exceed the ufual lize of the drops

of rain¹; which fhews that by the action of the wind, the congealed particles muft be forced tonbsp;adhere to each other j and, in faff, though thenbsp;fmall hail-ftones are more uniformly folid andnbsp;bular, the large ones almoft always confift of ^nbsp;harder nucleus, which is- furroundeci by a fofter fu^'nbsp;fiance, and fometimes by various diftinfl piecesnbsp;ice, juft agglutinated. Their fhape is feldomnbsp;fedlly globular.

If a veflel of an uniform ihape, and full of water� be expofed to the ambient air, and the decreafenbsp;water in it be meafured at the end of every daygt;nbsp;month, or year, or, in fhort, of any given periot^�nbsp;the evaporation which has taken place through th^¹quot;nbsp;period may be afeertained �, and it is generallynbsp;prefled by the number of inches and tenths: tho^�nbsp;if it be faid that the evaporation of a certain pondnbsp;one month be lo inches, the meaning is, thatnbsp;inches depth of water are evaporated in one month gt;nbsp;or, that if the water which has been evaporatednbsp;it in one month might be colleded and placed iit ^

Accounts of hail-ftones of a very large fize may j with in almoft all the works of natural philofophy, innbsp;periodical works, in accounts of voyages, amp;c. I have he� ^nbsp;affured by creditable eye-witnefles, that in the iflan^nbsp;Sicily hail-ftones have fometimes meafured more than tnbsp;inches in circumference. IDr. Halley gives an account^^^nbsp;hail-ftones that weighed 5 ounces each. It is np ^nbsp;then that falls of hail fometimes demolifh glafles, kill fe''�¹'nbsp;animals, and deftroy fruit, grain, amp;c.

with ftraight up fides, and having an horizontal lurface equal to the furface of the pond, the colledtednbsp;'vater would fill 10 inches depth of that veffel.

If a veffel for meafuring the evaporarion be left expofed, the furface of the water will defcend anbsp;^onfiderable way below the edge of it, in which cafe

fubfequent evaporation would be retarded. This indeed might be remedied by the addition of certainnbsp;'IHantities of water at ftated times ; but there is an-^ther inconvenience attending it, which is, that in-duff, amp;c. fall jn it, and thicken or cover thenbsp;'''ater. Therefore, the beft way is to note the evaporation either every day, or whenever it may benbsp;'Convenient, but to clean the veffel, and to changenbsp;'^0 water in it at Ihort intervals j for inftance, oncenbsp;^ iveek at lead. A veffel fit for fuch purpofe oughtnbsp;fo have an aperture not lefs than 8 or 10 inches innbsp;'diameter.

I'he quantity of evaporation from the furface of ��le fea or of the land, has been eftimated in certainnbsp;P^^ces only by a few fcientific perfons j but theirnbsp;^ftimates are feldom to be depended upon. Ge-^^ral dedudions, for extenfive trads, from partial,nbsp;^Oiall, and fometimes equivocal, experiments, can-Pot afford much fatisfadion, efpecially when thenbsp;^efolts of the experiments difagree from eachnbsp;Other.

The quantity of evaporation is various in dif-^^I'ent fpots. The furface of water furnifties upon whole the greateft quantity of vapour j thenbsp;D D 4nbsp;nbsp;nbsp;nbsp;land

land more or lefs, according as it is marfliy of rocky, or covered with vegetation, amp;c.

In hot climates, the evaporation is incompar^^^^ greater than in thofe which are colder. The e''�'nbsp;poration from places that are much expofed to thenbsp;wind and the fun, is likewife greater thannbsp;other places.

It was obferved in London, by Dr. Halley, that the evaporation of water, fituated in a room, outnbsp;the influence of the fun and of the wind, amounted?nbsp;in one year, to 8 inches. It was his opinion alfh?nbsp;that by the influence of the wind, the quantitynbsp;evaporation would have been trebled, and that th'^nbsp;again would have been doubled by the influence onbsp;the fun. Upon the whole, he reckons the anflU^^nbsp;quantity of evaporation for London, at 48 inchesnbsp;��Probably too great.

Dr. Hales eftimates the annual evaporation the furface of the earth only in England at 6,6 ^nbsp;inches f.'

Dr. Dobfon deduced from a mean of accurst� experiments made by hirnfejf during four yeat^�^nbsp;that the annual evaporation from the furface ^nbsp;water at Liverpool, amounts to 36,78 inches �

It has been calculated, that in one fummer�s about 5280 millions of tuns of water, are pro-Igt;ably evaporated from the furface of the Mediterra-��can*. It has alfo been calculated (omitting thenbsp;S^eat uncertainty to which fuch calculations are lia-that all the rivers, or at lead the nine principalnbsp;divers, which difcharge their waters into the Mediterranean, do not furnidr more than 1827 fnillions

tuns of water per day f. The deficiency is un-�loubtedly fupplied by the rain, which falls upon the fame fea, and by the current which is con-ft^ntly running from the Atlantic ocean into thenbsp;Mediterranean through the {freights of Gibraltar.

It may naturally be enquired by what means ''^ater, which is fo much heavier than air, is con-�'^erted into a fluid fo light as to float in air; andnbsp;how does it remain fufpended and difperfed theie-�'i) fometimes without the lead tendency to fepa*nbsp;ration.

Various hypothefes have been offered in expla-ttation of this fubjeft j, but I fhall not detain my reader by the account of opinions that are alwaysnbsp;�rifufHcient, and frequently abfurd. The moft rc-rriarlcable facts, which may affift the inquifitivenbsp;rriind in the inveftigation of the fubjedt, are as

ir the fleam of water be examined by means o'i lenfes or microfcopes,, no regular bodies or confi'nbsp;guration of particles will be diftingtiilhed in it.

There is an evident attradfion between water air, viz. the attradlion of cohefion ¹. If anbsp;bubble of air be introduced in a glafs veflTelnbsp;with boiled water, and inverted in water, �h�tnbsp;quantity of air will difappear in a day or two.

Hear, which diminifhes the attraftion of aggt^' gation between the particles of water, muftnbsp;courfe render the attraftion between air and watetnbsp;more adtive ; but, cateris paribus^ hot air is a bett^tnbsp;folvent of water, than colder air.. The coolingnbsp;hot atmofpherical air is generally accompaniednbsp;with a depofition of water, which, accordingnbsp;the quantity of water previoufly contained in th^nbsp;air, and the greater or lefs alteration of temperature�nbsp;aflumes the form of mifts, or clouds, or rain :nbsp;on the other hand, the heating of air is attendednbsp;with a diflipatioa of vapour, and an increahenbsp;tranfparcncy ; hence, as the fun rifes, thenbsp;of the night air, when no other cireumftance int^��¹

It is impoGible to annex more appropriate name� indefinite, or unfetded, ideas. Certain it is, that water vv¹nbsp;abforb a quantity of air, and that air abforbs a certainnbsp;tity of water; and to thofe abforbing powers we giv^nbsp;name of altraSiion or dijfolving property; whether theynbsp;really owing to the attrailion of cohefion, properly fo cal e 1nbsp;or not.

'^enes, is gradually diffipated, and the atmofphere clears up; hence, in this country, the foutherlynbsp;^fgt;d wefterly winds, which drive the air from warmernbsp;climates, generally bring rains or mifts; whereasnbsp;contrary effedt is moftly produced by northerlynbsp;eafterly winds, which bring the air from coldernbsp;^^gions. But the fame change of temperature Isnbsp;always accompanied with the fame diffipation ornbsp;^^pofition of water in the atmofphere.

It has been fully eftabliihed, by the refult of a va-*'�cty of experiments, that when water is converted into fteam or vapour, it abforbs a quantity of heat,nbsp;'�''hich is neceflary to its elaftic ftate �, (for the fteamnbsp;�f water is elaftic, viz. it may be comprefled, ornbsp;Expanded, by the addition or diminution of pref-^Ufe.) This quantity of heat is depofited whennbsp;fteam aflumes the form of water.

If you moiften part of your hand, and then blow ^pon it for the purpofe of increafing the evapora-hon, you will feel that part of the hand fenfiblynbsp;Pooled, viz. the water, in its aflliming the form ofnbsp;fteam, robs the hand of part of its lieat. If younbsp;place your hand over the fteam of boiling water,nbsp;��fte hand is much warmed by the heat which thenbsp;fteam depofits upon it in its reaffuming the form ofnbsp;'vater.

It is a common praflice amongft failors, to �Moiften one of their fingers by putting it into thenbsp;^outh, and then to expofe it above their head j bynbsp;^�ch rrieans they can tell which way the wind

blows; for that fide of the finger which is expofed to the wind, feels colder than the reft, the evaporation on that fide being promoted by thenbsp;wind.

Befides the abforption of heat, the evaporation oi �water (as has been fully afcertained by the verynbsp;able Profeffor Volta), is alfo attended with an ab-forption of eleftric fluid j and on the other hand, thenbsp;converfion of fteam into water is attended with ^nbsp;depofition of eleftric fluid. The experiments?nbsp;which prove thofe fafts, will be found in the thirdnbsp;part of thefe Elements, in the Se�lion for Ele^'nbsp;tricity.

It feems, therefore, that the formation of vapout? or clouds, or fogs, or rain, and fuch like phenO'nbsp;mena, depends upon the concurrence of all th^nbsp;above-mentioned circumftances, and perhaps th^nbsp;formation and duration of each phenomenonnbsp;particular depends upon the various degrees of thoiquot;^nbsp;different circumftances, which neceffary degrees arsnbsp;by no means known.

The moifture of the atmofphere, or rather th^t quantity of water which is not in perfedl folutioi�nbsp;with the air, but has not yet acquired the form �nbsp;water, is tiVeafured by an inftrument, called tbenbsp;hygrometer. The rain, or that quantity of waternbsp;v;hich falls from the clouds, or is depofited by th^nbsp;air in vifible drops, is meafured by means e�nbsp;another inftrumer.t, called the fhviometer ornbsp;2

The rain, which, as has been faid above, confifts the water that has been exhaled from the furfacenbsp;the terraqueous globe, either falls in very finallnbsp;particles of little gravity, in which cafe it is morenbsp;Ptoperly called dew¹y or mifl or fog-, or elfe it fallsnbsp;larger drops of various fizes, in which cafe it Isnbsp;properly called rain.

When the clouds are near, as is moftly the cafe �'r the winter feafon, or upon mountains, the dropsnbsp;rain are fmall, not having time fufficient to joinnbsp;to grow large. But when the clouds are verynbsp;^'gh, as is the cafe in the fummer feafon, or in hotnbsp;r^lirnates, the drops are much larger, and the rainnbsp;''Cry copious. A rain-gage, placed upon the fur-of the earth, receives a greater quantity ofnbsp;^^iri in the fame time, than a fimilar gage, whichnbsp;fituated higher up. A few feet difference ofnbsp;Perpendicular altitude make a confiderable dif-^^rence f. The quantity of rain is expreffed bynbsp;Inches and tenths; thus, if it be faid that 20,3nbsp;��ches of rain fell in one year in London, the

The deWy properly fpealcing, is that moifture which f^lls during the abfence of the fun, and without the neceffarynbsp;P¹^6fence of clouds.

been perfedtly flat, and all the rain that fell upon throughout that year, had remained upon it with'nbsp;.cut evaporation, draining, or abforption, the depthnbsp;of it would have amounted to 20,3 inches. Therefore, if a veflel open at top, and having flraigh¹'nbsp;up fides, be expofed to the atmolphcre fo asnbsp;receive the rain, and is fo conftru�ted as to preventnbsp;evaporation; the depth of water accumulated t�nbsp;that veflel, will fliew the quantity of rain for thenbsp;adjacent country, and the veflel itfelf is a raiit-

The quantity of rain which falls daily or nually in various parts of the world, has been, andnbsp;is, frequently meafured and regiftered; but t¹-might be wilhed that fuch obfervations were ind'¹nbsp;tuted in a great many more places ; for, confident!�nbsp;how unequal and partial rains are, we muft conclude, that the indication of a rain-gage will fert^^nbsp;for no great extent of circumjacent country.

The rains on the vicinity of hills or mountain^� or forefts, are generally more copious than in oth^tnbsp;places. In feveral places, efpecially within the tot-rid zone, the rain is feldom feen. It has beennbsp;ferted, as a real though Angular faft, that it nevetnbsp;rains in the kingdom of Peru; but that duringnbsp;of the year the atmofphere over the whole countt/nbsp;is obfcured by thick fogs, called garuas ¹.

�A. rain-gage is kept expofed over the apartments the Royal Society in London, and its contentsnbsp;noted frequently. It appears from that regider,nbsp;^hat a mean of the annual quantity of rain in Lon-amounts to little more than 21 inches, but anbsp;^^nfiderable inequality exifts between the quantitiesnbsp;the fingle years ; for fometimes, as in the yearnbsp;*79L the quantity of rain is about 15 inches, andnbsp;other times, as in the year 1774, as a!fo innbsp;*779, the rain amounts to 26 inches and up-'^ards.

At Townley, in the neighbourhood of the hills '^hich divide Lanca'fhire and Yorklhire, it is 41,516nbsp;^ches.

*' The annual quantity of rain,� as Dr. Dohjon objerves, � is a very uncertain tell of thenbsp;itioifture or drynefs of any particular feafon,nbsp;fituation, or climate. There may be little ornbsp;even no rain, and yet the air be conftantly dampnbsp;foggy; or there may be heavy rains, with

� a com-

� a comparatively dry (late of the atmofpherC� The fame depth of rain will like wife producenbsp;� different effetrs on the air, according as itnbsp;� upon a flat or hilly country; for large quantitiesnbsp;� foon quit the hills, or high grounds, wh¹^^nbsp;� fmaller quantities have more lading and poquot;'nbsp;� erful effedls on a flat country. Much alfonbsp;� pends upon the nature of the foil, whether da)nbsp;� or fand, whether firm or compaft, or loofenbsp;fpongy.�

� Is not evaporation, therefore, a more accurate � tefl: of the moifture or drynefs of the atmofph^¹^^�nbsp;� than the quantity of rain ¹ ?�

But if it be confidered that the evaporation the furface of water only, is far different fromnbsp;evaporation from the diverfified furface of a coUU'nbsp;try; the uncertainty of the latter method will app^^¹quot;nbsp;equally great.

The hygrometer Ihews, that in general moifture of the atmofphere is greater in lownbsp;tions, than in more elevated places: but.thenbsp;remarkable, and at the fame time the moftnbsp;countable, part of the fubjeeft is, that fometimcs�nbsp;(as has been obferved by fcientific perfons)nbsp;n'ountains and ocher elevated fituations, whilftnbsp;thermometer is fcationary, and the hygromcf^¹quot;nbsp;fiicws a confiderable degree of alt;ft:ual and cvc¹nbsp;increafing drync-fs, clouds are quickly fornnc gt;nbsp;and often a copious rain fucceeds ; wherc^�^

principal Ufes of the Atmofphere,^c. � 417 other times, a thick or clouded atmofpherenbsp;^�lckly clears up, and that without any apparent

It feems as if the vapour of water changed its 'Mature by being difperfed through the atmofphere;

we are certainly ignprant of that particular dif-P�fition in the atmofphere, which protluces fo great change. We find, for inftance, that clouds ofnbsp;'�^nnenfe extent, fometimes rife from the horizon;nbsp;^^at inftead of being driven by the exifting wind,nbsp;^^ey aftually change its direction j that other cloudsnbsp;quickly formed. A great ftorm enfues; thenbsp;'quot;ain is abundant �, every thing acquires a confidera-^le degree of moifture; yet an hour after, the fe-*'cnity of the air is reftored, and the natural procefsnbsp;evaporation becomes as vigorous as ever.

The quantity of evaporation from the land is, general, much lefs than the rain which falls uponnbsp;fame ; whereas, from the furface of the fea,nbsp;^*kes and rivers, the evaporation exceeds thenbsp;The like difference does alfo exift betweennbsp;and warm climates. But the aftion of thenbsp;'^^^tids, and the running of the fuperfluous rain-^3-ter from the land again into the fea, compenfatesnbsp;deficiencies, and keeps up a ufeful, neceffary,nbsp;^'^d admirable circulation.

We lhall now endeavour to explain the princl-and conftruftion of hygrometers, as alfo of rain-gage.

It has already been fliewn, that in virtue of ^ol. II,nbsp;nbsp;nbsp;nbsp;EEnbsp;nbsp;nbsp;nbsp;the

the attra�lion of cohefion or capillary attraftion� yarious fubftances are capable of abforbingnbsp;into their pores, or at leafl; of holding it attachednbsp;to their fiirface. If then the air contain a quanti�^nbsp;of moifture, and a certain other dry fubftancenbsp;a greater attraftion towards water than air hasgt;nbsp;then the moifture will quit the air, and will atta^^nbsp;itfelf to that other fubftance ; in confequence �nbsp;which that other fubftance will be enlarged innbsp;dimenfiQns, or will be increafed in weight,nbsp;by meafuring the diminifhed or increafed dim^*^nbsp;fions, or the increafed or dinninilbed weight ofnbsp;other fubftance, at different times, we acquit^nbsp;knowledge of the quantity of water which hasnbsp;depofited or abforbed by the air at thofe titn��nbsp;The inftrument in which a fubftance fit fornbsp;pyrpofe (called an hygrojcopic body) is fo fitn^*quot;^

and very feldom two inftruments, that are furnifhed with fuch fubftances, can be compared together.

Mr. De Luc, and Mr. De Sauflure, both gentlemen of great knowledge and ingenuity, have examined a vaft number of hygrofcopic fubftancesnbsp;in a great variety of circumftances j and, upon thenbsp;whole, the latter of thofe gentlemen found reafonnbsp;to prefer a hair¹ ; whilft the former prefers a verynbsp;fine flip of whale-bone cut acrofs the grain. Eithernbsp;of thofe fubftances is to be placed in a proper frame,nbsp;which fhews their elongations or contradlions to anbsp;Very minute quantity �, the inftrument, or at leadnbsp;that part of it which holds the hygrofcopic fub-ftance, is placed in water, which extends the fub-ftance to the utmoft, and the point where the extremity of the fubftance reaches, is marked uponnbsp;the inftrument, and is called the point of extremenbsp;^oifture. Then the inftrument is removed fromnbsp;the water, and is placed into a large veflel almoftnbsp;fi^ll of unllacked quick-lime, wherein it is kept fornbsp;^ few days; for as quick-lime has a confiderablenbsp;property of abforbing water copioufly but (lowly,nbsp;the air in that vefTel is very dry, and its degree ofnbsp;firynefs is conftantly the fame during fevera' months,nbsp;tiotwithdanding the opening of the velTel, whichnbsp;tt^rjft take place for putting in or taking out thenbsp;hygrometers. By this means the point of greateft

' drynejs is obtained. Then the diftance between this point and the point of greateft moifture, is di'nbsp;vided into one hundred parts, and thofe parts arenbsp;called the degrees of the hygrometer, or the degreesnbsp;of moifture

Thofe two forts of hygrometers are tolerably uniform, and pretty quick in their adtion. TwOnbsp;or more of them are alfo comparable within a fmallnbsp;difference. As upon the whole it appears thatnbsp;Mr. De Luc�s hygrometer has fome advantage¹nbsp;over that of Mr. De Sauffure�s, I Ihall thereforenbsp;defcribc it in Mr. De Luc�s own words. See fig¹nbsp;I. of Plate XV.

Thofe inftruments may be made of various lizesj but they are moftly made of about twice thenbsp;of the figure.

� Their frame will fufficiently be known front �� the figure} therefore I fhall confine myfelfnbsp;� the defcripdon of fome particulars. The flipnbsp;� whale-bone is rcprefented by a b, and at its endnbsp;a is feen a fort of -pincers, made only of a flattenednbsp;� bent wire, tapering in the part that holds thenbsp;� flip, and preffed by a Aiding ring. The end bnbsp;is fixed to a moveable bar r, which is moved bynbsp;� a fcrew for adjufting at firA the index. The end ^nbsp;� of the flip is hooked to a thin brafs wire}

From the point of greateft drynefs to that of greateft moifture, a flip of whale-bone will be increafeci about one-eighth of its leneth.

the other end of which is alfo hooked a very thin filver gilt lamina, that has at that end pincers fimi-lar to thofe of the Jlip, and which is fixed oy thenbsp;other end to the axis, by a pin in a propernbsp;hole. The fpring, d, by which the Jlip is ftretch-quot; ed, is made of filver-gilt wire j it aits on the Jlipnbsp;as a weight of about 12 grains, and with this ad-vantage over a weight (befides avoiding fomenbsp;other inconveniencies) that, in proportion as thenbsp;Jlip is weakened in its lengthening, by the pene-'' traiion of moifture, the fpring, by unbending atnbsp;quot; the fame time, lofes a part of its power. Thenbsp;' axis has very fmall pivots, the Jhoulders of whichnbsp;quot; are prevented from Coming againfl the frame, bynbsp;quot; the ends being confined, though freely, betweennbsp;the flat bearings of the heads of two /crews, thenbsp;quot; front one of which is feen near �. The feftionnbsp;quot; of that axis, of the fize that belongs to a flip ofnbsp;about 8 inches, is reprefented in fig. 2. j thenbsp;Jlip aits on the diameter a a, and the fpring on thenbsp;frnaller diameter b b*,

�A-ftcr an afliduous and judicious ufe of hygrome-made in the courfe of 20 years and upwards,' p)e formed fome very ufeful deduffions,nbsp;^'^hich I fhall fubjoin in his own words.

� From thofe determinations in hygrometry, fome great points are already attained in hygrology,

� meteorology, and chemiftry, of which 1 IhaH � only indicate the moft important^ ift. In thenbsp;'' phasnomenon of dew, the grafs often begins tonbsp;quot; be wet, when the air a little above it is ftiJl io *nbsp;� middle ftate of moifture; and extreme mcijitire isnbsp;� only certain in that air, when every folid expofc^nbsp;� to it is wet, sdly. The maximum of evapcratiot^ynbsp;� in a clofe fpace, is far from identical with thenbsp;maximum of moifture j this depending confiderably�nbsp;� though with the conftant exiftencc of the other�nbsp;quot; on the temperature common to the fpace and tonbsp;� the water that evaporates, jdly. The cafenbsp;� extreme moifture cxifting in the open tranfpareotnbsp;� air, in the day, even in the time of rain, isnbsp;quot; tremely rare : I have obferved it only once, thenbsp;� temperature being39�. 4thly. The air is dryernbsp;� dryer, as we afcend in the atmofphere; fo that it*nbsp;� the upper attainable regions, it is conftantly verfnbsp;� dry, except in the clouds. This is a fa�t certifit^^nbsp;� by Mr. De Sauflure�s obfervations and mio^'nbsp;� 5thly. If the whole atmofphere palled fromnbsp;� treme drynefs to extreme mofture, the quantitynbsp;� water thus evaporated would not raife the hei'nbsp;� rometer as much as half an inch. 6thly. LaftV'nbsp;� in chemical operations on cirs, the greateftnbsp;quantity of evaporated water that may be fop'nbsp;� pofed in them, at the common temperature o^nbsp;� the atmofphere, even if they were at extrew^nbsp;� moifture, is not fo much as ,-1-^- part of theirnbsp;� mafs. Thefe two lad very important propo-

frtions

The mean height, for the whole year, of De Luc�s hygrometer, expofed to the atmofphere innbsp;London, is about 79 degrees. It muft, however,nbsp;obferved, that hygrometers of every fort, evennbsp;above deferibed one of Mr. De Luc, are verynbsp;liable to be fpoiled by^ long expofure; as duftinbsp;Inaoke, infefts, amp;c. are apt to adhere to them;

which cafe their rate of going, or fenfibility, is altered confiderably. The proper aflion of Denbsp;Luc�s hygrometer may, in fome meafure, be pre-Lrved, by now and then placing the inftrument it!nbsp;'''�ater, and gently cleaning the furface of the whale-l*One flip, by means of an hair-pencil.�A fteadiernbsp;^nd more durable hygrometer is ftill a defideraturrtnbsp;'n natural philofophy.

Evaporation generates cold, and the quicker th� Evaporation takes place, the greater is the coldnbsp;'''hich is produced: therefore, if the bulb of anbsp;Ei^ermometer be juft moiftened, and then be ex-Pofed to the air, the mercury will defeend lower,nbsp;'''hen the evaporation is performed quickerj andnbsp;verja. Upon this principle Mr. Leflie hasnbsp;�^�nftru�ted an inftrument, tvhich fhews the quick-

nefs of evaporat'on. The inventor calls it hygrometer; but the quicknefs of evaporationnbsp;does not indicate the moifture of the air in allnbsp;cafes ¹.

The principle of the rain-gage has already been Ihewn in page 414. The rain-gage which i¹nbsp;moftly ufed, is delineated in fig. 3. of Platenbsp;It is an hollow vefleh of tined iron plates, japanned

infide and out. The whole machine confifts nlquot; three parts. A B C D is a cylindrical veffel,nbsp;the aperture of which the funnel F E ^ is nicelynbsp;fitted. The upper part of the funnel has an edg^nbsp;of brafs, which is perpendicular to the horizon, asnbsp;is fufficiently indicated by the figure.

This gage, when expo fed to tiie atmofphere, ceives the rain which goes through the aperture ^nbsp;of the funnel, into the receiver A B C D j out 0^nbsp;which it cannot evaporate, either out of the joi'�¹-ad, which is very clofe, or out of the holenbsp;whicii, befides it being fmall, is partly occupiednbsp;by the meafuring rod. The meafuiing rod GH ^nbsp;fattened to an hollow float H, of japanned tin plated;nbsp;which floats upon the water j and as the water fiH¹nbsp;the cylindrical veflel A DBC, fo the float is rafled,nbsp;and part of the meafuring rod comes our; and thenbsp;divifions of the rod, which are out of the funneh

See the defeription of this Hygrometer in Nicholicn � Journn!, vol. II. p. 461.

With refpeft to the divifions of the rod, it muft obferved, that when the edge of the funnel andnbsp;'�he cylindrical veflel are of the fame diameter, thennbsp;the divifions of the rod muft be only inches andnbsp;tenths, in order to fhew the quantity of rain innbsp;�fiches and tenths; but when the diameter of thenbsp;t^ylindrical veffel is lefs than that of the edge F E,nbsp;then the divifions muft be longer, becaufe an inchnbsp;^epth of rain, in an area of a certain diameter, willnbsp;he more than an inch depth in an area fmaller than

the divifions of the meafuring rod are made fo as to indicate the inches of rain that would be accu--tHolated in a cylindrical veffel whofe diameternbsp;^fl�alled the diameter of the brafs edge F E.

A crofs-bar with a' focket, through which the tt�eafuring-rod paffes, may be feen within the funnel.nbsp;quot;This ferves to render the divifions of the meafuringnbsp;tod more legible. When no water is contained innbsp;the gage, and of courfe the float refts upon the'nbsp;bottom B C, then the 0, or the beginning of thenbsp;'^f�vffions of the rod is even with the upper part ofnbsp;the above-mentioned crofs-bar.

tHE DESCRIPTION OF THE PRINCIPAL MACHINES�' WHICH DEPEND UPON THE FOREGOING SUBJECT�nbsp;OF FLUIDS.

IN laying down the theory of fluids, both and non-elaftic, I have defcribed as few itgt;^'nbsp;chines, and thofe of as Ample a conftruftion, asnbsp;nature of the fubjedl could admit of. 7�his I ha'^^nbsp;done, in the firft place, for the purpofe that thenbsp;der might not consider the knowledge of fuch fc^'nbsp;jecSts as unattainable, without the ufe of coftlynbsp;chines; and, fecondly, that the connexion ofnbsp;thepretical reafoning might not be interruptednbsp;the introdu�lion of long and complicatednbsp;fcriptions.

But it is now, however, neceflary to explain conftruftion and the ufe of thofe machines whichnbsp;bave been contrived for the purpofe either ofnbsp;Turing, or of elucidating, or, laftly, of applyingnbsp;our purpofes, the mechanical properties of flui^^'nbsp;And here we (hall beftow our attention more onnbsp;the principles than upon the variety of fuch m?'nbsp;chines.

The caufe of this ef�edt is die preflfure of the at-^^fphere ; for when the fyphon is full of liquor, the ^''^flure of the atmofphere at B and C keeps thenbsp;up in the legs of the fyphon ; and that pref-is partly counteracted by the perpendicular al-�'�^des of the liquor in thofe legs j but that coun-^��aftion is lefs at C than at B, becaufe the perpen-^cuJar altitude A C is lefs than A B; therefore

the atmofphere preffing at C, or (which is the fame thing) on the furface of the liquor in the velTel Fgt;nbsp;more than at B, forces the liquor to run throughnbsp;the fyphon.

It is evident that it is immaterial whether the diameters of the two legs be equal or not; pt�'nbsp;vided the difparity be not fo great as to introducenbsp;the obftrudtion from capillary attradlion, amp;c.-^nbsp;Whether the legs be bent in various dire�lions urnbsp;not, is alfo immaterial j provided the perpendicularnbsp;altitude of the difeharging leg be greater than thatnbsp;of the otiier.

It is alfo evident, from the theory, that the crane cannot aft if the perpendicular altitude of h*nbsp;legs exceed 3 2 feet or thereabout. Nor can a fy'photrnbsp;aft in vacuo.

The beft lyphons that are at prefent in ufe decanting liquors, have certain appendages whichnbsp;rentier their ufe more commodious. Fig. 5-Plate XV. reprefents one of the beft conftruC'nbsp;tion. It has a ftop-cock D at the difeharging apcf'nbsp;ture, and a fmall tube which runs along the outfiti^nbsp;of that leg, and communicates with the cavitynbsp;that leg juft above the ftop-cock. When the apciquot;'nbsp;ture C is fituated within the liquor, the ftop-coc^^nbsp;is doled, and the mouth which fucks the air oUtgt;nbsp;amp;c. is applied at E. Some of thofe fyphonsnbsp;no ftop-cock, in which cafe the aperture B muftnbsp;clofcd by the application of a finger,, whilft the air

If feveral threads of cotton, a bunch of grafs, or f^tue fimilar fubftance, be placed partly in a glafs ofnbsp;quot;'^tier, and the other part (being the longeft of thenbsp;^^o) be left hanging out of the glais, as is fhewn innbsp;%-iS- ofPlate XI.; the cotton or other fubftance willnbsp;�'adually abforb the water, in virtue of the capillarynbsp;^'^tralt;ftion ; and when the whole is moiftened fuffi-'^�ently, the cotton, or other fubftance, will ad as anbsp;%phon, and the water will keep dropping out ofnbsp;external part of it.

A little machine, called 'itantalus�s cup, ads '^Pon this principle, and its conftrudidh is as

'^'ater will rife into the leg D E of the fyphon, k does in the cup, and will drive the air fromnbsp;leg through the longer leg E G; but wlren thenbsp;. ^ter bas reached the upper part F of the fyphon,nbsp;not only run down and fill the other leo;nbsp;but it will keep running out at G, until thenbsp;P 'S quite emptied. A little figure is fometimesnbsp;^ ^^^d over the fyphon D F B, with the mouthnbsp;a little above F, which figure conceals thenbsp;^^Phon, and reprefents Tantalus, who is depriv-^f the water, when the wa^er has rifen fo

The reafon, which principally induced nne deferibe the above-mentioned cup, is, thatnbsp;adion explains a curious natural phenomenon,nbsp;that of intermitting or reciprocating fprings^ callednbsp;ebbing and flowing wells.

There are certain fprings or ftreams of watd which ifllie out of rocks, and are rather copiousnbsp;a certain time, then ftop, and, after a certainnbsp;riod, come out again. The intermitting period **nbsp;various, but fometimes it is very regular.nbsp;origin of thofe fprings is, with great probabili'-^^�nbsp;owing to the following conformation, or tonbsp;thing fimilar to it.

A A, fig. 19. Plate XV. reprefents the pendicular fedion of a hill, within which is a ca'^'

B B, and from this cavity a natural channel in the diredion BCDE, forming a naturalnbsp;The rain water, which defeends from the upPnbsp;part of the hill through various fmallnbsp;nbsp;nbsp;nbsp;�

G, G, G, gradually fills the cavity B B, ns the part BC of the channel, or fhorter kg '� .nbsp;fyphon ; but when the water gets above tuenbsp;of C, then a ftream will run through thenbsp;and out of it at E, until the cavity B B, as alfu ^nbsp;channel BCDE is quite emptied �, it beingnbsp;poled that the draining of the water through'nbsp;crevices G, G, G, cannot fupply the cavitynbsp;fo fall as it ife drained by the phannel B

Then the flow of water at E flops, until fo much 'vater is again accumulated in the cavity BB, as tonbsp;feach the level of C, at which time the flream reappears at E j and fo on.

There are feveral forts of pumps for drawing 'vater out of wells, fprings, amp;c.; but they may benbsp;I'educed to two forts, viz. the common pump, ge-*^erally called the fucking pump, and the forcingnbsp;pump.

Fig. 15. Plate XV. reprefents a pump of firfl; fort. A B is a cylindrical pipe open atnbsp;^oth ends, the lower of which is immerfed in thenbsp;''^ater of the well, amp;c. Towards the lower part,nbsp;at C, there is a ftopper with a hole and a valve,nbsp;^hich opens upwards when any fluid pufhes itnbsp;below, but is clofed by any fuperincumbentnbsp;^otce ¹, In the upper part of the tube there is a

A valve is a piece of mechanifm, that belongs almoft all forts of hydraulic and pneumatic engines. V alves arenbsp;'�lade of different forts, of which however the following arcnbsp;principal.

Fig. 12. Plate XV. reprefents a Hopple, with an ^'1 filk valve; viz. a narrow flip of oil filk is ftretchednbsp;the upper flat part of the ftopple, fo as to cover thenbsp;�^^�itral hole j and, being turned over the edge, is tied faft

pifton D, faftened to the handle or rod E, which generally is an iron rod. The pifton confifts of ^nbsp;piece of wood, nearly equal to the diameter of thenbsp;cavity of the pump; but being covered overnbsp;cylindrical part with leather, it fits pretty tightlynbsp;the cavity of the pump. In this pifton there is ^nbsp;hole and another valve, like the one at C, whichnbsp;alfo opens upwards. The adion of pumpi'^onbsp;confifts in alternately moving the pifton a certaif*nbsp;w^ay up and down, by which means thenbsp;afcends through the pump, and comes out ofnbsp;upper aperture, or out of the fpout F, when th?nbsp;upper part of the pump is furnilhed with fu*'^nbsp;veflel and fpout as is fhewn in the figure. Th^nbsp;aftion of this pump, depends upon the gravitynbsp;preffure of the atmofpherci hence it couldnbsp;poffibly aft in vacuo.

round the ftopple, as is indicated by the figure. In fig-a flat and thick piece of leather is adapted to the upper part of a ftopple, fo as to cover the central hole. It ha� ^nbsp;little prolongation oil one fide, which is faftened to th�nbsp;ftopple by means of a nail or fcrew, and a piece ofnbsp;is faftened to the upper part of the leather, in order to I�*'nbsp;it lay flat upon the hole. In fig. 14, the central holenbsp;made a little conical at its upper part, and is ftiut up bynbsp;conical piece of metal, which refts upon it by itsnbsp;gravity.

It is evident that a force from below vrill open any one thofe valves; but a force from above will fhut up the ap�''nbsp;ture more effeftually.

When the pifton is firft drawn upwards, the^-iir C D is rarefied ; hence the prefTure of the awnbsp;�^ofphere upon the furface of the water in the wellnbsp;forces the water to afeend a little way into the lowernbsp;Part of the pump; for inftance, as high as G.nbsp;'I'hen the pifton is puflied downwards, which con-^''adbing the diftance C D, forces fome air out of thenbsp;''�alve D through the pifton, but no air can get downnbsp;�^brough the valve at C ; hence the water remains

G. After this, the pifton is drawn upwards a f^cond time, which rarefies the air in CD ; in con-f^quence of which the water afeends higher withinnbsp;^!ie pump; thus, by degrees, the water gets abovenbsp;die valve C, and fills the fpace CD; and when thisnbsp;�^^kes place, then, by lowering the pifton, fomenbsp;^ater paftes through the valve D, and remainsnbsp;^kove the pifton ; then, on lifting up the pifton,nbsp;^kat water is raifed, and more water comes fromnbsp;the well through the valve C, amp;c.

It is hardly necelTary tp mention, that the height t'f the valve D, above the water of the well muftnbsp;exceed 32 feet. Indeed, on account of thenbsp;t^Operfedions to which thofe mechanifms are fub-that height can feldom exceed 20 feet.

1'he force which is required to work-a pump is the height to which the water is raifed, ahd asnbsp;d�e fquare of the diameter of the pump at thenbsp;place where the pifton vyorks; it being immaterialnbsp;''whether the reft of the pump be of the fame dia-�^cter or not.

n, nbsp;nbsp;nbsp;F Fnbsp;nbsp;nbsp;nbsp;Pumps

Pumps, in general, are worked not by apply*'�^ the power immediately to the rod at E; butnbsp;end of that rod is connefted with the fliorternbsp;of a lever, whilft the power is applied to the long^*quot;nbsp;arm of the lever; and fince the longer arm ofnbsp;lever is about five or fix times as long as the otb^''^nbsp;therefore the power is by this means increafed fi'��nbsp;or fix times.�It has been found fromnbsp;trials, that when the handle increafes the power .nbsp;times, when the diameter of the pump isnbsp;inches, and the water is to be raifed 30 feet hig^ �nbsp;the ordinary exertion of a labouring man cannbsp;it for a moderate continuance of time, and cannbsp;charge 27f gallons of water (Englifia wine

� Now, from the above-ftated particulars, it not be difficult to calculate the dimenfions of ^nbsp;pump, which will difcharge a given quantity ^nbsp;water at a certain height in a determinate tio�^ �nbsp;and what power will be required for the

as the preceding pump; but then, on lowering pifton, v.'hich in this pump is a folid piece witho�^nbsp;any valve or perforation, the water cannot get ^nbsp;it, but it is forced through the tube M N�nbsp;through the valve at P, into the veflel K K,nbsp;is called the air-vejfel or condenfing-vejfel. Thusgt; ^nbsp;repeated ftrokes of the pifton, the water is

to enter, and ro accumulate into the vefiel K K. driving the air out of it, through the pipe IGF,nbsp;But when the water has been raifed above thenbsp;aperture I of the pipe, then the air, inftead of being driven out, is condenfed in the upper part ofnbsp;the air-veffel; hence it begins to re-aft upon thenbsp;'vater by its elafticity; in confequence of which thenbsp;'v'ater is forced out of the pipe IHF, forming anbsp;jet, which rifes higher, or goes farther and farther,nbsp;according as the water is forced into the air-veffelnbsp;'vich greater quicknefs, and the air in the uppernbsp;part of the faid veffcl is contrafted into a narrowernbsp;fpace, by the rifing of the water at O, within thenbsp;veffel.�Some forcing-pumps have no air-veffel,nbsp;but convey the water through a Tingle uniform tubenbsp;to the required height.

The jet, when there an air-veffel, comes out without intermiffion; for whilft the pifton is afccnd-ing, the elafticity of the condenfed air continues tonbsp;act upon the water at O.

By means of this pump, the water may be raifed to any height, provided there be working powernbsp;adequate to the required effeft, and the parts of thenbsp;pump, and principally of the air- veffel, be fufficient-

If to the extremity F of the difeharging pipe, a dexible tube, either of leather, or of other pliablenbsp;gt;waterial, be adapted, fo as to render the jet capablenbsp;of being direfted towards any particular p-lace

The principle of fire-engines, which are commonly ufed in this country, and elfewhere, lot extinguifliing fires, is nothing more than what hasnbsp;been already defcribed. Their particular con-ftruftlons, which have been diverfified and improved by various able mechanics, differ only in 3nbsp;more or lefs compaft difpofidon of parts; mnbsp;having two or more forcing pumps j in havingnbsp;the levers capable of admitting feveral working-men, amp;c.

Water-pumps of every fort may be worked by other powers, befides the force of men. They mafnbsp;be worked by the wind, by horfes, by a ftearn-engine, by a river, amp;c. A vafl variety of mecha-nifms has been contrived for fuch purpofes, whichnbsp;may be feen in almofl: all the works on mechanics?nbsp;hydraulics, and other fubjefls allied to them; butnbsp;thofe mechanifms mull be contrived accordingnbsp;the particular circumftances of the fituations,nbsp;which they are to be ufed.

The water-works at London-bridge confift forcing-pumps, which are worked by the currentnbsp;of the river, viz. the current of the river turns ^nbsp;large vertical wheel, called the water-wheel,nbsp;axis of which has a number of cranks, which worknbsp;as many levers, and at the ends of thofe leversnbsp;faflened the rods of the forcing-pumps.

'vater is forced by them into a very ftrong con-denfing vcflel of iron, and from this veflel various pipes convey and difcharge the water to differentnbsp;parts of the town.

This fimple and elegant contrivance of the great Archimedes, is fhewn in fig. i8- Plate XV. Itnbsp;confifts of a fcrew-like tube, open throughout, andnbsp;faftened round an axis, which turns, together withnbsp;the tube, round the pivots A, B.

This machine being placed with its lower part in water, mult be inclined to the horizon at an anglenbsp;^f about 45 degrees; then by turning the handlenbsp;At, the machine muff be turned in the diredtionnbsp;^ a C ; viz. fo that the loweft aperture of the tubenbsp;Hiay go againft the water,; and by this means thenbsp;'''ater will be raifed from A, and will be difcharged

the upper aperture i, into a proper vcffel, S, '''hich muff be placed under it, to receive thenbsp;^ater, and to convey it wherever it may be re-

i'n order to underftand the aftion of this machine n muft be confidered, iff. That every fuccelllvenbsp;part or point in the length of the tube, is farthernbsp;and farther from the loweft part of the machine, ornbsp;i* nearer and nearer to the aperture i. adly. Thatnbsp;fmall quantity of water which is in the in-

to that identical part of the tube, when, by the turning of the machine, that part comes to thenbsp;higher fituation a ; but it muft pafs on to the nextnbsp;part of the tube, then to the next to that, and fonbsp;on. But thofe fuccelTive parts come nearer andnbsp;nearer to the aperture i; therefore that quantitynbsp;water muft pafs gradually from the loweft to thenbsp;higheft part of the tube, until it comes outnbsp;of the aperture i.

What has been faid of this quantity of water� may evidently be faid of the next, and, ��tnbsp;fhort, of all the water which is raifed by thenbsp;machine.

Inftead of the handle M, fometimes a pretty larg� wheel is affixed to the lov/eft part of the machit�^�nbsp;which, on account of the inclination, w ill be partlynbsp;immerfed in water; in confequence of which�nbsp;the machine will be turned by the water itfeU�nbsp;fuppofing that water to be a river, or runningnbsp;ftream.

Sometimes, inftead of one, two tubes are fixctl round the axis of this machine; but its conftm^'nbsp;tion has been altered various ways, which neednbsp;be particularly deftribed, fince the principlenbsp;of the machine remains unaltered.

Such machines are ufeful for raifing water to n� great heights; for when the elevation is confide^nbsp;ble, the m.achine, on account of its inclined pofit'�^nbsp;muft be long, heavy, and liable to be bent,nbsp;V/hich cafe its adlion would ceafe.

If a vertical grooved wheel, fixed in a frame, be fii^uated within the water at the bottonn of a well,nbsp;another fiinilar wheel, having a handle affixednbsp;its axis, be fitiiated in another frame at the uppernbsp;Part of the well; alfo an endlefs rope (viz. a ropenbsp;'''hofe two extremities are fpliced into each other)nbsp;pafied round both wheels; then, on turning thenbsp;^'andle, the w�heels and the rope will be caufed tonbsp;fgt;iove, viz. the rope will afcend on one fide, and willnbsp;'^^fcend on the other, paffing fucceffively throughnbsp;water of the wellj but the afcend ing part willnbsp;^arry up a quantity of water adhering to its ffirface;nbsp;�tid this water differs in quantity, according to thenbsp;^i2e of the rope, the depth of the well, and thenbsp;S^icknefs of the motion; viz. with a larger rope,nbsp;a lefs deep well and quickeft motion, a greaternbsp;�luanticy of water will be raifed, than otherwife.

In order to intercept the water at the top of the the upper wheel is inclofed in a pretty largenbsp;in the bottom of which there are two holes,nbsp;'^Iirough which the afcending and defcending partsnbsp;the rope pafs. To thefe holes are affixed twonbsp;tubes, which prevent the exit of the waternbsp;'^hich falls to the bottom of the box. There isnbsp;^ffo a lateral fpout on the fide of the box, dole tonbsp;I'I'C bottom, for the water to come out of �, and onnbsp;the

the broad Tides of the box there are two holes To'� the axis of the wheel. The nth and loth figuresnbsp;of Plate XV. exhibit a fedtion and a front vie'^'nbsp;of a machine of this fort, which was put upnbsp;in the year 1782,' on the caftle hill at Windfu'^�nbsp;�where the depth of the well is 95 feet *. '

The wheel H at the bottom' of the well is � lignum vitce, one foot in diameter. Its axis isnbsp;fteel, and turns with its extremities in fockcts ^nbsp;bell-metal.

The wheel EE at the top of the well is of itou gt; but its rim, with the grove which receives the rop^�nbsp;is of lead. The diameter of this wheel isnbsp;feet.

The axis dd is of flee!, and its extremities tu'U in bell-metal fockets, which are fixed in two upnbsp;right pofts AA, that fupport the machine. T isnbsp;handle affixed to the axis, which handle defcriue�nbsp;circle of 28 inches in diameter j h b is the wooonbsp;box, lined with lead, which inclofes the wheel ^nbsp;F F are the holes at the bottom of the box throUt?nbsp;�which the rope paffes. Their diameter is aboutnbsp;inches.

On the fanne axis dd, another wheel CC, of about four feet in diameter, is fixed. This wheel is ofnbsp;'''ood, loaded on the edge with lead, and it fervesnbsp;a fly to facilitate the motion.

With this identical machine, feveral experiments quot;'ere tried, the refljlt of which is as follows :

When the machine was worked flowly, viz. fo to malte about 30 revolutions of the handle innbsp;One minute, then very Ijttle water came up adheringnbsp;to the rope; and of this water a very fmall portionnbsp;quot;^as feparated from the rope within the box, fonbsp;to come out of the fpouc Z, in the fide of thenbsp;box.

When the revolutions of the handle were about 50 in a minute then a confiderable quantity ofnbsp;quot;'ater came up adhering to the rope 5 and on turn-the wheel E E round, the greateft part of thatnbsp;quot;'ater, having acquired a confiderable velocity,nbsp;fiew off in a tangent from the rope, and formed anbsp;Jet within the box. This water falling to the bottomnbsp;the box, came out of the fpout Z.nbsp;it was found that the utmoft'exertion of an ordi-nary working man, could not make more than 60nbsp;*quot;^quot;01011005 of the handle in a minute ; in whichnbsp;Cafe the rope moved at the rate of about 16nbsp;icet per fecond. With this velocity the quan-*��^7 of water that came out of the fpout Z, wasnbsp;^tiput fix gallons per minute : but it would have

been impoffible for the man to have workyd at that rate for more than three or four minutes.

This machine may evidently be placed aHant, viz. fo as to convey the v/ater from one place tQnbsp;another, which is not quite perpendicularly overnbsp;the former. The fame conftruction and almoft thenbsp;fame ex|)ence will adapt the machine to wells of dif'nbsp;ferent depths, though the effeds will not be alwaysnbsp;the fame.

More than one rope, or a broad band inftead of a rope, might be adapted to this machine, for whif!''nbsp;purpofe the wheels muft have more than one, or ^nbsp;broad, groove, amp;c.

The greateft difadvantage of this.-machine is, th^*^ the rope does not laid long. Its b'eing always wo*-dcilroys it very foon.�In putting on the rope, car^nbsp;muft be had to foke it well in water before itnbsp;fpliced ; other wife it will either be too tight, or

The efled which�arifes from that curious propo*� ty of non-elaftic fluids, viz, from their preffingnbsp;equal bottoms, according to their perpendicularnbsp;titudes, without any regard to their quantities,nbsp;been commonly called the hydrofatical paradox, ^nbsp;varbus machines, more or lefs complicated, ha'_^

^fikingly evident; but after the theoretical explanation which has been given of that property, ic ^cems ufelefs to employ more pages on the defcrip-kion of fuch machines. I fhall, however, add onenbsp;nf the lead complicated conftruftion. This is re-prefented in fig. 7. Plate XV. It is commonlynbsp;nailed the hy.droJiatical bellows.

It, confifts of two thick oval boards, each about ^6 inches brtjad and 18 inches long, joined bynbsp;naeans of leather, to open and Ihut like commonnbsp;bellows, excepting that they move parallel to eachnbsp;nther, A pipe B, about 3 feet high, is fixed intonbsp;^^e bellows at e.

Let fome water be poured into the pipe at 0, quot;'Inch will run Into the bellows, and feparate thenbsp;boards a little. Lay three weigh.ts b, c, d, eachnbsp;quot;'sighing too poynds, upon the upper board ; thennbsp;Pour more water into the pipe B, which will runnbsp;^nto the bellows, and will raife the board with allnbsp;fhe Weights upon it 5 and if the pipe be kept full,nbsp;Ptitil the weights are ralfed as high as the leathernbsp;quot;'hich covers the bellows will allow them, thenbsp;quot;'ater will remain in the pipe, and fupport all thenbsp;^^'ghts, even though it fhould weigh no more thannbsp;^ quarter of a pound, and they 300 pounds; nornbsp;quot;'ill all their force be able to caufe them to defcendnbsp;9nd force the water out at the top of the pipe.

�A. man may ftand upon the upper board, inftead ^Pthe weights, and he may raife himfclf by pour-Water into the pipe B j which will appear very

wonderful to unflcilled perfons; but the wonder wdl vanilh, if it be confidered tliac if the man raif*^*nbsp;himfell one tenth part of an inch, the waternbsp;defeend down alinoft the whole length of the pip^�nbsp;fo that the fmali quantity of water in the pipenbsp;balance the weight of th� man, becaufe theirnbsp;cities, or the fpace^ they mufl; move through,nbsp;inverfely as their weights; which renders theirnbsp;mentums equal.

I (hall not deferibe the various forts of millSj of other hydraulic engines, on three accountsnbsp;cipally, viz. firft becaufe thofe machines, thonS^j.nbsp;very ufeful, do not point out any new property ^nbsp;fluids, befides what have been already explaif^^^ �nbsp;fecondly, becaufe the deferiptions of thofenbsp;may be found in a variety of books, fuch asnbsp;tionaries of arts and fciences, tranfaftions of le^rn^nbsp;focietjes, treatifes on mechanics, on hydro(t3t'^^�nbsp;amp;c. and 3dly, becaufe, by the infertion ofnbsp;deferiptions, this work would be fwelled up tonbsp;enormous fize.�The following machine is notnbsp;commonly known.

Wherever tnere is tlie conveniency of a fa^ water, which is frequently the cafe in the vic'O'^5^nbsp;of hills, mountains, amp;c. there a machine for blo'^nbsp;ing the fire of a furnace may be eafily conftruc ^ ^

5nd it will it prove both ufefiil and lafting, almoft ''without any farther expence than that which attendsnbsp;original conftrudlion.

The dimenfions of fuch machines muft be fuited the circumftances of the fituation, fize of thenbsp;^^tnace, amp;c. but thofe particulars may be eafilynbsp;derived from the getieral principles of the con-^ruftion, which I llrall give in the words of Pro-Venturi, the gentleman who has given thenbsp;and moil recent explanation of thofe prin-'�'pies.

quot; Let BCDE, fig. 17. Plate XV. reprefent a pipe, through which the water of a canal AB,nbsp;falls into the lower receiver M N. The fides ofnbsp;the tube have openings all round, through whichnbsp;the air freely enters to fupply what the water car-ties down in its fall. This mixture of water and

^ir proceeds to ftrike a mafs of ftone Qj whence rebounding through the whole width of the receiver MN, the water feparates from the air,nbsp;and falls to the bottom at X Z, whence it is dif-charged into the lower channel or drain, by one

^ ^r more openings T, V. The air, being leis heavy than the water, occupies the upper partnbsp;cf the receiver, whence, being urged throughnbsp;the upper pipe O, it is conveyedi to the

quot; I formed one of thefe artificial blowing engines of a fmall fize. The pipe BD was two inchesnbsp;*ri diameter, and four feet in height. When the

water accurately filled the fedtion B C, antJ the lateral openings of the pipe B D E Cnbsp;� clofed, the pipe O no longer affordednbsp;� wind.� (See the note in page i8o of,nbsp;volume.)

� It is, therefore, evident, that in the open P'P^ quot; the whole of the wind comes from thenbsp;mofphere, and no portion is afforded bynbsp;� compofidon of water. Water cannot be deco^^nbsp;and transformed into gas, by the

parts. The opinions of Fabri and � have no foundation in nature, and are couC'''nbsp;� to experiment.

� cumflances proper to drive into the � M N, the greateft quantity of air, and tonbsp;� fure that quantity. The circumftances. ^nbsp;� favour the moft abundant produdion ofnbsp;*' are the following:

� I. In order to obtain the greateft efFelt;ft � the acceleration of gravity, it is neceffarynbsp;� the water fhould begin to fall at B C, ''/ithnbsp;� leaft poffible velocity j and that the heig^^*quot; ^nbsp;� th�e water FB fhould be no more than is ^

� tical velocity of this fedion to be produced hf � height or head equal to BC.nbsp;nbsp;nbsp;nbsp;^j-P

� 2. We do not yet know, by dired *' mem, the diftance to which the lateral coiflnbsp;3nbsp;nbsp;nbsp;nbsp;� nica^�

nication of motion between water and air-can extend itfelf; but we may admit, with confidence, that it can take place in a feftion double that ofnbsp;the original fcftion with which the water entersnbsp;the pipe. Let us fuppofe the feftion of the pipenbsp;B D E C, to be double the fedtion of.the waternbsp;at B C ; and in order that the ftream of fluidnbsp;may extend and divide itfelf through the wholenbsp;double fedlion of the pipe, fome bars, or a grate,nbsp;are placed in B C, to diftribute and fcatter thenbsp;water through the whole internal cavity of thenbsp;pipe.nbsp;nbsp;nbsp;nbsp;n

� ,3. Since the air is required to move in the pipe O, with a certain velocity, it muft benbsp;compreffed in the receiver. This compreiTionnbsp;w'ill be proportioned to the fum of the accelerations, which fliall have been deftroyed in thenbsp;inferior part K D of the pipe. 1 aking K Dnbsp;equal to one foot and a half, we Ihall have anbsp;prefllire fufircient to give the requifite velocitynbsp;in the pipe O. The fides of the portion KD, asnbsp;well as thofe of the receiver MN, muft be ex-aftly clofed In every part.

� 4. The lateral openings in the remaining part of the pipe B K, may be fo difpofednbsp;and multiplied, particularly at the upper part,nbsp;that the air may have free accefs w^ithin tfienbsp;tube. I will fuppofe them fo be fuch, thatnbsp;one.tenth part of a foot height of waternbsp;might be fufficient to give the neceflfary ve-

44^ nbsp;nbsp;nbsp;liejcription of the

*' loc^ty to the air at its introduftion through the � apertures. (i)

(I) � All thefe conditions being attended to, and f�P' poling the pipe B D to be cylindrical, it is required to dc'nbsp;� termine the quantity of air which paffes in a given tim^nbsp;� through the circular fedion, IC L. Let us take, in ftehnbsp;�KD = i,5; B C = BF = a; BD = By thenbsp;� common theory of falling bodies, the velocity in KL willnbsp;�be 7,76 v/ 0 * � J54 ; the circular fedion K ^nbsp;� = 0,785 ah Admitting the air in K L to have 21^'nbsp;� quired the lame velocity as the water, the quantity of th�nbsp;mixture of the water and air, which paffes in a fccoP^�nbsp;� through KL, is = 6,1 i/ ^ i� 1,4. Wenbsp;� dedud from the quantity (a amp;� 1,4) that heigl�*'nbsp;� which anfwers to the velocity the water muff lofe bynbsp;� portion of velocity which it communicates to the neWnbsp;� laterally and conflantly introduced ; but this quantitynbsp;� fo fmall, that it may be negleded in the calculation'nbsp;�^The water which paffes in the fame time of one fecoO*!nbsp;� through B C, is � 0,4nbsp;nbsp;nbsp;nbsp;\/ a 0,1. Confcqueihly�

� the quantity of air which paffes in one fecond thren^ � K L, will be � 6,1nbsp;nbsp;nbsp;nbsp; i � 1,4 � 0,4nbsp;nbsp;nbsp;nbsp; nbsp;nbsp;nbsp;nbsp;�

� taking the air itfelf, qven in its ordinary ftate of ootn � preH^oh, under the weight of the atraefphere. It will 1*�nbsp;proper, in pradical applications, to dedud one-fontnbsp;� from this quantity; iff, on account of the Ihocks whid'

� all its parts, have acquired the fame velocity as � water.�nbsp;nbsp;nbsp;nbsp;jP

If the pipe O do not difcharge the iwhole quantity of air afforded by the fall, the waternbsp;will defeend at X Z; the point K will rife innbsp;the pipe, the afflux of air will diminifli, andnbsp;part of the wind will iffue out of the lowernbsp;lateral apertures of the pipe B K¹.�¹

The direS:ion and the ftrength are the two particulars which may be required to be afeertained with relpe(ft to the wind.

The methods of determining the aftual direftion, by means of wind-vanes, or of the motion ofnbsp;clouds, amp;c. are too common and too obvious, tonbsp;need any particular defeription j but for the purpofenbsp;of meafuring the force of the windi feveral inftru-Oients have been contrived j fuch as a board fattened to the rod of a pendulum, which Ihews thenbsp;ftrength of the wind by the angle to which thenbsp;pendulum is caufed to deviate from the perpendi-. oolarj fuch alfo as a fmall windmill, which, bynbsp;^be number of revolutions that are performed in anbsp;amp;ven time, gives an eftimate of the force of thenbsp;^'nd, amp;c. but amongft all thofe inttruments, thenbsp;portable, lefs equivocal, and lefs complicated,

Venturi�s Experimental Enquiry on the lateral communication of motion in fluids. Prop, VIII.

450 nbsp;nbsp;nbsp;Dejcriptian of the

wind gage, is one which Vvas contrived by �f-James Lind of Windfor: this is delineated w fig. 8, Plate XV. which is about one-half o(nbsp;the real, or more ufual, fize of fuch inftrumenfs,-�nbsp;Philofophical Tranfa�lions, vol. 65, p. 353.

� This fimple inftrument confifts of two glafs tubes, A B, CD, of five or fix inches in length.*nbsp;Their bores, which are fo much the better alwaysnbsp;for being equal, are each about ths of an inchnbsp;in diameter. They are connefted together like anbsp;fyphon, by a fmall bent glafs tabe n b, the bore oinbsp;which is TrVth of an inch in diameter. On thenbsp;upper end of the leg A B, there is a tube of lattennbsp;brafs, which is kneed or bent perpendicularly outwards, and has its mouth open towards F. Onnbsp;the other leg C D is a cover, with a round hol� 0nbsp;in the upper part of it, -j-% ths of an inch in diameter. This cover, and the kneed tube are connetdet^nbsp;together by a flip of brafs cd, which not only giv^^nbsp;ftrength to the whole inftrument, but alfo ferves tonbsp;hold the fcale H I. The kneed tube and covernbsp;fixed on with hard cement, or fealing-wax. To thonbsp;fame tube is foldered a piece of brafs r, with nnbsp;round hole in it, to receive the fteel fpindle Knbsp;and at � there is juft fuch another piece of braBnbsp;Ibldered to the brafs hoop g h, which furround*nbsp;both legs of the inftrument. There is a fmaB

* They ought to be longer, as in feveral cafes the � a^vementioned length has been found infufficient.

fhoulde*quot;

principal Machines y nbsp;nbsp;nbsp;4^1

fiioulder on the fpindle at �, upon which the inftru-ftient refts, and a fmall nut at h to prevent it from being blown off the fpindle by the wind. The whole in-ftrument is eafily turned round upon the fpindle-by the wind, fo as always to prefent the mouth of the kneedi,nbsp;tube towards it. The lower end of the fpindle has anbsp;fcrew on it; by which it may be fere wed into the topnbsp;of a poft, or a ftand made on purpofe^ It alfo has anbsp;hole at L, to admit a fmall lever for ferewing it intonbsp;Wood with more readinefs and facility. A thin plate ofnbsp;brafs, k, is foldered to the kneed tube about half atlnbsp;iiTch above ,the round hole G, fo as to prevent rainnbsp;from /ailing into it. There is likewife a crookednbsp;tube A B, fig. 9. to be put on occafionally uponnbsp;the mouth of the kneed tube F, in order to prevent raiii from being blown into the mouth of thenbsp;wind-gage, when it is left out all night, or ex-� pofed in the time of rain. The force or momentumnbsp;of the wind may be afeertained by the afliftance ofnbsp;^his inftrument, by filling the tubes half-full ofnbsp;^ater, and pufhing the fcale a little up or down,nbsp;till the o of the fcale, when the inftrument is heldnbsp;perpendicularly, be on a line with the furface ofnbsp;the water, in both legs of the wind-gage. Thenbsp;inftrument being thus adjufted, hold it up perpen-tiicularly, and turning the mouth of the kneednbsp;tube towards the wind, obferve how much thenbsp;'''2ter is depreffed by it/in one leg, and how muchnbsp;�t is raifed in the other. The fum of the two is thenbsp;height of a column of water which the wind is ca-

pable of fuftaining at that time; and every body that is pppofed to that wind, will be preffed op'd!!nbsp;by a fcrce equal to the weight of a colurrn otnbsp;water, having its bafe equal to the furface that isnbsp;{cxpofed, and its height equal to the altitude ofnbsp;the column of water fuftained by the wind in thenbsp;' wind-gage. Hence the force of the wind upoonbsp;any body, where the furface oppofed to itnbsp;known, may be eafily found, and a ready compS'nbsp;rifon may be made betwixt the ftrength of onenbsp;gale of wind and that of another, by knowing thenbsp;heights of the columns of water, which the different winds were capable of fuftaining. Thenbsp;heights of the columns in each leg will be equal�nbsp;provided the legs are of equal bores ; ptherwife thenbsp;heights muft be calculated accordingly.

� The force of the wind may likewife be rnea-fured with this inftrument, by filling it until th^ water runs out at the hole G. For if we then hoIlt;inbsp;it up to the wind as before, a quantity of waternbsp;will be blown out; and, if both legs of the inftr*^'nbsp;ment are of the fame bore, the height of thecolum*^nbsp;fuftained will be equal to double the columnnbsp;water in either leg, or the fum of what is wantingnbsp;in both legs. But if the legs be of unequal bores�nbsp;then the heights muft be calculated accordingly.

� On land this inftrument may be left out pofed all night, amp;c. j but at fea it muft always benbsp;held up by the hand in a perpendicular pofiti^r''

whether

'''hether it be ufed when only half-full of water, or when quite full �, which laft will be frequentlynbsp;found to be the only praflicable method during thenbsp;'light.

� The ufe of the fmall tube of communication fig. 8. is to check the undulation of the wa-^cr, fo that the height of it may be read off fromnbsp;the fcale with eafe and certainty. But it is particularly defigned to prevent the water from beingnbsp;thrown up to a much greater or lefs altitude thannbsp;that which the wind can fuftain.

� The height of the column of water fuftained m the wind-gage being given, the force of the -wind upon a foot fquare is eafily had by thenbsp;following table, and confequently on any knownnbsp;furface.�

The fum is 23,958, which exprefTes the force of the wind when the height of the water in thenbsp;gage is 4,6 inches.

An7 alteration that can ufually take place in the �temperature of the water, makes no fenfible difference in this inftrument.

In frofty weather this gage cannot be ufed with common water. At that time fome other liquornbsp;muft be ufed, which is not fo fubje6t to freeze;nbsp;and, upon the whole, a faturated folution of com-tnon fait in water is the moft eligible; but in thatnbsp;Cafe (fince the fpecific gravity of a faturated fulu-tion of fait is to that of pure v/ater as 1,244 to i)nbsp;Che forces which are ftated in the preceding tablenbsp;Onuft be multiplied by 1,244. Thus, if in the preceding example the faturated folution of fait hadnbsp;been ufed inftead of water only, the force of thenbsp;'vind on a fquare foot, would have been 29,8nbsp;pounds ¹,

When fait-water is ufed, the force of the wind, which ftated in the table, muft be increafed in the proportion ofnbsp;G G 4nbsp;nbsp;nbsp;nbsp;the

The conftruftion of the barometer has been ro often varied at different times, and by differentnbsp;ingenious perfons, that a defcription of all h�nbsp;fhapes and varieties would be endlefs; but itnbsp;would at the fame time be ufelefs, fince few ofnbsp;thofe various conflruftions are really fufEcientlfnbsp;ufeful, either for the common purpofe of indicatingnbsp;the variations of the gravity of the atmolphere, ornbsp;for the purpofe of meafuring altitudes.

As the ufual perpendicular movement of the mercury in the barometer, upon the whole, hardlynbsp;amounts to two inches and a half, therefore thenbsp;principal objed of various ingenious perfons hasnbsp;been to extend the fcale, fo that very fmall varia'nbsp;tions might be rendered apparent.

One of the methods by which this objed has been accomplifhed, is reprefented in fig. 8nbsp;Plate XVI.

A B is a glafs tube about 5 or 6 feet long, at its lower end, and having an enlargement C D

the fpecific gravity of falt-water to that of common wat^r� thus, ufing the preceding example, we muft fay, as i : I?a44�nbsp;- '� ^3,958 to a fourth proportional, which muft be foun8 b/nbsp;multiplying the fecond term by the third, and then div-i(i|^Snbsp;the product by the firft term; but, the firft term beingnbsp;unity, we need only multiply 23,958 by 1,244.

the height of between aS and 31 inches above its lower extremity. This tube is filled with mercurynbsp;hiorh as about CD, viz. the middle of the en-largement of its cavity; and the upper part of it,nbsp;''iz. from the furface C D of the mercury, to anbsp;t^ertain place E, in the upper part G B of the tube,nbsp;Is filled with ringed fpirit of wine; the remainingnbsp;Ipace EB being a vacuum. F is a bafon contain-�fig quickfilver, wherein the lower end of the tubenbsp;ts immerfed.

When the mercury rifes in the barometer; for ^nftance, one inch in the enlargement CD, it isnbsp;Evident that a certain quantity of fpirit of winenbsp;itiufl: be forced by it into the part G B, which willnbsp;fill much more than one inch length of the tube GB,nbsp;firft becaufe one inch altitude of the cavity CDnbsp;Contains fpirit of wine enough to fill up fome inchesnbsp;length of the tube GB; and adly, becaufe onenbsp;*^ch perpendicular altitude of quickfilver is equiva-to feveral inches perpendicular altitude of fpiritnbsp;wine. By this means a fmall variation of th�nbsp;altitude of the mercury in C D, is indicated by anbsp;^Uch more apparent variation of the altitude of thenbsp;fipitit of wine in GB.

barometers, containing mercury and fpirits, or Mercury and water, or mercury and fome other li-have alfo been made of feveral parallel tubesnbsp;^onnefted together in a zigzag way; but I neednbsp;detain my reader by a particular defeription ofnbsp;filch barometers, fince they are all much more im-

perfect than the fimple ftraight mercurial barometer. Their imperfedtions principally arife from th� expanfion and contraftiop of the other fluidnbsp;the mercury, and from the vapour which beingnbsp;tricated from that other fluid, and occupyingnbsp;upper part of the tube, eounteradls in great me^'nbsp;lure the prefTure of the atmofphere.

The elongation of the fcale, or of the apparent motion of die barometer, has alfo been accompli^'nbsp;ed by inclining part of the mercurial barometer-Thus, in fig. 9. Plate XVI, the tube is ftraig*�*�nbsp;from the bafon B, to the altitude A, viz. abP'^*^nbsp;28 inches, but the reft, A C, is inclined tonbsp;horizon.nbsp;nbsp;nbsp;nbsp;^

Now, as the ordinary perpendicular motion ^ the quickfilver amounts to about three inch^�nbsp;which is equal to AD j therefore, when it movesnbsp;perpendicularly from A to D, but obliquely throO�'nbsp;A C, it muft run all the way from A to C, gt;n

fo that if the part A C be 12 inches long, viz-times as long as the part AD, then, whilft mercury in a ftraight barometer rifes one inchgt;nbsp;this flant barometer, it will run along fournbsp;length of the part A C j and of courfe thenbsp;alterations of the prefTure of the atmofphere ^nbsp;ihereby rendered more apparent. Yet thisnbsp;barometer is by no means fo accurate as a ftr^^�nbsp;one; and the caufes of its inaccuracy prinCip^nbsp;are the obliquity of the furface of the

part A C, the difficulty of obtaining, or of knowing, when the part AC is perfedtly ftraight,nbsp;the want of freedom in the motion of thenbsp;^uickfilver, which arifes from its attradion to-'^ards the glafs, and which increafes with the increaienbsp;^f the obliquity of the part AC.

Barometers are alfo made to move circular indexes; they have likewife been made with an ^rizontal elongation at the lower part of the tube jnbsp;always for the purpofe of extending the fcale. Butnbsp;^11 thofe conftruftions are attended with confiderablenbsp;iniperfedions �, fo that, upon the whole, the llraightnbsp;��iercurial barometer is the beft. Upon fuch anbsp;l�arometer for common purpofes, the altitude maynbsp;l^e commodioufly read off to the exadtnefs of one-liundredth part of an inch and on thofe which arenbsp;*)nade for meafuring altitudes, as mountains, amp;c.nbsp;gt;t may generally be read off within the 500th partnbsp;�fan inch.

I need not deferibe the ornamental part of the Common barometers, which is varied by the fancynbsp;every maker ; but a complete one is (hewn bynbsp;%� 14. Plate XVI.; two things, however, de-ferve to be mentioned, viz. the more ufual con:-ftfudeion of the lower part, or of the ciftern j andnbsp;nature of the nonius, which (in the beft con-ftruftion) is affixed to the index for the purpofe ofnbsp;indicating the fmall parts of an inch.

The lower part of the tube is fometimes bent and Enlarged, as is Ihewn by fig. 10. of Plate X^I.

in which conftrudion, when the barometer is to be removed from one place to another, the inftrumentnbsp;is turned gently upfide down, and the mercurynbsp;filling the whole tube, comes not higher than thenbsp;curvature A ^ but when the baroineter is fet ftraightnbsp;up againft a wall in the ufual way, then the quick-filver defcending a little way from the clofed uppetnbsp;end of the tube, fills the part A B, and rifes a litti^nbsp;way within the enlarged part B ; which in faftnbsp;the ciftern of the barometer. Sometimes the barometers are made with an open ciftern, in whichnbsp;cafe they aft well, but are not portable, unlefs the/nbsp;be carried ftraight up, and very gently, fromnbsp;place to another.

The moft portable barometers of the cotf' mon fort, have a little bag made of a piecenbsp;bladder, tied round their lower extremity, Thgt;*nbsp;bag and tube are filled with mercury, and no p^�^nbsp;of that mercury is expofed to the armofpherei bn*quot;nbsp;the atmofphere preffes upon the outfide of the bag�nbsp;which anfwers the fame purpofe. To tholenbsp;barometers a ferew S, fig. 13. Plate XVl-affixed to the frame, which, when the baronaetetnbsp;is to be carried from place to place, is ferewed upnbsp;wards by applying the hand to the milled headnbsp;by which means the prefllire of the ferew agat*^nbsp;the bag, pufhes the mercury into the tube, fi^^nbsp;the whole length of the tube, and renders the �ftnbsp;ftrument quite poftable.

the above-mentioned conftruftion of cifterns, when the mercury rifes in the tube, it muft fall in thenbsp;t^iftern; in confequence of which the altitude ofnbsp;the mercury Ihould always be reckoned from thenbsp;Outface of the mercury in the ciftern j this, how-excepting in barometers for meafuring altitudes, is in general not taken notice of j fince thenbsp;^�fference is not great.

The principle of what is commonly, though improperly, called nonius, may be better explained by trieans of an example. This curious contrivance isnbsp;great ufe; and in fad it has been applied to anbsp;Sreat variety of philofophical, and principally ofnbsp;3ftronomical, inftruments ¹ ².

Suppofe that a fcale, as AB, fig. 11. Plate XVI. ts divided in inches only, and that the parts of annbsp;*uch (for inftance, the quarters) be required to benbsp;ttreafured by means of a nonius: C D is the no-t^'us, viz. a little fcale, moveable over, or along, thenbsp;of the fcale AB. The conflrudion of thisnbsp;*^unius is fuch, that the diftance CD, which is equalnbsp;three inches, is divided into four equal parts;

whereaSj on fhe fcale, the fame length is divide^ into three equal parts; fo that the divifions of th^nbsp;nonius are to thofe of the fcale as 4 to j. Therefore the parts, or divifions, of the nonius arenbsp;Ihorter than the divifnans of the fcale,nbsp;each part of the nonius muft be equal to thKe'nbsp;quarters of each divifion of the fcale; hence thenbsp;firft divifion of the nonius, which lies h�'nbsp;fween o and !gt; is one-quarter of an inch fhorte*'nbsp;than the next divifion of the fcale; the fecondnbsp;divifion of the nonius is half an inch diftant fr^*^nbsp;the next divifion of the fcale; and the third divifi�*'nbsp;of the nonius is three-quarters of an inch dift�*'^nbsp;from the next divifion (meaning always towardsnbsp;right-hand) of the fcale.

Now, when I am to meafure the diftance Ef' by the application of the fcale, I find it equalnbsp;four inches; but if I want to meafure the dd'nbsp;tance E G, the fcale will Ihew that it is more th^**nbsp;four inches, but not how much more ; now, innbsp;der to find how much more than four inches tb�nbsp;diftance EG is, I move the nonius forward untilnbsp;edge D coincides with G. (Here the diftance Enbsp;is not placed clofe to the fcale and nonius, onlynbsp;avoid confufion) and in that cafe, I find thatnbsp;third divifion of�the nonius coincides with

��the divifions of the fcale; but that divifion 01 nonius, as has been fhewn above, was threenbsp;ters of an inch diftant from the next divifion ^ ^nbsp;fcale ; therefore the nonius has now been adv^anc^nbsp;three quarters-of an inch, as is ftiewn by fig*

What has been faid of this nonius may be eadly applied to explain the principle of every other no-; viz. as by this nonius we have the quartersnbsp;an inch, becaufe the fame ipace of three inchesnbsp;divided into three equal parts on the fcale, andnbsp;'��to four equal parts on the nonius; fo wc maynbsp;^'^e the tenth� of an inch if the fame fpace ofnbsp;5 inches be divided into 10 equal parts on thenbsp;I'^tiius i fo alfo we may have the hundredths of annbsp;if the feme fpace, which is divided into 9-^�nths of an inch on the fcale be divided, into 10nbsp;^Ual parts on the nonius; and fo forth.

The barometers for meafuring mountains, or al-htudes in general, muft be made with much greater ^'^curacy than thofe of the common fort j their fcalenbsp;be longer ; the mercury in the.ciftern muft benbsp;f^ifed by means of a fcrew always to the fame mark,nbsp;order that the divifions of the fcale may indicatenbsp;real altitudes of the furface of the mercury in thenbsp;above that of the mercury in the ciftern.nbsp;alfo muft be furnilhed with a ftand capablenbsp;^^Pporcing them in a perpendicular fituation ;�nbsp;� otherwife they cannot be fufpended ftraight upnbsp;^^-tlie fidcs ofmountains; and great care muft benbsp;^d to render fuch inftruments as portable and as fe~nbsp;^*'0 as poflible.

Various contrivances have been made and exe-^^^d for the attainment of fuch objefts. The lateft

and perhaps the beft, but by no means the fimpleft� was made by Mr. Haas; I ftiall, however, briefly^nbsp;' defcribe the conftrudtion of the portable barometer�nbsp;contrived and conftruamp;ed by the late very ingeniof�nbsp;philofophical inftrument-maker, Mr. Jeffe Ratnf*nbsp;den, which have been iifed by various philofoph*''nbsp;cal gentlemen, and efpecially by Colonel Roy in hi�nbsp;numerous meafurements. Fig. 20. and 21. ofnbsp;XVI. exhibit a barometer of this conftruftio*��nbsp;both in the fituation proper for obfervation,nbsp;packed up.

� The principal parts of this inftrument arc ^ fimple ftraight tube, fixed into a wooden ciftc�^|*nbsp;� A, which, for the conveniency of carrying�

� Ibut with an ivory fcrew B, and that being *' moved, is open when in ufe. Fronting rh'*nbsp;quot; aperture is diftin�tly feen the coincidence of th^nbsp;� gage-mark, with a line on the rod of annbsp;float, fwimming on the furface of the quickffl'^^�^�nbsp;� which IS raifed or deprefled by a brafs fcrew ^ ^nbsp;quot; the bottom of the ciftern. From this, as' anbsp;� point, the height of the column is readilynbsp;quot; fured on the fcale D attached to the frame� ^

� ways to 3^ ' s- part of an inch, by means of a ** nius E, moved with rack-work. Anbsp;� meter F is placed near the ciftern, whofenbsp;� heretofore was ufually inclofed within the wo� ^

The air-pump is an inftrument which ferves to draw, or pump, the air out of any velTel which isnbsp;properly adapted to if. This noble engine is onenbsp;^f the principal inftruments which have, fince thenbsp;*^iddleof the 17 th century, contributed to the rapidnbsp;advancement of natural philofophy, by affording thenbsp;^�ans not only of verifying what had been advancednbsp;^rid conjectured by feveral learned perfons concern-the atmofphere ; but likewife of trying a greatnbsp;�^any experiments, and of afcerta!ining a vaft num-of new and interefting facts.

The original principle or conftrudlion of the air-PUmp is fimilar to that of the common water-pump '''hich wc have already defcribed j excepting thatnbsp;parts of the air-pump muft be executed with.

very great accuracy, for the pui-pofe of intercepting the paflage of the air, where that is not wanted�nbsp;and which, on account of the prelTure of the at*nbsp;mofphere and the fubtlety of the air, cannot benbsp;well intercepted, without the utmoft mechanicalnbsp;accuracy.

The firft conftru�lion of the air-pump was very imperfeft, but a variety of improvementsnbsp;gradually removed its imperfeftions, and multgt;quot;nbsp;plied its varieties, fo that at prefent there ar^nbsp;various forts of air-pumps in ufe, which at^nbsp;more or lefs complicated, more or lefs effcftnalnbsp;in exhaufting, and more or lefs expenfive. Tb�nbsp;hiftory of moft of its improvements and fhapcs�nbsp;makes a very entertaining article in variousnbsp;books, and efpecially in the Encyclopaedia Bti'nbsp;tannica, under the article Pneumatics �, but fevet^^nbsp;of thofe improvements � need not be noticednbsp;prefent, fince they have been fuperfeded by bett^*^nbsp;contrivances. The defcription of the particul^^nbsp;conftrudlions, at lead; of the moft: ufoful, maynbsp;found in the above-mentioned article, or in oth^^nbsp;works that are mentioned in the note. Wenbsp;only defcribe the principle of the fimpleftnbsp;which is now in ufe, for the purpofe of givl^^nbsp;the ftudent a clear idea of the principal partsnbsp;that exhaufting engine, and ftiall then fubjoin tb�nbsp;defcription of an improved one which was lately

�^rinci^al Machines, ^c. nbsp;nbsp;nbsp;40

that conftruction has not, as far as I knoWj been defcribed in any other publication *.

Fig.

� The air-pump was firft invented by Otto Guericke, a gentleman of Magdeburgh in Germany, about the yearnbsp;*^54quot; (Schottus. Mech. Hydraulico-Pneum.) Soon after,nbsp;Guericke�s contrivance was imitated and greatly irni-proved, in England, by the celebrated and indefatigable Mr.nbsp;fioyle (fee his works), who was affifted by feveral eminentnbsp;perfons, and efpecially by Dr. Hook, a gentleman of a moltnbsp;inventive mechanical genius. But the want of Ikill in thenbsp;then exifting workmen, and the deficiency of feveral articles, flill rendered the air-pump a very imperfedl infiru-ment, until Mr. Hawkelbee produced an improved andnbsp;elegant engine of that fort, which has been copied by manynbsp;srtifts here and elfewhere, and is even at preferit in ufenbsp;aniongft philofopherS� (See the defcription of it in Dr.nbsp;�efagulier�s Philofophical Works.) Another pump, fome-t''hat different, was alfo conftrudled by Gravefande. (Seenbsp;his Courfe of Phiiofophy.) But a very capital improve-ttient of the air-pump was made in almoft all its parts, bynbsp;the late famous engineer, Mr. John Smeaton; (fee his de-h^tiption in the 47th vol. of the Philofophical Tranfadtions);nbsp;and a well-made pump of that fort, undoubtedly, is one of thenbsp;heft now extant; yet, after the interval of about 25 years,nbsp;this conftru61:ion was followed by feveral other contrivances,nbsp;lonie of which are certainly fuperior to it. The beft ofnbsp;thofe latter contrivances are, a pump by Mr. Haas; (fee itknbsp;t^onftruiftion in the 73d vol. of the Philolbphical Tranfac-tioijs); an air-pump by Mr. Prirtce of Bofton in America jnbsp;(Encyclopaedia Britannica, article Pneumatics); one bynbsp;Cuthbeitfon, an eminent philofophical-inftrumentnbsp;H M 2nbsp;nbsp;nbsp;nbsp;maker.

Fig. i8. of Plate XVI. exhibits the fitnpleft fort of air -pump. AB is the brafs barrel, whichnbsp;is reprefented as being tranfparent for the purpofcnbsp;of fliewing the conftrudion of the internal parts*nbsp;The infide of the barrel is as perfecftly cylindrical a�nbsp;can be made, and very fmooth. The barrel is opennbsp;at top, or if furnifhed with a cover, that cover isnbsp;perforated for the paffage of the rod F G, and ofnbsp;the air. The bottom B of the barrel is accuratelynbsp;clofed by a flat piece of brafs, excepting a fmallnbsp;hole, which pafles through the faid piece, and communicates with the cavity of the glafs receiver Djnbsp;which is cemented into the piece C, and out ofnbsp;which the air is to be pumped. The fmall hole innbsp;the flat bottom of the barrel is covered by a flip ofnbsp;oil-filk, which is ftrained over it j whence it appears?

maker, at preferit in London; (Encyclopedia BritanniC^i article Pneumatics.) A very good improvement of th�nbsp;air-pump was made in France by M. Lavoifier, and othernbsp;fcientific perfons, which rendered that engine capablenbsp;exhaufting to a very great degree; but it is faid, thatnbsp;that conftrudlion is difficultly executed, and eafily putnbsp;of order.

The fixth vol. of the Tranfadtions of the Royal Iri^ Academy contains the defcription of an air-pump, contrivenbsp;by the Rev. James Little, of Lacken, in the county onbsp;Mayo. This paper, befides the particular defeription of tl��nbsp;inftrument, contains leveral good obfervations onnbsp;neral fubje� of air-pumps, and apparatus.

that air may pafs from the receiver Dj into the barrel; but it cannot go from the latter into thenbsp;former. E is a pifton, viz. a folid piece of brafs,nbsp;Covered over with leather foked in oil, or othernbsp;greafy matter, which fitting the cavity of the barrelnbsp;Very accurately, may be moved up or down allnbsp;^long the barrel, by means of the rod F G, withoutnbsp;admitting any air between the furface of the barrelnbsp;3nd that of the pifton. But there is a hole, indicated by the dotted lines at E, which pafles throughnbsp;the pifton, and has its upper end covered withnbsp;^ ftrained flip of oil-filk, fimilar to the valve at thenbsp;bottom B of the cylinder. The valve in the piftonnbsp;permits the air�s paflage from E to G, but not thenbsp;Contrary way. If the hand be applied to the handlenbsp;and the pifton be moved alternately up andnbsp;down the cylinder, the veflfel D will thereby benbsp;�'�adually exhaufted of air^ and the procefs of it is asnbsp;follows:

When the pifton is drawn upwards, the Ipace betw�een the lower part of it and the bottom of thenbsp;Cylinder is enlarged, and the air in it is rarefied j-quot;'bereas the air in the receiver D is denfer thannbsp;*^hat; therefore the elafticity or expanfive propertynbsp;this air prefl�s againft the lower part of the oil-

which is within the cylinder preflfes upon the ^Ppcr fide of it �, hence part of the air of the ve��lnbsp;^ pafles into the barrel, and of courfe the quantitynbsp;air in D is diminiihed. Then, by deprefllng

H H 3 nbsp;nbsp;nbsp;the

the pifton, the (quantity of air which is between it and the bottom of the pifton is condenfed ; hencenbsp;ic preffes againft the lower fide of the valvenbsp;more than the atmoipheric air preffes on the iipP^''nbsp;fide of the fame; therefore the greateft partnbsp;that air paffes through that valve into the atmof'nbsp;iphere. When the pifton is drawn upwards thenbsp;lecond time, the like effeift takes place, and thenbsp;air of the veffel D is diminilhed a little morenbsp;Thus, by repeating the movement of the pifton�nbsp;the veffel D is gradually exhaufted of air to a cet'nbsp;tain degree, which is the utmoft limit of the pump ^nbsp;exhaufting power j and that degree is expreffed h/nbsp;the proportion which the air that laftly remain^nbsp;in the vefi�l D, bears to that which was atnbsp;in it. Thus, if the remaining air is one-tenthnbsp;of the original quantity, the pump is faid to hav^^nbsp;rarefied the air ten times ; for, in fad, thenbsp;maining quantity of air in D, fills up ten tim^*nbsp;the fpace which it occupied before thenbsp;hauftion.

* It will be eafily comprehended, that if the valves m ^ pifton and at the bottom of the barrel could be openednbsp;the utmoft freedom, the quantity of air, which remainednbsp;the veffel D, after every ftroke of the pifton, would be^^nbsp;that quantity which was in it, previous to that ftroke, 3�nbsp;Capacity of the veffel D is to the fum of the capacit�^�nbsp;that veffel, and of the barrel.

A more particular examination of the parts as 'Veil as operations of this pump, -will'point out thenbsp;powers, the defed, and the improvements of air*nbsp;pomps in general.

As the capacity of the barrel is generally fmall in proportion to that of the veflel, out of which the airnbsp;�s to be exhaufted in feveral experiments, the exhauf.nbsp;tion will proceed but flowly ; therefore, in ordernbsp;^0 expedite the operation, pumps have been madenbsp;'vith two barrels, which are moved alternately bynbsp;Cleans of a wheel with a handle, and racks affixednbsp;^0 the rods of the piftons. Both barrels commu-iiicate with the fame receiver, and the exhauftionnbsp;goes on as quick again as when one barrel isnbsp;Ufed.

-The receiver cemented to the piece B C, at the bottom of the barrel, cannot be adapted to a ^reatnbsp;'variety of experiments j therefore, inftead of that,nbsp;barrel or barrels have been made to communi*nbsp;with the fam.e duct which opens in the middlenbsp;a pretty large and flat metal plate. Then a glafsnbsp;feceiver of any required lize, within certain limits,nbsp;placed with its aperture upon that plate, and isnbsp;^^haufted, amp;c.�In order to prevent the admiffionnbsp;''f air, between the edge of the receiver and thenbsp;plate of the pump, it was formerly ufed to inter*nbsp;Pofe a piece of wet leather, which, however, wasnbsp;^ound to be prejudicial on feyeral accounts j hencenbsp;leather is now feldom ufed ; but the edges ofnbsp;receiver, as alfo the furface of the plate, arenbsp;H H 4nbsp;nbsp;nbsp;nbsp;grouncf

ground fo very flat and fmooth, that when the receiver is placed upon the plate, no air can through, efpecially if the leaft film of oil be inter-pofed, or be placed on the outfide of the edge of

Both thofe improvements, viz. the double barrel and the place, are feen in fig. 17. Plate XVI.

By infpedting fig. 18. Plate XVI. it will alfo be eafily underftood, that when the air which rc*nbsp;mains within the veflel D, is fo far rarefied as notnbsp;to have force fiifficient to open the valve at th�nbsp;bottom of the barrel, then the pump cannot eX*nbsp;hauft the veflel any farther. This efFeft is alf*�nbsp;partly produced by the air which remains betweennbsp;the pifton and the bottom of the barrel, when thenbsp;pifton is down. Now in order to avoid thefe in'nbsp;conveniences, feveral contrivances have been made?nbsp;and it is the different nature of thofe contrivancesnbsp;that forms the variety of thofe air-pumps whichnbsp;have been mentioned above.

Mr. Haas�s laft air-pump (for this is not the fame as was contrived by the fame perfon fornenbsp;time ago, and which is delcribed in the yjd vol-of the Philofophical Tranfaftions) is Ihewn i*^nbsp;Plate XVI. fig, 2, and 5. The wooden frame 0^nbsp;the machine is lufficiently apparent in fig. 2. Therenbsp;are two barrels in it, which by turning the handlenbsp;H, round the axis A, about .one turn and a hal^nbsp;one way, and then as much the other ''vay�nbsp;are worked alternately j for within the wooden

BB, there is on the axis A, a wheel with teeth, �which catch into the teeth of the racks, which arenbsp;affixed to the rods of the piftons.

The two barrels communicate with a common duT, which opens in the middle of the Plate � P.nbsp;This plate is firmly fixed upon a wooden pillarnbsp;that proceeds from the Hand or pedeftal of thenbsp;tiiachinc. O, O, at the lower part of the machine,nbsp;are two veffels affixed to the ends of the barrels,nbsp;and their office is to receive the oil which graduallynbsp;paffes from the infide of each barrel through thenbsp;'quot;alve at the bottom.

Fig. 1. is one-eighth of the real fize; and fig. 5. which exhibits a feftion of one of thenbsp;barrels, is one-fourth of the real fize.

At the bottom V of the barrel, there is a valve which opens outwards, viz. the air may be forcednbsp;fi'orn the infide of the barrel into the atmofphere,nbsp;but cannot go the contrary way.

The form of the pifton is pretty well indicated the figure. It confifts of two pieces of brafsnbsp;Screwed together, and holding between them cir-'^ular pieces of leather, the edges of which rubnbsp;^Eainft the cavity of the barrel. There is a valvenbsp;the pifton, through which the air may pafs fromnbsp;��he upper part of the barrel into the lower, butnbsp;�^ot nice verja. The rod of the pifton is quitenbsp;htiooth and cylindrical; it paffes through, what isnbsp;^^lled, a collar of leathers, viz. through a holenbsp;in many'pieces of leather, which are contained

in a brafs box Z, on the top of the barrel.¹ Several holes are feen towards the upper part ofnbsp;the barrel, which communicate with a cavity, ioquot;nbsp;dicated by two dark lines, that runs all round thenbsp;tipper part of the barrel, and communicates withnbsp;the duff D of communication with the plate of thenbsp;machine.

When the phton is drawn upwards, the air may pafs, though not very freely, from the upper tonbsp;the lower part of the barrel, through the valve it^nbsp;the pifton �, but when the pifton is raifed fo highjnbsp;as that its lower furface be higher than the above-mentioned holes, then the air from the receiver�nbsp;which flarid^ on the plate, coming through thenbsp;dud D, may freely pafs into the barrel j fornbsp;that cafe there is neither valve nor any thing elfenbsp;that obllruds its paflage. Then on depreffing th^nbsp;pifton, the air which has entered the barrel bein^nbsp;comprelTed towards the lower part of the barrehnbsp;will be forced out of it through the valve atnbsp;It is owing to the freedom with which the airnbsp;pafs from the receiver which ftands on the plal^^�nbsp;into the ban el, that this pump rarihes to a vef)fnbsp;confiderable degree.

Thefe leathers as well as thofe of the pifton, are welj foked in hog�s lard (fome workmen foke them in oilnbsp;tallow). The latter fit the barrel, and the former fit tb�nbsp;outfide of the pifton rod, fo well as not to allow the pafl^�

It will appear on the lead refledion, that no pump can pofllbly remove all tlie air from any receiver 5 for the quantity of air which is expelled atnbsp;each ftroke of the pifton, is only a portion ofnbsp;''^hat was in the receiver previous to that ftroke jnbsp;and therefore a much greater quantity of air fimilarnbsp;denfity to that which was laft expelled, multnbsp;remain in the receiver. So that a great degree ofnbsp;rarefadion, but not a complete exhauftion, is allnbsp;that can be expeded from the beft pump; whereasnbsp;the torricellian vacuum is much more completenbsp;than what is made by an air-pump.

When a pump of the common fort rarefies the air of a receiver 2CO or 160 times, it may be con-fidered as a very good inftrument of the kind. Thenbsp;Very beft pumps now extant, will rarefy the air 600nbsp;even 800 times; but I am unwilling to ftate thenbsp;titmoft effed of thofe conftrudions; IJnce a verynbsp;trifling difference generally produces a confiderablenbsp;alteration in the refult. The pump being recentlynbsp;put together, the valves being more or lefs ftrain-cd, the want of a due quantity of oil, between thenbsp;moving parts of the engine, and various other particulars, render the pump more or lefs capable ofnbsp;rarefying the air of a receiver j and generally theynbsp;rarefy to a great degree at firft, but foon lofc thatnbsp;power.

The various methods of eftimating the quantity of air which remains in the receiver after a certain

adion of the pump, or of meafuring the rarefadion, will be fliewn in the fequel.

The glafs receivers for an air-pump are of dif-ferent fizes, aGr'ording to the nature of the experiments. Some of them are open at top, and their upper aperture there is fometimes applied *nbsp;flat brafs plate, which is ground very frnooth, or 3nbsp;focket is cemented j to which plate or focket variousnbsp;apparatufes are affixed.

Sometimes the receivers are not fet immediately on the plate of the pump, but they are fet ounbsp;another plate, which has a pipe with a flop-cock)nbsp;that may be ferewed into the centre of the princip^^nbsp;plate P. With this apparatus the air of the receivciquot;nbsp;may be rarefied as well as if the receiver ftood upoUnbsp;the principal plate j and when that is done, bynbsp;turning the ftop-cock, and unferewing it from th^nbsp;middle of the principal plate, that receiver, havingnbsp;the air rarefied, may be removed together with thenbsp;filial] plate, and leave the pump ready for other experiments. This auxiliary plate, with its pipe andnbsp;ftop-cock,. is commonly called a transferrer. Seenbsp;fig. 19. Plate XVI.

Of the various experiments which are ufually performed with the air-pump, and which are de-feribed in almoft all the works on Natural Phi'nbsp;lofophy, I fhall briefly deferibe a few only, as theynbsp;will be quite fufficlenc to indicate the general modsnbsp;of making fuch experiments.

place

Place the glafs receiver upon the plate P of the pump, as appears at fig. 2. taking care thatnbsp;both the edge of the receiver and the plate, be quitenbsp;^lean, and fmearing the former with a very frnallnbsp;t^Uantity of oil then work the pump by turning thenbsp;handle H of the machine alternately as far as it willnbsp;go one way, and as far as it will go the other way.nbsp;After a few ftrokes you will find, upon trial, that thenbsp;glafs receiver adheres very firmly to the plate fornbsp;3-s the air is partly withdrawn from the infide of thenbsp;^�eceiver, the preflure of the atmofphere on the out-hde becomes manifeft. The adhefion of the receiver to the plate, increafes in proportion as younbsp;Continue to w'ork the pump.

There is, in every air-pump, a ferew-nut on the of communication between the barrel and thenbsp;Receiver; which may be opened Occafionally, ianbsp;^fder to let the external air enter the cavity of thenbsp;�quot;cceiver: fo that if, in the above-mentioned cafe,nbsp;^his ferew-nut be opened, the air will rufh innbsp;'^Ith an audible noife; in confequence of whichnbsp;adhefion of the receiver to the plate will benbsp;*'ct�ioved.

^nder fuch a receiver, or other receivers of dif-ctcnt forms, a variety of things may be placed,.

on rarefying the air, different effefts will take ^lace j but in deferibing thofe experiments, it will

fufficient to fay that certain effefts are produced y Certain fubftanccs in vacuo, or in the exhaufted-Receiver; meaning fuch a vacuum as may be produced

duced by the air-pump for a more perfef� vacuum is always denominated the torricelU^^nbsp;vacuum.

An exhaufted receiver does not appear different from what it does before the exhauftion. Ohjed^nbsp;may be feen in it and through it, juft as well in onenbsp;cafe as in the other.

A lighted candle placed under the receiver of the pump will go out after a few ftrokes of the

Animals die fooner or later in the receiver of th� air-pump. Infefls die lateft in it, viz.nbsp;the lapfe of fome hours. A dog, a cat, a rabbit? *nbsp;trioufe, a bi.^d. See. begin to fhew figns ofnbsp;�afinefa after a few ftrokes of the pifton ; the nn^nbsp;eafinefs, the quickening of the refpiration, andnbsp;panting for want of air, increafe gradually jnbsp;miting, bleeding at the mouth and Ooftrils, lofsnbsp;ftrength, and fwelllng of the body, fuccecd ; butnbsp;thofe difagreeable fymptoms laft not many minut^*'nbsp;for death foon clofes the feene.

If previous to their death, air be admitted the receiver, by opening the fcr�w-nut, the anim�^^nbsp;generally revive, provided the rarefa�lion hasnbsp;broken any vital parr.

If water be placed in a glafs under the recei'^^^ of the pump, on working the machine, the wat^^nbsp;will at firft appear full of air-bubbles, then tho/� a�tnbsp;bubbles enlarge, and coming out of the water,

*t the appearance of boiling. By rarefying the ^ir, and of courfe removing the preffure of the at-i^ofphere from the furface of the water, the airnbsp;'''hich is ufuaJly contained in it is expanded in virtue of its elafticity, and efcapes from the water,nbsp;^'''hich efcape gives the appearance of boiling; fornbsp;the water does not acquire any heat by it.�Thenbsp;thing happens with feveral other fluids. Ifnbsp;fiflies be contained in the water, the rarefafhion ofnbsp;the air kills them, and breaks their air-bladdersu^nbsp;Kven the minute infefts that are frequently feen innbsp;vinegar, are deprived of life if the vinegar be ex-pofed to the exhauftion of the air-pump.

Shrivelled fruit, under the receiver, are generally fwelled by the exhauflion, and appear very plump,nbsp;'vhilft they remain in it.

A bladder, containing a very fmall quantity of and having its neck tied up, when placed undernbsp;the redeiver, will, on exhaufting the receiver, fweljnbsp;^�P and appear quite full; the reafon of which is,nbsp;that when the prefllire of the atmolphere is re-ttioved from the out�de of the bladder, the internalnbsp;expands itfelf.

Fig. 4. of Plate XVI. reprefents a little ma-chine confifting of two little fets of mill-fails, a and gt; which are of equal weights, are unconnedlednbsp;V'lth each other, and turn with equal freedom uponnbsp;their axes. Each fet has four thin fails, fixed intonbsp;^he axii j thofe of the mill a have their planes perpendicular to the axis, thofe of h are pai'^allel to '

their axis; in confequence of which when the a turns round in corr.mon air, it is little refitted bynbsp;the air, whereas the other is refitted in a confi'nbsp;derable degree. There is a pin in each axle nearnbsp;the middle of the irarne, which goes quite throughnbsp;the axle, and ttands out a little on each fide ofnbsp;upon thefe pins, the ttider may be made to beargt;nbsp;and fo hinder the mills from going, when the ftrongnbsp;Ipring c is fet or bent againft th� oppofite ends oinbsp;the pins.

This little machine ferves to fhew the refittanc^ which air offers to the motion of bodies, whichnbsp;fiftancc is proportionate to the furface that the bocffnbsp;prefents direftjy before the air.

For this purpofe the above-mentioned little chine, with the fprings bent and fet upon the axl^��nbsp;is fituated upon the plate of the pump, and a re*nbsp;ceiver is placed upon it; but this receivernbsp;have a focket, with a fet or collar of leathers,nbsp;mented to its upper aperture, and a long wirenbsp;pafs through a hole in the leathers, like the rodnbsp;the pitton in fig. 5; and it mutt be fo fituatednbsp;the wire of the receiver may be pufhed downnbsp;adtly upon the Aider and difcharge it fromnbsp;pins; in confequence of which the mills beingnbsp;pelled by the fpring, will be caufed to turn round-Now if this operation be performed when thenbsp;ceiver is full of air, it will be found that the mitt ^nbsp;will turn round much longer than the other, fot

Place the glals, AB, fig. i. Plate XVI.-open at both ends, upon the plate of the pump over thenbsp;hole, amp;c. and place your hand flat and clofe tonbsp;. the upper aperture B of it. On exhaufting thatnbsp;glafs, you will find that the hand is preflTed with anbsp;weight which increafes in proportion as you cofl'nbsp;tinue to work the pump, and the adhefion isnbsp;great, that the hand cannot be removed, unle^*nbsp;the ferew-nut be opened, and the air let into thenbsp;glafs.

The cups which are ufed by furgeons for bleed' ing, are often applied to the flelh, by means ofnbsp;exhaufting fyringe, which is nothing more than ^nbsp;fmall barrel with pifton and valves, exaftly like th^nbsp;one deferibed in page 468. This fyringe is ferewednbsp;to the neck of the cup, whilft the oppofite andnbsp;much larger aperture of the cup is applied to th^nbsp;lurface of the body, amp;c.

If inftead of applying the palm of the hand, tie a piece of bladder over the aperture B of th^nbsp;above-mentioned glafs, on working the pump, whi^^nbsp;removes the prelTure from the under part of th^nbsp;piece of bladder, the preflTure on the external P^'^��nbsp;of it will become very manifeft; for the bladd^*^nbsp;will be hollowed by it, and at laft it will be brok^itnbsp;with confiderable noife.

cups, which, when joined together, form a globe, the cavity of which communicates with the at-tnofpherkal air, through the pipe E, when thenbsp;ftop-cock D is open, otherwife it is abfolutelynbsp;clofed *.

Join the two hemifpheres j ferew the end of the pipe E, into the centre hole of the plate of thenbsp;air-pump, and open the ftop-cock D. In this fi-tuation work the pump fo as to exhauft the globenbsp;A B; then lliut up the ftop-cock D, unferew thenbsp;pipe E, with the globe from the pump, and ferewnbsp;the piece C upon the pipe E. The globes nownbsp;being exhaufted, the preflure of the atmofpherenbsp;�'vill force the two hemifpheres, A and B, verynbsp;powerfully againft each �ther; fo that if twonbsp;ftrong\men, applying their hands, one at thenbsp;tipper ring A, and the other at the lower ring C,nbsp;Endeavour to feparate them, they will find it verynbsp;^lifficult; for if the diameter of the hemifpheres benbsp;^ur inches, there will be required a force equalnbsp;to little lefs than 200 pounds to pull them afunder.nbsp;^f the globe, thus exhaufted, be fufpended bynbsp;Either of the rings to an hook within the receivernbsp;�f an air-pump, and that receiver be exhaufted, the

the aperture more effe�l;ually ; but when they are well made, their edges are ground properly, a little oil fmeared overnbsp;the edges is quite fufficient for the purpofe.

two

two het�iifpheres will f�parate immediately � fhev?'* ingj in a moft convincing mannet, that they adhered to each other merely in confequence of tbsnbsp;prelTure of the atmofphere.

If you place a barometer under a tall glafs re* ceiver of the air-pump, and rarefy the air by working the pump, you will find that the quickfilvernbsp;defcends gradually in the tube of the barometer;nbsp;for as the quickfilver is kept up in the barometernbsp;by the prefllire of the atmofphere on the furface ofnbsp;the quickfilver of the ciftern, and its altitude isnbsp;proportionate to that prefllire, therefore, accordingnbsp;as the prelTure is diminiflred, fo the quickfilver de-fcends in the tube. Now, from what has beennbsp;fhewn above in chap. VIII. it appears, that if thenbsp;prefllire upon the ciftern of the barometer be reduced to one half, the height of the mercury i^nbsp;the tube will alfo be reduced to one half} if tha*nbsp;prefllire be reduced to one quarter of its origin^^'nbsp;quantity, then the altitude of the mercury in thenbsp;tube will likewife be reduced to one quarter of thenbsp;original altitude; in fliort, the altitude of the mercury in the tube of the barometer under the receiver of the pump, is an exadt meafure of thenbsp;prefllire on the ciftern, or of the quantity of elafti^nbsp;fluid that remains in the receiver, or of the elaf-ticity of that fluid j for the latter is proportionate tonbsp;the former. Hence the barometer becomes a verynbsp;good gage of the power of the air-pump, or of thenbsp;degree of rarefadion; for the altitude of thenbsp;^nbsp;nbsp;nbsp;nbsp;mercuty

ttiercury in its tube, is to the altitude of the fame at any period of the rarefadtion, as the entire capacity of the receiver, or as the air of the ufualnbsp;lt;^-enfity, is to the denfity or quantity of the air in thenbsp;receiver at that period ; fo that if the mercury innbsp;the barometer flood originally at 30 inches height,nbsp;andj after working the pump a certain time, itnbsp;ftands at the altitude of one inch, the conciufion is,nbsp;that the air within the receiver has been rarefied 30nbsp;times, or that the air which remains in the receivernbsp;is the 30th part of that which was in it before thenbsp;ivorking of the pump, fince one inch is the 30thnbsp;part of 30 inches. Thus alfo, if the mercury innbsp;the barometer is found to fland one tenth of an inch'nbsp;above that of the ciflern, the conciufion is, thlit thenbsp;air has been rarefied 300 times, amp;c.

Upon this principle three gages have been con-ftrudled, viz. she Jhort barometer gage, the long barometer gage, and the fyphon gage.

The fliort barometer gage is nothing more than the lower part of a barometer, viz. a tube of aboutnbsp;^ Or 9 inches in length, filled with mercury, andnbsp;iiTimerfed with its aperture into a fmall quantity ofnbsp;tnercury contained in a glafs veflel, which formsnbsp;the ciflern. This gage is either placed under thenbsp;toceiver upon the principal plate of the pump, ornbsp;^t IS placed under a feparate fmail receiver, upon anbsp;httle auxiliary plate, which fome air-pumps havenbsp;^itprefsly for that purpofe, as in fig. ly- Plate XVf.nbsp;�t is evident that this gage, not being equal to a

whole barometer, will not Ihew the very fmall degree of rarefaftion j but we are feldom interefted concerning thofe fmall degrees,� and in general thisnbsp;gage will begin to fhew the rarefadion when aboutnbsp;three quarters of the air have been removed fromnbsp;the receiver, viz. when the air has been rarefied tillnbsp;its remaining elafticity is notable to fupport.thatnbsp;column of mercury. This gage has a fcale ofnbsp;inches and parts of an inch affixed to the tube�nbsp;which ffiews the precife altitude of the mercurynbsp;in it.

The long barometer gage is a tube of about 33 inches in length, open at both ends, having its lows'�nbsp;end immerfed in a ciftern of quickfilver, whichnbsp;fixed on the pedeftal, or lower part of the frame ofnbsp;the pump (for the tube itfelf reaches from tha^^nbsp;place to the height of the plate). The upper ape^'nbsp;ture of the tube communicates, by means of a brafsnbsp;tube, with the infide �f the pump.

This in fidb is an empty barometer, which filled with quickfilver by withdrawing the air fro^^nbsp;it through its upper aperture; and if the pumpnbsp;could produce a perfeft vacuum, the mercurynbsp;this long gage would rife as high as it does in ^nbsp;common barometer \ but as the pump cannot sX'nbsp;hauft fo far, therefore the difference of altitude between the mercury of the long gage, and that of ^nbsp;common barometer, ffiews the quantity of air thatnbsp;remains in the receiver. This difference of ah'^nbsp;tude is ffiewn by a fcale of inches and parts 0

�nches, which is always affixed to the long barometer gage. As the altitude of the mercury in a common barometer, is to the contemporaneous altitude of the mercury in the long barometer gage,nbsp;fo is the whole quantity of air which was in the receiver before the rarcfaftion, to that quantity whichnbsp;has been drawn out of it.

The fyphon gage is nothing more than the fliort barometer gage, except that inftead of terminatingnbsp;in a little cittern, in this gage the tube is bent andnbsp;tifes upwards with its aperture, which by means ofnbsp;a brafs tube is made to communicate with the.infidenbsp;of the pump ; fo that the afcending leg of the tubenbsp;performs the office of a cittern j hence, in rarefyingnbsp;the air, the mercury defcends from the clofed endnbsp;of the tube, and rifes into the afcending leg; therefore the altitude of it in one leg above its altitudenbsp;'n the other leg (which leg in fa�t is the cittern)nbsp;fhews the degree of rarefadion, and this altitude isnbsp;denoted by an annexed fcale of inches and parts ofnbsp;loches. Such a gage is partly teen at g, fig. 2.nbsp;Plate XVI.

The above-mentioned gages evidently Indicate die ^lafticity of the fluid, which remains in the receivernbsp;�f the pump after a certain degree of rarefaftion jnbsp;^od it is immiaterial whether that elaftic fluid be air,nbsp;vapour of water, or other elaftic fluid �, but therenbsp;is another gage, which from its fhape was called, thenbsp;t-ear-gage, by its inventor, Mr. Smeaton, and whichnbsp;Utew's (not at th� adual time, but after'the read-1 I 4nbsp;nbsp;nbsp;nbsp;miffion

minion of air into the receiver) how much air was left in the receiver in the preceding rarefadtion.

The pear-gage confifts of a glafs veflel A, fig-Plate XVI. which has a finall projecting orifice Bgt; and at the other end is extended into a tube clofcdnbsp;at D j the capacity of this tube is the hundredthnbsp;part of the capacity of the whole veflel. Tliis gag?nbsp;is fiifpended, with its aperture downwards, to thenbsp;lower end of a flip-wire (viz. a wire which pafiesnbsp;through a collar of leathers) within a glals r?'nbsp;ceiver of the pump, and exactly under it, a littlenbsp;cup, containing quickfilver, is placed upon the platenbsp;of the pump. When the pump has been workednbsp;to the intended degree, the air in the pear-gage isnbsp;evidently rarefied as much as it is in the receiver*nbsp;In that ftate, by lowering the flip-wire, the pear-gag?nbsp;is let down till its aperture B has reached the bottom of the mercury. This done, the external a'*quot;nbsp;is admitted into the receiver; but it cannot be admitted into the pear-gage, becaufe the aperture Bnbsp;of that gage is now immerfed in the quickfilver; b?'^nbsp;the prefliure of the atmofphere on the lurface of th?nbsp;quickfilver, forces that fluid metal into the pear-gag?gt;nbsp;and fills it up to a certain degree E ; then th?nbsp;tipper part D E of the gage will contain all th^

the degree to which the rarefadion of the air had been carried. For inftan�e, if we find that thenbsp;part D E of the gage, which is filled with air abovenbsp;the quickfilver, is the 500th part of the whole, wenbsp;may conclude, that the air in the receiver had beennbsp;rarefied 500 times, amp;c.

But a very confiderable difference muft be re-rnarked between the indications of this, and of the preceding gage?.

When the receiver contains no other fluid befldes air, then the pear-gage and the other gages indicatenbsp;the fame degree of rarefadion j but if the receivernbsp;contain the vapour of water, or of other liquor,nbsp;then the pear-gage will indicate a much greater degree of rarefadion than the other gages 5 becaufqnbsp;the vapour which has elafticity fufficient to fupplynbsp;the place of air in the receiver, on the readmiffionnbsp;of air, is condenfed into a fpace vaftly fmaller thannbsp;the fame quantity of rarefied air can be condenfednbsp;intoj fo that the pear-gage (hews the quantity of �irnbsp;done which had been left in the receiver j whereasnbsp;the other gages fhew the quantity of elafdc fluidnbsp;t''hich is adually remaining in the receiver.

Fig. 16. Plate XVI. reprefents a veffel proper for weighing air. It is a glafs veffel in the fliapenbsp;of a Florence fiafk, having a focket of brafs with anbsp;ftop-cock cemented on its neck. The aperture Anbsp;of the brafs part is formed into a ferew, whichnbsp;bts the fcrew in die middle of the plate of thenbsp;pump.

This vcfl�l, being fcrewed on the pump, and the ftop-cock B being opened, is exhaufted �, thennbsp;the ftop-rcock is turned fo as to fliut up the aperture, the Veflel is unferewed from the pump, andnbsp;js weighed in an accurate pair of fcales. This done,nbsp;t})e ftop-cock B is opened, and the air is admittednbsp;into the veflel, which is then weighed again, innbsp;which ftate it will be found to weigh more than itnbsp;did in its exhaufted ftate. The difference of thenbsp;two weights is the weight of a quantity of air, of thenbsp;aftual denfity of the atmofphere, equal in bulk tonbsp;the capacity of the veffel. Yet, fince no air-pumpnbsp;produces a perfeeft vacuum, the above-mentionednbsp;veffel, in what we have called its exhaufted ftategt;nbsp;does aftually contain a fmall quantity of air, whichnbsp;renders the refult inaccurate. But this inaccuracynbsp;may be corredled in a very eafy manner, by obferv-ing the precife degree pf rarefadion, as indicated bynbsp;the gage, and allowing for the remaining quantitynbsp;of air. Thus, for inftance, fuppofe that the gag*^nbsp;indicates that the air has been rarefied 8o times�nbsp;therefore the air which remains in the veffel, is thenbsp;8oth part of its whole capacity, In this ftate letnbsp;the veffel weigh 9000 grains, and when full of alt�nbsp;let it w'eigh 9160 grain.s, the difference of whichnbsp;weights is 160 grains, and this is the weight of�nbsp;quantity of air .equal to .^�ths of the capacitynbsp;the glafs; therefore the 160 grains muft be iti-creafed by the 80th part of that number, viz. egt;f

If inftead of weighing common air, in the above-mentioned veflel, it be required to weigh fome other fort of permanently elaftic fluid, the operation mufl;nbsp;proceed as above, excepting that before the flop-cock B be opened, previoufly to the fecond weighing, the end A mufl be fcrewed or faflened to thenbsp;neck of a bladder, or other receiver, full of thatnbsp;other fort of elaflic fluid j fo that the veflTel may benbsp;filled with it, inftead of common air. It is thennbsp;Weighed again, amp;c.

The principle of the condenfing engine will be �cafily comprehended ; for if in the exhaufling engine, fig. 18. Plate XVI. the valves be reverfed,nbsp;viz. the valves at B, and at G in the piflon, benbsp;turned upfide down, that engine will become anbsp;Condenfing engine fince in that cafe, when thenbsp;piflon is drawn towards the air will rufli throughnbsp;the valve at E, into the barrel; and when afterwardsnbsp;the piflon is pufhed downwards, the air of thenbsp;barrel will be pufhed through the valve at B, andnbsp;'vill be condenfed into the veffel D. Yet an exhaufling fyringe is made in a manner flill morenbsp;hmple j fee fig. 15, of Plate XVI. The cylindernbsp;has one valve at its lower aperture B, which opens

outwards; the pifton is not perforated, but folid; and there is a hole on the fide of the barrel, at C-When the pifton is drawn upwards, a vacumnnbsp;formed in the lower part of the barrel; but as foonnbsp;as the lower part of the pifton is railed above thenbsp;hole C, the aii rufhes through that hole, andnbsp;fills the barreli then, on lowering the pifton, thenbsp;air is condenfed into the lower part of the barrel�nbsp;and is forced out at B, into any veflel, to whichnbsp;that end of the fyringe is fcrewed. With this fy-ringe the air is condenfed into the infide of a watetnbsp;fountain, or of a wind-gun, which inftruments arrnbsp;fo commonly defcribed in philofophical works, amp;c-that tliey need not be inferted in this place. But fotnbsp;the purpofe of performing a variety of philofophicalnbsp;experiments in condenfed air, fuch a fyringe isnbsp;adapted to a frame and apparatus, as at fig. i-Plate XVII. and this apparatus is commonly denominated a condenfing engine.

CD is abrafs condenfing fyringe, which, when by applying the hand at Z, the pifton is moved alternately up and down, forces the air through the bralsnbsp;pipe D N F, into the glafs receiver A B. This receiver muft be very thick, and well annealed : it i�nbsp;fet with its fmooth and flat edge on the plate of thenbsp;machine, which is fimilar to the plate of an ait'nbsp;pump ; a thick piece, L M, of brafs, is applied in ^nbsp;fimilar manner to the upper aperture of the glnlsnbsp;receiver, and a flip-wire palTes through a collarnbsp;leathers in t|ii3 brafs piece. As the force of th^

^ondenfed air would lift up the brafs piece, L M, from over the receiver,, or lift up the latter from thenbsp;plate, fo the receiver and brafs piece are .kept downnbsp;by the crofs piece of wood G H, which is adjuftednbsp;by means of the fcrew-nuts on the fteady pillars 1,1^.

There is a gage, EF, annexed to this machine, '''hich indicates the condenfacion of the air withinnbsp;the receiver and tube of communication, It con-fids of a ftrong and narrow giafs tube hermeticallynbsp;t^lofed at E, and connefted with the brafs pipenbsp;of communication at F. A fmall quantity of quick-diver fills up a Ihort part of the cavity about thenbsp;*^iddle of the tube, and the fpace between the mer-'^Ury and the clofed end E of the tube, contains airnbsp;of the ufual denfity, Now when the air is condcnfednbsp;the receiver, in the tube of communication,amp;c. thenbsp;�Mercury is thereby impelled farther towards E, andnbsp;die contraftion of that fpace, which is fhewn by annbsp;Annexed fcale, fhews the degree of condenfation;nbsp;for inftance, if the air which is contained in thatnbsp;fpace, is, by the condenfation, forced into half thenbsp;Tace it occupied before, the conclufion is, that thenbsp;within the receiver is as denfe again as it wasnbsp;previous to the condenfation j and this is generallynbsp;^xpreffed by faying, that then the receiver doesnbsp;'�ontain two atmofpheres ; if the air at E be con-drafted into a quarter of its original fpace, then fournbsp;^tnnofpheres have been forced into the receiver;

j, * condenfation is inverfely as the fpace occupied by ^ air at the extremity E of the gage.

Certain air-pumps, as that of Mr. Smeaton, and the firft which was contrived by Mr. Haas, can benbsp;made to exhauft or to condenfe at pleafure, whichnbsp;is done by changing the communication betweennbsp;the cylinders and the plate of the pump j for as mnbsp;thofe pumps the air is r..refied towards one end, andnbsp;is condenfed tow'ards the other end of each barrel�nbsp;the machine will exhauft if the former end of th^nbsp;barrel be made to communicate with the plate ofnbsp;the pump, and the latter with the atmolphere ; buCnbsp;it will become a condenfer, if the latter end of thenbsp;barrel be made to communicate with the hole ii^nbsp;the centre of the plate, and the former with th^nbsp;atmofphere.

t 495 3

CONTAINING THE PRINCIPLES OF CHEMISTRY, AND particularly THE DESCRIPTION OF THE PRINCIPAL OPERATIONS AND APPARATUS.

-/CHEMISTRY is the fcience which endeavours to afeertain the number, the quantities, andnbsp;the properties, of the conftituent principles of allnbsp;natural bodies. It alfo endeavours to form new ornbsp;artificial compounds.

The feparation of the component principles of a body from one another, is called analyfis. Thenbsp;formation of compound bodies from fimpler fub*nbsp;ftances, is called Jynthefis.

Both the analyfis and the fyrithefis are performed by means of certain operations, which are therefore called chemical operations, or chemical pro-

It has been faid above, page 19. that there is a Mutual attradlion between the parts of the fame fub-ftance, which is called attraftion of aggregation jnbsp;^nd that there is, like wife, a mutual attradion be-tween the heterogeneous parts of difterent bodies,nbsp;''^htch, when it is merely fwperficial, is called

attraPlion of cohefiou-, but it is called altraBion of affinity, or of compofition, when it produces an intermixture ot two or more heterogeneous ftib-ftances, and a change of fome, at leaft, of theirnbsp;properties.

Now it muft be remarked, that the affinity of one fubftaiice to another, differs in degree according to the different fubftances j and it is upon thenbsp;difference of thole affinities that the operations ofnbsp;chemidry are eftabliffied; for if the affinity betweennbsp;two bodies were equal to the affinity between anynbsp;two other bodies, chemidry could not exid. Thusnbsp;for indance, it is known that A and B have anbsp;certain degree of attraction or affinity towards eachnbsp;other; alfo, that there is a greater affinity betweennbsp;A and C; and a much greater affinity between Cnbsp;and D. Now, if I wifh to analize a certain body�nbsp;which is a compound of A and B, I mix that bodynbsp;with the body C, in confequence of which, as Cnbsp;has' a greater affinity to A than to B, the givennbsp;body will be decompofed ; and one of its ingredients, viz. A, will form a new compound with Cgt;nbsp;whild the other ingredient B w ill be left by itfelf-Then I mix the new' compound of A and C, withnbsp;D, in confequente of which this new compoundnbsp;?ill be decompofed, C will adhere to D, and A

�ppofite to the attraftion of affinity; for the weaker One of them becomes, the greater power will benbsp;gained by the other.

The attraftion of affinity afls more powerfully Iri proportion as the quantity of concadt between thenbsp;different bodies is inCreafed; hence the adtion between two bodies that have a certain affinity, is weaknbsp;Or imperceptible when both the bodies are in a hardnbsp;folid ftate; it becomes ftronger when the bodiesnbsp;are foftened by means of heat, (which diminifhesnbsp;the attradlion of aggregation) or when they are pulverized and intermixedftronger ftill, when onenbsp;of the bodies is in a fluid ftate; and it will becomenbsp;as adlive as polfible, when both the bodies are in anbsp;fluid ftate. Therefore, in order to decompofe, ornbsp;to compole, different bodies, it is neceffary to pulverize, or to heat, or to mix, or, in fliort, tonbsp;perform diverfe operations with a variety of neceffary inftruments, according as may be requirednbsp;fly the nature and properties of the different articles, Hence the whole fubjedt of chemiftry con-flfts, I ft, of the art of performing the neceffary operations ; and adly, of the knowledge of the principal fadls, which have been afcertained by means ofnbsp;thofe operations. The fecond of thofe objedts isnbsp;'''hat immediately belongs to the prefent part ofnbsp;rflpfe elements of natural philofophy, which treats ofnbsp;rfle peculiar properties of bodies ; we fhall nevef-rhelefs premife a competent accoum of the principalnbsp;Operations, through which moft of efie peculiar pro-

perties of bodies have been afcertained, and by the means of which new difcoveries may be made.

mortars, pcflles, ftones and muller, are either ot wood, or metal, or glals, or porcelain, or marble, otnbsp;agate, amp;c. according to the hardnefs and other pfo-perties of the articles that are to be pulverized. Butnbsp;thefe miift be confidered amongft the preliminarynbsp;operations j for they only alter the bulk, and not thenbsp;nature of the articles; fince every particle of a pu*'nbsp;verized body is a fmall whole of that bodyj whereasnbsp;the real chemical operations deftroy the aggregationnbsp;of bodies^ feparate their conftituent principles, forntnbsp;new compounds, and alter fome of, if not all, the'tnbsp;properties.

The feparation of the finer parts of bodies frorf� the coarflr, which may want farther pulverization?nbsp;is performicd by means offtfting, or wajhing.

A fteve, for fifting, generally confifts of a cyhn' drical band of thin wood, or metal, having acroBnbsp;its middle a perforated diaphragm of fllk, or lo^'nbsp;ther, or hair, or vvire.

Sieves are of difi�rent flzes and different fineness' Fig. 3. of Plate XVII. fhews a fieve of the beftnbsp;. conftrudlion. It confifts of three parts. A, Bgt;nbsp;The middle part B is properly the fieve; D isnbsp;perforated diaphragm, through which the powd^'^

paffes; C is a bottom which may be put on, or taken off, the lower part of B, and ferves to receive the powder that paffes through the fieve j Anbsp;is a top or lid, which is placed on the upper partnbsp;of B, and ferves to prevent the falling off, or thenbsp;diffipation into the air, of the materials. When all ,nbsp;the three parts are together, the Ihape of the fievenbsp;is as in fig. 7. Plate XVII.

By walking, one may feparate powders of an uniform finenefs much more accurately than by means of the fieve; but it can only be ufed for fuch fub-ftances as are not acted upon by the fluid whichnbsp;is ufed. The powdered fubftance is mixed with,nbsp;and is agitated in, water, or other convenient fluid ;nbsp;the liquor is allowed to fettle for a few moments,nbsp;and is then decanted off; the coarleft powder remains at the bottom of the veffel, and the finernbsp;paffes over with the liquor. By repeated decantations in this manner, various fediments are obtainednbsp;of different degrees of finenefs; the laft, or thatnbsp;which remains longefl; fufpended in the liquor, being the fineft.

, Filtration is a finer fpecies of fifting. It is fifcing through the pores of paper, or flannel, or finenbsp;linen, or fand, or pounded glafs, or porous ftones,nbsp;and the like; but it is ufed only for feparatinnbsp;fluids from folid or groflilh particles, that maynbsp;happen to be fufpended in them, ancl not chemicallynbsp;combined with the fluids. Thus fait water cannotnbsp;be deprived of its ^It by filtration; but muddy

500 nbsp;nbsp;nbsp;Principles of Chemijiryy and

water may. No folid, even in the form of powder, will pafs through the above-mentioned filtering fubftances j hence, if water or other fluid, containing fand, infe�ts, mud, amp;c. be placed in a bag, or hollow veflel, made of any of thofe fubftances, the fand, amp;c. will remain upon the filter,nbsp;and the liquor will pafs clear through the filter, andnbsp;may be received in a veflel placed under it *.

Lixiviation is the feparation by means of water, or other fluid, of fuch fubftances as are foluble innbsp;that fluid, from other fubftances which are notnbsp;foluble in it. Thus, if a certain mineral confiftnbsp;of fait and fand, or fait and clay, amp;c. the given

� Filtering paper is paper without fize., For this pur-pofe the piece of paper is ihaped into the form of a cone, and is placed into a funnel, in order to fupport it, oth�rwife,nbsp;when wet, it would eafily break. \

Filtering ftones and filtering bafons, either natural or artificial, for the purpofe of purifying water, are not un-frequently ufed in this and other countries. Rocky mountains, beds of fand, gravel, amp;c. are natural filters.

The compofition for making filtering bafons for purifying water, confifts of equal parts of tobacco-pipe clay, and coarfenbsp;fea, river, drift, or pit fand. The bafons are formed andnbsp;turned on a potter�s wheel. They fliould be about ^ of annbsp;inch thick. When the veflels are of the ufuat degree ofnbsp;drynefs, the whole putfide and infide furface muft be fliavednbsp;�r turned off on a potter�s wheel j and, when perfedtly dry,nbsp;thofe bafons are burnt or baked ia a potter�s kiln after thenbsp;ufoal Bianner,

body

Dejcription of the principal Operations^ ^c. 501 body being broken into powder, is placed in water,nbsp;which will diflblve the fait, and keep it fufpended,nbsp;whilft the earthy matter falls to the bottom of thenbsp;velfel, and, by means of decantation, may be fe-parated from the fluid. If the fait, or other fub-ftance, which is diflTolved in the fluid, be requirednbsp;to be feparated from it, then recourfe mufl: benbsp;had to

Evaporation, which feparates a fluid from a folid, or a more volatile fluid from another which is lefsnbsp;volatile.

Simple Evaporation, properly fpeaking, is ufed when the more volatile or fluid fubftance is notnbsp;to be preferved; and, in that cafe, the evaporationnbsp;is performed in velTels of wood or glafs, or porcelain or metal, amp;c. which are either Amply ex-pofed to the air, or are placed upon a fire, morenbsp;' or lefs aftive, according to the nature of the fub-ftances.

When the fluid, which is evaporated, mufl: be preferved, then the operation is called diftillation,nbsp;^nd is to be performed in other veflels, which arenbsp;Called retorts, alemhics, fills, amp;c. made either ofnbsp;giafs, or porcelain, or metal, amp;c.

The office of thofe veflels is to condenfe the vapour into a liquid form, and to convey it into a recipient. The evaporation is performed by means of ^cat j�the condenfation by means of cold therefore the body of any of thofe veffels, which receivesnbsp;the materials, mufl be placed upon a fire, or hot

502 nbsp;nbsp;nbsp;Principles of Cbemijlry, and

place; but that part of the velTel which condenfes the vapour, and is hence called the refrigeratory^nbsp;muft be rendered fufficiently cool for the pur-pofe.

Fig. 2. Plate XVII. reprefents a retort. In this diftilling inftrument, the materials are placednbsp;In the body E A F, and the bottom A is placednbsp;upon the fire*. The vapours which rife from thenbsp;materials at E F, pafs through the tube EEC,nbsp;which being at fome dlftance from the fire, andnbsp;therefore cooler, condenfes the vapour into liquidnbsp;drops, which, on account of the inclination of thenbsp;tube B C, run down into the recipient D, which isnbsp;adapted to the neck of the retort f. Thus the folidnbsp;part of the materials in E A F remains in the retort, and the fluid, part paflTes over into the receiver.

* In order to prevent its breaking, the bottom of the retort is generally covered with fome adhefive fubftance,nbsp;which can Hand the fire, fuch as clay, a mixture of lime andnbsp;clay, amp;c. this is callednbsp;nbsp;nbsp;nbsp;the retort; or the retort is

placed in a bafon of fand or water, and this baton is then placed immediately upon the lire.

f The receiver muft not, in moft cafes, be clofed very accurately upon the neck of the retort; for that may occa-flon the burfting of the inftrument; but when that accuratenbsp;clofing is practicable, it may be accomplifhed by the appi*quot;nbsp;cation of wet paper, or wet rags, or a mixture of wax andnbsp;turpentine, or a mixture of whitening and oil, amp;c.

This

This inftrument is ufed when the quantity of materials is fmall; and the vapours may eafily be condenfedj otherwife an alembic, fuch as fig. 4.nbsp;Plate XVII. is ufed. This inftrument confifts ofnbsp;two parts. A B is the body which receives thenbsp;materials. AC is the capital, which is joined clofenbsp;to the body. The upper part of the capital isnbsp;formed into a bafon C, in which cold water isnbsp;placed, which condenfes the vapour in the cavity i,nbsp;fo that the drops of liquor fall in the grove 0, 0,nbsp;and come out of the tube D into the recipient. Innbsp;diftilleries and other large works, the capital has notnbsp;the bafon or refrigeratory C; but the tube D isnbsp;made very long, and is lhaped into a Icrew-likenbsp;form, called a worm, which is placed into a tub ofnbsp;�Water, and has its aperture out on one fide of thenbsp;tub. Then that worm and tub forms the refrigeratory.

When the materials which are evaporated in the body of the diftilling veflels, concrete not in a fluidnbsp;but in a folid form, within the neck of the retortnbsp;Or tube, amp;c. then that diftillation is more properlynbsp;Called Jublimation.

By the above means one fluid may be feparated from other materials j but it often happens that innbsp;biftillation feveral fluids are produced, fome ofnbsp;which are permanently elaftic,, and all or moft ofnbsp;them may be required to be preferved. In thisnbsp;cafe, another fort of apparatus muft be ufed,nbsp;which is callednbsp;nbsp;nbsp;nbsp;'

The apparatus for Pneumato-chemical Dijlillations. See fig. 5. Plate XVII. A is a tubulated retort¹,nbsp;adapted to the recipient B, which has two necks.nbsp;To the upper neck of this recipient is fitted a bentnbsp;tube C D E, whofe other extremity reaches as farnbsp;as very near the bottom of the recipient G. Thisnbsp;recipient has three necks a, b, c, into the firft ofnbsp;which the end of the tube D E is fitted ; into thenbsp;fecond, b, an open tube, which reaches very nearnbsp;the bottom of G, is fitted; and to the laft neck,nbsp;a crooked tube is adapted, which opens and dif'nbsp;charges the elaflic fluid into a proper receiver.nbsp;Sometimes two or three,- or more, veflTels, like G,nbsp;are interpofed; viz. inftead of the crooked tube F,nbsp;a tube, like CDE, is adapted to the veflel G, andnbsp;to the next which is fimilar to it, and fo on ; thennbsp;the crooked tube F is applied to the lafl neck of thcnbsp;lafl of thole veffels.

When this apparatus is properly conneded, the materials are put into the retort through the hoknbsp;O,' and a proper degree of heat is applied to thenbsp;bottom of the retort i then the products will benbsp;collected in different parts, yiz. what is fiiblimed,nbsp;or concreted, in a compad form, adheres to thenbsp;neck of the retort j the fluid of eafieft condenfatioi^nbsp;is colleded into the receiver B j the elaftic vapours,

'vhich are condenfable in water, will be combined with the diftilled water, which muft be.placed at thenbsp;bottom of the vefiel G, and thofe which are notnbsp;fufceptible of being thus abforbed, pafs throughnbsp;the tube F into a proper receiver, or they may benbsp;made to pafs through other fucceflive veffels fimilarnbsp;to G, in which fuch other fluid may be placed,nbsp;as may be capable of abforbing one or more ofnbsp;the permanently elaftic fluids. The tube H fervesnbsp;to admit fome atmofpheric air, in cafe the water innbsp;G fliould abforb the produced elaftic fluid toonbsp;tjuickly.

In certain cafes of mixtures, the produce is merely an elaftic fluid, which is required to benbsp;collefted. For this purpofe, the veffcl reprefe'ntednbsp;in fig. 6. Plate XVII, is very ufefuh It confiftsnbsp;of a body A, to which a perforated ftopple, withnbsp;the crooked tube C, is adapted. The materialsnbsp;are placed in A, and the elaftic fluid which isnbsp;generated, pafles through BCD, into a propernbsp;teceiver.

Such receiver, and the reft of the apparatus proper for receiving, meafuring, mixing, and performing other operations on permanently elafticnbsp;floids, is delineated in fig. 8. Plate XVII.

B C D E is a wooden trough, having a ftielf G, and filled with water as high as about annbsp;tfich or two above the Ihelf. There are feveralnbsp;�lafs jars, or receivers, as H, I, K, L, which fervenbsp;for retaining, mixing, meafuring, and otherwife

ufing the permanently elaftic fluids. Thofe jars are firft filled with water in the trough, then they arenbsp;turned upfide down, and being lifted up gently, fonbsp;as not to elevate their aperture above the water,nbsp;they are placed upon the Ihelf, as reprefented at G.nbsp;Then if a velTel full of air be placed with its aperture downwards into the water of the trough, andnbsp;there it be turned upfide down, juft under one of thenbsp;jars full of water, the air or permanently elaftienbsp;fluid being the lighter fluid of the two, will afcendnbsp;into the latter velTel, and all or part of the water willnbsp;come out of it, according to the quantity of air introduced.

For the purpofc of rendering this operation more commodious, fome holes are feen in the flielflnbsp;which are the apertures or apexes of .as many inverted funnels, or little domes dug out of the thick-nefs of die fnelf; fo that v/hen a veffel full of air isnbsp;inverted under one of thofe holes, whereupon a jatnbsp;full of water is placed as at G, the air will corn^nbsp;cut cf the former veftel, and palTing through thenbsp;hole in the flielf, will enter the latter veffel.

At F there is reprefented a jar which receive* the air that is generated from the materials in thenbsp;phial M, fimilar to the phial, fig. 6. There thenbsp;phial is reprefented as heated by the flame of *nbsp;candle, which in feveral experiments muft be done�nbsp;in order to afuft the extrication of the elaftie flpi'^*nbsp;This fluid is conveyed 'through the crooked tube�^nbsp;and is difeharged under one of the holes of the fttell

tln-oog*^

through which it paffes into the receiver I, and in proportion as the elaftic fluid afcends under the formnbsp;of bubbles, the water fubfides.

A fmall glafs veUel L, capable of containing about an ounce meafure, is ufed as a meafure of a per-rnanently elaftic fluid j for if this phial be fuc-cefTively filled and inverted under a large jar, wenbsp;ttiay thereby throw into that jar any requirednbsp;quantity of an elaftic fluid, or as many meafures ofnbsp;One elaftic fluid, and as many of another, as wenbsp;pleafe.

When a glafs jar is partly filled with an elaftic fluid, we may meafure the quantity of that fluid bynbsp;*�ieafuring the diarheter and altitude, or the capacity of that part of the veflfel, in the ufual geometrical way of gauging vefTels. But for the fake ofnbsp;Sreater expedition and accuracy, the contents of anbsp;'^cflTel are fometimes marked on the outfide of it.nbsp;Thus the tube, or narrow veflTel, K, is marked onnbsp;the outfide, fhewing the fpace which is occupiednbsp;each fuccefiive meafure. of air, fuch as is contained in the meafuring phial L. Such a veffel asnbsp;^ is moftly employed for examining the purity ofnbsp;t^onamon or refpirable air. This is done by mix-a certain quantity, as a meafure or two, of re-^Pirable air, with a certain quantity of anothernbsp;permanently elaftic fluid, or of fome other fub-^3nce capable of occafioning a diminution of thenbsp;^tilk of the elaftic fluid, and then meafuring the di-^tiinution i for the purity of the refpirable fluid is

proportionate to that diminution. 1'he parts of a meafure are foraetimes marked upon the tube K.nbsp;itfelf, and at other times are afeertained by the external and occafional application of a divided fcale.nbsp;The tube K, or in general any fuch veflel as isnbsp;ufed for afeertaining the purity of refpirable air, isnbsp;called an Eudiometer.

It is fometimes required to remove an inverted jar with its contents from the flielf of the trough �nbsp;this is done by the ufe of a lhallow pan or dilhgt;nbsp;�which is immerged in the water of the trough, andnbsp;the jar is flipped in it; then the whole may be removed and placed wherever it may be convenientnbsp;as at P. In this cafe the fhallow pan performs thenbsp;office of a flnall trough j and for Inch purpofes fe-veral diflies or pans of different fizes Ihould be hadnbsp;in readinefs.

Some elaftic fluids are inflammable, and in order to try their inflammability a fmall phial may benbsp;filled with any of them, and after having ftopp^^nbsp;its aperture with a finger, it may be removed ftoctinbsp;the water; then being brought with its aperturenbsp;near the flame of a candle, the finger is removed,nbsp;and the elaftic fluid will take fire, as may be clearlynbsp;feen in the dark, and even in the day light. Whennbsp;the quantity is not very fmall, a pretty large jar�Snbsp;filled with it, and the palm of the hand is apph^^^nbsp;to the aperture; in that fituation the jar is removednbsp;from the water, and is turned with the aperturenbsp;wards. Then having in readinefs a twilled

^ nbsp;nbsp;nbsp;with

^ith a bit of lighted wax taper at its extremity, the hand is removed, and the lighted taper is dipped innbsp;the veflel, amp;c. as fhewn at

Some of the permanently elaftic fluids are ab-forbed by water; therefore they cannot be confined by water. For fuch fluids, it becomes neceffary tonbsp;ufe a troiigh full of quickfilver; but on accountnbsp;of the price and weight of the mercury, a muchnbsp;flu aller trough and fmaller glafs vefl�ls muft benbsp;tifed-

The folution of falts in water, the diflfolution of Unetallic and other fubftances in different menflrua,nbsp;Require a variety of veffels, whofe form, viz. whethernbsp;upen or clofe, or deep, amp;c. is eafily fuggefled bynbsp;the nature of the articles.

When a fait is diffolved in water or other fluid, and by evaporation the fluid is driven off, the faknbsp;gradually acquires the folid form, and in doing thisnbsp;tt arranges its particles in a particular manner} as,nbsp;fl^r inffance, fome falts arrange themfelves under thenbsp;form of cubes, other under the form of globules,nbsp;The fame thing happens with fome earthynbsp;particles, and feveral other fubftances. Now thisnbsp;Spontaneous regular arrangement is called cryjlali-

Veffels, generally open, but fometimes clofed, employed for fuch cryftalizations j and the cryF

talization of fome fubftances requires a certain temperature, that of others requires an higher, ornbsp;a lower temperature ; hence the charged vefie^�nbsp;muft be placed in cool places, amp;c.

The fufion of metallic fubftances by means of heat, requires veflels fufficiently ftrong to refiftnbsp;fire. Thofe veflels are moftly, if not always, mad^nbsp;of earthenware or porcelain, or a mixture of cla/nbsp;and powder of black-lead. They are called cruc*'nbsp;hies, and their more ufual fhapes are reprefentednbsp;fig. 9. Plate XVII.

Some of thofe crucibles have covers likewife earthenware ; but fometimes the fufed metal rnn^nbsp;be expofed to a current of air. In that cafe th^nbsp;proper crucibles are fliallow and broad, as at f�'nbsp;10. Plate XVII. Thefe are called cuppels,nbsp;they are formed either of calcined bones, mix^^nbsp;with a fmall quantity of clay, or of a mixture ^nbsp;clay and black-lead powder. But the cupP^^^nbsp;muft not be placed in a clofe furnace, or be f*^*^nbsp;rounded by coals; for in that cafe the requi'quot;^nbsp;current of air could not have accefs to the fuJ^^nbsp;metal. They are therefore placed under a lore ^nbsp;oven of earthenware, which is called anbsp;nbsp;nbsp;nbsp;^

reprefented at fig. 13. Plate XVII. and the containing the cupples, amp;c. is expofed to thenbsp;of the proper furnace.nbsp;nbsp;nbsp;nbsp;^

The various degrees of heat, which are requi��^ for the performance of chemical operations�nbsp;from the heat of a fmall wax taper, to that 01

moft powerful furnace, render a variety of fireplaces or furnaces necefiary for a chemifr. Thofe furnaces are either open at top, or they are covered with v/hat is called a dame, and have a chimney, or tube, to carry off^ the heated air, fmoke, amp;c.nbsp;They are fometimes fupplied with air from thenbsp;natural adlion of the fire, which rarefies the airnbsp;about the ignited fuel, and the rarefied air becoming fpecifically lighter, afeends into the chimney, and other colder, and confecjuently heavier,nbsp;air, is forced by the atmofphere to enter at thenbsp;lower part of the furnace. Some furnaces arenbsp;fupplied with air by means of bellows; and thofenbsp;are applied for forging iron, or for reducing metalsnbsp;froni the � ore, which is called fnetting. Sec.nbsp;Hence the furnaces derive their various names,nbsp;and are called fimple, or open, furnaces �, reverberatory furnaces j wind, or air, furnaces; blaft,nbsp;or bellows, furnaces; forges; fmelting furnaces,nbsp;6tc.*

When a pan full ofjand, or of water, is placed over a common furnace, and a retort, or othernbsp;'^effel, is placed in the fand, or water j that modenbsp;^f applying heat is called a fund bath, or ivaternbsp;hath.

* The particular defeription of the various furnaces may feen in a variety of chemical works: Macquiar�s Dic-*^ionary of Chemiftry, and Lavoifier�s Elem. of Chem. arenbsp;foiiic of tlie beft for this purpofe.

There

There are feveral other chemical operations, eJi-prcffions, and tools, which are f� obvious, common,* or fimple, as to need little or no particular explana*nbsp;tion. The following are the moft remarkable.

The dry way ol' performing chemical operations, is when ftrong degrees of heat are ufed, and thenbsp;humid way is when fluid folvents, and at moft lo^nbsp;degrees of hear, are ufed.

Combuftion is when a body is burned with the afliftance of refpirable air. Deflagration is whennbsp;the combuftion is attended with little explofionsnbsp;or cracklings. Detonation is a pretty loud report.

The word mixture is commonly underftood ; but the mixing of bodies, which have a great affinity tonbsp;each other, requires a variety of precautions j f�^nbsp;fometimes fuch mixtures are attended with heat,nbsp;ebullition, explofions, and fuch like dangerousnbsp;effe�t. They muft, according to the nature ofnbsp;the materials, be made either flowly, or fuddenly�nbsp;in open velTels, or clofed phials �, they muft fomO'nbsp;times be affifted by agitation, ftirring, heating; nndnbsp;at other times muft be left undifturbed j but thonbsp;time and the mode of adopting any one or moronbsp;of thofe particular applications, muft be learnednbsp;from pra�ice, and from a competent knowledgenbsp;the nature of the Ingredients.

kept

When a fubftance, which has an a,ffinity to another fubflance. Is mixed with as much of that other fubftance, as its affinity will enable it to holdnbsp;in corr',bination, then the former fubftance is faidnbsp;to be Jaturated, or the mixture to have attained thenbsp;point of Jaturation. If the mixture contain anbsp;greater proportion of either fubftance, then thatnbsp;mixture is faid to contain an excefs of, or to be fur-charged with that other fubftance. The fame thingnbsp;muft be underftood of the compounds of morenbsp;than two fubftances, '

The grand principle of all chemical procelTeS) which enables us to decompofe certain bodies, and to compound others, is that everynbsp;bns, a ceHsin peculiar affinity for other Jubffances, bulnbsp;7tot in equal degree.

This principle, though long known, could nob however, be univerfally applied to explain allnbsp;variety of chemical phenomena, on account of thonbsp;undifcovered nature of feveral powerful agentsnbsp;nature, and on account of the fuppofed aiSionnbsp;others which have no real exiftence.

The wrong or confufed knowledge relative heat, fire, air, light, amp;c. rendered a varietynbsp;fads abfolutely, inexplicable ; certain effeds aP'nbsp;peared to be contradidory j fome feemed to havenbsp;nothing to 3o with the principle of affinities,nbsp;others were explained upon the fuppofednbsp;of an inflammable principle called pblogiffon.

The modern phifofophers (I mean fince the year *7oo, or thereabout), affifted by the difcoveries�

the knowledge, and even the errors, of their pre-decelTors, having inveftigated, with infinite labour and ingenuity, the nature of thofe powerful naturalnbsp;agents, have found reafon to explode the fuppofednbsp;exiftence of the phlogifton, and have been able tonbsp;form a theory, which is incomparably more genera),nbsp;lefs complicated, and more fatisfadory, than anynbsp;other preceding theory.

This theory confiders every procefs, which produces a change of fome or of all the properties of the bodies in aftion, as depending on the variousnbsp;eledtive attradlions of thofe bodies, or of theirnbsp;components j and, in general, the refult of everynbsp;fuch procefs is the decompofition of certain compound bodies, and the formation of others.

Not only the mixtures of metallic fubftances with acids or alkalies; the formation of foaps, thenbsp;formation of compound falts, the purification ofnbsp;metals, and fuch other operations as are performednbsp;m chemical laboratories j but whatever compofi-don or decompofition, with change of properties�nbsp;mkes place in nature, fuch as the burning of com*'nbsp;buftible bodies, the rafting of iron, the evaporationnbsp;of water, animal refpiration, the growth of animalnbsp;and vegetable bodies, their fermentations and putre-faftions, amp;c. have, in great meafure, been provednbsp;depend, (and, by analogy, we are led to believenbsp;^hat they do all depend) upon the eledlive attradbionsnbsp;Qf the various ingredients.

this d�ftrine; but thofe wili be found in the next Chapter; for in this we muft flate fome general ob-fervations on the nature of the primitive or ele-msntaiy fubftanccs, which are the agents in all natural arid chemical procefTes. A lift of thofe fub-flances has been inlerted in the firft volume of thisnbsp;work, as alfo in the prefent volume, pages 15 andnbsp;16, to which the reader is referred.

The light which is perceived by our eyes, is fup-pofed to be the effeft of a peculiar fluid, which proceeds from the fun, a candle, a fire, or othernbsp;luminous objelt;ft. We cannot confine it in veflels�nbsp;nor can we weigh it, nor meafure its quantity, excepting in fome degree by comparifon, viz. of twonbsp;luminous bodies, we may determine which is thenbsp;moft luminous. But light feems to enter intonbsp;combination with certain bodies, and by that coOi'nbsp;bination to produce particular effeds; for iiiftanccjnbsp;plants that are kept growing in the dark, lofe theirnbsp;green colour, and become white or pale. Plantsnbsp;which grow in confined places, always endeavournbsp;to turn their tops and tender branches towards thenbsp;light; �their flavour, their vigour, their fragrance�nbsp;are much greater when they have been expofed Wnbsp;much light.in the courfe of their vegetation, thaunbsp;otherwife.�There are likewife feveral other effcdl*nbsp;produced by light in various chemical procelTes.

Or�lefs quantity of it is contained in bodies of every fort. It paffes through all forts of bodies, butnbsp;eafier through fome, fiich as the metals, thannbsp;through others, fuch as charcoal, wood, amp;c. hencenbsp;certain bodies are faid to be better or worfe conduc~nbsp;tors of heat than other bodies.

Caloric enters into combination with various fub¹ ² fiances; viz. it poffeffes peculiar affinities; and vcwfi/nbsp;ingenious methods have been difeovered for afeer-taining the comparative quantities of it, which arenbsp;abforbed, retained, or difengaged in a grettt varietynbsp;of proceffes. As a mixture of two fubftances muftnbsp;naturally have a greater bulk, than either of themnbsp;fingly ; fo by the acceffion of caloric a body is enlarged in its din)enfions, and, of courfe, from theirnbsp;being placed farther from each other, the attra�lionnbsp;of aggregation between the conftituent particles ofnbsp;that body is weakened ; hence every body is ex-.nbsp;Panded by heat, and is rendered more or lefs con-fiftent by the acceffion of various degrees of caloric. Amongft thofe various degrees of confif-tency, we diftinguifh three principal ftates, viz.

folid, the liquid, and the aeriform ftate. Thus water, according as more and more caloricnbsp;Communicated to it, affumes, firft the folid ftatenbsp;ice, next that of fiuid water, and then the aeriform ftate, or what is called vapour ². If preffurc,

/ nbsp;nbsp;nbsp;quot;1nbsp;nbsp;nbsp;nbsp;��nbsp;nbsp;nbsp;nbsp;,,nbsp;nbsp;nbsp;nbsp;II .1nbsp;nbsp;nbsp;nbsp;IPnbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;Inbsp;nbsp;nbsp;nbsp;I

It is not unlikely that by a further c.xpanfion, and per-aps by the combination with the eletSlric, or other fiuid,

or the contaft of other bodies, which have a greater affinity for caloric, come into contadt with a lub-ftance in a (late of vapour, that fubftance becomesnbsp;a liquid, and then a folid, harder and harder.

Certain bodies, when they have acquired a quantity of caloric fufficient to give them an aeriform ftate, hold it with fo much'force, that neithernbsp;preffure, nor the contadt of colder bodies, can takenbsp;it aw'ay, and convert them into a liquid; in that cafenbsp;they are faid to ht fcrmanentiy elqftic fluids, other wilenbsp;they are called vapours.

When caloric is communicated to a body, th^t body will abforb as much of it as its peculiar afH'nbsp;nicy will enable it to abforb, and the reft will tendnbsp;to expand itfelf equally through all the furroundingnbsp;bodies.�The former portion is called combined cd'nbsp;lork, and the latter has been called free caloric, be-caufe its tranfitlon to other bodies becomes fenfibl�nbsp;from the effedls it produces on thofe bodies; vi^'nbsp;thofe other bodies are expanded! or foftened, or !gt;'nbsp;quified by.it. This effedt of expanding bodies fur'nbsp;nifties the beft means of meafuring heat or free caloric ; and the Thermometer adts upon this principle*nbsp;The quantity of combined caloric is meafured irinbsp;the fame manner as, by analyzing, we feparate, andnbsp;meafure, the quantity of any other ingredient; viZ-the vapour of water may become more permanently elaft'Cjnbsp;at Icafl: fo as not to be conclenfable into fluid water inerd/nbsp;by riicchanical^ireffure, or cooling.

the given body A is mixed with fbme other body Bj that has a greater attraftionj or affinity, for A,nbsp;than A has for caloric; in confequence of whichnbsp;that latent, or combined caloric of A, is feparatcdnbsp;from it, and becomes free caloric, or fenfible heat;nbsp;and its quantity may be meafured from the effeft itnbsp;produces on the Thermometer, or upon other contiguous bodies.nbsp;nbsp;nbsp;nbsp;I

The eleBric fluid feems to be another remarkable agent in nature. Its a�lion feems to be very ex-tenfive. It has no perceivable weight, nor can wenbsp;exhibit it by itfelf. It paflcs more or lefs freelynbsp;through certain bodies, and not at all, or perhapsnbsp;difficultly, through others. Hence the former bodies are called conduBors, and the latter non-con~nbsp;duBors, of el��lricity. It is developed or abforbednbsp;in a variety of natural and artificial procefles: hencenbsp;it feems to have peculiar affinities; but the faftsnbsp;�which have been difcovered, though numerous, donbsp;not enable us to form any diftind and compre-henfive notions with refpecl; to its real and ge-'neral agency.

'The magnetic fluid is much more hypothetical, and more partial in its adion, than any of thenbsp;^brmer. This is fuppofed to be a fluid which, excepting in very few cafes, affeds iron alone, or fuchnbsp;bodies as contain iron, and produces thofe effedsnbsp;which are called magnetic, and which are all reducible to two, viz. to an actradion (not an attradionnbsp;of affinity) between certain parts of ferrugineous

bodies, and to a repulfion between certain other parts of the fame bodies.�We have no knowledgenbsp;of this fluid entering into combination with anynbsp;body, nor of its producing any other effeft.

Of thofe four natural agents, viz. heat, light, eledricity, and magnetifm, particular notice will benbsp;taken in the next volume. What has Been alreadynbsp;faid concerning their nature, is fufficient to illuftratenbsp;the fubjed of the remaining pages of the prefentnbsp;volume.

There feem to be only three principal and permanently elaftic fluids in nature, each of which confifls of a Ample fubftance combined with caloric,nbsp;and, probably, with light:�they are called oxygen air,nbsp;hydrogen gas, and azotic gas, or nitrogen gas ¹ j andnbsp;their bafes, or peculiar conftituents, independent ofnbsp;the caloric and light, are called oxygen, hydrogen,nbsp;and azote, or nitrogen. But there are feveral othernbsp;aerial fluids, fome of which are combinations of thenbsp;above-mentioned three, with other fubftances. Thenbsp;following lift contains their number, their names,nbsp;and the ingredients of them all, befides caloric andnbsp;light.

The name air has been more particularly given to the rcfpirahle fluids} whereas the v/ord gai is a more generalnbsp;appellation for permanently elaftic fluids, particularlynbsp;thofe of a fuft'ocating; quality.

Carlonated ley drogen gas, confifting of hydrogen, and the bafe of carbonic acid gas.

Hydrogen gas of marJhss, confiftlng of hydrogen and different proportions of azote.

Thofe are the principal elaftic fluids, or thofe t\rhich occur more commonly. Mixtures of twonbsp;or more of them are infinite in number j. but thenbsp;ingredients may be feparaced more or kfs by various means, and thus; their quantities may be afcer-tained.' Thofe means muft be derived from theirnbsp;peculiar properties; for inflance, if a mixt elafticnbsp;fluid be agitated in water, the water will abforbnbsp;that which is of a faline quality, and will leave thenbsp;ether by itfelf. Then the latter, by the applicationnbsp;of a lighted candle, will fliew whether it be infiam-mable, or capable of alTifling combuftion, or incapable of it, amp;c.

The purity of the atmofpherical fluid, which is various at different times and places, ds tried by ex-pofing to a determined quantity of it, fuch fub-flances as have great affinity fur the oxygen part vnbsp;for by this means the atmofpheric air is decom-pofed, the oxygen combines with the other fub-ftance, and the azotic gas remains by itfelf; andnbsp;its quantity determines the purity of the a'ir, ornbsp;rather the ratio of azote to oxygen ; for the air maynbsp;be rendered unfit for refpiration by the fufpenfio'^nbsp;of other fubftanccs, which do not diminifli the pfO'nbsp;portion of oxygen in it.

charcoal, and feems to be a fimple fubdance ; for it has never been decompofed. Icexifts in vegetables,nbsp;as alfo in animal bodies, and may be feparated fromnbsp;the oily and volatile principles by diftillation, as alfonbsp;from the faks, by wafliing in pure water.

Sulphur feems to be a pure fubftance. It exifb principally amongft minerals, but feme of it alfonbsp;exifts in vegetable and animal bodies.

Phojphcrus cannot be decompofed, and of courfc it may be confidered as a fimple fubftance.

The burning of phofphorous, of fulphur, or of carbon, is not a decompolition of thofe bodies, butnbsp;a combination of thofe bodies with oxygen, whichnbsp;combination increafes their weight, renders themnbsp;milcible with water, and gives them a ftrong four*nbsp;take ; viz. they become the phofphoric acid, the Jul~nbsp;phuric acid, and the carbonu acidfo that thenbsp;accelfion of oxygen turns them into acids; andnbsp;hence the oxygen derives its name, which, fromnbsp;its Greek origin, means the acidifying principle.-�nbsp;The heat and the light which attend the com-buftion, are derived from the oxygen air which de-pofits them, when it lofes ib aeriform ftate, andnbsp;combines with the pholphorous, or the fulphur, ornbsp;the carbon.

In a fimilar manner oxygen combines with a variety of other fubftances, which combination isnbsp;called oxidation and the compounds, accordingnbsp;to the different proportions of oxygen, have different properties, and different generic names, be-

The combination of a very fmall quantity of oxygen conftitutes what are called oxides-, with morenbsp;oxygen the combinations are called �weak acids fnbsp;with a quantity ftill greater of oxygen, the deno-minations are made to terminate in cus, viz. wenbsp;iay the nitrous acidi the fulfhurcv.s acid, amp;c. Whennbsp;the quantity of oxygen is as much as will completely faturate the bafes, t;h� appellations terminate in ic-, viz. we fay the yiitric acid, the JidphHricnbsp;acid, amp;c. and, laftly, when the combinations contain more oxygen than is necefliiry for their fatura-fion, then thofe ftates are exprefled by annexingnbsp;the word oxygenated to the peculiar name of thenbsp;acid.

All the articles, which follow fhojphorus in the lift of pages 15 and 16, as far as the 'zoonic radical,nbsp;are capable of abforbing oxygen enough to givenbsp;them an acid tafte, as alfo other properties peculiarnbsp;to acids s hence they form the various acids, which ,nbsp;derive their appellations from the names of theirnbsp;peculiar radicals

Some of thofe radicals (as the muriatic) are only recltoned fisch from analogy ; for they cannot be exhibitednbsp;ill an uncoiiblned ftacc, tike Julphur and phofphorus, whichnbsp;are the radicals of the fulphuric, and of the phofphoric,nbsp;acids.

of Cberaijlry. nbsp;nbsp;nbsp;525

Tihe articles of the lift, amp;c. which follow the Koonic radical, and as far as gold, are called metallk

fubjianees :

and animal, acids, according to the nature of their radicals. Acids in general have a four tafte, have a powerful alEnitynbsp;for alkalies, and redden certain blue vegetable colours.

The mineral acids are the fulphuric (formerly called the vitriolic) acid, the nitric acid, the.muriatic acid (formerlynbsp;called \.hs marine acid), the carbonic acid hformeily callednbsp;the aerial' acid, or fixed air), the pliofphoric acid,_ which isnbsp;likewite an animal acid, it being found amongll animal matters, as well as among minerals, the acid of borax, thenbsp;fluoric acid, the arfenic acid, the molybdic acid, the tung-ftenic acid, and the cromk acid. Thcie laft four are alfanbsp;Called metallk acids.

Every one of die vegetable acids feems to have a compound balls, confining of carbon and hydrogen, but in different proportions. All their radicals may be decompofed, but they cannot be compounded from fimpler fubftancesnbsp;and it is on account of this circumftance that they ar�nbsp;reckoned amongft the primitive fubllances. They arenbsp;dillingiiilhcd from each other by their peculiar affinities fornbsp;alkalies, or earths, or metallic fubftances. The vegetablenbsp;acids are the acetic, or vinegar, the acid of tartar, the em-Pyreunaatic acid of tartar, the oxalic or acid of lorrel, thenbsp;acid of galls, tfie citric or lemon acid, the malic or acid ofnbsp;apples, the benzoic, or the acid of the flowers of benjamin,nbsp;�he empyreumatic acid of wood, the empyreumatic acid ofnbsp;fugar, the acid of camphor, and the fuberic or acid ofnbsp;tork.

The animal acids, excepting the phcfphoiic, likewife *eem to have their bafes or radicals compounded of carbon,

Juhftances: they cannot combine with as much oxygen as the preceding radicals ; hence they cannbsp;only form oxides, formerly called metaliic calces-,nbsp;yet from thofe we mufl: except the firfb four, viz.nbsp;arfenic, molibdenite, amp;c. which can combine withnbsp;fo much oxygen, as actually to acquire fome evidentnbsp;acid properties. The others alfo .have differentnbsp;affinities for oxygen. Thofe which come firft innbsp;the lift, have a greater affinity for oxygen than thofenbsp;which follow. The laft four, viz. mercury, filver,nbsp;platina, and gold, have lefs affinity for oxygen thannbsp;any of the reft; for the oxides of thofe metals maynbsp;be deprived of the oxygen; that is, may be reducednbsp;into their fimple or metallic ftates, by heat alone jnbsp;whereas the oxides of the other metallic fubftances,nbsp;cannot be deprived of their oxygen by heat alone,nbsp;but the procefs muft be affifted by the contadl ofnbsp;hydrogen, phofphorus, and azote, in different numbers andnbsp;different proportions. The animal acids are, the acid nfnbsp;milk, the acid of fugar of milk, the formic or acid of ants,-the pruffic acid, vizi the colouring matter of Pruffian blue,nbsp;which is obtained from dried blood, hoofs, amp;c. the febacicnbsp;or acid of fat, the bombic or acid of filk-vvorms, the laccicnbsp;or the acid of waxy matter, and the zoonic, or the acid cX-tradted from animal matter by means of lime, Thofe actd*nbsp;arc alfo diftinguifhed from each other by their peculiar afS'nbsp;nities,. and their bafes or radicals may be decompounded,nbsp;but cannot be compounded from fimpler fubftances.

of Chcinlfify. � nbsp;nbsp;nbsp;�nbsp;nbsp;nbsp;nbsp;527

The

* The iiietalllc fubffances are difl-inguifhed by iheir ab-folute opacity, great fpecific gravity, brilliaix:y, anti t3u6fl-Jity ; but this laft property is very ,imperfelt;Sly poffelTeiJ by all thofe which precede iron in the lid, and which are, on thatnbsp;account, called feml-metals. Ail the metallic fubflances become liquid in certain peculiar degrees of heat. They have,nbsp;difFerent fpecific gravities, (fee the table of Specific Gravitynbsp;in page 75, and follow'ing), different colours, and differentnbsp;degrees of dudliiity; they have c.ho peculiar affinities fornbsp;other fubftances. We (hall briefly fubjoin a few of theirnbsp;more remarkable cbarafferiflic properties,; commencingnbsp;with the moft perfect of the'metals, and which has the leaffnbsp;affinity for oxygen.

Gold has an orange or reddilh yellow colour; is the heavieft metallic fubftance, platina excepted ; it melts atnbsp;about 5^37* Fahrenheit�s Thermometer; is the moftnbsp;perfecl, ductile, tenacious, and unchangeable of all thenbsp;known metals. Its proper foivents are the nUro-muriaiknbsp;acid, [aqua regia), and the oxy-muriatic acid.

Platina, Its colour is white; it is the moft ponderous roetal. Ry itfelf it refifts the fire of ordinary furnaces, andnbsp;can only be fefed by means of powerful burning glaffes, ornbsp;tn a fire urged by a current of oxygen air. It maybe alloyednbsp;�tvith moft metallic fubftances, and in that ftate may benbsp;fitfed with much greater facility. It is not afteSed by dienbsp;action of the atmofpherc. Its proper foivents are the famenbsp;3s thofe of gold.

Silver has a pure white colour, It is malleable and Very ductile, though not quite fo much as gold. It fufes at

528 nbsp;nbsp;nbsp;Sketch of the modern �Theory

The feven fubftances which follow gold in the lift, are called earths^ or earthy Juhftances ; \\z.ftlic3y

about 4717� of Fahrenheit�s Thermometer. It may be alloyed with feveral metals. It is diffolved by various acids,nbsp;^fpecially by the nitric.

Mercury. Its colour is like that of bright poliftied filver. It is the heavieft metallic fubftance next to gold andnbsp;platina. It is a folid in a temperature under the 72� beloWnbsp;friezing water. It is a liquid between that degree and 60C*nbsp;of Fahrenheit�s Thermometer; but above that degree itnbsp;becomes a vapour, or an elaftic fluid. The nitric acid is itsnbsp;beft folvent.

Copper has a brownifh- red colour ; is malleable, flexible, and duftile ; though not fo much as filver. It melts atnbsp;4587� of I'ahrenheit�s Thermometer. By expofure to thenbsp;fire it changes colour, and becomes firft blue, then yellow,nbsp;and lafily violet. It gives agreenifli-blue tinge to the flamenbsp;of burning coals. It is diflbluble, more or lefs, in moft ofnbsp;the acids. With the acetous acid it forms verdigris. Coppetnbsp;mav be united to moft metallic fubftances, forming variousnbsp;ufeful compounds.

Lead has a blueifti white colour, and is the heavieft metal, after gold, platina, and mercury. It melts at 540quot;.nbsp;furface is readily oxidated. It is diflblved by moft acids-Its oxides form various ufeful colouring pigments.

Tin comes neareft to the colour of filver ; but its furfac^ is foon tarniihed. It is very dudile, flexible, and whe�nbsp;bent crackles in a peculiar manner. It fufes at 41Cquot;,nbsp;is pretty readily oxidated. It is diflblved more or lefs bynbsp;Kioft acids.

moll ufeful, moft abundant, and the moft diffufed, metal in nature. Iron (excepting a few equivocal cafes) thenbsp;only metal fufceptible of magnetifm. It is eafily oxidated,nbsp;and its colour changes according to the degree of oxygenation. It is found combined with a variety of fubftance^nbsp;fromfome of which it cannot be feparated without verynbsp;great difficulty; hence we have iron of different qualitiesnbsp;and of different fufibility. Call iron melts at about 17977�.nbsp;Its union with carbon forms Jieel.

Zinc. Its colour is between the colour of filver and that of lead. It has very little dudlility. It fufes as foon as itnbsp;becomes red hot, (viz. when the heat is about loTt)quot;) tMbnnbsp;with the accefs of air it inflames and fublimes in whitenbsp;flocks of oxide, called philofophical wool, or pompholix. Itnbsp;Unites with feveral metals. With copper it forms brafs.

Antimony is a v/hitifh' brilliant femi-melkl, not eafy of fufion, but when fufed it emits a white fume called argentinenbsp;/now, oc flowers of antimony. The ftate in which this femi-inetal is generally feen in commerce, and in which ftate itnbsp;-is improperly called antimony, is in combination withnbsp;fulpbur.

Bifmuth (otherwife called tln-ghfs) is white, with a lhade nf red inclining to yellow. By means of the hammer it maynbsp;be reduced into powder. It fufes eafier than tin. Whennbsp;expofed to a ftrong heat, it burns with a b�ue flame, andnbsp;fublimes in ayellowifh fmoke, which condenfes and formsnbsp;the fowers of bifmuth. The nitric acid is its beft folvent,nbsp;�ts combinations with various metallic fubftances, formnbsp;pewter, folders, printer�s types, amp;c.

Cobalt is white, inclining to bluifti grey, and, when tar-niflied, to red. In a red heat it is malleable to a certain de-

lhall

is not eafily oxidated. When expofed to the fire in con-jun�ion with borax, or foda, amp;c. and earthy fubftances, tinges them blue. Its oxide, fufed with fand and pot-afhgt;nbsp;forms a blue glafs, which, when finely pounded, is called/malt-' Nic^ely in its pure ftate, has a greyifli white colour.nbsp;is magnetic in a very fmall degree ; hence it is thought tonbsp;contain iron. It is malleable in a confiderable degree, andnbsp;is flowly oxidated in a ftrong heat. The nitric acid is itsnbsp;beft folvent.

Manganefe is of a greyifli white colour, but it is fo eafily oxidated, as to be readily darkened by expofure to the air gt;nbsp;it falls into powder, and becomes a perfect oxide of a darknbsp;brown or black colour. Indeed it is in that ftate that W^nbsp;always find it. This oxide, expofed to a pretty ft.ong heatnbsp;in proper vedels, yields a very great quantity of oxygennbsp;air. This metallic fubftance is lefs fufible than iron, andnbsp;unites, by fufion, with every one of the metals, exceptnbsp;mercury.

Uranite is of a dark ft'cel or iron grey colour. Nitrous acid didblves it; but its oxide is infoluble in alkalies, whichnbsp;circumftance diftinguiflies it from the oxide of tungften,nbsp;which it refembles in colour.

Sylvanitey or Tellurite, is of a dark grey colour, inclining to red. It has a confiderable degree of dudlility and mal'nbsp;leability; is the nioft fufible metallic body, excepting mercury. It readily unites with mercury and fulphur. Itnbsp;diflbluble in nitrous acid, in the fulphuric acid, and in nitro*nbsp;muriatic acid.

Titanite is imperfefliy known. Its oxide, which was formerly taken for a red fori, is but fparingly found united

of Chemiftry. nbsp;nbsp;nbsp;531

ihall add two more which have been lately dlfco-

vered

to other minerals, and from certain phenomena, which at-teed its diflblutions and precipitations, it appears to be the oxide of a new metallic fubftance, to which the name ofnbsp;iitamie has been given 5 but it feems that it was never fairlynbsp;reduced to a metallic ftate.

Ghremt has a whitifh grey, fliining, appearance. It is obtained from a mineral called Siberian red lead. It yieldsnbsp;a particular acid, of a ruby red colour, which contains twonbsp;thirds of its weight of oxygen.

Tungden is fuppofed to be the oxide of a particular me-, tallic fubftance ; for it does not appear to have ever beennbsp;fairly reduced to a metallic ftate. It is, of a fteel greynbsp;colour, very hard and brittle. It affords a peculiar acid.

Molybdenite is a fubftance of a metallic luftre, which marks paper like plumbago [black lead). It is oxidated innbsp;a red heat, but it cannot be fufed without a very powerfulnbsp;fire. Its white or red oxide gives evident marks of acidnbsp;properties.

Arfenic is naturally white, inclining to blue; but it fpeedily becomes pale yellow, and then greyifti black bynbsp;expofure to the atmofphere. In a metallic ftate arfenic isnbsp;of a blackifh grey colour; it is brittle, and in its fra�turenbsp;refembles fteel. If arfenic be placed upon burning Coals,nbsp;it burns with a blueifh white flame, and is volatilized intonbsp;a white oxide, which attaches itfelf to the chimney, amp;c.nbsp;By this means arfenic is extra�led from various mineralsnbsp;with which it is found combined. This oxide, which isnbsp;fufible in water, is the white arfenic of commerce. Thisnbsp;volatilized oxide has a fmell refembling that of garlic, andnbsp;is exceedingly dangerous to animals. Arfenic by itfelfnbsp;fufes difficultly, but by fufion it may be united to moftnbsp;MM2nbsp;nbsp;nbsp;nbsp;metals.

Sketch of the modern 'theory

vered in fmall quantities, viz. glucmet and aguj-tine *.

The

metals. When faturated with oxygen, it conftitutes an acid which may exift in a concrete form, but it readilynbsp;attradls moifture from the atmofphere, and thereby becomesnbsp;a Huid.

* The earths are dry, brittle, inodorous, uninflammable, and fparingly foluble in water.

Silica is the earth which forms the principal ingredient of flints, rock cryftal, and feveral gems. It is rough, andnbsp;when finely pounded, a very minute quantity of it may benbsp;kept difiblved in water. 1�he only acid which ads uponnbsp;it, is the fluoric. It is infufible by itfelfj but in a ftrongnbsp;heat the fixed alkalies fufe it readily, and form glafs.

yirgil., or pure clay, otherwife called alumine, (for with the fulphuric acid it forms alum) in its pure ftate is white,nbsp;finooth, of an unctuous feel, and is dilFufible in water.nbsp;When heated it diminiflies in bulk, is hardened, and is rendered indifFufible in water. It may be hardened fo as tonbsp;ftrike fire with fteel. This moft ufeful property enablesnbsp;us to form bricks, pots, and a variety of utenfils, commonlynbsp;known under the name of earthen-ware.

Baryt, or Ponderous Earth, (from its confiderable fpecific gravity) is infufible when pure. Cold water diflblves anbsp;25th part, and boiling water one half, of its weight. It isnbsp;foluble in alcohol, and is highly poifonous. See lesnbsp;Annales de Chimie XXI. It has a greater affinitynbsp;for muriatic acid, than any of the other earths, or thenbsp;alkalies.

Strontian, when pure, is not fufible in the fire, but it only glitters with a phofphoric flame; it may however benbsp;fufed in conjundion with moft of the other earths. It is

of Chemijiry. nbsp;nbsp;nbsp;533

The laft three articles .of the lift are called alkalies, they have a peculiar tafte as well as other pe.r culiar properties. Pot-afh and foda are called/winbsp;alkalies, becaufe they cannot be rendered volatile

dillblved readily in the nitric and muriatic acids ; and forms, by the addition of the fulphurlc acid, an infoluble precipitate.

Lime, when pure, is called quick lime, or pure calcareous earth. Is infufible by itfelf, but it may be fufed in con- 'nbsp;jundlion with fdica and argil. Lime is purified by Jongnbsp;expofure to a ftrong heat, by which means it becomesnbsp;white, moderately hard and brittle. It has a hot burningnbsp;tafte, renders violets green, and corrodes animal and vegetable fubftances. By the application of water it becomesnbsp;hot, burfts, and becomes Jlaked lime, which, when mixednbsp;with fand, or dry mould, he. forms the mortar commonlynbsp;ufed for building. Slaked lime will be found to have ab-forbed 287 grains of w'ater for every 1000 grains of its original weight. Water cannot hold in folution more thannbsp;one yopdth part of its weight of lime, and in that ftate itnbsp;is called lime water.

Magnefta, when puoe, is white and very light. It combines with all the acids. It is infufible by itfelf.

Jargonia is a peculiar earth obtained from two gems; viz. the jargon and the hyacinth. It is infoluble in water.nbsp;In hardnefs and roughnefs it refembles filica. It is infufiblenbsp;by itfelf. It unites with the nitric, the carbonic, and thenbsp;fulphuric, acids.

Glucine is fuppofed to be a peculiar earth obtained from two gems; vi;^ the ieryl, or aqua marina, and thenbsp;emerald.

But it mufl; be obferved, that the alkalies are placed in the lift of fimple fubftances, rather be-caufe they form a particular clafs of bodies, whichnbsp;are endued with remarkable and peculiar properties } for they feem to be compounds of Amplernbsp;fubftances. Indeed, the ammoniac has been provednbsp;to conlift of 807 parts of azote, and 193 parts ofnbsp;hydrogen; alfo the two fixed alkalies are ftronglynbsp;fufpefted of being formed from a combination ofnbsp;azote with fome unknown bafes.

The three alkalies, the acids, and the combinations, in which they enter in fufftcient quantities, are called JaltSy or Jdine JubJlances j for a Jaline fub-ftance, in its extended chemical fenfe, means anbsp;fubftance that has fome tafte, and is foluble innbsp;water.

Thus we have endeavoured to give fome idea of the primitive, or elementary fubftances; fuch as

Agujline is fuppofed to be a peculiar earth obtained frorti a rnineral that refembles the beryl. It is not foluble innbsp;water, and it becomes hard in the fire.

* Alkalies have an acrid, urinous tafte ; change the vegetable blye colours into a green; combine with acids, and form neutral falts; viz. falts that have neither the properties of acids, nor of alkalies. As the alkalies appear to benbsp;derived principally from azote, therefore azote has been alfonbsp;called the alkaligen principle,

may

of Chemijlry. nbsp;nbsp;nbsp;S3S

may be deemed fufBcient for a ftudent of natural philofophy. A full account of their properties,nbsp;affinities, combinations, amp;c. will be found in variousnbsp;recent publications written profeflcdly on the fubjeflnbsp;of chemiftry ¹.

See Lavoifier�s Elements of Chemiftry. Jacquin�s Elements of Chemiftry. Briflbn�s Phyfical Principles ofnbsp;Chemiftry. Fourcroy�s Chemiftry. Gren�s I�rincipks ofnbsp;Modern Cherniftry. Lagrange�s Manual of a Conrfe ofnbsp;Chemiftry; and feveral other large works: to which maynbsp;be added, a very ufeful little book } viz. Parkinfon�s Chemical Pocket Book, or Memoranda Chemica.

IT Is perhaps fcarcely fufpe�led by mod of my readers, that almofl: every phenomenon,nbsp;which takes place about us, and which is attendednbsp;with fome change of property in the bodies concerned, is in faft a chemical procefs; viz. it doesnbsp;aftually depend upon, and is regulated by, the lawsnbsp;of affinity. Heating, cooling, fires, and every fortnbsp;of combuftion �, our refpiration, our digeftion, thenbsp;formation, decompofition, and fecretion,. of thenbsp;various animal fluids; evaporations, diflblutions,nbsp;and fermentations; the operations carried on in thenbsp;various arts of dyeing, bleaching, tanning, amp;c. arenbsp;all depending on the various affinities of bodies.nbsp;Infinite is the number and the variety of the particular procefles; and even the account of a feledtnbsp;number of them, is what fills up many large andnbsp;learned works. In thefe elements we can only attempt to deferibe the moft remarkable of thofe pre-ceflTes ; viz. fuch as are more general or more in-terefling, and which may not only elucidate thenbsp;general theory of chemiftry, but may alfo affift

Combuflion, in its modern enlarged fenfe, means every operation in which oxygen air is decompofed,nbsp;its radical j viz. the oxygen, is abforbed, and itsnbsp;other two components, caloric and light, are feenbsp;at liberty, or enter into other combinations. Therefore refpiration, the oxydation of metallic bodies,nbsp;and, in fhort, the oxidation of all, other fubftances,nbsp;arc different degrees of combuftlon. Thofe bodies,nbsp;which have fo much affinity for oxygen, as to benbsp;able to decompofe oxygen air, are called comhuftihlenbsp;boaies.

When the oxygen air is decompofed flowly, the heat is imperceptible, becaule the caloric is diffi-pated as foon as generated. When the decompo-fition goes on fader, the bodies concerned becomenbsp;fenfibiy warm. A quicker decompofition of thenbsp;oxyen air heats the bodies fo as to render themnbsp;red hot; (this temperature is equal to about 1000�nbsp;of Fahrenheit�s Thermometer) which date is callednbsp;ignition. When the procefs is attended with thenbsp;produdlion of certain fluids, as hydrogen, volatile

Whoever wifhes to examine this fubjeft at large, may perufe fome of the valuable vrorks which are mentioned innbsp;the note at the end of the preceding chapter; as alfo a variety of works written expreffively on the arts of dyeingjnbsp;leaching, amp;c,

oilsj amp;c. and the decompofition of oxygen asf affords a fufEcient developement of caloric i thennbsp;the above-mentioned fluids themfelves are ignitednbsp;and decomprofed, which conftitutes the ftame^ and isnbsp;thence called inflammation. The qurckeft decom-pofltion of oxygen air is attended with a very quicknbsp;extrication of caloric, a fudden expanfion of thenbsp;contiguous bodies, and of courfe with a fuddennbsp;Roife ; hence it is called detonation. A quicknbsp;fuccefTion of little detonations, is called decrepi-tatioriy or deflagration.

Combuflions are generally attended with the de* compofition and formation of feveral compounds;nbsp;viz. the carbon, which naturally exifts in vegetable and anim.al fubftances, unites with part of thenbsp;oxygen, and forms carhonic acid gas; fome of thenbsp;neutral falts are decompofed, and an alkali is leftnbsp;intermixed with what fixed matter remains after thenbsp;combuftion, amp;c.

T wo principal faefts mufl; be particularly remarked in this place. Firfl;, that t;ie greateft part of the heat, which is yielded in combuftion, comes fromnbsp;the decompofition ot the oxygen air; and fecondly,nbsp;that the oxygen air is the general, and the onlynbsp;fubftance, which by its decompofition, amp;c. cannbsp;produce combuftion. In fadt, where no oxygc*^nbsp;air exifts, as in vacuo, in azotic gas, in hydrogennbsp;gas, amp;c. there combuftion cannot take place; annbsp;animal cannot refpire, a metallic body cannot be,-

oxidated, or in general a combuftlble body cannot burn; for inftance, a piece of charcoal, expofed tonbsp;a ftrong fire in a clofe veflel, will not thereby benbsp;altered.

The atmofpherical air is ufeful for thofe pur-pofes, fo far as it contains oxygen air. When that portion of oxygen, which is about a quarter of thenbsp;atmorpherlcal fluid, has been more or lefs, or entirely, feparated, the remainder will accordingly benbsp;found lefs fit, or quite unfit for refpiration, fornbsp;combuftlon, amp;c. Hence will appear the neceffitynbsp;of ventilating towns, houfes, fhips, amp;c.

If you place a lighted wax taper under a glafs receiver, which is inverted with its aperture innbsp;Water, and is fituated upon the fhelf of the tub,nbsp;fig. 8. plate XVII. you will find that as the flamenbsp;decompofes the oxygen air, and of courfe lefs andnbsp;lefs of that air remains within the receiver, fo thenbsp;flame becomes gradually fmaller, lefs afii ve, and at laftnbsp;ceafes to burn. After the cooling of the apparatus,nbsp;you will find the water to have rifen within the receiver, and to occupy the place of the decompofednbsp;oxygen air j viz. about one quarter of the originalnbsp;bulk of the common air. The remaining azoticnbsp;gas is unfit for combuftion. This gas containsnbsp;a fmall quantity of carbonic acid gas, which hasnbsp;been formed by the union -of the carbon of thenbsp;''^ax with fome of the oxygen. This carbonic acidnbsp;may be fepara'ted from the azotic gas by

aglcadon in Urne water, which abforbs it, and leaves the azotic.gas by itfelf¹.

If the glafs receiver be filled with pure oxygen air, the wax taper will be found to burn for a longernbsp;time, with a much more adlive and luminous flame;nbsp;and the air will difappear almoft entirely, exceptingnbsp;only the carbonic acid gas which has been formed,nbsp;and a fniall portion of oxygen air which remainsnbsp;mixed with the acid gas.

The moft aftive fire which we can polfibly produce, is obtained by palling a current of oxygen air, inftead of common air, through burning coals,nbsp;or other combuftibles.

For the fupport of animal life, a conftant fupply of heat is indifpenfably neceflary, and the caloric,nbsp;which produces that heat, is derived from the de-cornpofition of oxygen air in the courfe of refpira-tion, A certain quantity of carbonated hydrogennbsp;gas is fuppofed to be difengagcd from the blood innbsp;the lungs ; the oxygen of the air, which is infpired.

Gun powder may be fired in vacuo, and compofitions of gun-pov;der, nitre, amp;c. may be made to burn under water ; but in thofe cafes the oxygen,' neceflary for the corn-bullion, is afforded by the nitre, or by fome other fait analogous to it, In facl, if nitre be put by itfelf in an earthen-W'are retort, aud the retort be expofcd to a fire fufficient tonbsp;render it flrongly red hot, or rather white hot, the nitrenbsp;will yield abundance of oxygen air, which may be received

ccmbines with the hydrogen, and with the carbon of the above-mentioned gas, and parts with its caloric; thus carbonic acid gas and water is produced,nbsp;(for, as it will be Ihewn in the fequel, water confiftsnbsp;of oxygen and hydrogen). The caloric v/hich isnbsp;dlfengaged in this procefs, expands itfelf throughnbsp;the adjoining parts, and fupplies the heat ncceffarynbsp;for animal life.

If the atmofpherical fluid confifted entirely of Oxygen air, then a much greater quantity of heatnbsp;quot;'ould be produced by refpiration than is neceflarynbsp;for the fupport of animal life, the combuftion ofnbsp;bodies would likewife proceed too rapidly, and ofnbsp;Courfe decompofitions of every fort would go oilnbsp;'^^ith ufelefs precipitation; hence we may thankfullynbsp;admire the juft and temperate conftitution of thenbsp;^trnofpherical air.

One of the moft remarkable difeoveries of modern '^oies, is the decompofition and compofition of water,nbsp;''^hich was formerly confidered as ah elementary oamp;nbsp;brnple fubftance. This decompofition has been ef-fefted tv.'o ways principally; viz. by placing the vapour of water in contaft with certain ignited bodies,

by means of eledricity. The moft fatisfacftoiy Methods of decompofing, and of compofing it, arcnbsp;'^Wly deferibed by M- Briflbn, in the followingnbsp;'^ords :

fufedj about I of an inch in diameter *, -was placed acrofs a furnace GFED, in a pofition fomewhatnbsp;inclined, and to its upper extremity was adapted anbsp;glafs retort A, containing a known quantity of distilled water, and refting on a furnace V V. To thenbsp;lower extremity of the glafs tube F, was applied anbsp;w'orm S S, connedbed with the double tubulatednbsp;fiafk H ; and to the other aperture was adapted anbsp;bent glafs tube K K, deftined to convey the gas tonbsp;an apparatus proper for determining the quality andnbsp;quantity of it. When the whole was thus arrangenbsp;ed, a fire was kindled in the furnace CFED, andnbsp;maintained in fuch a manner as to bring the glaS�nbsp;tube EF to a red heat, but without fufing it: atnbsp;the fame time, as much fire was maintained in thenbsp;furnace VVXX, as to keep the water in the retort A, in a continual ftate of ebullition.

� In proportion as the water in the retort Agt; aflumed the ftate of vapour by ebullition, it fillednbsp;tlie interior part of the tube EF, and expelled thenbsp;atmofpheric air, which was evacuated by the worntnbsp;S S, and the tube K K. The fteam of the waternbsp;was afterwards condenfed by cooling in the wortr^nbsp;S S, and fell, drop by drop, in the ftate of water�

^ nbsp;nbsp;nbsp;into

into the tubulated dalle H. When the whole of the water in the retort A, was evaporated, and thenbsp;liquor in the veflel had been fuffered to drain offnbsp;completely, there was found in the flafle H, anbsp;quantity of water exaflly equal to that which wasnbsp;in the retort A ; and there had been no difengage-ment of any gas; fo that this operation was merelynbsp;a common diftillation, which gave abfolutely thenbsp;fame refult as if the water had never been broughtnbsp;to a date of incondefcence in paffing through thenbsp;glafs tube EF.

2. � Every thing being arranged as in the preceding experiment, 28 grains of charcoal reduced to fragments of a moderate fize, and which hadnbsp;been previoufly expofed for a long time to a whitenbsp;heat in clofe veflels, were introduced into the glafsnbsp;tube EF. The operation was then conduced asnbsp;before, and the water in the retort A, kept in anbsp;continual date of ebullition, till it was totally evaporated.

� The water in the retort A, was diddled, as in the preceding experiment; and being condenfed innbsp;the worm S S, had fallen, drop by drop, into thenbsp;fladc H ; but at the fame time there had been dif-engaged a confiderabl'e quantity of gas, whichnbsp;efcaped through the tube K K, and was colledlednbsp;in a proper apparatus. When the operation wasnbsp;finifhed, there was found notliing in tire tube F F,nbsp;but a few alhes; and the 28 grains of charcoal hadnbsp;totally difappeared.

There were found two different kinds of gas; viz. 144 cubic inches of carbonic acid gas, weighing 100 grains, and 380 cubic inches of a verynbsp;light gas, weighing 13,7 grains. T'his laft gas tooknbsp;fire on being applied to a lighted body in contadtnbsp;with the air.

in examining afterwards the Weight of the w'ater which had pafled into the flafk, it was foundnbsp;lefs than that in the retort A, by 85,7 grains. Innbsp;this experiment, therefore, 85,7 grains of water,nbsp;and 28 grains of charcoal, formed carbonic acidnbsp;gas, equal to 100 grains, and a peculiar gas fuf-ceptible of inflammation, equal to 13,7 grains.

�We have already faid, that to form 100 grains of carbonic acid gas, 72 grains of oxyg�n muft benbsp;united to 28 grains of charcoal or carbon. Thenbsp;^28 grains of charcoal pur into the glafs tube E F,nbsp;took, therefore, from the water, 7 2 grains of oxygen, fince there was formed carbonic acid equal tonbsp;100 grains.

� It appears therefore that 85,7 grains of water are compofed of 72 grains of oxygen, and 13,7nbsp;grains of a fubftance, forming the bafe of a gas fuf-ceptible of inflammation.

3. � The apparatus being arranged as above, inftead of the 28 grains of charcoal, 274 grains of thin (havingsnbsp;of iron, rolled up in a fpiral form, were introduced into

as before; and in the like manner the whole of t^ water in the retort A, was made to evaporate. ,

� In this experiment there was difengaged only one kind of gas which was inflammable : there wasnbsp;obtained of it about 406 cubic inches, weighingnbsp;15 grains. The 274 grains of iron, put into thenbsp;tube E F, were found to weigh above what theynbsp;did when introduced, 85 grains, and the water firftnbsp;employed was diminillied 100 grains.

The volume of thefe iron flravings was found to be greatly enlarged. The iron was fcarcely anynbsp;longer fufceptible of attraftion by the magnet 5 itnbsp;dilTolved without effervefcence in acids: in a word,nbsp;it was in the ftate of a black oxide, like that whichnbsp;has been burnt in oxygen air.

� In this experiment there Was a real oxidation of the iron by the water, entirely fimilar to thatnbsp;efFedled in the air by the aid of heat; 100 grains ofnbsp;Water were decompofed, and of thsfe 100 grains,nbsp;85 united to the iron, to reduce it to the ftat$nbsp;of black oxide: thefe 8 5 grains, therefore, werenbsp;oxygen; the remaining 15 grains combined withnbsp;caloric, and formed an inflammable gas. It hencenbsp;follows, that water is compofed of oxygen, and thenbsp;bafe of inflammable gas, in the proportion of 85 tonbsp;J 5, or of 17 to 3.

� Water, therefore, befides oxygen, which Is one of its principles, and which is common to itnbsp;with a great many other fubftances, contains anothernbsp;peculiar to itfelf, and which is its ccuiftituent radical.

This radical has been called hydrogen; viz. th: generator of water and the combination of this radical with caloric, is diftinguifhed by the name ofnbsp;hydrogen gas.

4. � Recompofition of Water. � Take a widemouthed glafs balloon A, fig. 12. Plate XVII. capable of containing about 30 pints, and cement to its mouth a fmall plate of copper B C, havingnbsp;above it a Cylinder of the fame metal, 0^ D, piercednbsp;with three holes to receive three tubes. The firftnbsp;of thefe, ^H, is deftined to be connedfed, at its extremity h, with an air-pump, in order that thenbsp;balloon A, may be exhaufted of air. The fecondnbsp;tube gg, communicates by its extremity MM,nbsp;with a refervoir of oxygen gas, and is deftined tonbsp;convey it into the ballon A. The third tube zDd,nbsp;communicates by the extremity N N, with a refervoir of hydrogen gas: the extremity z of this tubenbsp;terminates in an aperture fo fmall as fcarcely tonbsp;admit a very delicate needle. It is through thisnbsp;aperture that the hydrogen gas, contained in the refervoir, is to pafs into the balloo.'; A. In the nextnbsp;place, the fmall pjate BC is pierced with a fourthnbsp;hole, into which is inferted with cement, a glalsnbsp;tube, through which palfes a wire F L, having atnbsp;its extremity L, a fmall ball deftined to make annbsp;cleiftric fpark pafs between the ball and the extremity of the tube that conveys the hydrogen gas intonbsp;the balloon A. Each of the three tubes has anbsp;cock, r, r, H.

� That the gafes may be conveyed in a very dry (late through the tubes which conduft themnbsp;into the balloon A, and that they may be deprivednbsp;of water as much as poffible, you muft put intonbsp;the fwelled parts M M, and N Nj of the tubes,nbsp;feme fait capable of attrading the moiflure withnbsp;great adtivity. Thefe falts fhould be only coarfelynbsp;pounded, in order that they may not form a mafs,nbsp;and that the gafes may pafs freely through the in*nbsp;terhices left between the fragments. You muft benbsp;provided with a fufficient quantity of very purenbsp;oxygen gas, and nearly a triple volume of hydrogen gas, equally pure. To obtain it in this ftate,nbsp;and free from all mixture, you muft extrad it fromnbsp;Water, decompofed by means of very pure and ductile iron.

� When every thing has been thus prepared, adapt to the air-pump the tube h H, and exhauftnbsp;the air in the large balloon A; then fill it withnbsp;oxygen by means of the tube gg, and, by anbsp;certain degree of preffure, force the hydrogen gas tonbsp;pafs into the balloon A, through the extremity ofnbsp;the tube z D d; then kindle this gas by means ofnbsp;an eledric fpark ; and if you renew the quantity ofnbsp;each of thefe two gafes, the combuftion may be continued for a long time.

� In proportion as the combuftion proceedsi, ''ater is depofited on the internal furface of thenbsp;balloon A: the quantity of this water graduallynbsp;Jucreafes, and it unites into large drops, which

� The fura of the weights of the gafes employed, and the weight of the water formed, were found conbsp;be equal, within a 200 th part. It was bynbsp;experiment of the fame kind, that Lavoifier afcer-tained, that 85 parts, by weight, of oxygen, andnbsp;15 parts, alfo by weight, of hydrogen, are requirednbsp;�to compofe an hundred parts of water.

� Thefe phenomena of the decompofition, and rccompofition of water, are continually effefted before our eyes, by the temperature of the atmofphere,nbsp;and the agency of compound affinities. It is thisnbsp;decompofition which gives rife, at leaft in a certainnbsp;degree, to the phenomena of fpirituous fermentation, thofe of putrefaftion, and thofe even ofnbsp;getation.�

The diffolution of metallic fubftances in acids b a very important and remarkable operation of ch^'nbsp;miftry. When a metal is placed in a fluid acid�nbsp;capable of diflblving it, heat and effervefcence (vi^'nbsp;a dh�ngagement of gas) frequently takes place, andnbsp;the gas is either the nitrous, or the fulphurous acid,nbsp;amp;c. according to the nature of the acid j the metalnbsp;gradually diminiflies in bulk, and at lafl; none ofnbsp;it is ta be feen. The liquor thus loaded with thenbsp;metallic fubftance, is called the folution ofnbsp;mtal. If an alkali, or certain other fubftances, benbsp;added to the folution, tlie metallic fubftance will be

feparated from the fluid, and will fall to the bottom of the veflei. This is called the precipitat-e, andnbsp;the alkali or other fubftance that has been added tonbsp;the folution, is called the precipitant. The precipitate, in certain cafes, appears in a metallic ftate, viz.nbsp;a powder, or cruft of the original metal; but it generally appears in the form of a fait; viz. quite def-titute of the metallic appearance: it is, in fhort, annbsp;oxyde of the metal, which may be reduced to anbsp;metallic ftate by depriving it of the oxygen. Thisnbsp;laft procefs is called teduElion.

Such are the general phenomena of metallic dif-lt; folutions, and the operations of affinity feem to benbsp;fimple and evident; but a clofer examination ofnbsp;particular diflblutions, and of the fads which attendnbsp;each of them, fliew that the fubje�l: is much morenbsp;intricate than it may at firft fight appear. In fhort,nbsp;it is manifefted by a variety of experiments, thatnbsp;Water is abfolutely necelTary for every diflblution jnbsp;that the water is decompofed as well as the metalnbsp;and the acid, and that new compounds are therebynbsp;formed. Nearly the fame thing may be faid ofnbsp;redudlions j but the number of ingredients of de-compofitions and compofitions, which a6l; and arenbsp;produced in every particular cafe, are in partnbsp;known, and in part guefled at. Several elegantnbsp;experiments in elucidation of this fubjed, whic.Hnbsp;fiiew the above-mentioned neceffary prefence ofnbsp;water, and a variety'of collateral particulars, were

Some idea of the primitive fubftances has been given in the preceding chapter; but by far thenbsp;greater number, if not all, the bodies which naturally occur to our fenfes, are compounds of fe-veral of the primitive fubftances j and their ingredients are in great meafure to be afcertained by trials,nbsp;and by employing other fimpler and determinatenbsp;fubftances.

Each of the three kingdoms of nature are divided by the chemifts into fubordinate divifions. Thenbsp;mineral .is divided into earthy, metallic, faline, andnbsp;bituminous, minerals; of which a general idea hasnbsp;been given in the preceding pages, excepting thenbsp;bituminous; but thefe feerh to have a doublenbsp;origin j viz. they feern to partake of the mineralnbsp;and of the vegetable kingdom ; for they are foundnbsp;to contain feveral of thofe ingredients which belongnbsp;principally to vegetables, and perhaps to animalsnbsp;too.

* See Mrs. Fulhame�s ElTay on Combuftion, amp;c. London 1794. See alfo a fliort account of Dr. Woodhoufe�s Experiments in the Philofophical Magazine, vol. VII. p. 83.nbsp;and the Chemical Works mentioned at the end of the preceding chapter, in which the particular phenomena that attend a variety of diflblutions and redudions will be found,

' nbsp;nbsp;nbsp;chiefly

chiefly from water, which is decompofed by the powers of vegetation, and its components enternbsp;into new combinations.

an eflTential principle of plants, and enters into the formation of their refins, oils, artd mucilage.nbsp;Part of the oxygen forms the acid juices of vegetables, and another part is expelled, when thenbsp;plants are expofed to a ftrong light, in the formnbsp;of oxygen air; but when the plants are in thenbsp;dark, as at night, then they give out principallynbsp;the carbonic acid gas. The common air whichnbsp;furrounds a plant contributes to its vegetation, bynbsp;affording it oxygen in certain cafes, as alfo by de-pofiting moifture upon, or taking it away from,nbsp;its furface, according to circumftances. Nitrogennbsp;is likewife abforbed by plants.

Light, caloric, and carbon, do alfo feem to enter into combination with vegetables, and to be ne-ceflary for their growth.

Moll of thofe principles may be extraded, by decompofition, from all plants ; but, befides thofe,nbsp;there are feveral others which may be extraeffednbsp;from particular plants.

Though we find that moft plants are refolvible into the above-mentioned principles ; yet it muftnbsp;be acknowledged that the chemical art cannotnbsp;irnitate, or form, any vegetable, no more than itnbsp;can form any animal, part. The real proportionnbsp;of the ingredients, the manner of combining them,

and probably the neceffary concurrence of other eleinenrs, are far from being afcertained.

By the decompofition of plants (I do not mean an extreme decompofition) feveral ufeful fubftancesnbsp;are obtained j the moft remarkable of which wenbsp;fhall bi'iefly enumerate.

The/apis the general, or more abundant, fluid of a plant, from which the various peculiar juices,nbsp;refuis, oils, amp;c. of the plant, are fecreted, bynbsp;the organifm of the plant and the powers of ve^nbsp;getation.

The mucilage, which forms the bafis of mofl: vegetable produdtions, has the following peculiar properties, It is infipidj is foluble in water, but not in alcohol ; is coagulable by the adbion of weak acids,nbsp;and of metallic folutions.

Gum is a confiftent fubftan�ce, foluble in water. It is found concreted in certain places on the furfacenbsp;of plants, and is fuppofett to be only inlpifliatednbsp;mucilage.

Oils are diftinguilhed into fxed or fai oils; viz, fuch as contain mucilage, and cannot be renderednbsp;volatile without a confiderable degree of heat jnbsp;and into volatile oils, which contain aroma^ ornbsp;the odoriferous part of the plant. By diftillationnbsp;oils yield a phlegm, an acid, a fluid, or lightnbsp;oil, a , confiderable quantity of hydro-carbonatenbsp;gas� carbonic acid gas, and leave in the retort a

refidouW

refidimm which does not afFord any alkali, as the afhes of moft vegetables do. The volatile oilsnbsp;aftbrd a greater proportion of hydrogen gas, andnbsp;the fixed .oils a greater proportion of carbonic acidnbsp;gas; for this gas is in great meafure derived fromnbsp;the mucilage.

Reftns feem to be oils concreted by the combination with oxygen. They are inflammable, fo-luble in alcohol, and in oils, but not in water.

Gum reftns feem to be mixtures of mucilage and of refins j for they are partly foluble in water, andnbsp;partly in alcohol.

Fcccula feems to be little different from mucilage. The principal circumftance, in which they feem to differ, is, that fecula is not foluble in coldnbsp;water.

Vegetable glutent is an adhefive fubftance, obtained principally from the flour of farinaceous plants, by forming a pafte of that flour, andnbsp;kneading it in water, until it no longer tinges thenbsp;Water.

Sugar is an effential fait, which may be ex-tradted In various quantities from different plants.

Albuminous Matter of Vegetables, is a flocculerit matter, which is extracted from the juice of certain plants, and in fonie meafure refembles thenbsp;white of an egg, whence it has derived itsnbsp;name.

The different acids, which mdy be obtained

from

The conftituent principles of plants have different affinities; but the proportion of thofe principles innbsp;a living plant, is fuch as to balance their peculiarnbsp;affinities and the excefs or defedl of each principle is eafily expelled or abforbed by the adlionnbsp;of vegetation. But when vegetation ceafes, thennbsp;the adlion of the atmofphere, which heats or cools,nbsp;or oxygenates, or dries up, or moiftens, the vegetable fubftances, foon dillurbs that juft proportionnbsp;of ingredients, and produces a variety of effe�ls. Ifnbsp;the vegetable abound only in moifture, a dry airnbsp;and ventilation will dry it up ; and fuch is the cafenbsp;with wood, feeds, amp;c. When the vegetables arenbsp;very juicy, and thofe juices contain a variety of principles, then thofe principles begin to feparate, thenbsp;heavieft go to the bottom, the moft volatile flynbsp;away, an inteftine motion is thereby produced, newnbsp;combinations Lake placcy amp;c. This decompofltionnbsp;in general is called fermentation. In different ftatesnbsp;of it different effefls are produced, and from thofenbsp;Ciffedls it derives three different names; viz. of vinous, acid, and putrid, fermentation.

The Vinous Fermentation, or Spiritous Fermentation, * In order to produce this fermentation, the expreffed juice of grapes (and the fame thing withnbsp;little difl�rence may be faid of the juices of feveralnbsp;other fruits) is placed in an �pen velTel, or vat,

and is kept gently warm, as about 70� of Fahrenheit�s Thermometer. The liqour foon grows turbid, and an inteftine motion takes place through the whole mafs, attended with a copious difchargcnbsp;of carbonic acid gas, and a frothy iubftance callednbsp;yeaft. After a day or two, and fometimes longer,nbsp;the phenomena gradually diminifn, and ceafe almoftnbsp;entirely. In that date the liquor is pretty clear,nbsp;and will be found to have acquired a vinous taftenbsp;and odour j and the thickeft orquot; more confidentnbsp;part will be found fettled at the bottom of thenbsp;vefTcl. Now if the progrefs of diflblution benbsp;ftopped, which is done by feparating the clearnbsp;liquor from the thick fediment, by preventing thenbsp;accefs of air to it, by placing it in a coolernbsp;fituation, amp;c. then the liquor remains with littlenbsp;alteration in the date of wine. But if the whole benbsp;left undidurbed, the fermentation will pals on to thenbsp;next dage; viz. to

The acetous Fermentation. This confids in the abforption of oxygen from the atmolpherej andnbsp;the refult is vinegar, or the acetous acid.

In the putrid Fermentation the colour of the vegetables changes j they grow pretty hot, and a mixture of gafes is difengaged; viz. of azote,nbsp;hydrogen, carbonic- acid, and ammoniacal, gafes.nbsp;This procefs completes the diffolution of the vegetable fubdances.

Wine, Or fermented liquors, yield, by didilla-tion, an infiammable and odoriferous liquor,

Alcohol feems to be formed from an intimate combination of hydrogen and carbon, and is perfe�l-ly mifcible with water.

Alcohol mixed with the fulphuric, or the nitric, or other acid, and then diftillcd, yields the lighteft liquid known. This liquid is called ether,nbsp;to which the name of the acid is added ; viz. it isnbsp;called the fulphunc, or the nitric, or the muriatic,nbsp;or the acetic ether, according to the nature of thenbsp;acid which has been employed for its produftion.

Ether feems to be formed from a combination of the oxygen of the acid, with the carbon and thenbsp;hydrogen of the alcohol. It has a peculiar fmell,nbsp;is very volatile, and highly inflammable. If ethernbsp;be mixed with an equal bulk of water, about anbsp;quarter of it will be dilTolved by the water; the othernbsp;three quarters, which are purer than previous tonbsp;the mixture, will be found to fwim upon thenbsp;water.

Animal fubftances, whether folid or fluid, confift of^ for they are refolvable into, the followingnbsp;principles; viz. azote, carbon, hydrogen, oxygen,nbsp;phofphorus, and lime. The various, but unknown,nbsp;proportions, the number, and the arrangement ofnbsp;thofe ingredients, conftitute the blood, the milk,nbsp;the gall, the bones, the mufcles, the fat, and allnbsp;the other parts of animal bodies. But with refpe^tnbsp;to the fafts which have been afeertained, or the

conjeftures which have been offered, relative to the original formation, growth, fecretion, form, fuu-ation, and other properties of thofe animal parts,

I muft unavoidably refer.the reader to the works of the anatomical and chemical writers: we fhall,nbsp;however, fubjoin a Ihort account of the naturalnbsp;procefs of the putrefaftion of animal fubftances,nbsp;with which we fhall clofe the prefent volume.

An animal, like a vegetable, when deprived of life, begins to undergo a decompofition or lepara-tion of its conftituent principles; and this decompo-fition is afllfted and promoted by a moderatenbsp;warmth, by moifture, and by the accefs of air. Itnbsp;muft be obferved, however, that animal diffolutionnbsp;does not go through the vinous and acetic ftates ofnbsp;fermentation ; but it proceeds direftly to the putrid,nbsp;principally on account of its containing more azote,nbsp;and much ammonia j excepting a few animal fluids,nbsp;which, by proper treatment, may be caufed to undergo a vinous or acid fermentation.

The colour and the confiftence of dead animals firft begin to diminifli, and. an unpleafant odour isnbsp;exhaled. The colour, after having become pale,nbsp;changes to blue and green, then to dark brown, according as the parts become lefs conftftent, and thenbsp;putrid effluvium becomes more penetrating, naufe-ous, and injurious. This produflion of gafes gradually increafes in pungency and variety j and,nbsp;from the feparation of phofphorous, it is often attended with a phofphorefcent light. The mafs of

matter, already become very foft, fwells, and, laftly, produces carbonic acid gas. When all the moftnbsp;volatile parts have been difengaged, the fixed radicals, containing fome hydrogen, form a brown,nbsp;fofc, earthy matter, which, if left expofed to thenbsp;atmofphere, becomes, in procefs of time, a powdery pale fubfrance; but if mixed with mould,nbsp;forms foil fit for vegetation.

The putrid proccfs of animal fubftances may be checked or prevented by various means, fuch asnbsp;placing the fubftances in cold fituations, freezing,nbsp;drying up the mioiilure w'hich is neceffary for fermentation, introducing refinous fubftances, placingnbsp;the fubftances in fpirit of wine, amp;c.

r G A B C D E F o ^ nbsp;nbsp;nbsp;�

m��-

Fii). 22.

Nmnencal JVanies.^................		� 2*^	quot;'2^'			��I*quot;'		f th 5 .	16^	^6^	L 7^		8Tquot;
Literal Names_____________________	C		D	%��E	E	F	%V(5	G	^g'-a	A	^V�'B	B	C
Tib ratio ns in one Seeond.---------	128,4	1^1.	144,4	154.	160,6	171,2	180,5	1,92,6	20.5,4	214.	228,3	240,8	256,8
(	3�00.	3375.	3200.	3000.	2880.	2700.	2560.	2400.	2250.	2160.	2025.	1920.	1800.
ISflportional lerujths ot the SPinrfs-j		16	8	6	4	3	32	2	5	3	9	8	1
	1- A-	IG	9	6	6	4	45	quot;3	8	5	16 -i	16	2
t/ie Antes or an (Jctave.............	A-	^�-^�	�	^0 ^�e	-0-	0	^0^	��J	^fcni	Cl ^		-0-	� nbsp;nbsp;nbsp;1 J

�^'�e.dfi*

JfBasire tc .

Keat,	100 grains of	100 grains of	100 grains of	100 grains of
Keat,	ipiricto 5 grains or water.	fpirit to 10 grains of water.	fpirit CO 1 5 grains of water.	fpirit to zo grains of water.
	0,84995	0,85957	0,86823	0,87585
35	0,84769	0,85729	0,86587	0^87357
40	0,84539	0,85507	0,86361	0,87134
45	0,84310	0,85277	0,86131	0,86907
5� 55	0,84076	0,85042	0,85902	0,86676
5� 55	0,83834	0,84802 '	0,85664 0,85430	0,86441
60	0,83599	0,84568	0,85664 0,85430	0,86208
65	�0,83362	0,84334	� 0-85=93	0,85976
70	0,83124	0,84092	0,84951	0,85736
75	0,82878	0,83851	0,84710	0,85493
80	0,82631	0.83603	0,84467 nbsp;nbsp;nbsp;,	0,85248
85	0,82386	C�83355	0,84221	0,85006
90	, 0,82142	0,83111	0,83977	0,84762
95	0,81888	0,82800	0,83724	0,84511
lOO	0,81643	0,82618	0,83478	0,84262

Heat.	ICO grains of	100 grains of	100 grains of	100 grains of
Heat.	to 23 grains of water.	fpirit to 30 grains of water.	fpiritto 35 grains of water.	fpiritto 40 grains of water.
30�. 35	0,88282 0,88059	0,88921 0,88701	0,89511 0,89294	0,90054 0,89839
40	0,87838	0,88481	0,89073	0,89617
45	0,87613	0,88255	0.88849	0,89396
So	0,87384	0,88030	0,88626	0,89174
	0,87150 0,86918	0,87796 0,87568	0,88393 0,88169	0,88945 0,88720
05	0,86686	�gt;87337'	0,87938	0,88490
70	0,86451	0,87105	0,87705	0,88254
80 85	0,86212 � 0,85966	0,86864 0,86623	0,87466 0,87228	0,88018 0,87776
80 85	0,85723	0,86380	0,86984'	0,87541
90	0,85483	o,86i 39	0,86743	0,87302
95	0,85232	0,85896	0,86499	0,87060
.100	0,84984	0,85646	0,86254	0,86813 1

	lOO grains	10c grains of	100 grains of	---�..... J 100 grains of
Heat.	fpirit to 65 grain?	fpiritto7o grains	fpirit to 7^ trains	fpirit to 80 grain*
	of water.	of water.	of water, '	of water.
	0,92217	0,92563	0,92889	0,93191
3-5	0,92009	0,92355	0,92680	0,92986
40	0,91799	0,92151	0,92476	0,92783
45	0.91584	0,91937	10,92264	0,92570
50	0,91370	0 9I723	0,92050	0,92358
55	0.91 14	0,91502	0,91837	0,92145
60	0,90927	0,91287	0,91622	^�gt;91933
65	0,90707	0,91066	ogt;9i4oo	0,91715
70	0,90484	0,90847	0 91181	0)91493
75	0,90252	0,90617	0,90952	0,91270.
80	0,9002 I	0,90383	0,90723	0.91042
85	. 0,89793	0,90157	0,90496	0,90818
SO	0,89558	0,89925	0,90270	0,90590
95	0,89322	0,89688	0,90037	0,90358
100	' 0,89082	0,89453	0,89798	0,90123
	ICO grain? of	100 grains of	ICO grains of	100 grains of
Hear.	fpirit to 85 grain:	fpirit to 90 grains	fpirit to q q grains	fpirit to 100
	of water.	of water.	of water.	grains of water,.
go�	0,93474	0.93741	0,93991	0,94222
35	0,93274	0,93541	0,93790	0,94025
40	0,93072	ogt;9334'	0,93592	0,93827
45	0,92859	0,93131	0,93382	0,93621
5�	0,92647	0,92919	0,93177	0,93419
55	0.92436	0,92707	0,92963	0,93208
60	0,92225	0,92499	0,92758	0,93002
65	0,92010	0,92283	0,92546	0,92794
70	0,91793	0,92069	0,92333.	0,92580
75	0,91569	0,91849	0,921 I�	0,92364
80	0,91340	0,91622	0,91891	0,92142
85	0,91119	0,91403	o,'9i670	0,91923
90	0,90891	0,91177	0,91446	0,91705
95	0,90662	0,90949	0,91221	0,9148 [
100	0,90428	0,90718	0,90992	0,91252

	9SS'ainsoffpirit	90 grains of fpirit	S5 grains of fpirit	80 grains of fpirit
	to loo grains	to 100 grains	to IOO grains	to IOO grains
	of water.	of water.	of water.	of water.
30�	0,94447	0,94675	0,Q4020 ,	0.95173
35	0.94249	0.944^4	0.94734	0,94988 '
	0,9:pO\|,-3	0,94295	0.94547	0,94802
4s	0,93860	0,94096	0.94348	0,94005
SO	0,936158	0,93897	0,94149	0,94414
60	0,934,2	0,93696	0,93948	0,94213
	0.93247	0.93493	0,93749	0,94018
�S	0.93-40	0.93285	0,93546	0,93822
70	0,92828	0.93076	093337 �	0,93616
75	0,92613	0,92865	0,93132	0,93413
S_r-	0,92393	0,92646	0,92917	0,93201
	0.92179	0,92432	0,92700	0,92989
90	0,91962	0,92220	0.92491	0,92779
9S	0,91740	0,91998'	0,92272	0,92562
100	0,91513	0,91769	0,92047	0,92346
�
	75 grains offpirU	70grains of fpirit	6^ grains of fpirit	60 grains of fpirit
	to ioo grains-	to IOO grains	to IOO grains	to IOO grains
	of water.	of water*	of water.	of water.
30�	0,95429	0,95681	0,95944	0,96209
35	0,95246	0,95502	0,95772	0,96^48
40	0,95060	0,95328	0 95602	0.95879
45	0,94871	� 0,95143	0,95423	0.95705
SO	0,94683	0,94958	0.95243	0,95534
55	0,94486	0,94767	0,95057	0.95357
60	0,94296	0,94579	0,94876	0,95181
^5	0,94099	0,94388	0,94689	0,95000
70	0,93898	0,94193	0,94500	0,94813
75	0,93695	0.93989	0,94301 .	0,94623
�O	0,93488	0,93785	0,94102	0,94431
85	0 93282	0,93582	0,93902	0.04236
90	0,93075	0,93381	0,93703	0.94042
95	0,92858	0,93170	0.93497	0,93839
J 00	0,92646	0,92957	0,93293	0,93638

Heat.	of fpirit	10 grains of i^pirit	5 grains of fpirit
Heat.	to loo.grains , of water.	to 100 grains of water.	to 100 grains of water.
30�	0,98412	0.98804	0,99334
35	0,98397	0,98804	0 99344
40	0,98373	0,98795	o.-99j45
45	0,98338	0,98774	0,99338
SO	0,98293	0,98743	0,99316
55	0,98239	0,98702	0,99284
60	0,98176	0,98654	0,99244
^5	0,98106	0,98594	0,99194
70	0,98028	0,98527	0,99134
75	0,97943	0,98454	0,99066
80	0,97845	0,98367	0,98991
85	0,97744	0,98281	0,98912
90	0,97637	0,98185	0,98824
95	0,97523	0,98082	0,98729
loo	0,97401	0,97969	0,98625

Inches.	Words annexed.
31-	Very dry. Hard froft.
30gt;5-	Settled fair. Settled froft.
3�-	Fair. Froft.
29^5-	Changeable.
29.	Rain. Snow.
28,5.	Much rain. Much fnow.
28.	Stormy weather.

Altitudes in miles.			Correfpondent denfities.
0		�	1
7	�	�	I , nbsp;nbsp;nbsp;4
14		�	I TS-
21	��	��
28	��	�	TT'S^
35	�	�-	1
42		-r-	X quot;�W S�
49	�	�	X TTTTTT
56 amp;c.			I TTTT'5' amp;c.

'lt;T nbsp;nbsp;nbsp;�		�
J � , '	-4�	- O	�O	� .n m .
			��

NATURAL PHILO SO PHf.

PART IL or THE PECULIAR PROPERTIES OF BOjDIESj

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