'223 nbsp;nbsp;nbsp;--FERGUSON, JAMES. Lectures on select subjects in mechanics,

hydrostatics, hydraulics, pneumatics and optics. With the use of the globes, the art of dialing and the calculation of the mean times of newnbsp;and full moons and eclipses. 5th ed. London, 1776. Calf (rebacked). With 36nbsp;folding pits. � (Some foxings).nbsp;nbsp;nbsp;nbsp;65._

Good copy. � J. Ferguson, 1710-1776. �As the inventor and improver of astronomical and other scientific apparatus, he claims a place among the most remarkable men of science of his country.�nbsp;. Mills, cranes, wheel-carriages, engines for driving piles, hydraulic machines etc.

Puh�ijhed hy the fame Author.

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LECTURES

SELECT SUBJECTS

The USE of the GLOBES, The ART of DIALING,

The Calculation of the Mean Tim^of New and Full Moons and Eclipses.

By JAMES FERGUSON, F.R.S.

Printed for W. Strahan, J. and F. Rivington, J. Hinton, L, Hawes and Co. S. Crowder, T, Longman, B. Law, G, Robinson, T. Cadell, and E. Johnston.nbsp;MDCCLXXVI.

;i nbsp;nbsp;nbsp;:

Heaven has infpired your Royal Highnessnbsp;with luch love of ingeniousnbsp;and ufeful arts, that you notnbsp;only ftudy their theory, butnbsp;have often condefcended tonbsp;honour the profeflbrs of mechanical and experimentalnbsp;philofophy with your pre-A 3 fence

fence and particular favour j I am thereby encouraged tonbsp;lay myfelf and the followingnbsp;work at your Royal Highness�s feet y and at the famenbsp;time beg leave to exprefs thatnbsp;veneration with which I am,

PREFACE.

Jiy VER Jince the days of the Lord Chancellor Bacon, natural philofophy hath been more and more cultivated in England. That great genius firf Jet out withnbsp;taking a general furvey of all the naturalnbsp;fciences, dividing them into difinSl branches,nbsp;which he enumerated voith great exaStnefs.nbsp;He inquired fcriipuloufy into the degree ofnbsp;knowledge already attained to in each, andnbsp;drew up a li/i of what fill remained to benbsp;difcovered: this was the fcope of his firf undertaking. Afterward he carried his viewsnbsp;A 4nbsp;nbsp;nbsp;nbsp;much

PREFACE.

much farther, and Jhewed the necejjity of an experimental philofophy, a thing never beforenbsp;thought of As he was a prqfef 'ed enemy tonbsp;fyfiems, he confderedphilofophy, no otherveifenbsp;than as that part of knowledge which cou'nbsp;tributes to make men better and happier : henbsp;feems to limit it to the knowledge of thingsnbsp;ufeful, recommending above all the fudy ofnbsp;nature, and foewing that no progrefs can benbsp;made therein, but by collehling fabis, andnbsp;comparing experiments, of which he pointsnbsp;out a great number proper to be made.

But notwithfanding the true path to fcience was thus exablly marked out, the old notionsnbsp;of the fchools fo flrongly pof 'ejfedpeople's mindsnbsp;at that time, as not to be eradicated by anynbsp;new opinions, how rationally foever advanced,nbsp;until the illufrious Mr. Boyle, the frjlnbsp;who purfued Lord Bacon�s plan, begannbsp;to put experiments in praBice with annbsp;afiduity equal to his great talents. Next,nbsp;the Royal Society being efablifoed, thenbsp;true philofophy began to be the reigning tajienbsp;of the age, and continues fo to this day.

PREFACE.

The immortal Sir Isaac Newton m-Jijled even in his early years, that it vuas high time to h^ni/Jj vague conjehlures andnbsp;hypothefes from natural philofophy, and tonbsp;bring that fcience under an entire fubje��ionnbsp;to experiments and geometry. He frequentlynbsp;called it the experimental philofophy,yi asnbsp;to exprefs fignificantly the difference hetvoeennbsp;it and the numberlefs fyfems vahich hadarifennbsp;merely out of the conceits of inventive brains :nbsp;the one fubfjling no longer than the fpirit ofnbsp;novelty lofts \ the other never failing vuhilftnbsp;the nature of things remain unchanged.

The method of teaching and laying the foundation of phyfics, by public courfes ofnbsp;experiments, veas fir ft undertaken in thisnbsp;kingdom, I believe, by Dr. John Keill,nbsp;and ftnee improved and enlarged by Mr.nbsp;Hauksbee, Dr. DesaGuliers, Mnnbsp;Whiston, Mr. Cotes, Mr. Whiteside,nbsp;Dr. Bradley, our late Regius and Savi~nbsp;Han profeffor of Hftronorny, and the Reverend Dr. Bliss his fuccejfor.-��

PREFACE.

Nor has the fame been negle�icd by Dr. James, and Dr. David Gregory, Sirnbsp;Robert Stewart, and after him Mr,nbsp;Maclaurin.��Dr. Helsham in Ireland, Meffieurs s�Gravesande andnbsp;Muschenbroek, and the Abb�Noj.i.'E'Tnbsp;in France, have alfo acquired juf applaufenbsp;thereby.

The fubfance of my own attempt in this way of infrumental infruliion, thefollowingnbsp;fheets fexcluftve of the qftronomical part)nbsp;vaillfhew; the fatisfallion they have generally given, read as lellures to differentnbsp;audiences, affords me fome hope that they maynbsp;be favourably received in the fame form bynbsp;the Public.

I ought to obferve, that though the five lafi leliures connot be properly faid to concern experimental philofophy, I confidered, however,nbsp;that they were not of fo different a clafs, butnbsp;that they might, without much impropriety,nbsp;be fubjoined to the preceding ones.

PREFACE.

My apparatus (part of which is defcrihed hcrci and the ref in a ¹ former work) isnbsp;ratherfmpk than magnificent; which isnbsp;owing to a particular point I had in �view-at firf fetting out, namely, to avoid all fu~gt;nbsp;perfuity, and to render every thing asnbsp;plain and intelligible as I thought the fub^nbsp;jedi would admit of.

Aftronomy explained upon Sir Isaac Newton'� principles, and made eafy to thofe who have not fiudiednbsp;mathematics.

The plates muft open to the left-hand, fronting the right-hand pages in the following order.

CONTENTS.

LECTURE VII.

LECTURE XII.

Shewing how to calculate the mean time of any new or full moon., or eclipfe from the creation of thenbsp;world to the year of Cbrijl 5800.

LEG-

LECTURES

SELECT SUBJECTS.

AS the dcfign of the firfl: part of this courfe is to explain and demonhrate thofenbsp;laws by which the material univerfe is governed,nbsp;regulated, and continued; and by which thenbsp;various appearances in nature are accounted for;nbsp;it is requifite to begin with explaining the properties of matter.

By the word matter is here meant every thing Matter, that has length, breadth, and thicknefs, and what,nbsp;refills the touch.

The inherent properties of matter are folidity,its pro-inadlivity, mobility, and divifibility. nbsp;nbsp;nbsp;perties.

The folidity of matter arifes from its having sojjjjjty. length, breadth, thicknefs; and hence it is thatnbsp;all bodies are comprehended under fome lhapenbsp;or other, and that each particular body hindersnbsp;all others from occupying the fame part of fpacenbsp;which it pofleffeth. Thus, if a piece of woodnbsp;or metal be fqueezed ever fo hard between twonbsp;plates, they cannot be brought into contradl.

And even water or air has this property ; for if a fmall {quantity of it be fixed between any other

IcaaivJty. ^ lecond property of matter is inaSiivity, or paffivenefs ; by which it always endeavours tonbsp;continue in the ftate that it is in, whether of reftnbsp;or motion. And therefore, if one body containsnbsp;twice or thrice as much matter as another bodynbsp;does, it will have tvyice or thrice as much inactivity ; that is, it will require twice or thrice asnbsp;much force to give it an equal degree of motion,nbsp;or to flop it after it hath been put into fuch anbsp;motion.

That matter can never put itfelf into motion is allowed by all men. For they fee that a ftone,nbsp;lying on the plane furface of the earth, nevernbsp;removes itfelf from that place, nor does any onenbsp;imagine it ever can. But moft people are aptnbsp;to believe that all matter has a propenfity tonbsp;fall from a ftate of motion into a ftate of reft;nbsp;becaufe they fee that if a ftone or a cannon-ballnbsp;be put into ever fo violent a motion, it foon flops;nbsp;not confidering that this ftoppage is caufed,nbsp;I. By the gravity or weight of the body, whichnbsp;finks it to the ground in fpite of the impulfe;nbsp;and, 2. By the refiftance of the air through whichnbsp;it moves, and by which its velocity is retardednbsp;. every moment till it falls.

A bowl moves but a fhort way upon a bowl-ing-green; becaufe the roughnefs and uneven-nefs of the grafly fofface foon creates fridtion encyergh tb flop it. But if the green were per-fedtly le^el, atid covered with polilhed glafs, andnbsp;the bowl wete perfedlly hard, round, and fmooth,nbsp;it w��M go a great way farther; as it wouldnbsp;have nothing but the air to refift it; if then thenbsp;air were taken away, the bowl would go onnbsp;without any fridlion, and confequently without

any diminution of the velocity it had at fetting out: and therefore, if the green were extendednbsp;quite around thfe earth, the bowl would go on,nbsp;round and round the earth, for ever.

If the bowl were carried feveral miles above the earth, and there proje�led in a horizontalnbsp;direflion, with fuch a velocity as would makenbsp;it move more than a femidiameter of the earth,nbsp;in the time it would take to fall to the earth bynbsp;gravity; in that cafe, and if there were no refilling medium in the way, the bowl would notnbsp;fall to the earth at all; but would continue tonbsp;circulate round it, keeping alv^ays in the famenbsp;tract, and returning to the fame point fromnbsp;which it was projefted, with the fame velocitynbsp;as at firft. In this manner the moon goes roundnbsp;the earth, although fhe be as una(5live and deadnbsp;as any ftone upon it.

The third property of matter is mohility *, for Mobility, we find that all matter is capable of being moved,nbsp;if a fufficient degree of force be applied to overcome its inadlivity or refillance.

The fourth property of matter is divifibility^ Divifibi-of which there can be no end. For, fince matter can never be annihilated by cutting or breaking,nbsp;we can never imagine it to be cut into fuch fmallnbsp;particles, but that if one of them be laid on anbsp;table, the uppermoll fide of it will be furthernbsp;from the table than the undermoft fide. Moreover, it would be abfurd to fay that the greateftnbsp;mountain on earth has more halves, quarters, ornbsp;tenth parts, than the fmalleft particle of matternbsp;has.

We have many furprifing inftances of the fmallnefs to which matter can be divided by art;nbsp;of which the two follow'ing are very remarkable.

I, If

1. nbsp;nbsp;nbsp;If a pound of filver be melted with a finglenbsp;grain of gold, the gold will be equally dilfulednbsp;through the whole filver; fo that taking onenbsp;grain from any part of the mafs (in which therenbsp;can be no more than the 5760th part of a grainnbsp;of gold) and diffolving it in aqua fortis, thenbsp;gold will fall to the bottom.

2. nbsp;nbsp;nbsp;The gold beaters can extend a grain of goldnbsp;into a leaf containing 50 fquare inches; and thisnbsp;leaf may be divided into 500000 vifible parts.nbsp;For an inch in length can be divided into 100nbsp;parts, every one of which will be vifible to thenbsp;bare eye: confequently a fquare inch can benbsp;divided into looco parts, and 50 fquare inchesnbsp;into 500000, And if one of thefe parts benbsp;viewed with a microfcope that magnifies thenbsp;diameter of an obje�t only 10 times, it willnbsp;magnify the area 100 times; and then the 100thnbsp;part of a 500000th part of a grain (that is, thenbsp;50 millionth part) will be vifible. Such leavesnbsp;are commonly ufed in gilding ; and they are fonbsp;very thin, that if 124500 of them were laid uponnbsp;one another, and prelfed together, they wouldnbsp;not exceed^one inch in thicknefs.

Yet all this is nothing in comparifon of the lengths that nature goes in the divifion of matter. For Mr, Leewenhoek tells us, that there arenbsp;more animals in the milt of a fingle cod-fifh,nbsp;than there are men upon the whole earth: andnbsp;that, by comparing thefe animals in a microfcope with grains of common fand, it appearednbsp;that one fingle grain is bigger than four millionsnbsp;of them. Now each animal mull have a heart,nbsp;arteries, veins, mvtfcles, and nerves, otherwifenbsp;they could neither live nor move. How inconceivably fmall then muft the particles of theirnbsp;blood be, to circulate through the fmalleft ramifications

It has been found by calculation, that a particle of their blood mull be as much fmaller than anbsp;globe of the tenth part of an inch in diameter, asnbsp;that globe is fmaller than the whole earth �, andnbsp;yet, if thefe particles be compared with the particles of light, they will be found to exceednbsp;them as much in bulk as mountains do finglenbsp;grains of fand. For, the force of any bodynbsp;ftriking againft an obftacle is direftly in proportion to its quantity of matter multiplied intonbsp;its velocity : and fince the velocity of the particles of light is demonftrated to be at leaft anbsp;million times greater than the velocity of a cannon-ball, it is plain, that if a million of thefenbsp;particles were as big as a fingle grain of find,nbsp;we durft no more open our eyes to the light,nbsp;than we durft expofe them to fand flaot point-blank from a cannon.

That matter is infinitely divifible, in a mathe- Platei, matical fenfe, is eafy to be demonftrated. For, Fig. I.nbsp;let AB be the length of a particle to be divided;nbsp;and let it be touched at oppofite ends by the parallel lines CD and EF, which, fuppofe to benbsp;infinitely extended beyond D and F. Set offnbsp;the equal divifions 5C, G H, HI, amp;c. on thenbsp;line E F, towards the right hand from B; and fibnity�ofnbsp;take a point, as at R, any where toward the left matternbsp;hand from A, in the line CD: Then, from this Proved,nbsp;point, draw the right lines RG, RH, RI, amp;c.nbsp;each of which will cut off a part from the particle AB. But after any finite number of fuchnbsp;lines are drawn, there will ftil! remain a part, asnbsp;A P, at the top of the particle, which can nevernbsp;be cutoff: becaufe the lines DD and beingnbsp;parallel, no line can ever be drawn from thenbsp;point R to any point of the line E F that willnbsp;B 2nbsp;nbsp;nbsp;nbsp;coincide

coincide with the line R D. Therefore the particle contains more than any finite number of parts.

A fifth property of matter is attraStion, which feems rather to be infufed than inherent. Ofnbsp;this there are four kinds, viz. cohejion, gravita-rnbsp;tion, magnetifm., and deimcity.

Cohef.on. The attraction of cchefion is that by which the fmall parts of matter are made to flick and cohere together. Of this we have feveral in-flances, fome of which follow.

1. nbsp;nbsp;nbsp;If a fmall glafs tube, open at both ends, benbsp;dipt in water, the water will rife up in the tubenbsp;to a confiderablc height above its level in thenbsp;bafon: which mull be owing to the attractionnbsp;of a ring of particles of the glafs all round innbsp;the tube, immediately above thofe to which thenbsp;water at any inftant riles. And when it has rifennbsp;fo high, that the weight of the column balancesnbsp;the attraction of the tube, it rifes no higher.nbsp;This can be no ways owing to the preflure of thenbsp;air upon the water in the bafon; for, as the tubenbsp;is open at top, it is full of air above the water,nbsp;which will prefs as much upon the water in thenbsp;tube as the neighbouring air does upon anynbsp;column of an equal diameter in the bafon. Be-fides, if the fame experiment be made in annbsp;exhaufted receiver of the air-pump, there willnbsp;be found no difference,

2. nbsp;nbsp;nbsp;A pieee of loaf-fugar will draw up a. fluid,nbsp;and a fpunge will draw in water : and on thenbsp;fame principle fap afeends in trees.

3. nbsp;nbsp;nbsp;If two drops of quicklilver be placed nearnbsp;each other, they will run together and becomqnbsp;o.ne large drop.

4. nbsp;nbsp;nbsp;If two pieces of lead be feraped clean, andnbsp;pvelTed together with a twili, they will attraft

each other fo ftrongly, as to require a force much greater than their own weight to feparatenbsp;them. And this cannot be owing to the preffurenbsp;of the air, for the fame thing will hold in annbsp;exhaufted receiver.

5. nbsp;nbsp;nbsp;If two poliflted plates of marble or brafsnbsp;be put together, with a little oil between themnbsp;to fill up the pores in their furfaces, and preventnbsp;the lodgement of any air; they will cohere fonbsp;ftrongly, even if fufpended in an exhaufted receiver, that the weight of the lower plate willnbsp;not be able to feparate it from the upper one. Innbsp;putting thefe plates together, the one ftiould benbsp;rubbed upon the other, as a joiner does twonbsp;pieces of wood when he glues them.

6. nbsp;nbsp;nbsp;If two pieces of cork, equal in weight, benbsp;put near each other in a bafon of water, they willnbsp;move equally fall: toward each other with annbsp;accelerated motion, until they meet: and then,nbsp;if either of them be moved, it will draw thenbsp;other after it. If two corks of unequal weightsnbsp;be placed near each other, they will approachnbsp;with accelerated velocities inverfely proportionate to their weights ; that is, the lighter corknbsp;will move as much fafter than the heavier, as thenbsp;heavier exceeds the lighter in weight. Thisnbsp;Ihews that the attraclion of each cork is in diredtnbsp;proportion to its weight or quantity of matter.

This kind of attra�fion reaches but to a very fmall diftance; for, if two drops of quickfilvernbsp;be rolled in duft, they will not run together,nbsp;becaufe the particles of duft keep them out ofnbsp;the fphere ot each other�s attradlion.

Where the fphere of attradion ends, a repuU Repul-five force begins i thus, water repels moft bodies fdl they are wet; and hence it is, that a fmallnbsp;B 3nbsp;nbsp;nbsp;nbsp;needle^

needle, if dry, fwims upon water; and flies walk upon it without wetting their feet.

The repelling force of the particles of a fluid is but fmall; and therefore, if a fluid be divided,nbsp;it eafily unites again. But if glafs, or any othernbsp;hard fuhftance, be broke into fmall parts, theynbsp;cannot be made to flick together again withoutnbsp;being firft wetted: the repulfion being too greatnbsp;to admit of a re-union.

The repelling force between water and oil ig fo great, that we find it almofl; impoflible to mixnbsp;them fo, as not to feparate again. If a ball ofnbsp;light wood be dipt in oil, and then put iritp water, the water will recede fo as to form a channelnbsp;of fome depth all around the ball.

The repulfive force of the particles of air is fo great, that they can never be brought fo near to-gather by condenfation as to make them flick ornbsp;cohere. Hence it is, that when the weight ofnbsp;the incumbent atmofphere is taken off from anynbsp;fmall quantity of air, that quantity will diffufe it-felf fo as to occupy (in comparifon) an infinitelynbsp;greater portion of fpace than it did before.

JttraSiiou of gravitation is that power by which diftant bodies tend towards one another.nbsp;Of this we have daily inftances in the fallingnbsp;of bodies to the earth. By this power in thenbsp;earth it is, that bodies, on whatever fide, fall innbsp;lines perpendicular to its furface; and confe-quently, on oppofite fides, they fall in oppofitenbsp;diredions; all towards the center, where thenbsp;force of gravity is as it were accumulated : andnbsp;by this power it is, that bodies on the earth�snbsp;furface are kept to it on all fides, fo that theynbsp;cannot fa^ from it. And as it ads upon all bodies in proportion to their refpedive quantitiesnbsp;of matter, without any regard to their bulks or

If two bodies which contain equal quantities of matter,were placed at ever fo great a diftancenbsp;from one another, and then left at liberty in freenbsp;fpace; if there were no other bodies in the uni-verfe to affed them, they would fall equally fwifcnbsp;towards one another by the power of gravity,nbsp;with velocities accelerated as they approachednbsp;each other ; and would meet in a point whichnbsp;was halfrway between them at firft. Or, if twonbsp;bodies, containing unequal quantities of matter,nbsp;were placed at any diftance, and left in the famenbsp;manner at liberty, .they would fall towards onenbsp;another with velocities which would be in annbsp;inverfe proportion to their refpedive quantitiesnbsp;of matter; and moving fafter and fafter in theirnbsp;mutual approach, would at laft meet in a pointnbsp;as much nearer to the place from which thenbsp;heavier body began to fall, than to the placenbsp;from which the lighter body began to fall, asnbsp;the quantity of matter in the former exceedednbsp;that in the latter.

All bodies that we know of have gravity or weight. For, that there is no fuch thing as po-fitive levity, even in fmoke, vapours, and fumes,nbsp;is demonftrable by experiments on the air-pump ; which fhews, that although the fmokenbsp;of a candle afcends to the top of a tall receivernbsp;when full of air, yet, upon the air�s being ex-haufted out of the receiver, the fmoke falls downnbsp;to the bottom of it. So, if a piece of wood benbsp;immerfed in ajar of water, the wood will rife tonbsp;the top of the water, becaufe it has a lefs degreenbsp;of weight than its bulk of water has: but if thenbsp;jar be emptied of water, the wood falls to thenbsp;bottpm.

As every particle of matter has its proper gravity, the effea; of the whole muft be in proportion to the number of the attradiing particles jnbsp;that is, as the quantity of matter in the wholenbsp;body. This is demonftrable by experiments onnbsp;pendulums j for, if they are of equal lengths,nbsp;whatever their weights be, they vibrate in equalnbsp;times. Now it is plain, that if one be double ornbsp;triple the weight of another, it muft require anbsp;double or triple power of gravity to make icnbsp;move with the fame celerity : juft as it wouldnbsp;require a double or triple force to projeft a bullet of twenty or thirty pounds weight with thenbsp;fame degree of fwiftnefs that a bullet of tennbsp;pounds would require. Hence it is evident,nbsp;that the power or force of gravity is always proportional to the quantity of matter in bodies,nbsp;whatever their bulks or figures are.

Gravity alfo, like all other virtues or emanations which proceed or ilTue from a center, de-creafes as the diftance multiplied by itfelf in-creafes: that is, a body at twice the diftance of another, attraifts with only a fourth part of thenbsp;force-, at thrice the diftance, with a ninth part;nbsp;at four times the diftance, with a fixteenth part-,nbsp;and fo on. This too is confirmed by cornparingnbsp;the diftance which the moon falls in a minute,nbsp;from a right line touching her orbit, with thenbsp;diftance through which heavy bodies near thenbsp;earth fall in that time. And alfo by comparingnbsp;the forces -vvhich retain Jupiter�s moons in theirnbsp;orbits, with their reipedtive diftances from Jupiter. Thefe forces will be explained in thenbsp;next ledture.

The velocity which bodies near the earth acquire in defeending freely by the force of gravity, is proportional to the times of their defeent.

For, as the power of gravity does not confift in a fingle impulfe, but is always operating in anbsp;conftant and uniform manner, it muft producenbsp;equal effeds in equal times ; and confequently innbsp;a double or triple time, a double or triple effeft.nbsp;And fo, by ading uniformly on the body, muftnbsp;accelerate its motion proportipnably to the timenbsp;of its defcent.

To be a little more particular on this fubjcd, let us fuppofe that a body begins to move withnbsp;a celerity cOnftantly and gradually increafing, innbsp;fuch a manner, as would carry it through a milenbsp;in a minute ; at the end of this fpace it will havenbsp;acquired fuch a degree of celerity, as is fufficientnbsp;to carry it two miles the next minute, though itnbsp;Ihould then receive no new impulfe from thenbsp;caufe by which its motion had been accelerated :nbsp;but if the fame accelerating caufe continues, itnbsp;will carry the body a mile farther; on whichnbsp;account, it will have run through four miles atnbsp;the end of two minutes �, and then it will havenbsp;acquired fuch a degree of celerity as is fufficientnbsp;to carry it through a double fpace in as muchnbsp;more time, or eight miles in two minutes, evennbsp;though the accelerating force ffiould afl; upon itnbsp;no more. But this force ftill continuing to operate in an uniform manner, will again, in annbsp;equal time, produce an equal effebl; and fo, bynbsp;carrying it a mile furthc-, caufe it to movenbsp;through five miles the third minute �, for, thenbsp;celerity already acquired, and the celerity ftillnbsp;acquiring, will have each its complete effed:,nbsp;Hence we learn, that if the body Ihould movenbsp;one mile the firft minute, it would move threenbsp;miles the fecond, five the third, feven the fourth,nbsp;sine the fifth, and fo on in proportion,

And

And thus it appears, that the fpaces defcribed in fucceffive equal parts of time, by an uniformlynbsp;accelerated motion, are always as the odd numbers I, 3, 5, 7, p, amp;c. and confequently, thenbsp;whole fpaces are as the fquares of the times, or ofnbsp;the laft acquired velocities. For, the continuednbsp;addition of the odd numbers yields the fquaresnbsp;of all numbers from unity upwards. Thus, i isnbsp;the firft odd number, and the fquare of i is i ;nbsp;3 is the fecond odd number, and this added tonbsp;1 makes 4, the fquare of 2 ; 5 is tiie third oddnbsp;number, which added to 4 makes 9, the fquarenbsp;of 3 ; and fo on for ever. Since, therefore, thenbsp;times and velocities proceed evenly and conftant-ly as I, 2, 3, 4, amp;c. but the fpaces defcribed innbsp;each equal times are as i, 3, 5, 7, amp;c. it is evident that the fpace defcribed

In 3 minutes - i-f 3-1-5� 9r:fquare of 3 In4minutes 1-1-3-1-54-7=: 16rcfquare of 4,amp;c.

As heavy bodies are uniformly accelerated by the power of gravity in their defcenr, it isi plainnbsp;that they mult be uniformly retarded by thenbsp;fame power in their afcent. Therefore, the velocity which a body acquires by falling, is fuffi-cient to carry it up again to the fame heightnbsp;from whence it fell: allowance being made fornbsp;the refinance of the air, or other medium innbsp;which the body is moved. Thus, the body Dnbsp;in rolling down the inclined plane AB willnbsp;acquire fuch a velocity by the time it arrives at

B, as will carry it up the inclined plane BC, al-mofl; to Ci and would carry it quite up to C, if the body and plane were perfedly fmooth, andnbsp;the air gave no refiftance.�So, if a pendulumnbsp;were put into motion, in a fpace quite free ofnbsp;air, and all other refiftance, and had no fridionnbsp;on the point of fufpenfion, it would move fornbsp;ever: for the velocity it had acquired in fallingnbsp;through the defcending part of the arc, wouldnbsp;be ftill fufficient to carry it equally high ip thenbsp;afcending part thereof.

The cefiter of gravity is that point of a body The cen-in which the whole force of its gravity or weight ter of is united. Therefore, whatever fupports thatnbsp;point bears the weight of the whole body ; andnbsp;Vvhilft it is fupporced, the body cannot fa!! ;nbsp;becaufe all its parts are in a perfedl equilibriumnbsp;^bout that point.

An imaginary line drawn from the center of gravity of any body towards the center of thenbsp;earth, is called the line of direction. In this line and linenbsp;all heavy bodies defcend, if not obftrucled. of direc-

Since the whole w'eight of a body is united in its center of gravity, as chat center afcends ornbsp;dcfcends, we muft look upon the whole body tonbsp;do fo too. But as it is contrary to the nature ofnbsp;heavy bodies to afcend of their own accord, ornbsp;not to defcend when they are permitted; wenbsp;may be fure that, unlefs the center of gravitynbsp;be fupported, the whole body will tumble ornbsp;fall. Hence it is, that bodies ftand upon theirnbsp;bafes when the line of diredlion falls within thenbsp;bafe ; for in this cafe the body cannot be madenbsp;to fall without firft raifmg the center of gravitynbsp;higher than it was before. Thus, the incliningnbsp;body ABCDy whofe center of gravity Is E, Fig. 3.nbsp;ftands firmly pn its bafe CD IK, becaufe the line

of direftion E F falls within the bafe. But if a weight, as ABGH, be laid upon the top of thenbsp;body, the center of gravity of the whole bodynbsp;and weight together is raifed up to /; and then,nbsp;as the line of diredtion / D falls without the bafenbsp;at D, the center of gravity I is not lupported ;nbsp;and the whole body and weight tumble downnbsp;together.

Hence appears the abfurdity of people�s rifing haftily in a coach or boat when it is likely tonbsp;overiet: for, by that means they raife the center of gravity fo far as to endanger throwing itnbsp;quite out of the bafe; and if they do, theynbsp;overfet the vehicle effedually. Whereas, hadnbsp;they clapt down to the bottom, they wouldnbsp;have brought the line of diredlion, and confe-quently the center of gravity, farther within thenbsp;bafe, and by that means might have faved them-felves.

The broader the bafe is, and the nearer the line of direftion is to the middle or center of it,nbsp;the more firmly does the body ftand. On thenbsp;contrary, the narrower the bale, and the nearernbsp;the line of direftion is to the fide of it, the morenbsp;eafily may the body be overthrown, a lefs changenbsp;of pofition being fupneient to remove the linenbsp;of diredlion out of the bafe in the latter cafenbsp;than in the former. And hence it is, that anbsp;fphere is fo eafily rolled upon a horizontal plane jnbsp;and that it is fo difficult, if not impoffible, tonbsp;make things vrhich are lharp-pointed to ftandnbsp;upright on the point.�From what hath beennbsp;laid, it plainly appears that if the plane be inclined on which the heavy body is placed, thenbsp;body will Aide down upon the plane whilft thenbsp;line of diredlion falls within the bafe; but it willnbsp;tpmble or roll down when that line falls without

the bafe. Thus, the body A will only Aide down the inclined plane C D, whilft the body Bnbsp;rolls down upon it.

When the line of diredlion falls within the bafe of our feet, we Hand �, and moft: firmly whennbsp;it is in the middle: but when it is out of thatnbsp;bafe, we immediately fall. And it is not onlynbsp;pleafing, but even furprifing, to reflecfl uponnbsp;the various and unthought-of methods and pof-tures which we ufe to retain this pofition, or tonbsp;recover it when it is loft. For this purpofe wenbsp;bend our body forward when we rife from anbsp;chair, or when we go up flairs; and for thisnbsp;purpofe a man leans forward when he carries anbsp;burden on his back, and backward when he carries it on his breaft ; and to the right or left fidenbsp;as he carries it on the oppofite fide. A thou-fand more inftances might be added.

The quantity of matter in all bodies is in ex� act proportion to their weights, bulk for bulk.nbsp;Therefore, heavy bodies are as much more denfenbsp;or compaft than light bodies of the fame bulk,nbsp;as they exceed them in weight.

All bodies are full of pores, or fpaces void of'fl'hoilies matter: and in gold, which is the heavicft ofnbsp;all known bodies, there is perhaps a greaternbsp;quantity of fpace than of matter. For the particles of heat and inagnetifm find an cafy paflagcnbsp;through the pores of gold ; and even water kfelfnbsp;has been forced through them. Befides, if wenbsp;confidcr how eafily the rays of light pafs throughnbsp;fo folid a body as glafs, in all manner of directions, we flaall find reafon to believe that bodiesnbsp;are much more porous than is generally imagined.

All bodies are fome way or other affefled by 'f heat j and all metallic bodies are expanded i

proportion of the expanfion of feveral metals, according to the beft experiments I have beennbsp;able to make with my pyrometer, is nearly thus:nbsp;Iron and fteel as 3, copper 4 and an half^nbsp;brafs 5, tin 6, lead 7. An iron rod 3 feet longnbsp;is about one 70th part of an inch longer innbsp;fnmmer than in winter.

rometer. aught I know) of a new conftrudlionj a de-fcription of it may perhaps be agreeable to the reader.

fixed four brafs ftuds B,C,D,L', and two pins, one at F and the other at H. On the pinnbsp;F turns the crooked index E I, and upon thenbsp;pin H the ftraight index G K, againft which anbsp;piece of watch-fpring R bears gently, and fonbsp;prefles it towards the beginning of the fcale MiV,nbsp;over which the point of that index moves. Thisnbsp;fcale is divided into inches and tenth parts of annbsp;inch : the firft inch is marked 1000, the fecondnbsp;2000, and fo on. A bar of metal O is laid intonbsp;notches in the top of the ftuds C and D -, onenbsp;end of the bar bearing againft the adjuftingnbsp;fcrew P, and the other end againft the crookednbsp;index Ef at a 20th part of its length from itsnbsp;center of motion F.�Now it is plain, that how-�nbsp;ever much the bar O lengthens, it will movenbsp;that part of the index El, againft which it bears,nbsp;juft as far: but the crooked end of the famenbsp;index, near H, being 20 times as far from thenbsp;center of motion F as the point is againftnbsp;which the bar bears, it will move 20 times asnbsp;far as the bar lengthens. And as this crookednbsp;end bears againft the index G K 2X. only a 20thnbsp;part of the whole length GS from its center of

motion H, the point S will move through 20 times the fpace that the point of bearing near Hnbsp;does. Hence, as 20 multiplied by 20 producesnbsp;400, it is evident that if the bar lengthens but anbsp;400th part of an inch, the point S will move anbsp;whole inch on the fcale �, and as every inch isnbsp;divided into 10 equal parts, if the bar lengthensnbsp;but the I oth part of the 400th part of an inch,nbsp;which is only the 4000th part of an inch, thenbsp;point S will move the tenth part of an inch,nbsp;which is very perceptible.

To find how much a bar lengthens by heat, firft lay it cold into the notches of the ftuds, andnbsp;turn the adjufting fcrew P until the fpring Rnbsp;brings the point S of rhe index Gif to the beginning of the divifions of the fcale at M: then,nbsp;without altering the fcrew any farther, take offnbsp;the bar and rub it with a dry woollen cloth tillnbsp;it feels warm; and then, laying it on where itnbsp;was, obferve how far it pufhes the point 5 uponnbsp;th� fcale by means of the crooked index E /;nbsp;and the point S will fhew exaftly how much thenbsp;bar has lengthened by the heat of rubbing. Asnbsp;the bar cools, the fpring R bearing againft thenbsp;index �fG, will caufe its point S to move gradually back towards M in the fcale ; and whennbsp;the bar is quite cold, the index will reft at A/,nbsp;where it was before the bar was made warm bynbsp;rubbing. The indexes have fmall rollers undernbsp;them at I and K; which, by turning round onnbsp;the fmooth wood as the indexes move, makenbsp;their motions the eafier, by taking off a greatnbsp;part of the fridion, which would otherwife benbsp;on the pins F and H, and of the points of thenbsp;indexes themfelves on the wood.

Befides the univerfal properties above men- Mafne-tioned, there are bodies which have properties

peculiar to themfelves: fuch as the loadftone*, in which the moft remarkable are the Ie : i. Itnbsp;actrafts iron and ftecl only. 2. It conftantlynbsp;turns one of its lides to the north and anothernbsp;to the fouth, when fufpended by a thread thatnbsp;does not twift. 9. It communicates all its properties to a piece of fteel when rubbed upon it,nbsp;without lofing any itfelf.

According to Dr. HeJfljamh experiments, the attradlicn of the loadftone decreafes as thefquarenbsp;of the diftance increafcs. Thus, if a loadftonenbsp;be fufpended at one end of a balance, and coun-terpoifed by weights at the other end, and ^nbsp;fiat piece of iron be placed beneath it, at thenbsp;diftance of four tenths of an inch, the ftone willnbsp;immediately defcend and adhere to the iron.nbsp;But if the ftone be again removed to the famenbsp;diftance, and as many grains be put into thenbsp;fcale at the other end as will exadtly counterbalance the attraflion, then, if the iron be broughtnbsp;twice as near the ftone as before, that is, onlynbsp;two tenth parts of an inch from it, there mullnbsp;be four times as many grains pul into the fcalenbsp;as before, in order to be a juft counterbalancenbsp;to the attradtive force, or to hinder the ftonenbsp;from defcending and adhering to the iron. So,nbsp;if four grains will do in the former cafe, therenbsp;tnuft be fixteen in the latter. But from fomenbsp;later experiments, made with the greateft accuracy, it is found that the force of magnetifinnbsp;decreafes in a ratio between the reciprocal of thenbsp;fquare and the reciprocal of the cube of the di-ffance-, approaching to the one or the other, asnbsp;the magnitudesof the attracting bodies are varied.nbsp;Eleftd- Several bodies, particularly amber, glafs, jet,nbsp;chy. fealing-wax, agate, and almoft all preciousnbsp;ftones, have a peculiar property of attradling

and repelling light bodies when heated by rubbing. This is called eleSrical attraction,, in which the chief things to be obferved are, i. Ifnbsp;a glafs tube about an inch and a half diameterjnbsp;and two or three feet long, be heated by �rubbing, it will alternately attraft and repel all lightnbsp;bodies when held near them. 1. It does notnbsp;attraft by being heated without rubbing.nbsp;3. Any light body being once repelled by thenbsp;tube, will never be attrafted again till it hasnbsp;touched fome other body. 4. If the tube benbsp;rubbed by a moift hand, or any thing that isnbsp;Wet, it totally deftroys the elcflricity. 5. Anynbsp;body, except air, being interpofed, flops thenbsp;eledlricity. 6. The tube attrabfs ftronger whennbsp;rubbed over with bees-wax, and then with a drynbsp;woollen-cloth. 7. When it is well rubbed, ifnbsp;a finger be brought near it, at about the dif-tance of half an inch, the effluvia will fnapnbsp;ngainfl the finger, and make a little cracklingnbsp;hoife; and if this be performed in a dark place,nbsp;there will appear a little flafh of light.

� have already mentioned it as a hecef- All bodies fary confequence arifing from the dead- equally in-hefs or inadivity of matter, that all bodiesnbsp;endeavour to continue in the flate they are in, lt;,r reft,nbsp;whether of refl or motion. If the body A were Plate II.nbsp;placed in any part of free fpace, and nothing **nbsp;cither drew or impelled it any way, it would fornbsp;ever remain in that part of fpace, becaufe itnbsp;Could have no tendency of itfelf to remove anynbsp;from thence. If it receives a fingle im--Cnbsp;nbsp;nbsp;nbsp;pulfgs

pulfe any way, as fuppofe from ^/towards B, it will go on in that direftion j for, of itfelf, itnbsp;could never fwerve from a right line, nor ftopnbsp;its courfe.�When it has gone through the fpacenbsp;A Bt and met with no refiftance, its velocitynbsp;will be the fame at B at it was at A: and thisnbsp;velocity, in as much more time, will carry itnbsp;through as much more fpace, from B to C-, andnbsp;fo on for ever. Therefore, when we fee a bodynbsp;in motion, we conclude that fome other fub-ftance muft have given it that motion ; andnbsp;when we fee a body fall from motion to reft, wenbsp;conclude that fome other body or caufe ftopt it.

As all motion is naturally redtilineal, it appears, that a bullet projedted by the hand, or fhot from a cannon, would for ever continue tonbsp;move in the fame diredlion it received at firft, ifnbsp;no other power diverted its courfe. Thereforenbsp;when we fee a body move in a curve of any kindnbsp;whatever, we conclude it muft be a�led upon bynbsp;two powers at leaft; one piutting it in motion,nbsp;and another drawing it off from the redilinealnbsp;courfe it would otherwife have continued tonbsp;move in : and whenever that power, which bentnbsp;the motion of the body from a ftraight line intonbsp;a curve, ceafes to ad, the body will again movenbsp;on in a ftraight line touching that point of thenbsp;curve in which it was when the adion of thatnbsp;power ceafed. For example, a pebble movednbsp;round in a fling ever fo long a time, will fly offnbsp;the moment it is fee at liberty, by flipping onenbsp;end of the fling cord; and will go on in a linenbsp;touching the circle it deferibed before : whichnbsp;line would adually be a ftraight one, if thenbsp;earth�s attradion did not affed the pebble, andnbsp;bring it down to the ground. This ftiews thatnbsp;the natural tendency of the pebble, when put

into motion, is to continue moving in a ftraight line, although by the force that moves the flingnbsp;it be made to revolve in a circle.

The change of motion produced is in propor-The ef-tion to the force impreiTed: for the effeds of^�'^' natural caufes are always proportionate tonbsp;force or power of thofe caufes.

By thefe laws it is eafy to prove that a body will defcribe the diagonal of a fquare or parallelogram, by two forces conjoined, in thenbsp;fame time that it would defcribe either of thenbsp;fides, by one force fingly. Thus, fuppofe thenbsp;body yf to reprefent a fliip at fca and that it is Fig.nbsp;driven by the wind, in the right line yf B, withnbsp;fuch a force as would carry it uniformly from ^nbsp;to S in a minute: then fuppofe a ftream or current of water running in the diredtion ^ D, withnbsp;fuch a force as would carry the fhip through annbsp;equal fpace from yf to D in a minute. By thefenbsp;two forces, ading together at right angles tonbsp;each ocher, the fliip will defcribe the line ARCnbsp;in a minute: which line (becaufe the forces arenbsp;equal and perpendicular to e.ach other) will benbsp;the diagonal of an exad; fquare. To confirmnbsp;this law by an experiment, let there be a woodennbsp;fquare ABCD fo contrived, as to have the part p-BEFC made to draw out or pufli into the fquarenbsp;at pleafure. To this part let the pully H benbsp;joined, fo as to turn freely on an axis, whichnbsp;will be at H when the piece is pulhed in, andnbsp;at h when it is drawn out. To this part let thenbsp;ends of a ftraight wire k be fixed, fo as to movenbsp;along with it, under the pulley; and let the ballnbsp;G be made to Hide eafily on the wire, A thread

is fixed to this ball, and goes over the pulley to 7; by this thread the ball may be drawn upnbsp;On the wire, parallel to the fide AD, when thenbsp;C 2nbsp;nbsp;nbsp;nbsp;part

part B EFC is pufhed as far as it will go into the fquare. But, if this part be drawn out, itnbsp;will carry the ball along with it, parallel to thenbsp;bottom of the fquare D C. By this means, thenbsp;ball G may either be drawn perpendicularly upward by pulling the thread ?�, or moved horizontally along by pulling out the part BE FC^nbsp;in equal times, and through equal Ipaces; eachnbsp;power afting equally and feparately upon it.nbsp;But if, when the ball is at G, the Upper end ofnbsp;the thread be tied to the pin 1, in the corner yinbsp;of the fixed fquare, and the moveable partnbsp;BEFG be drawn our, the ball will then be actednbsp;upon by both the powers together: for it willnbsp;be drawn up by the thread towards the top ofnbsp;the fquare, and at the fame time be carried with itsnbsp;wire k towards the right hand 5C, moving allnbsp;the while in the diagonal line L; and will benbsp;found at g when the Aiding part is drawn out asnbsp;far as it was before; which then will have caufednbsp;the thread to draw up the ball to the top of thenbsp;infide of the fquare, juft as high as it was before,nbsp;when drawn up fingly by the thread withoutnbsp;moving the Aiding part.

If the adling forces are equal, but at oblique angles to each other, fo will the fides of thenbsp;parallelogram be: and the diagonal run throughnbsp;by the moving body will be longer or fhorter,nbsp;according as the obliquity is grater or fmaller.nbsp;Thus, if two equal forces adl conjointly upon thenbsp;Fig. 4. body one having a tendency to move itnbsp;through the fpace AB in the fame time that thenbsp;other has a tendency to move it through an equalnbsp;fpace AB', it will defcribe the diagonal AGCnbsp;in the fame time that either of the fingle forcesnbsp;would have caufed it to defcribe either of thenbsp;fides. If one of the forces be greater than thenbsp;2nbsp;nbsp;nbsp;nbsp;other.

other, then one fide of the parallelogram will be fo much longer than the other. For, if one forcenbsp;fingly would carry the body through the fpacenbsp;AE, in the fame time that the other would havenbsp;carried it through the fpace AD, the joint adionnbsp;of both will carry it in the fame time throughnbsp;the fpace AHF, which is the diagonal of thenbsp;oblique parallelogram AD E F.

If both forces ad upon the body in fuch a manner, as to move it uniformly, the diagonalnbsp;deferibed will be a ftraight line but if one ofnbsp;the forces ads in fuch a manner as to make thenbsp;body move fafter and fafter, then the line deferibed will be a curve. And this is the cafenbsp;of all bodies which are projeded in redilinealnbsp;diredions, and at the fame time aded upon bynbsp;the power of gravity ; which has a conftant tendency to accelerate their motions in the diredionnbsp;wherein it ads.

From the uniform projedile motion of bodies in The laws ftraight lines, and the univerfal power of gravity of Acnbsp;or attradion, arifes the curvilineal motion of all P^=*oetarynbsp;the heavenly bodies. If the body A be projedednbsp;along the ftraight line AFH in open fpace, pig. 5,nbsp;where it meets with no refiftance, and is notnbsp;drawn afide by any power, it will go on fornbsp;ever with the fame velocity, and in the famenbsp;diredion. But if, at the fame moment thenbsp;projedije force is given it at A, the body 5 begins to attrad it with a force duly adjufted*,nbsp;and perpendicular to its motion at A, it will thennbsp;be drawn from the ftraight line AFH, and forced

* To make the projeQile force a juft balance to the gravitating power, fo as to keep the planet moving in a circle, it muft give fuch a velocity as the planet would acquire bynbsp;gravity when it had fallen through half the femidiaiaeter ofnbsp;that circle.

e 3 nbsp;nbsp;nbsp;to

to revolve about S in the circle AFW-, in the fame manner, and by the fame law, that a pebble is moved round in a fling. And if, whennbsp;the body is in any part of its orbit (as fuppofenbsp;at K) a fmaller body as L, within the fphere ofnbsp;attradion of the body K, be projeded in thenbsp;� right line L AI, with a force duly adjufted, andnbsp;perpendicular to the line of attradion LK-, then,nbsp;the fmall body L will revolve about the largenbsp;body K in ��he orbit A'O, and accompany it innbsp;its whole courfe round the yet larger body S.nbsp;But then, the body K will no longer move innbsp;the circle ATJVfor that circle will now benbsp;defcribed by the common center of gravity between K and L. Nay, even the great body 5nbsp;will not keep in the center; for it will be thenbsp;common center of gravity between all the threenbsp;,nbsp;nbsp;nbsp;nbsp;bodies 5, K, and Z-, that will remain immove

able there. So, if we fuppofe S and K conneded by a wire P that has no weight, and K and Lnbsp;conneded by a wire q that has no weight, thenbsp;common center of gravity of all thefc threenbsp;bodies will be a point in the wire P near S\nbsp;which point being fupported, the bodies will benbsp;all in equilibria as they move round it. Though

their moving forces regulated as above. In this cafe, whilft the earth goes round the fun innbsp;the dotted circle RFUPFX, amp;c. the fun will Thenbsp;go round the circle ABD, whole center C is curves de-the common center of gravity between the funnbsp;and earth : the right line (3 t? reprefenting the volvingnbsp;mutual attra�lion between them, by which they aboutnbsp;are as firmly connected as if they were fixed atnbsp;the two ends of an iron bar ftrong enough tonbsp;hold them. So, when the earth is at e, the gravity,nbsp;fun will be at �; when the earth is at T, the funnbsp;will be at F-, and when the earth is at j-, the funnbsp;will be at G, amp;c.

Now, let us take in the moon q (at the top of the figure) and fuppofe the earth to have no pro*nbsp;grefllve motion about the fun �, in which cafe,nbsp;whilft the moon revolves about the earth in hernbsp;orbit �210C2D, the earth will revolve in thenbsp;circle 5 13, whofe center R is the common center of gravity of the earth and moon �, they being connefted by the mutual attra�lion betweennbsp;them in the fame manner as the earth and lunnbsp;are.

But the truth is, that whilft the moon revolves about the earth, the earth is in motion aboutnbsp;the fun : and now, the moon will caule thenbsp;earth to deferibe an irregular curve, and not anbsp;true circle, round the fun-, it being the commonnbsp;center of gravity of the earth and moon th.it willnbsp;then deferibe the fame circle which the earthnbsp;would have moved in, if it had not been attended by a moon. For, fuppofing the moonnbsp;to deferibe a quarter of her progreffive orbitnbsp;about the earth in the time that the earth movesnbsp;from e to �; it is plain, that when the earthnbsp;comes to �, the moon will be found at r -, innbsp;which time, their common center of gravitynbsp;C 4nbsp;nbsp;nbsp;nbsp;will

will have defcribed the dotted arc R i T, the earth the curve R 5 f, and the moon the curvenbsp;q 14 r. In the time that the moon defcribesnbsp;another quarter of her orbit, the center of gravity of the earth and moon will defcribe the dotted arc F 2 U, the earth the curve f 6 g, thenbsp;moon the curve r 15 r, and fo on�And thus,nbsp;whilft the moon goes once round the earth innbsp;her progreffive orbit, their common center ofnbsp;gravity defcribes the regular portion of a circlenbsp;RiFzU^V 4 J'F-, the earth the irregular curvenbsp;R^f6g']h^i., and the moon the yet morenbsp;irregular curve y 14?� 15^ i6^ 17 u-, and then,nbsp;the fame kind of tracks over again.

The center of gravity of the earth and moon is 6000 miles from the earth�s center towards thenbsp;moon ; therefore the circle 513 which the earthnbsp;defcribes round that center of gravity (in everynbsp;eourfe of the moon round her orbit) is 12000nbsp;miles in diameter. Confequently the earth isnbsp;12,000 miles nearer the fun at the time of fullnbsp;moon than at the time of new. [See the earth atnbsp;/ and at h-l

To avoid confufion in fo fmall a figure, we have fuppofed the moon to go only twice and anbsp;half round the earth, in the time that the earthnbsp;goes once round the fun : it being impofllble tonbsp;take in all the revolutions which (he makes in anbsp;year, and to give a true figure of her path, un-lefs we fhould make the femidiameter of thenbsp;earth�s orbit at leaft 95 inches; and then, thenbsp;proportional femidiameter of the moon�s orbitnbsp;would be only a quarter of an inch.^�For a truenbsp;figure of the moon�s path, I refer the reader tonbsp;my treatife of aftronomy.

If the moon made any complete number of revolutions about the earth in the time that the

earth makes one revolution about the fun, the paths of the fun and moon would return intonbsp;themfelves at the end of every year �, and fo benbsp;the fame over again : but they return not intonbsp;themfelves in lefs than 19 years nearly j in whichnbsp;time, the earth makes nearly 19 revolutionsnbsp;about the fun, and the moon 235 about the earth.

If the planet J be attrafted towards the fun, with fuch a force as would make it fall from Anbsp;to B, in the time that the projectile imptiifenbsp;would have carried it from A to F, it will de-feribe the arc AG by the combined aCtion of thefenbsp;forces, in the fame time that the former wouldnbsp;have caufed it to fall from A to B, or the latternbsp;have carried it from A to F. But, if the projectile force had been twice as great, that is, fuch asnbsp;would have carried the planet from A to H, innbsp;the fame time that now, by the fuppofition, itnbsp;carries it only from A to F-, the fun�s attractionnbsp;muft then have been four'times as ftrong as formerly, to have kept the planet in the circlenbsp;ATtV-, that is, it muft have been fuch as wouldnbsp;have caufed the planet to fall from A to �,nbsp;which is four times the diftance of A from B, innbsp;the time that the projeftile force fingly wouldnbsp;have carried it from A to H, which is only twicenbsp;the diftance of A from F¹. Thus, a double projectile force will balance a quadruple power ofnbsp;gravity in the fame circle ; as appears plain bynbsp;the figure, and (hall foon be confirmed by annbsp;experiment.

The whirling-table is a machine contrived for pj^te iv. fhewing experiments of this nature. A A is z Fig. i.nbsp;ftrong frame of wood, B a winch or handle

Here the arcs AG, AI muft be fuppofecl to be very fmall; othervvife which is equal to HI, will be morenbsp;than quadruple to A B, which is equal to F G.

fixed on the axis C of the wheel A round which is the catgut firing F, which alfo goes round thenbsp;fmall wheels G and F, eroding between themnbsp;and the great wheel B. On the upper end ofnbsp;the axis of the wheel G, above the frame, isnbsp;fixed the round board d, to which the bearernbsp;MS X may be fattened occafionally, and removed when it is not wanted. On the axis of thenbsp;wheel H is fixed the bearer NT Z: and it isnbsp;eafy to fee that when the winch B is turned, thenbsp;wheels and bearers are put into a whirling mo-

Each bearer has two wires, W, X, and T, Z� fixed and ferewed tight into them at the ends bynbsp;nuts on the outfide, And when thefe nuts arenbsp;un!crev\ jd, the wires may be drawn out in order to change the balls U and F, which Aidenbsp;upon the wires by means of brafs loops fixed into the balls, which keep the bails up from touching the wood below them. A ttrong filk linenbsp;goes through each ball, and is fixed to it at anynbsp;length from the center of the bearer to its endnbsp;as occafion requires, by a ntit-fcrew at the top ofnbsp;the ball; the fliank of the ferew goes into thenbsp;center of the ball, and preffes the line againftnbsp;the under fide of the hole that it goes through.nbsp;�The line goes from the ball, and under a fmallnbsp;pulley fixt in the middle of the bearer; then upnbsp;through a focket in the round plate (fee S and T)nbsp;in the middle of each bearer; then through anbsp;flit in the middle of the fquare top (O and P)nbsp;of each tow'er, and going over a fmall pulley onnbsp;the top, comes down again the fame way, and isnbsp;at latt fattened to the upper end of the focketnbsp;fixt in the middle of the above-mentioned roundnbsp;plate. Thefe plates S and T have each fournbsp;round holes near' their edges /or letting them

Aide up and down upon the wires which make the corners of each tower. The balls and platesnbsp;being thus conneited, each by its particularnbsp;line, it is plain that if the balls be drawn outward,nbsp;or towards the ends Mand JV of their refpedivenbsp;bearers, the round plates 5 and F will be drawnnbsp;up to the top of their refp��live towers O and P.

There are feveral brafs weights, fome of two ounces, fome of three, and fome of four, to benbsp;occafionally put within the towers 0 and P, uponnbsp;the round plates 5 and F: each weight havingnbsp;a round hole in the middle of it, for going uponnbsp;the fockets or axes of the plates, and is flit fromnbsp;the edge to the hole, for ailov/ing it to be diptnbsp;over the aforefaid line which comes from eachnbsp;ball to its refpedtive plate. (See Fig. 2.)

I. Take away the bearer MX, and take the Fig- i. ivory ball to which the line or fdk cord I isnbsp;faftened at one end ; and having made a loop onnbsp;the other end of the cord, put the loop oyer anbsp;pin fixt in the center of the board d. Then,

motion, you will fee that the ball does not imme-diately begin to move with the board, but, on i^^gp the account of its inadtivity, it endeavours to conti- ftate it isnbsp;nue in the ftate of reft which it was in before.� gt;quot;�nbsp;Continue turning, until the board communicatesnbsp;an equal degree of motion with its own to thenbsp;ball, and then turning on, you will perceive thatnbsp;the ball will remain upon one part of the board,nbsp;keeping the fame velocity with it, and having nonbsp;relative motion upon it, as is the cafe with everynbsp;thing that lies loofe upon the planefurface of thenbsp;earth, which having the motion of the earthnbsp;communicated to it, never endeavours to remove

from that place. But flop the board fuddenly by hand, and the ball will go on, and continue to revolve upon the board, until thenbsp;friftion thereof Hops its motion : which Ihews,nbsp;that matter being once put into motion wouldnbsp;continue to move for ever, if it met with nonbsp;refiftance. In like manner, if a perfon Handsnbsp;upright in a boat before it begins to move, henbsp;can Hand firm -, but the moment the boat fetsnbsp;off, he is in danger of falling towards that placenbsp;which the boat departs from : becaufe, as matter, he has no natural propenfity to move. Butnbsp;when he acquires the motion of the boat, let itnbsp;be ever fo fwift, if it be fmooth and uniform, henbsp;will ftand as upright and firm as if he was onnbsp;the plain fliore; and if the boat ftrikes againftnbsp;any obftacle, he will fall towards that obftacle ;nbsp;on account of the propenfity he has, as matter,nbsp;to keep the motion which the boat has put himnbsp;into.

2. Take away this ball, and put a longer cord to it, which may be put down through the hollow axis of the bearer MX, and wheel G, andnbsp;fix a weight to the end of the cord below thenbsp;machine ; which weight, if left at liberty, willnbsp;draw the ball from the edge of the whirling-board to its center.

Draw off the ball a little from the center, and turn the winch; then the ball will go round andnbsp;round with the board, and will gradually fly offnbsp;farther and farther from the center, and raife upnbsp;the weight below the machine : which fliewsnbsp;that all bodies revolving in circles have a tendency to fly off from thefe circles, and mufl: havenbsp;fome power afting upon them from the center ofnbsp;motion, to keep them from flying off. Stop thenbsp;machine, and the ball will continue to revolve

for fome time upon the board; but as' the friction gradually flops its motion, the weight afting upon it will bring it nearer and nearer to thenbsp;center in every revolution, until it brings itnbsp;quite thither. This fhews, that if the planetsnbsp;met with any refiftance in going round the fun,nbsp;its attraftive power would bring them nearernbsp;and nearer to it in every revolution, until theynbsp;fell upon it.

3.' Take hold of the cord below the machine with one hand, and with the other throw the ballnbsp;upon the round board as it were at right anglesnbsp;to the cord, by which means it will go roundnbsp;and round upon the board. Then obfervingnbsp;with what velocity it moves, pull the cord below the machine, which will bring the ball nearernbsp;to the center of the board, and you will fee thatnbsp;the nearer the ball is drawn to the center, thenbsp;fafter it will revolve ; as thofe planets which arenbsp;neareft the fun revolve fafter than thofe whichnbsp;are more remote ; and not only go round fooner,nbsp;becaufe they defcribe fmaller circles, but evennbsp;move fafter in every part of their refpedivenbsp;circles.

4* Take away this ball, and apply the bearer MX, whofe center of motion is in its middle atnbsp;w, direcftly over the center of the whirling-boardnbsp;Then put two balls {V and U) of equalnbsp;weights upon their bearing wires, and havingnbsp;fixed them at equal diftances from their refpedivenbsp;centers of motion w and x upon their filk cords,nbsp;by the fcrew nuts, put equal weights in thenbsp;towers 0 and P. Laftly, put the catgut firingsnbsp;E and F upon the grooves G and H of the fmallnbsp;wheels, which being of equal diameters, will givenbsp;equal velocities to the bearers above, when thenbsp;winch B is turned: and the balls JJ and V will

fly off towards M and N �, and will raife the weights in the towers at the fame inftant. Thisnbsp;Ihews, that when bodies of equal quantities ofnbsp;matter revolve in equal circles with equal velo-�nbsp;cities, their centrifugal forces are equal.

5. Take away thefe equal balls, and inftead of them, put a ball of fix ounces into the bearernbsp;MX, at a fixth part of the diftance w x from thenbsp;center, and put a ball of one ounce into the op-pofite bearer, at the whole diftance x y, whichnbsp;is equal to w z from the center of the bearer jnbsp;and fix the balls at thefe diftances on their cords,nbsp;by the fcrew nuts at top ; and then the ball f/,nbsp;which is fix times as heavy as the ball V, will benbsp;at only a fixth part of the diftance from its center of motion �, and confequently will revolve innbsp;a circle of only a fixth part of the circumferencenbsp;of the circle in which V revolves. Now, let anynbsp;equal weights be put into the towers, and thenbsp;machine be turned by the winch �, which (as thenbsp;catgut firing is on equal wheels below) willnbsp;caufe the balls to revolve in equal times ; but Vnbsp;will move fix times as fall as �7, becaufe it revolves in a circle of fix times its radius; andnbsp;both the weights in the towers will rife at once.nbsp;This fhews, that the centrifugal forces of revolving bodies (or their tendencies to fly off from thenbsp;circles they deferibe) are in direft proportion tonbsp;their quantities of matter multiplied into theirnbsp;refpedlive velocities ; or into their diftances fromnbsp;' the centers of their refpeftive circles. For, fup-poGng {7, which weighs fix ounces, to be twonbsp;inches from its center of rnotion w, the weightnbsp;multiplied by the diftance is 12 : and fuppofingnbsp;y, which weighs only one ounce, to be 12 inchesnbsp;diftant from the center of motion x, the weightnbsp;I ounce multiplied by the diftmee la inchesnbsp;5nbsp;nbsp;nbsp;nbsp;is

is 12. And as they revolve in equal times, their velocities are as their diftances from the center,nbsp;namely, as i to 6.

If thefe mo balls be fixed at equal diftances from their refpedive centers of motion, theynbsp;will move with equal velocities; and if thenbsp;tower O has 6 times as much weight put into itnbsp;as the tower P has, the balls will raife theirnbsp;weights exadly at the fame moment. Thisnbsp;(hews that the ball U being fix times as heavy asnbsp;the ball F, has fix times as much centrifugalnbsp;force, in defcribing an equal circle with an equalnbsp;velocity.

6. If bodies of equal weights revolve in equal A double circles with unequal velocities, their centrifugal yelocitynbsp;forces are as the fquares of the velocities. Tonbsp;prove this law by an experiment, let two balls de, is aquot;nbsp;U and F of equal weights be fixed on their cords bai�ancenbsp;at equal diftances from their refpedive centers I?nbsp;of motion w and x and then let the catgutnbsp;firing E be put round the wheel K (whofe cir- gravity,nbsp;cumference is only one half of the circumferencenbsp;of the wheel H or G) and over the pulley s tonbsp;keep it tight �, and let four times as much weightnbsp;be put into the tower P, a^ in the tower O.

Then turn the winch P, and the ball F will revolve twice as fall as the ball U'm a. circle of the fame diameter, becaufe they are equidiftant fromnbsp;the centers of the circles in which they revolve;nbsp;and the weight in the towers will both rife atnbsp;the farne inftanr, which (hews that a double velocity in the farne circle will exa�lly balance anbsp;quadruple power of attradion in the center ofnbsp;the circle. For the weights in the towers maynbsp;be confidered as the attra�live forces in the centers, ading upon the revolving balls-, which,

moving in equal circles, is the fame thing as if they both moved in one and the fame circle.

7. If bodies of equal weights revolve in unequal circles, in fuch a manner that the fquares of the times of their going round are as thenbsp;cubes of their diltances from the centers of thenbsp;circles they defcribe their centrifugal forces arenbsp;inverfely as the fquares of their diftances fromnbsp;thofe centers. For, the catgut firing remainingnbsp;as in the laft experiment, let the diftance of thenbsp;ball V from the center x be made equal to twonbsp;of the crofs divifions on its bearer ; and the diftance of the ball U from the center w be threenbsp;and a fixth part; the balls themfelves being, ofnbsp;equal weights, and V making two revolutionsnbsp;by turning the winch, in the time that U makesnbsp;one : fo that if we fuppofe the ball V to revolvenbsp;in one fecond, the ball U will revolve in twonbsp;feconds, the fquares of which are one and four:nbsp;for the fquare of i is only i, and the fquare ofnbsp;2 is 4 -, therefore the fquare of the period ornbsp;revolution of the ball V, is contained four timesnbsp;in the fquare of the period of the ball XJ. Butnbsp;the diftance of V, is 2, the cube of which is 8,nbsp;and the diftance of^t/is gf, the cube of whichnbsp;is 32 very nearly, in which 8 is contained fournbsp;times �, and therefore, the fquares of the periodsnbsp;of V and U are to one another as the cubes ofnbsp;their diftances from x and w, which are the centers of their refpeflive circles. And if thenbsp;weight in the tower 0 be four ounces, equal tonbsp;the fquare of 2, the diftance of V from the center X; and the weight in the tower P be 10nbsp;ounces, nearly equal to the fquare of 3i, the diftance of U from w ; it will be found upon turning the machine by the winch, that the balls Unbsp;and V will raife their itfpedive weights at

the

tlie fame inftant of time. Which confirms that famous obfervation of Kepler, viz. That�thenbsp;fquaresof the times in which the planets go roundnbsp;the fun are in the fame proportion as the cubes ofnbsp;their diftanccs from him ; and that the fun�s at-traftion is inverfely as the fquare of the diftancenbsp;from his center: that is, at twice the diftance,nbsp;his attraflioh is four times lefs; and thrice thenbsp;diftance, nine times lefs *, at four times the diftance, fixteen times lefs; and fo on, to the re-moteft part of the fyftem.

8. Take off the catgut firing E from the �reat wheel D and the fmall wheel i�, and letnbsp;the firing F remain upon the wheels .D and G.

Take away alfo the bearer MX from the whirling-board di and inftead thereof put the machine AB upon it, fixing this machine to the center of the board by the pins c and J, in fuch Fig. 3.nbsp;a manner, that the end ef may rife above thenbsp;board to an angle of 30 or 40 degrees. In the Theab-upper fide of this machine are two glafs tubes furdiryofnbsp;and clofe flopt at both ends; and eachnbsp;tube is about three quarters full of water. Innbsp;the tube ah a little quickfilver, which naturallynbsp;falls down to the end a in the water, becaufenbsp;it is heavier than its bulk of water; and in thenbsp;tube ^ is a fmall cork which floats on the topnbsp;of the water at e, becaufe it is lighter; and itnbsp;is fmall enough to have liberty to rife or fallnbsp;in the tube. While the board b with this machine upon it continues at reft, the quickfilvernbsp;lies at the bottom of the tube a, and the corknbsp;floats on the water near the top of the tube b. Bur,nbsp;upon turning the winch, and putting the machine in motion, the contents of each tube willnbsp;fly off towards the uppermoft; ends (which arenbsp;farthefl from the center of motion) the heavieftnbsp;Dnbsp;nbsp;nbsp;nbsp;witU

with the greateft force. Therefore the quick ^ filver in the tube a will fly oflr quite to the endnbsp;�, and occupy its bulk of fpace there, excludingnbsp;the water from that place, becaufe it is lighternbsp;than quickfilver 5 but the water in the tube bnbsp;flying off to its higher end e, will exclude thenbsp;cork from that place, and caufe the cork to de-fcend towards the lowermoft end of the tube,nbsp;where it will remain upon the loweft end of thenbsp;water near h; for the heavier body having thenbsp;greater centrifugal force, will therefore pofTefsnbsp;the uppermoft part of the tube; and the lighternbsp;body will keep between the heavier and thenbsp;lowermoft part.

This demonftrates the abfurdity of the Garte-fian dodrine of the planets moving round the fun in vortexes: for, if the planet be morenbsp;denfe or heavy than its bulk of the vortex, it willnbsp;fly off therein, farther and farther from the fun jnbsp;if lefs denfe, it will come down to the loweftnbsp;part of the vortex, at the fun: and the wholenbsp;vortex itfelf muft be furrounded with fomethingnbsp;like a great wall, otherwife it would fly quite off,nbsp;planets and all together.�But while gravity ex-ifts, there is no occafion for fuch vortexes; andnbsp;when it ceafes to exift, a ftone thrown upwardsnbsp;will never return to the earth again.

If one bo- 9� a body be fo placed on the whirling-dy moves board of the machine (Fig. i.) that the center of round gravity of the body be diredly over the centernbsp;another, of the board, and the board be put into ever fonbsp;them mufta motion by the winch 5, the body willnbsp;movenbsp;nbsp;nbsp;nbsp;turn round with the board, but will not remove

�rai'ity. of motion, the centrifugal force of all parts of 1nbsp;nbsp;nbsp;nbsp;the

the body will be equal at equal diftances from its center of motion, and therefore the body willnbsp;remain in its place. But if the center of gravitynbsp;be placed ever fo little out of the center of motion, and the machine be turned fwiftly round,nbsp;the body will fly off towards that fide of thenbsp;board on which its center of gravity lies. Thus, pjg,nbsp;if the wire C with its little ball B be taken awaynbsp;from the demi-globe A, and the flat fide ef ofnbsp;this dembglobe be laid upon the whirling-boardnbsp;of the machine, fo that their centers may coincide ; if then the board be turned ever fo quicknbsp;by the winch, the demi-globe will remain wherenbsp;it Was placed. But if the wire C be fcrewed intonbsp;the demi-globe at d, the whole becomes onenbsp;body, whofe center of gravity is now at or nearnbsp;d. Let the pin c be fixed in the center of thenbsp;whirling-board, and the deep groove h cut in thenbsp;fiat fide of the demi-globe be put upon the pin,nbsp;fo as the pin may be in the center oi A {See Fig.

5. where this groove is reprefented at and let the whirling-board be turned hy the winch,nbsp;which will carry the little ball B (Fig. 4.) withnbsp;its wire C, and the demi-globe A, all round thenbsp;center-pin f F, and then, the centrifugal force ofnbsp;the little ball 5, which weighs only one ounce,nbsp;will be fo great, as to draw off the demi-globenbsp;yf, which weighs two pounds, until the end ofnbsp;the groove at e ftrikes againfl; the pin r, andnbsp;fo prevents the demi-globe A from going anynbsp;farther: otherwife, the centrifugal force of Bnbsp;would have been great enough to have carriednbsp;A quite off the whirJing-board. Which (hews,nbsp;that if the f n v/ere placed in the very center ofnbsp;the orbits of the planets, it could not poffiblynbsp;remain there; for the centrifugal forces of thenbsp;planets would carry them quite off, and the funnbsp;D 2nbsp;nbsp;nbsp;nbsp;with

with them; efpecialJy when feveral of them happened to be in any one quarter of the heavens. For the lun and planets are, as much connedednbsp;by the mutual attraction that fubfifts betweennbsp;them, as the bodies A and B are by the wire Cnbsp;which is fixed into them both. And even ifnbsp;there were but one fingle planet in the wholenbsp;heavens to go round ever fo large a fun in thenbsp;center of its orbit, its centrifugal force wouldnbsp;foon carry off both itfelf and the fun. For, thenbsp;greateft body placed in any part of free fpacenbsp;might be eafily moved; becaufe if there were nonbsp;other body to attrafl. it, it could have no weightnbsp;or gravity of itfelf; and confequently, though itnbsp;could have no tendency of itfelf to remove fromnbsp;that part of fpace, yet it might be very eafilynbsp;moved by any other fubftance.

lo. As the centrifugal force of the light body B will not allow the heavy body A to remain innbsp;the center of motion, even though it be 24 timesnbsp;as heavy as B-, let us now take the ball A (Fig.nbsp;6.) which weighs 6 ounces, and conneft it bynbsp;the wire C with the ball B, which weighs onlynbsp;one ounce; and let the fork E be fixed into thenbsp;center of the whirling-board : then hang thenbsp;balls upon the fork by the wire C in fuch a rnan-ndr, that they may exaftly balance each other;nbsp;which will be when the center of gravity betweennbsp;them, in the wire at d, is fupported by the fork.nbsp;And this center of gravity is as much nearer tonbsp;the center of the ball A, than to the center of thenbsp;ball B, as A is heavier than B, allowing for thenbsp;weight of the wire on each fide of the fork.nbsp;This done, let the machine be put into motionnbsp;by the winch ; and the balls A and B will gonbsp;round their common center of gravity d, keeping their balance, becaufe either will not allow

Of central Forces,

the other to fly off with it. For, fuppofing the ball E to be only one ounce in weight, and thenbsp;ball A to be fix ounces; then, if the wire C werenbsp;equally heavy on each fide of the fork, the centernbsp;of gravity d would be fix times as far from thenbsp;center of the ball E as from that of the ball A^nbsp;and confequently E will revolve with a velocitynbsp;fix times as great as A does ; which will give Bnbsp;fix times as much centrifugal force as any Anglenbsp;ounce of A has : but then, as E is only onenbsp;ounce, and A fix ounces, the whole centrifugalnbsp;force of A will exaftly balance the whole centrifugal force of E : andi therefore, each body willnbsp;detain the other fo as to make it keep in itsnbsp;circle. This Ihews that the fun and planets muffnbsp;all move round the common center of gravitynbsp;of the whole fyftem, in order to preferve that juftnbsp;balance which takes place among them. For,nbsp;the planets being as unaflive and dead as thenbsp;above balls, they could no more have put them-felves into motion than thefe balls can; nor havenbsp;kept in their orbits without being balanced atnbsp;firft with the greatefl; degree of exaftnefs uponnbsp;their common center of gravity, by the Almightynbsp;hand that made them and put them in motion.

Perhaps it may be here alked, that fince the center of gravity between thefe balls mull benbsp;fupported by the fork E in this experiment,nbsp;vohat prop it is that fupports the center of gravity of the folar fyftem, and confequently bearsnbsp;the weight of all the bodies in it; and by whatnbsp;is the prop itfelf fupported ? The anfwer is eafynbsp;and plain; for the center of gravity of our ballsnbsp;muft be fupported, becaufc they gravitate towards the earth, and would therefore fall to it:nbsp;but as the fun and planets gravitate only towardsnbsp;D 3nbsp;nbsp;nbsp;nbsp;one

one another, they, have nothing elfe to fall to, 3,, and therefore have no occafion for any thing tonbsp;fupport their common center of gravity; and ifnbsp;they did not move round that center, and confe-quently acquire a tendency to fly off from it bynbsp;their motions, their mutual attraftions wouldnbsp;foon bring them together; and fo the wholenbsp;would become one mafs in the fun: which wouldnbsp;alfo be the cafe if thsir velocities round the funnbsp;were not quick enough to create a centrifugalnbsp;force equal to the fun�s attraftion.

But after all this nice adjuftment, it appears evident that the Deity cannot withdraw his regulating hand from his works, and leave themnbsp;to be folely governed by the laws which he hasnbsp;impreft upon them at firft. For if he Ihouldnbsp;once leave them fo, their order would in timenbsp;come to an end ; becaufe the planets muff ne-ceffarily difturb one another�s motions by theirnbsp;mutual attra�lions, when feveral of them are innbsp;the fame quarter of the heavens; as is often thenbsp;cafe: and then, as they attratff the fun morenbsp;towards that quarter than when they are in anbsp;manner difperfed equably around him, if he wasnbsp;not at that time made to defcribe a portion of anbsp;larger circle round the common center of gravi ty,nbsp;the balance would then be immediately de-ftroyed; and as it could never reftore itfelf again,nbsp;the whole fyftem yvould begin to fall together,

Of this difturbance we have a very remarkable inftance in the comet which appeared lately; andnbsp;which, in going laft up before from the fun, wentnbsp;lb near to Jupiter, and was fo affedted by hisnbsp;attraftion, as to have the figure of its orbit muchnbsp;changed; and not only fo, but to have its period

altered, and its courfe to be different in the heavens from what it was laft before.

II. Take away the fork and balls from the Fig. 7, whirling.board, and place the trough JB thereon, fixing its center to the center of the whirling-board by the pin H. In this trough are twonbsp;balls D and E, of unequal weights, connedednbsp;by a wire �; and made to Aide eafily upon thenbsp;wire C ftretched from end to end of the trough,nbsp;and made faff by nut-fcrews on the outfide of thenbsp;ends. Let thefe balls be fo placed upon the wirenbsp;C, that their common center of gravity^ may benbsp;diredly over the center of the whirling-board.

Then, turn the machine by the winch, ever fo fwiftly,and the troughand balls will go round theirnbsp;center of gravity, fo as neither of the balls will flynbsp;offj becaufe, on account of the equilibrium, eachnbsp;ball detains the other with an equal force adingnbsp;againft it. But if the ball E be drawn a littlenbsp;morp towards the end of the trough at it willnbsp;remove the center of gravity towards that endnbsp;from the center of motion and then, uponnbsp;turning the machine, the little ball E will fly off,nbsp;and ftrike with a confiderable force againfl: thenbsp;end J, and draw the great ball B into the middlenbsp;of the trough. Or, if the great ball D be drawnnbsp;towards the end B of the trough, fo that the center of gravity may be a little towards that endnbsp;from the center of motion, and the machine benbsp;turned by the winch, the great ball D will fly off,nbsp;and ftrike violently againft the end B of thenbsp;trough, and will bring the little ball E into thenbsp;middle of if. If the trough be not made verynbsp;ftrong, the ball D will break through it.

12. The reafon why the tides rife at the fame 9^ tlie abfolute time on oppofue fides of the earth, andnbsp;P 4nbsp;nbsp;nbsp;nbsp;confe^uently

confequently in oppofite diredions, is made abundantly plain by a new experiment on thenbsp;whirling table, Thecaufeof theirrifingon the fidenbsp;next the mpon every one underftands to be owingnbsp;to the mpon�s attradion: but why they ihouldnbsp;rife on the oppofite fide at the feme time, wherenbsp;there is no moon to attrad them, is perhaps notnbsp;fo generally underftood. For it would feemnbsp;that the moon Ihould rather draw the waters (asnbsp;it were) clofcr to that fide, than raife them uponnbsp;it, jliredly contrary to her attradive force. Letnbsp;the circle abed reprefent the earth, with its fidenbsp;� turned toward the moon, which will then at-trad the waters fo, as to raife them from c to g.nbsp;But the queftion is, why Ihould they rife as highnbsp;at that very time on the oppofite fide, from a to,nbsp;e? In order to explain this, let there be a platenbsp;AB fixed upon one end of the flat bar Z)C; withnbsp;fuch a circle drawn upon it as abed (in Fig. 8.)nbsp;to reprefent the round hgure of the earth andnbsp;fea; and fuch an ellipfis as efgk fo reprefent thenbsp;fwelling of the tide at e and g, occafioned by thenbsp;influence of the moon. Over this plate AB letnbsp;the three ivory balls e,f, g, be hung by the fdknbsp;lines h, i, k, faftened to the tops of the crookednbsp;wires H, /, K, in fuch a manner, that the bail atnbsp;e may hang freely oyer the fide of the circle e,nbsp;which is fanheft from the moon M (at the othernbsp;fnd pf the bar); the ball at � may hang freelynbsp;pver the center, and the ball at ^ hang over thenbsp;fide of the circle g, which is neareft the moon.nbsp;The ball � may reprefent the center of the earth,nbsp;the ball g fome water on the fide next the moon,nbsp;and the ball e fome water on the oppofite fide.nbsp;On the back of the moon M is fixt the Ihorc barnbsp;N parallel to the horizon, and there are threenbsp;holes in it above the l�tle weights f, q, r. A

Of the ^idesl

filk thread o is tied to the line h clofe above the ball and pafling by one fide of the moon Af,nbsp;goes through a hole in the bar iV, and has thenbsp;weighty hung to it. Such another thread � isnbsp;tied to the line i, clofe above the ball �, andnbsp;pairing through the center of the moon Af andnbsp;middle of the bar N, has the weight ? hung tonbsp;it, which is lighter than the weight p. A thirdnbsp;thread is tied to the line h, dole above the ballnbsp;e, and pafling by the other fide of the moon Af,nbsp;through the bar iV, has the weight r hung to it,nbsp;which is lighter than the weight q.

The ufe of thefe three unequal weights is to reprefent the moon�s unequal attraftion at different diftances from her. With whatever forcenbsp;Ihe attrads the center of the earth, Ihe attradsnbsp;the fide next her with a greater degree of force,nbsp;and the fide fartheft from her with a lefs. So,nbsp;if the weights are left at liberty, they will drawnbsp;all the three balls towards the moon with different degrees of force, and caufe them to makenbsp;the appearance Ihewn in Fig. lo-, by which Fig. lo.nbsp;means they are evidently farther from each othernbsp;than they would be if they hung at liberty by thenbsp;lines h, i, k; becaufe the lines would then hangnbsp;perpendicularly. This fhews, that as the moonnbsp;attrads the fide of the earth which is neareft hernbsp;with a greater degree of fofce than (he does thenbsp;center of the earth, Ihe will draw the water onnbsp;that fide more than Ihe draws the center, and fonbsp;caufe it to rife on that fide: and as Ihe draws thenbsp;center more than Ihe draws the oppofite fide,nbsp;the center will recede farther from the furface ofnbsp;the water on that oppofite fide, and fo leave it asnbsp;high there as (he raifed it on the fide next to her.nbsp;for, as the center will be in the middle between

the

the tops of the oppofite elevations, they muft of courfe be equally high on both fides at the famenbsp;time.

But upon this fuppofition the earth and moon would foon come together: and to be fure theynbsp;would, if they had not a motion round theirnbsp;common center of gravity, to create a degree ofnbsp;centrifugal force fufficient to balance their mutual attraftion. This motion they have; for asnbsp;the moon goes round her orbit every month, atnbsp;the diftance of 240000 miles from the earth�snbsp;center, and of 234000 miles from the center ofnbsp;gravity of the earth and moon, fo does the earthnbsp;go round the fame center of gravity every monthnbsp;at the diftance of 6000 miles from it; that is,nbsp;from it to the center of the earth. Now as thenbsp;earth is (in round numbers) 8000 miles in diameter, it is plain that its fide next the moon isnbsp;only 2000 miles from the common center of gravity of the earth and moon; its center 6000nbsp;miles diftant therefrom; and its farther fide fromnbsp;the moon loooo. Therefore the centrifugalnbsp;forces of thefe parts are as 2000, 6000, andnbsp;10000; that is, the centrifugal force of any fidenbsp;of the earth, when it is turned from the moon,nbsp;is five times as great as when it is turned towardsnbsp;the moon. And as the moon�s attra�lion (ex-preft by the numbers 6000) at the earth�s center-keeps the earth from flying out of this monthlynbsp;circle, it muft be greater than the centrifugalnbsp;force of the waters on the fide next her; andnbsp;confequently, her greater degree of attraflion onnbsp;that fide is fufficient to raife them ; but as hernbsp;attradlion on the oppofite fide is lefs than thenbsp;centrifugal force of the water there, the excefsnbsp;of this force is fufficient to raife the water juft as

high

'Ibi EartUs Motton demonjlraud. nbsp;nbsp;nbsp;45

Kigh on the oppofite fide.�To prove this expe-Fig. 9. rimentally, let the bar D C with its furniture benbsp;fixed upon the whirling-board of the machinenbsp;(Fig. I.) by pulhing the pin P into the centernbsp;of the board which pin is in the center of gravity of the whole bar with its three balls e,f, g,nbsp;and moon M, Now if the whirling-board andnbsp;bar be turned flowly round by the winch, untilnbsp;the ball � hangs over the center of the circle, asnbsp;in Fig. II. the ball g will be kept towards thenbsp;moon by the heavieft weight p, (Fig. 9.) andnbsp;the ball e, on account of its greater centrifugalnbsp;force, and the lefier weight r, will fly off as farnbsp;to the other fide, as in Fig. 11. And fo, whilfl;nbsp;the machine is kept turning, the balls e and gnbsp;will hang over the ends of the ellipfis I f k. Sonbsp;that the centrifugal force of the ball e will exceed the moon�s attradion juft as much as hernbsp;atcraftion exceeds the centrifugal force of thenbsp;ball whilfl her attradlion juft balances the centrifugal force of the ball �, and makes it keepnbsp;in its circle. And hence it is evident that thenbsp;tides muft rife to equal heights at the fame timenbsp;on oppofite fides of the earth. This experiment, to the bell of my knowledge, is entirelynbsp;new.

From the principles thus eftablilhed, it is The evident that the earth moves round the fun, and j��nbsp;not the fun round the earth ; for the centriAigalnbsp;law will never allow a great body to move round iiraud.nbsp;a finall one in any orbit whatever �, fpeciallvnbsp;when we find that if a fmall body moves roundnbsp;a great one, the great one muft alfo move roundnbsp;the common center of gravity between them two.

And it is well known that the quantity of matter in the fun is 227000 times as great as the quantity of matter in the earth. Nov/, as the fun�s

diftance

diftance from the earth is at leaft 81,000,000 of miles, if we divide that diftance by 227,000, wenbsp;lhall have only 357 for the number of miles thatnbsp;the center of gravity between the fun and earthnbsp;is diftant from the fun�s center. And as thenbsp;fun�s femidiameter is 4 of a degree, which, at fonbsp;great a diftance as that of the fun, muft be nonbsp;lefs than 381500 miles, if this be divided bynbsp;357, the quotient will be 10684, which fhewsnbsp;that the common center of gravity between thenbsp;fun and earth is within the body of the fun ;nbsp;and is only the 10684 part of his femidiameternbsp;from his center toward his furface.

All globular bodies, whofe parts can yield, and which do not turn on their axes, muft benbsp;perfefl fpheres, becaufe all parts of their furfacesnbsp;are equally attradled toward their centers. Butnbsp;all fuch globes which do turn on their axes willnbsp;be oblate fpheroids; that is, their furfaces willnbsp;be higher, or farther from the center, in thenbsp;cquatoreal than in the polar regions. For, asnbsp;the equatoreal parts move quickeft, they muftnbsp;have the greateft centrifugal force; and willnbsp;therefore recede fartheft from the axis of motion. Thus, if two circular hoops A B andnbsp;Fig. 12. CD, made thin and flexible, and croffing onenbsp;another at right angles, be turned round theirnbsp;axis EF by means of the winch m, the wheel n,nbsp;and pinion 0, and the axis be loofe in the polenbsp;or interfe�lion e, the middle parts A^ B, C, Dnbsp;will fwell out fo as to ftrike againft the fides ofnbsp;the frame at F and G, if the pole f, in finkingnbsp;to the pin E, be not ftopt by it from finkingnbsp;farther : fo that the whole will appear of an ovalnbsp;figure, the equatoreal diameter being confide-rably longer than the polar. That our earth isnbsp;of this figure, is demonftrable from adual mea-

furement of fome degrees on its furface, which are fotind to be longer in the frigid zones thannbsp;in the torrid: and the difference is found to benbsp;fuch as proves the earth�s equatoreal diameternbsp;to be 36 miles longer than its axis.�Seeing then,nbsp;the earfh is higher at the equator than at thenbsp;poles, the fea, which like all other fluids naturally runs downward (or towards the placesnbsp;which are nearell the earth�s center) would runnbsp;towards the polar regions, and leave the equatoreal parts dry, if the centrifugal force of thenbsp;water, which carried it to thofe parts, and fonbsp;raifed them, did not detain and keep it fromnbsp;running back again towards the poles of thenbsp;earth,

pare them together, we may do this either founda-with refpeft to the quantities of matter they�'�quot;�^ contain, or the velocities with which they arenbsp;moved. The heavier any body is, the greaternbsp;is the power required either to move it or to flopnbsp;its motion: and again, the fwifter it moves, thenbsp;greater is its force. So that the whole momentnbsp;turn or quantity of force of a moving body is thenbsp;refult of its quantity of matter multiplied by thenbsp;velocity with which it is moved. And when thenbsp;produdls arifing from the multiplication of thenbsp;particular quantities of matter in any two bodies �nbsp;by their refpedlive velocities are equal, the momenta or intire forces are fo too. Thus, fup-pofe a body, which we fhall call A, to weigh 40nbsp;pounds, and to move at the rate of two miles

in a minute; and another body, which we flial! call 5, to weigh only four pounds, and to movenbsp;20 miles in a minute; the entire forces withnbsp;�which thefe two bodies would ftrike againft anynbsp;obftacle would be equal to each other, and therefore it would require equal powers to flop them.nbsp;For 40 multiplied by 2 gives 80, the force ofnbsp;the body A: and 20 multiplied by 4 gives 80,nbsp;the force of the body B.

Upon this eafy principle depends the whole of mechanics; and it holds univerfally true,nbsp;that when two bodies- are fufpended on anynbsp;inacliine, fo as to a�t contrary to each other; ifnbsp;the machine be put into motion, and the perpendicular afcent of one body multiplied intonbsp;its weight, be equal to the perpendicular defcentnbsp;of the other body multiplied into its weight,nbsp;thofe bodies, how unequalfoever in their weights,nbsp;will balance one another in all fituations : for,nbsp;as the whole afcent of one is performed in thenbsp;fame time with the whole defcCnt of the other,nbsp;their refpeflive velocities mull be diredlly as thenbsp;fpaces they move through ; and the excefs ofnbsp;weight in one body is compenfated by the excefsnbsp;How to of velocity in the other.�Upon this principle itnbsp;compute is eafy to compute the power of any mechanicalnbsp;the power engine, whether Ample or compound ; for it isnbsp;. but only finding how much fwifter the powernbsp;wfem *' moves than the weight does (1. e. how much far-gine. ther in the fame time) and juft fo much is thenbsp;power increafed by the help of the engine.

In the theory of this fcience, we fuppofe all planes perfectly even, all bodies perfedly Imooth;nbsp;levers to have no weight, cords to be extremelynbsp;pliable, machines to have no friftion *, and innbsp;fhort, all imperfections mull be fet afide until

The Ample machines, ufually called mechanical powers, are fix in number, viz, the lever, the chanicnbsp;wheel and axle, the pulley, the inclined plane, the powers,nbsp;wedge, and the fcrew.�They are called mecha-nical powers, becaufe they help us mechanicallynbsp;to raiie weights, move heavy bodies, and overcome reliftances, which we could not effedl without them.

I. A lever Is a bar of iron or wood, one part The U-of which being fupported by a prop, all the wr. other parts turn upon that prop as their centernbsp;of motion; and the velocity of every part ornbsp;point is direftly as its diftance from the prop.nbsp;Therefore, when the weight to be raifed at onenbsp;end is to the power applied at the other to raifenbsp;it, as the diftance of the power from the propnbsp;is to the diftance of the weight from the prop,nbsp;the power and weight will exadtly balance ornbsp;counterpoife each other: and as a common levernbsp;has next to no fridion on its prop, a verynbsp;little additional power will be fufiicient to raifenbsp;the weight.

There are four kinds of levers, i. The common fort, where the prop is placed betweennbsp;the weight and the power; but much nearer tonbsp;the weight than to the power. 2. When thenbsp;prop is at one end of the lever, the power at thenbsp;other, and the weight between them. 3. Whennbsp;the prop is at one end, the weight at the other,nbsp;and the power applied between them. 4. Thenbsp;bended lever, which differs only in form fromnbsp;the firft fort, but not in property. Thofe of thenbsp;firft and fecond kind are often ufed in mechanical engines; but there are few inftances in whichnbsp;the third fort is ufed.

A common balance is by fome reckoned a le^'�l* of the firft kind �, but as both its ends are atnbsp;equal diftances from its center of motion, theynbsp;move with equal velocities j and therefore, aSnbsp;it gives no mechanical advantage, it cannot properly be reckoned among the mechanical powers.

A lever of the firft kind is reprefented by the bar ABC, fupported by the prop D. Its principal ufe is to loofen large ftones in the ground,nbsp;or raife great weights to fmall heights, in ordernbsp;to have ropes put under them for railing themnbsp;higher by other machines. The parts AB andnbsp;B C, on different fides of the prop D, are callednbsp;the arms of the lever : the end A of the fhorternbsp;arm A B being applied to the weight intendednbsp;to be raifed, or to the refiftance to be overcome jnbsp;and the power applied to the end C of the longernbsp;arm B C.

In making experiments with this machine, the Ihorter arm AB muft be as much thicker thannbsp;the longer arm B C, as will be fufficient to balance it on the prop. This fuppofed, let P re-prefent a power, whofe gravity is equal to inbsp;ounce, and fF a weight, whofe gravity is equalnbsp;to 12 ounces. Then, if the power be 12 timesnbsp;as far from the prop as the weight is, they willnbsp;exaftly counterpoife ; and a fmall addition tonbsp;the power P will caufe it to defeend, and raifenbsp;the weight IV-, and the velocity with which thenbsp;power defeends will be to the velocity withnbsp;which the weight rifes, as 12 to i : that is,nbsp;diredly as their diftances from the prop; andnbsp;confequently, as the fpaces through which theynbsp;move. Hence, it is plain that h man, who bynbsp;his natural ftrength, w'ithout the help of anynbsp;machine, could fupport an hundred weight, willnbsp;by the help of this lever be enabled to fupport

twelve hundred. If the weight be lefs, or the power greater, the prop may be placed fo muchnbsp;farther from the weight; and then it can benbsp;raifed to a proportionably greater height. Fornbsp;univerfally, if the intenfity of the weight multiplied into its diftance from the prop be equalnbsp;to the intenfity of the power multiplied into itsnbsp;diftance from the prop, the power and weightnbsp;will exadly balance each other �, and a little addition to the power will raife the weight. Thus,nbsp;in the prefent inftance, the weight IF is 12nbsp;ounces, and its diftance from the prop is i inch ;nbsp;and 12 multiplied by i is 12 ; the power P isnbsp;equal to i ounce, and its diftance from the propnbsp;is 12 inches, which multiplied by i is 12 againjnbsp;and therefore there is an equilibrium betweennbsp;them. So, if a power equal to 2 ounces be applied at the diftance of 6 inches from the prop,nbsp;it will juft balance the weight W-, for 6 multiplied by 2 is 12, as before. And a power equalnbsp;to 3 ounces placed at 4 inches diftance from thenbsp;prop would be the fame -, for 3 times 4 is 125nbsp;and fo on, in proportion.-

The Jlatera or Roman Jleelyard is a lever of Thejieth this kind, and is ufed for finding the weights ofnbsp;different bodies by one fingle weight placed atnbsp;different diftances from the prop or center ofnbsp;motion D. For, if a fcale hangs at A, the extremity of the fhorter arm A B, and is of fuch a.nbsp;weight as will exactly counterpoife the longernbsp;arm B C-, if this arm be divided into as manynbsp;equal parts as it will contain, each equal to A B,nbsp;the fingle weight P (which we may fuppofe tonbsp;be I pound) will ferve for weighing any thingnbsp;as heavy as itfeif, or as many times heavier asnbsp;there�are divifions in the arm B C, or any quantity between its own weight and that quantity.

As for example, if P be i pound, and placed at the firft divifion i in the arm BC, it willnbsp;balance i pound in the fcale at A: if it be removed to the fecond divifion at 2, it will balance 2 pounds in the fcale : if to the third, 3nbsp;pounds �, and fo on to the end of the arm B C.nbsp;If each of thefe integral divifions be fubdividednbsp;into as many equal parts as a pound containsnbsp;ounces, and the weight P be placed at any ofnbsp;thefe Wxlivifions, fo as to counterpoife what isnbsp;in the fcale, the pounds and odd ounces thereinnbsp;will by that means be afcertained.

To this kind of lever may be reduced feveral forts of inflruments, fuch as fciflars, pinchers,nbsp;fnuffers; which are made of two levers aftingnbsp;contrary to one another : their prop or center ofnbsp;motion being the pin which keeps them together.

In common pradlice, the longer arm of this lever greatly exceeds the weight of the fhorter :nbsp;which gains great advantage, becaufc it adds fonbsp;much to the power.

A lever of the fecond kind has the weight cond kind between the prop and the power. In this, asnbsp;of lever,nbsp;nbsp;nbsp;nbsp;gg former, the advantage gained is as

the diftance of the power from the prop to the diftance of the weight from the prop: for thenbsp;refpedlive velocities of the power and weight arenbsp;in that proportion ; and they will balance eachnbsp;other when the intenfity of the power multiplied by its diftance from the prop is equal tonbsp;the intenfity of the weight multiplied by its diftance from the prop. Thus, if yf 5 be a levernbsp;on which the weight W oi 6 ounces hangs at thenbsp;diftance of i inch from the prop G, and a powernbsp;P equal to the weight of i ounce hangs at thenbsp;end B, 6 inches from the prop, by the cord

C D going over the fixed pulley E, the power will juft 1�upport the weight: and a fmall addition to the power will raife the weight, i inchnbsp;for every 6 inches that the power delcends.

This lever fhews the reafon why two men carrying a burden upon a flick between them,nbsp;bear unequal fliares of the burden in the in-verfe proportion of their diflances from it. Fornbsp;it is v/ell known, that the nearer any of them isnbsp;to the burden, the greater lhare he bears of it;nbsp;and if he goes diredlly under it, he bearsnbsp;the whole. So, if one man be at G, and thenbsp;other at P, having the pole or flick ^B reflingnbsp;on their (lioulders �, if the burden or weight Wnbsp;be placed five times as near the man at G, as itnbsp;is to the man at P, the former will bear fivenbsp;times as much weight as the latter. This isnbsp;likewife applicable to the cafe of two horfes ofnbsp;unequal ftrength to be fo yoked, as that eachnbsp;iiorl'e may draw a part proportionable to hisnbsp;ftrength-, which is done by fo dividing the beamnbsp;they pull, that the point of traftion may be asnbsp;much nearer to the flronger horfe than to thenbsp;weaker, as the ftrength of the former exceedsnbsp;that of the latter.

To this kind of lever may be reduced oars, rudders of Ihips, doors turning upon hinges,nbsp;cutting-knives which are fixed at the point ofnbsp;the blade, and the like.

If in this lever we fuppofe the power and The third weight to change places, fo that the power maynbsp;be between the weight and the prop, it willnbsp;come a lever of the third kind : in which, thatnbsp;there may be a balance between the power andnbsp;the weight, the intenfny of the power inuft exceed the intenfuy of the weight, juft as muchnbsp;as the diftance of the weight from the prop ex-H 2nbsp;nbsp;nbsp;nbsp;ceeds

ceeds the diftances of the power from it. Thus, let E be the prop of the lever A B, and hP anbsp;weight of I pound, placed 3 times as far fromnbsp;the prop, as the power P adts at F, by thenbsp;cord C going over the fixed pulley D ; in thisnbsp;cafe, the power muft be equal to three pounds,nbsp;in order to fupport the weight.

To this fort of lever are generally referred the bones of a man�s arm : for when we lift anbsp;weight by the hand, the] mufcle that exerts itsnbsp;force to raife that weight, is fixed to the bonenbsp;about one tenth part as far below the elbow asnbsp;the hand is. And the elbow being the centernbsp;round which the lower part of the arm turns,nbsp;the mufcle muft therefore exert a force ten timesnbsp;as great as the weight that is raifed.

As this kind of lever is a difadvantage to the moving power, it is never ufed but in cafes ofnbsp;neceflity -, fuch as that of a ladder, which beingnbsp;fixed at one end, is by the ftrength of a man�snbsp;arms reared againft a wall. And in clock-work,nbsp;where all the wheels may be reckoned levers ofnbsp;this kind, becaufe the power that moves everynbsp;wheel, except the firft, adts upon it near thenbsp;center of motion by means of a fmall pinion,nbsp;and the refiftance it has to overcome, adts againftnbsp;the teeth round its circumference.

The fourth kind of lever differs nothing from the firft, but in being bended for the fake ofnbsp;convenience. ACB \sz lever of this fort, bendednbsp;at C, which is its prop, or center of motion.nbsp;P is a power adling upon the longer arm AC nx.nbsp;F, by means of the cord D E going over thenbsp;pulley G ; and IV is a weight or refiftance adtingnbsp;upon the end B of the fhorter arm B C. If thenbsp;power is to the weight, as C P is to C F, theynbsp;are in eqiiilibrio. Thus, fuppofe fV to be 5

pounds a�l;ing at the diftance of one foot from the center of motion C, and P to be i poundnbsp;afting at F, five feet from the center C, thenbsp;power and weight will juft balance each ether.

2. The fecond mechanical power is the wheel Tlie and axle, in which the power is applied to thenbsp;circumference of the wheel, and the weight isnbsp;railed by a rope which coils about the axle as thenbsp;wheel is turned round. Here it is plain thatnbsp;the velocity of the power muft be to the velocitynbsp;of the weight, as the circumference of the wheelnbsp;is to the circumference of the axle: and confe-quently, the power and weight will balance eachnbsp;other, when the intenfity of the power is to thenbsp;intenfity of the weight, as the cicumference ofnbsp;the axle is to the circumference of the wheel.

Let 5 be a wheel, C D its axle, and fuppofe pjg, the circumference of the wheel to be 8 times asnbsp;great as the circumference of the axle j then, anbsp;power P equal to i pound hanging by the cordnbsp;/, which goes round the wheel, will balance anbsp;weight fF of 8 pounds hanging by the rope K,nbsp;which goes round the axle. And as the friction on the pivets or gudgeons of the axle isnbsp;but fmall, a fmall addition to the power willnbsp;caufe it to defeend, and raife the weight: butnbsp;the weight will rife with only an eighth part ofnbsp;the velocity wherewith the power defeends, andnbsp;confequently, through no more than an eighthnbsp;part of an equal fpace, in the fame time. If thenbsp;wheel be pulled round by the handles S, S, thenbsp;power will be increafed in proportion to theirnbsp;length. And by this means, any weight maynbsp;be raifed as high as the operator pleafes,

To this fort of engine belong all cranes for raifing great weights; and in this cafe, thenbsp;wheel may have cogs all round it inftead of han^nbsp;dies, and a fmali lantern or trundle may be madenbsp;to v/ork in the cogs, and be turned by a winch jnbsp;which will make the power of the engine to exceed the power of the man who works it, asnbsp;much as the number of revolutions of the winchnbsp;exceed thofe of the axle A when multipliednbsp;by the excefs of the length of the winch abovenbsp;the length of the femidiameter of the axle,nbsp;added to the femidiameter or half thicknefs ofnbsp;the rope K, by which the weight is drawn up.-�nbsp;Thus, fuppofe the diameter of the rope andnbsp;axle taken together, to be 13 inches, andconle-quently, half their diameters to be 6 4 inches �, fonbsp;that the weight PF will hang at 6 4- inches perpendicular diftance from below the center ofnbsp;the axle. Now, let us fuppofe the wheel A B,nbsp;which is fixt on the axle, to have 80 cogs, andnbsp;to be turned by means of a winch 6 ~ inchesnbsp;long, fixe on the axis of a trundle of 8 ftaves ornbsp;rounds, working in the cogs of the wheel.�nbsp;Here it is plain, that the winch and trundlenbsp;would make 10 revolutions for one of the wheelnbsp;AB-, and its axis D, on which the rope K windsnbsp;in raifing the weight hFand the winch beingnbsp;no longer than the fum of the femidiameters ofnbsp;the great axle and rope, the trundle could havenbsp;no more power on the wheel, than a man couldnbsp;have by pulling it round by the edge, becaufenbsp;the winch would have no greater velocity thannbsp;the edge of the wheel has, which we here fuppofe to be ten times as great as the velocity ofnbsp;the rifing weight: fo that, in this cafe, thenbsp;power gained would be as 10 to i. But if thenbsp;length of the winch be 13 inches, the power

gained will be as 20 to i : if 19 f inches (which is long enough for any man to work by) thenbsp;power gained would be as 30 to i ; that is, anbsp;man could raife 30 times as much by fuch annbsp;engine, as he could do by h(s natural ftrengthnbsp;without it, becaufe the velocity of the handle ofnbsp;the winch would be 30 times, as great as the velocity of the rifing weight; the abfolute forcenbsp;of any engine being in proportion of the velocitynbsp;of the power to the velocity of the weight raifednbsp;by it.�But then, juft as much power or advantage as is gained by the engine, fo much time isnbsp;loft in working it. In this fort of machines it isnbsp;requifite to have a ratchet-wheel G on one endnbsp;of the axle, with a catch H to fall into its teeth ;nbsp;which will at any time fupport the weight, andnbsp;keep it from delcending, if the perfon who turnsnbsp;the handle ftiould, through inadvertency or care-lefthefs, quit his hold whilft the weight is raifing.

And by this means, the danger is pn vented which might otherwife happen by the running downnbsp;of the weight when left at liberty.

3. The third mechanical power or engine con- The /�/-fifts either of one moveable pully, or a fyfiem of^^y-pulleys j fome in a block or cafe which is fixed, and others in a block which is moveable, andnbsp;rifes with the weight. For though a finglenbsp;pulley that only turns on its axis, and moves notnbsp;out of its place, may ferve to change the di-redfion of the power, yet it can give no mechanical advantage thereto but is only as the beamnbsp;of a balance, whole arms are of equal length andnbsp;weight. Thus, if the equal weights W and P Fig. g,nbsp;hang by the cord E B upon the pulley J, whofenbsp;frame b is fixed to the beam H1, they will counj,nbsp;terpoife each other, juft in the fame manner asnbsp;if the cord were cut in the middle, and its twonbsp;E 4nbsp;nbsp;nbsp;nbsp;ends

ends hung upon the hooks fixt in the pulley a� A and /?, equally diftant from its center.

But if a weight /F hangs at the lower end of the moveable block p of the pulley D, and thenbsp;cord G F goes under that pulley, it is plain thatnbsp;the half G of the cord bears one half of thenbsp;weight IV, and the half F the other ; for theynbsp;bear the whole between them. Therefore,nbsp;whatever holds the upper end of either rope,nbsp;fuftains one half of the weight: and if the cordnbsp;at F be drawn up fo as to raifc the pulley D to C,nbsp;the cord will then be extended to its wholenbsp;length, all but that part which goes under thenbsp;pulley : and confequently, the power that drawsnbsp;the cord will have moved twice as far as thenbsp;pulley D with its weight W rifes; on whichnbsp;account, a power whofe intenfity is equal to onenbsp;half of the weight will be able to fupport it,nbsp;becaufe if the power moves (by means of a fmallnbsp;addition) its velocity will be double the velocitynbsp;of the weight; as may be feen by putting thenbsp;cord over the fixt pulley C (which only changesnbsp;the diredion of the power, without giving anynbsp;advantage to it) and hanging on the weight P,nbsp;which is equal only to one half the weight fVjnbsp;in which cafe there will be an equilibrium, and anbsp;little addition to P will caufe it to defcend, andnbsp;raife W through a fpace equal to one half of thatnbsp;through which P defcends.�Hence, the advantage gained will be always equal to twice thenbsp;number of pulleys in the moveable or undermofl:nbsp;block. So that, when the upper or fixt blocknbsp;u contains two pulleys, which only turn on theirnbsp;axes, and the lower or moveable block U contains two pulleys, which not only turn upon theirnbsp;axes, but alfo rife with the block and weight;nbsp;the advantage gained by this is as 4 to thenbsp;5nbsp;nbsp;nbsp;nbsp;working

�working power. Thus, if one end of the rope K MO fixed to a hook at /, and the ropenbsp;paffes over the pulleys N and i?, and under thenbsp;pulleys L and P, and has a weight T, of onenbsp;pound, hung to its other end at T, this weightnbsp;will balance and fupport a weight IV oi fournbsp;pounds hanging by a hook at the moveablenbsp;block t/, allowing the faid block as a part of thenbsp;weight. And if as much more power be added,nbsp;as is lufEcient to overcome the friftion of thenbsp;pulleys, the power will defcend with four timesnbsp;as much velocity as the weight rifes, and confe-quently through four times as much fpace.

The two pulleys in the fixed block X, and the two in the moveable block T, are in thenbsp;fame cafe with thofe laft mentioned; and thofenbsp;in the lower block give the fame advantage tonbsp;the power.

As a fyftem of pulleys has no great weight, and lies in a fmall compafs, it is eafily carriednbsp;about; and can be applied, in a great manynbsp;cafes, for railing weights, where other enginesnbsp;cannot. But they have a great deal of fridionnbsp;on three accounts : i. Becaufe the diameters ofnbsp;their axes bear a very confiderable proportion tonbsp;their own diameters; 2. Becaufe in workingnbsp;they are apt to rub againfl one another, or againftnbsp;the fides of the block; 3. Becaufe of the ftiffnefsnbsp;of the rope tTiat goes over and under them.

4. The fourth mechanical power is the in-Thetn' dined plane and the advantage gained by it isnbsp;as great as its length exceeds its perpendicular^nbsp;height. Let A B bez. plane parallel to the hori- Plat. VI,nbsp;zon, and C Da plane inclined to it; and fuppofenbsp;the whole length C D to be three times as greatnbsp;as the perpendicular height G f F: in this cafe,nbsp;the cylinder E will be fupported upon the plane

CD, and kept from rolling down upon it, by 3 power equal to a third part of the weight ofnbsp;the cylinder. Therefore, a weight may be rollednbsp;up this inclined plane with a third part of thenbsp;power which w'ould be fufficient to draw it up bynbsp;the fide of an upright wall. If the plane wasnbsp;four times as long as high, a fourth part of thenbsp;power would be fufficient; and fo on, in proportion. Or, if a weight was to be raifed from anbsp;floor to the height G F, by means of the machinenbsp;A BCD, (which would then act as a half wedge,nbsp;where the refiftance gives way only on one fide)nbsp;the machine and weight would be in equilibria whennbsp;the power applied at G F was to the weight tonbsp;be raifed, as G F to G F ; and if the power benbsp;increafed, fo as to overcome the friftion of thenbsp;machineagainft the floor and weight, the machinenbsp;will be driven, and the weight raifed : and whennbsp;the machine has moved its whole length uponnbsp;the floor, the weight will be raifed to the wholenbsp;height from G to F.

The force wherewith a rolling body defcends upon an inclined plane, is to the force of its ab-folute gravity, by which it would defcend perpendicularly in a free fpace, as the height ofnbsp;the plane is to its length. For, fuppofe the planenbsp;Fig. 2. A B to be parallel to the horizon, the cylinder Cnbsp;will keep at reft upon any part of the planenbsp;where it is laid. If the plane be fo elevated.nbsp;Fig. 3. that its perpendicular height D is equal to halfnbsp;its length A B, the cylinder will roll down uponnbsp;the plane with a force equal to half its weight;nbsp;for it would require a power (afting in the di-redlion of A B) equal to half its weight, to keepnbsp;Fig. 4. it from rolling. If the plane A B ho elevated,nbsp;fo as to be perpendicular to the horizon, the cylinder C will defcend with its whole force of

gravity, becaufe the plane contributes nothing to its fupport or hindrance; and therefore, itnbsp;would require a power equal to its whole weightnbsp;to keep it from defcending.

Let the cylinder C be made to turn upon Fig. 5. flender pivots in the frame D, in which there isnbsp;a hook e, with a line G tied to it: let this line gonbsp;over the fixed pulley H, and have its other endnbsp;tied to the hook in the weight /. If the weightnbsp;of the body /, be to the weight of the cylindernbsp;C, added to that of its frame D, as the perpendicular height of the plane L M is to its lengthnbsp;ji B, the weight will juft fupport the cylindernbsp;upon the plane, and a fmall touch of a fingernbsp;will either caufe it to afcend or defcend withnbsp;equal cafe : then, if a little addition be made tonbsp;the weight /, it will defcend, and draw the cylinder up the plane. In the time that the cylindernbsp;moves from A to 5, it will rife through thenbsp;whole height of the plane ML ', and the weightnbsp;will defcend from H to K, through a fpace equalnbsp;to the whole length of the plane AB.

If the machine be made to move upon rollers or fridtion-wheels, and the cylinder be fupportednbsp;upon the plane C 5 by a line G parallel to thenbsp;plane, a power fomewhat lefs than that whichnbsp;drew the cylinder up the plane will draw thenbsp;plane under the cylinder, provided the pivots ofnbsp;the axes of the fridion-wheels be fmall, and thenbsp;wheels themfelves be pretty large. For, let thenbsp;machine ^ 5 C (equal in length and height tOp; gnbsp;ABM, Fig. 5.) move upon four wheels,nbsp;two whereof appear at D and E, and the thirdnbsp;under C, whilft the fourth is hid from fight bynbsp;the horizontal board a. Let the cylinder F benbsp;laid upon the lower end of the inclined planenbsp;C B, and the line G be extended from the framenbsp;of the cylinder, about fix feet parallel to thenbsp;Inbsp;nbsp;nbsp;nbsp;plane

�2 nbsp;nbsp;nbsp;Of the mechanical Powers.

plane C B; and, in that direction, fixed to a hook in the wall; which will fupport the cylinder, andnbsp;keep it from rolling off the plane. Let one endnbsp;of the line H be tied to a hook at C in the machine, and the other end to a weight K, fome-what lefs than that which drew the cylinder upnbsp;the plane before. If this line be put over thenbsp;fixed pulley I, the weight K will draw the machine along the horizontal plane L, and undernbsp;the cylinder F; and when the machine has beennbsp;drawn a little more than the whole lengthnbsp;the cylinder will be raifed to d, equal to the perpendicular height A B above the horizontal partnbsp;at A. The reafon why the machine muft benbsp;drawn further than the whole length C A is, be-caufe the weight F rifes perpendicular to C B.

To the inclined plane may be reduced all hatchets, chifels, and other edge-tools whichnbsp;are chamfered only on one fide.

equally inclined planes D E F and C E F, joined Fig. 8. together at their bafes e E F O : then D C is thenbsp;whole thicknefs of the wedge at its back ABCD,nbsp;where the power is applied : F F is the depth ornbsp;heighth of the wedge : D F the length of one ofnbsp;its fides, equal to C F the length of the othernbsp;fide ; and O F is its lliarp edge, which is enterednbsp;into the wood intended to be fplit by the forcenbsp;of a hammer or mallet ftriking perpendicularlynbsp;on its back. Thus, ABb is a wedge drivennbsp;Fig. 9. into the cleft CDE of the wood FG.

When the wood does not cleave at any dif-tance before the wedge, there will be an equilibrium between the power impelling the wedge downward, and the refittance of the wood adt-ing againft the two fides of the wedge when thenbsp;power is to the refiftance, as half the thicknefs

of the wedge at its back is to the length of either of its fides; becaufe the refiftance then adls perpendicular to the fides of the wedge. But, whennbsp;the refiftance on each fide afts parallel to thenbsp;back, the power that balances the refiftances onnbsp;both fides will be as the length of the wholenbsp;back of the wedge is to double its perpendicular height.

When the wood cleaves at any diftance before the wedge (as it generally does) the power impelling the wedge will not be to the refiftance ofnbsp;the wood, as the length of the back of the wedgenbsp;is to the length of both its fides ; but as halfnbsp;the length of the back is to the length of eithernbsp;fide of the cleft, eftimated from the top or adtingnbsp;part of the wedge. For, if we fuppofe the w'edgenbsp;to be lengthened down from h to the bottom ofnbsp;the cleft at �, the fame proportion will hold;nbsp;namely, that the power will be to the refiftance,nbsp;as half the length of the back of the wedge is tonbsp;the length of cither of its fides: or, whichnbsp;amounts to the fame thing, as the whole lengthnbsp;of the back is to the length of both the fides.

In order to prove what is here advanced concerning the wedge, let us fuppofe the wedge to be divided length wife into two equal parts �, andnbsp;then it will become two equal inclined planes �,nbsp;one of which, as a igt; c, may be made ufe of as a Fig. 7;nbsp;half wedge for feparating the moulding c d fromnbsp;the wainfcot AB. It is evident, that when thisnbsp;half wedge has been driven its whole length a cnbsp;between the wainfcot and moulding, its fide a cnbsp;will be at e d-, and the moulding will be fepa-rated to � ^ from the wainfcot. Now, from whatnbsp;has been already proved of the inclined plane, itnbsp;appears, that to have an equilibrium between thenbsp;power impelling the half wedge, and the refiftance of the moulding, the former muft be to the

letter, as 0 ^ to 0 r; that is, as the thicknefs of the back which receives the ftroke is to the lengthnbsp;of the fide againft which the moulding a�ts.nbsp;Therefore, fince the power upon the half wedgenbsp;is to the refiftance againft its fide, as the halfnbsp;back a b h x.0 the whole fide a c, it is plain, thatnbsp;the power upon which the whole wedge (wherenbsp;the whole back is double the half back) muft benbsp;to the refiftance againft both its fides, as thenbsp;thicknefs of the whole back is to the length ofnbsp;both the fides �, fuppofing the wedge at the bottom of the cleft; or as the thicknefs of the wholenbsp;back to the length of both fides of the cleft,nbsp;when the wood fplits at any diftance before thenbsp;wedge. For, when the wedge is driven quitenbsp;into the wood, and the wood fplits at ever fonbsp;fmall a diftance before its edge, the top of thenbsp;wedge then becomes the afbing part, becaufe thenbsp;wood does not touch it any where elfe. Andnbsp;fince the bottom of the cleft muft be confiderednbsp;as that part where the whole ftickage or refiftancenbsp;is accumulated, it is plain, from the nature ofnbsp;the lever, that the farther the power afts fromnbsp;the refiftance, the greater is the advantage.

Some writers have advanced, that the power of the wedge is to the refiftance to be overcome,nbsp;as the thicknefs of the back of the wedge is tonbsp;the length only of one of its fides; which feemsnbsp;very ftrange: for, if we fuppofe yf 5 to be anbsp;ftrong inflexible bar of wood or iron fixt into thenbsp;ground at C B, and D and E to be two blocks ofnbsp;marble lying on the ground on oppofite fides ofnbsp;the bar ; it is evident that the block D may benbsp;feparated from the bar to the diftance d, equal tonbsp;a b, by driving the inclined plane or half wedgenbsp;ab 0 down between them �, and the block E maynbsp;be feparated to an equal diftance on the othernbsp;fide, in like manner, by the half wedge c d 0.

But the power impelling each half wedge will be to the refiftance of the block againft its fide, asnbsp;the thicknefs of that half wedge is to its perpendicular height, becaufe the block will be drivennbsp;off perpendicular to the fide of the bar J iS.nbsp;Therefore the power to drive both the halfnbsp;wedges is to both the refiftances, as both thenbsp;half backs is to the perpendicular height of eachnbsp;half wedge. And if the bar be taken away, thenbsp;blocks put clofe together, and the two halfnbsp;wedges joined to make one; it will require asnbsp;much force to drive it down between the blocks,nbsp;as is equal to the fum of the feparate powersnbsp;adling upon the half wedges when the bar wasnbsp;between them.

To confirm this by an experimenr, let two pig. ii. cylinders, as and CD, be drawn towards onenbsp;another by lines running over fixed pulleys, andnbsp;a weight of 40 ounces hanging at the lines belonging to each cylinder : and let a wedge ofnbsp;40 ounces weight, having its back juft as thick asnbsp;either of its fides is long, be put betw'cen thenbsp;cylinders, which will then aft againft each fidenbsp;with a refiftance equal to 40 ounces, whilft itsnbsp;own weight endeavours to bring it down andnbsp;feparate them. And here, the power of thenbsp;wedge�s gravity impelling it downward, w'ill benbsp;to the refiftance of both the cylinders againft thenbsp;wedge, as the thicknefs of the wedge is to doublenbsp;its perpendicular height; for there will then benbsp;an equilibrium between the weight of the wedgenbsp;and the refiftance of the cylinders againft it, andnbsp;it will remain at any height between them ; requiring juft as much power to pufh it upwardnbsp;as to pull it downward.�If another wedge ofnbsp;equal weight and depth with this, and only halfnbsp;as thick, be put between the cylinders, it willnbsp;require twice as much weight to be hung at the

ends of the lines which draw them together, to keep the wedge from going down between them.nbsp;That is, a wedge of 40 ounces, whofe back isnbsp;only equal to half its perpendicular height, willnbsp;require 80 ounces to each cylinder, to keep it innbsp;an equilibrium between them: and twice 80 isnbsp;160, equal to four times 40. So that the powernbsp;will be always to the refiftance, as the thicknefsnbsp;of the back of the wedge is to twice its perpendicular height, when the cylinders move off innbsp;a line at right angles to that perpendicular.

The beft way, though perhaps not the neateft, that I know of, for making a wedge with itsnbsp;appurtenances for fuch experiments, is as fol-Fig. II. lows. Let KILM and LMNO be two flatnbsp;pieces of wood, each about fifteen inches longnbsp;and three or four in breadth, joined together bynbsp;a hinge at L M-, and let P be a graduated archnbsp;of brafs, on which the faid pieces of wood maynbsp;be opened to any angle not more than 60 degrees,nbsp;and then fixt at the given angle by means ofnbsp;the two fcr�ws a and h. Then, IK NO willnbsp;reprefent the back of the wedge, L M its fliarpnbsp;edge which enters the wood, and the outfides ofnbsp;the pieces KILM and LMNO the two fides ofnbsp;the wedge againft which the wood a6ts in cleaving. By means of the faid arch, the wedge maynbsp;be opened fo, as to adjuft the thicknefs of itsnbsp;back in any proportion to the length of either ofnbsp;its fides, but not to exceed that length: and anynbsp;weight as p may be hung to the wedge upon thenbsp;hook M, which weight, together with the weightnbsp;of the wedge itlelf, may be confidered as thenbsp;impelling power; wliich is all the fame in the experiment, whether it be laid upon the back ofnbsp;the wedge, to pulh it down, or hung to its edge tonbsp;pull it down.�Let AB and CD be two woodennbsp;cylinders, each about two inches thick, where

they touch the outfides of the wedge; and let rheir ends be made like two round flat plates, tbnbsp;keep the wedge from flipping off cdgewife fromnbsp;between them. Let a fmall cord with a loop onnbsp;one end of it, go over a pivot in the end of eachnbsp;cylinder, and the cords S and 7quot; belonging to thenbsp;cylinder yf 6 go over the fixt pulleysnbsp;nbsp;nbsp;nbsp;and JT, and

be faftcned at their other ends to the bar w x, on which any weight asZ may be hung at pleafure.nbsp;In like manner, let the cords ^and R belongingnbsp;to the cylinder CD go over the fixt pulleys F and Unbsp;to the bar vu,on which a weight^equal to Z maynbsp;be hung. Thefe weights, by drawing the cylinders towards one another, may be confidered asnbsp;the reflftance of the wood acting equally againftnbsp;oppofite Tides of the wedge-, the cylinders thern-felves being fufpended near, and parallel to eachnbsp;other, by their pivots in loops on the linesnbsp;which lines may be fixed to hooks innbsp;the ceiling of the room. The longer thefe linesnbsp;ste, the better; and they Ihould never be iefs thannbsp;four feet each. The farther alfo the pulleysnbsp;^fh and XfF are from the cylinders, the truernbsp;will the experiments be : and they may turnnbsp;upon pins fixed into the wall.

In this machine, the weights Tand Z, and the weight p, may be varied at pleafure, fo as to benbsp;adjufted in proportion of double the wedge�s perpendicular height to the thicknefs of its back ;nbsp;and when they are fo adjufted, the wedge will benbsp;in eq^uilibrio with the reflftance of the cylinders.

The wedge is a very great mechanical power, fince not only wood but even rocks can be fpUcnbsp;by it; which would be impoflible to eff��t by thenbsp;lever, wheel and axle, or pulley; for the forcenbsp;of the blow, or ftroke, fliakes the cohering parts,nbsp;and thereby makes them feparate the more eafily,nbsp;Fnbsp;nbsp;nbsp;nbsp;6. The

6. The fixth and laft mechanieal power is thd fcrew; which cannot properly be called a fimplenbsp;machine, becaufe it is never ufed without thenbsp;application of a lever or winch to aflift in turning it: and then it becomes a compound enginenbsp;of a very great force either in preffing the partsnbsp;of bodies clofer together, or in raifing greatnbsp;weights. It may be conceived to be made bynbsp;cutting a piece of paper(Fig. 12.) intonbsp;the form of an inclined plane or half wedge, andnbsp;then wrapping it round a cylinder AB (Fig. 13).nbsp;And here it is evident, that the winch Enbsp;muft turn the cylinder once round before thenbsp;weight of refiftance D can be moved from onenbsp;fpiral winding to another, as from i to f: therefore, as much as the circumference of a circlenbsp;defcribed by the handle of the winch is greaternbsp;than the interval or diftance between the fpirals,fonbsp;much is the force of the fcrew. Thus, fuppofingnbsp;the diftance between the fpirals to be half an inch,nbsp;and the length of the winch to be twelve inches-,nbsp;the circle defcribed by the handle of the winchnbsp;where the power ads will be 76 inches nearly, ornbsp;about 152 half inches, and confequently 152 timesnbsp;as great as the diftance between the fpirals: andnbsp;therefore a power at the handle, whofe intenfitynbsp;is equal to no more than a Angle pound, will balance 152 pounds ading againft the fcrew; andnbsp;as much additional forxe, as is fufficient to overcome the fridion, will raifethe 152 pounds; andnbsp;the velocity of the power will be to the velocitynbsp;of the weight, as 152 to 1. Hence it appears,nbsp;that the longer the winch is, and the nearernbsp;the fpirals are to one another, fo much thenbsp;greater is the force of the fcrew.

A machine for flnewing the force or power of the fcrew may be contrived in the following

irianner. Let the wheel C have a fcrew a b on pig. i,j.. its axis, working in the teeth of the wheel X),nbsp;which fuppofe to be 48 in number. It is plain,nbsp;that for every time the wheel C and fcrew a b arenbsp;turned round by the winch A., the wheel D willnbsp;be moved one tooth by the fcrew j and therefore, in 48 revolutions of the winch, the wheelnbsp;D will be turned once round. Then, if the .cirrnbsp;cumference of a circle defcribed by the handle ofnbsp;the winch A be equal to the circumference of anbsp;groove e round the wheel D, the velocity of thenbsp;handle will be 48 times as great as the velocitynbsp;bf any given point in the groove. Confequentlyj

groove e, and has a weight �f 48 pounds hung to it below the pedeftal EF, a power equal tonbsp;one pound at the handle will balance and fupportnbsp;the w'eight.�To prove this by experiment, letnbsp;the circumferences of the grooves of the t^heelsnbsp;C and D be equal to one another; and then ifnbsp;a Weight H of one pound be fufpended by a linenbsp;going round the groove of the wheel C, it willnbsp;balance a weight of 48 pounds hanging by thenbsp;line G �, and a fmall addition to the weight Hnbsp;will caufe it to defcend, and fo raife up the othernbsp;weight.

If the line G, inilead of going round the groove e of the wheel D, goes round its axle /jnbsp;the power of the machine will be as much in-creafed, as the circumference of the groove enbsp;exceeds the circumference of the axle : which,nbsp;fuppofing it to be fix times, then one pound atnbsp;ZXwill balance 6 times 48, or 288 pounds hungnbsp;to the line on the axle; and hence the power ornbsp;advantage of this machine will be as 288 to i.nbsp;That is to fay, a man, v;ho by his naturalnbsp;ftrength could lift an hundred weight, will benbsp;F 2nbsp;nbsp;nbsp;nbsp;able

But the following engine is ftill more powerful, oni alccount of its having the addition of four pulleys: and in it we may look upon allnbsp;the mechanical powers as combined together,nbsp;Plate VII. oven if we take in the balarice. For, as the axisnbsp;Fig. 1. D of the bar AB is in its middle at C, it is plainnbsp;that if equal weights are fufpended upon any twonbsp;A combi- pins equi-diftant from the axis C, they will coun-nation of tgrpoife each other.�It becomes a lever bynbsp;hanging a fmall weight P upon the pin n, and anbsp;weight as much heavier upon either of the pinsnbsp;hf c, d, e, ox f as is in proportion to the pins being fo much nearer the axis. The wheel andnbsp;axle FG is evident; fo is the fcrew E whichnbsp;takes in the inclined plane, and with it the halfnbsp;wedge. Part of a cord goes round the axle, thenbsp;reft under the tower pulleys K, over the uppernbsp;pulleys L, n, and then it is tied to a hook at mnbsp;in the lower of moveable block, on which thenbsp;weight IV hangs.

In this machine, if the wheel F has 30 teeth, it will be turned once round in thirty revolutions of the bar AB, which is fixt on thenbsp;axis D of the fcrew E: if the length of the barnbsp;is equal to twice the diameter of the wheel, thenbsp;pins a and n at the ends of the bar will move 60nbsp;times as faft as the teeth of the wheel do ; andnbsp;confequently, one ounce at P will balance 60nbsp;ounces hung upon a tooth at q in the horizontalnbsp;diameter of the wheel. Then, if the diameter ofnbsp;the wheel F is ten times as great as the diameternbsp;of the axle G, the wheel will have 10 times thenbsp;velocity of the axle ; and therefore one ounce Pnbsp;at the end of the lever AC will balance 10 rimesnbsp;60 or 600 ounces hung to the rope fl which goes

round

round the axle. Laftly, if four pulleys be added, they will make the velocity of the lower blocknbsp;and weight W, four times lefs than the velocity of the axle : and this being the laft powernbsp;in the machine, which is four times as great asnbsp;that gained by the axle, it makes the wholenbsp;power of the machine 4 times 600, or 2400.

So that a man who could lift one hundred weight in his arms by his natural ftrength, would benbsp;able to raife 2400 times as much by this engine.�But it is here as in all other mechanicalnbsp;cafes �, for the time loft is always as much as thenbsp;power gained, becaufe the velocity with whichnbsp;the power moves will ever exceed the velocitynbsp;with which the weight rifes, as much as the in-tenfity of the weight exceeds the intenfity of thenbsp;power.

The fridlion of the fcrew itfelf is very confi-derable v and there are few compound engines, but what, upon account of the fridlion of nbsp;nbsp;nbsp;^

the parts againft one another, will require a third part more of power to work them when loaded,nbsp;than what is fufEcient to conftitute a balancenbsp;between the weight and the power.

AS thefe engines are fo univerfally ufeful, it would be needlefs to make any apology for deferibing them.

In a common breafi mill, where the fall of Plate VII, water may be about ten feet, A 4 is the great Fig.nbsp;wheel, which is generally about in or 18 feet in ,

diameter, reckoned from the outermoft edge of any float board at a to that of its oppofite float atnbsp;k. To this wheel the water is conveyed throughnbsp;a channel, and by falling upon the wheel, turnsnbsp;it round.

On the axis B B oi this wheel, and within the mill houfe, is a wheel T, about 8 or 9 feet diameter, haying 61 cogs, which turn a trundle �nbsp;containing ten upright flaves or rounds ; andnbsp;when thele are the number of cogs and rounds,nbsp;the trundle will make 6^�-g- revolutions for onenbsp;revolution of the wheel.

The trundle is fixt upon a ftrong iron axis called the fpindle, the lower'end of which turns innbsp;a brafs foot, fixt at �, in the horizontal beam STnbsp;called the bridge-tree; and the upper part of thenbsp;fpindle turns in a wooden bufh fixt into the nethernbsp;millftone which lies upon beams in the floor TT.nbsp;The top part of the fpindle above the bufli isnbsp;fquare,and goes into a fquare hole in a flrong ironnbsp;crofs ah cd., (fee Fig. 3.) called the rynd ; undernbsp;which, and clofe to the bufh, is a round piece ofnbsp;thick leather upon the fpindle, which it turnsnbsp;round at the fame time as it does the rynd.

The rynd is let into grooves in the under fur-face of the running millftone G (Fig. 2.) and fo turns it round in the fame time that the trundle Enbsp;is turned round by the cog-wheel T. This mill-llone has a large hole quite through its middle,nbsp;called the eye of the ftone, through which thenbsp;middle part of the rynd and upper end of thenbsp;fpindle may be feen ; whilft the four ends of thenbsp;rynd lie hid below the ftone in their grooves.

The end T of the bridge-tree T S (which fup-ports the upper millftone G upon the fpindle) is fixed into a hole in the wall; and the end 5 is letnbsp;into a beam called the brayer, whofe end R.

remains

Of Water-Mills.

remains fixt in a mortife: and its other end ^ hangs by a ftrong iron rod P which goes throughnbsp;the floor TT, and has a fcrew-nut on its top atnbsp;O; by the turning of which nut, the end ^ofnbsp;the brayer is raifed or depreffed at plcafure; andnbsp;confequently the bridge-tree TS and upper mill-ftone. By this means, the upper millftone maynbsp;be fet as clofe to the under one, or raifed as highnbsp;from ir, as the miller pleafes, The nearer thenbsp;millftones are to one another, the finer they grindnbsp;the corn, and the more remote from one another,nbsp;the coarfer.

The upper millftone G is inclofed in a round box which does not touch it any where; andnbsp;is about an inch diftant from its edge all around.nbsp;On the top of this box ftands a frame for holding the hopper k k, to which is hung the (hoe Inbsp;by two lines fattened to the hind-part of it, fixednbsp;upon hooks in the hopper, and by one end ofnbsp;the crook-ftring K fattened to the fore-part of itnbsp;at i-, the other end being twitted round the pin L.nbsp;As the pin is turned one way, the ttring drawsnbsp;up the (hoe clofer to the hopper, and lb leflTensnbsp;the aperture between them ; and as the pin isnbsp;turned the other, way, it lets down the (hoe, andnbsp;enlarges the aperture.

If the (hoe be drawn up quite to the hopper, no corn can fall from the hopper into the mill;nbsp;if it be let a little down, fome will fall: and thenbsp;quantity will be more or lefs, according as thenbsp;Ihoe is more or lefs let down. For the hopper isnbsp;open at bottom, and there is a hole in the bottomnbsp;of the Ihoe, not direftly under the bottom of thenbsp;hopper, but forwarder towards the end i, overnbsp;the middle of the eye of the millftone.

There is afquare hole in the top of the fpindle, p-in which is put the feeder e: this feeder (as the F 4nbsp;nbsp;nbsp;nbsp;fpindle

fpindle turns round) jogs the (hoe three times in each revolution, and fo caufes the corn to runnbsp;conidantly down from the hopper through the (hoe,nbsp;into the eye of the milldone, where it falls uponnbsp;the top of the rynd, and is, by the motion of thenbsp;rynd, and the leather under it, thrown below thenbsp;upper (lone, and ground between it and thenbsp;lower one. The violent motion of the donenbsp;creates a centrifugal force in the corn goingnbsp;round with it, by which means it gets farther andnbsp;farther from the center, as in a fpiral, in everynbsp;revolution, until it be thrown quite out; and,nbsp;being then ground, it falls through a fpout iW,nbsp;called the mill-eye, into the trough N.

When the mill is fed too fad, the corn bears up the done, and is ground too coarfe; and be-rnbsp;fides, it clogs the mill fo as to make it go toonbsp;(low. When the mill is too (lowly fed, it goesnbsp;too fad, and the (tones by their attrition are aptnbsp;to drike fire againd one another. Both whichnbsp;inconveniences are avoided by turning the pin Lnbsp;backwards or forwards, which draws up or letsnbsp;down the (hoe; and fo regulates the feeding asnbsp;the miller fees convenient.

The heavier the running milldone is, and the greater the quantity of water that falls upon thenbsp;wheel, fo much the fader will the mill bear to benbsp;fed j and confequently fo much the more it willnbsp;grind. And on the contrary, the lighter thenbsp;done, and the lefs the quantity of water, fo muchnbsp;(lower mud the feeding be. But when the donenbsp;is confiderably wore, and become light, the millnbsp;mud be fed (lowly at any rate; otherwife thenbsp;flone will be too much born up by the cornnbsp;under it, which will make the meal coarfe.

1 he quantity of power required to turn n licavy milldone is but very little more than what

is fufRcient to turn a light one: for as it is fup-ported upon the fpindle by the bridge-tree S T, and the end of the fpindle that turns in the brafsnbsp;foot therein being but fmall, the odds arifingnbsp;from the weight is but very inconfiderable in itsnbsp;adtion againft the power or force of the water.nbsp;And befides, a heavy ftone has the fame advantage as a heavy fly; namely, that it regulatesnbsp;the motion much better than a light one.

In order to cut and grind the corn, both the upper and under millftones have channels ornbsp;furrows cut into them, proceeding obliquely fromnbsp;the center towards the circumference. And thefenbsp;furrows are cut perpendicularly on one fide andnbsp;obliquely on the other into the ftone, whichnbsp;gives each furrow a fharp edge, and in the twonbsp;ftones they come, as it were, againft one another like the edges of a pair of fcilTars: and fonbsp;cut the corn, to make it grind the eafier when itnbsp;falls upon the places between the furrows.nbsp;Thefe are cut the fame way in both ftones whennbsp;they lie upon their backs, which makes them runnbsp;crols ways to each other when the upper ftone isnbsp;inverted by turning its furrowed furface towardsnbsp;that of the lower. For, if the furrows of bothnbsp;ftones lay the fame way, a great deal of the cornnbsp;would be driven onward in the lower furrows,nbsp;and fo come out from between the ftones without being either cut or bruifed.

When the furrows become blunt and fliallow by wearing, the running ftone muft be takennbsp;up, and both ftones new drett with a chifel andnbsp;hammer. And every time the ftone is taken up,nbsp;therp muft be fome tallow put round the fpindienbsp;upon the bulb, which will foon be melted bynbsp;the heat the fpindle acquires from its turningnbsp;and rubbing againft the bulh, and fo will get in

The bulh muft embrace the fpindle quite clofe, to prevent any fhake in the motion, whichnbsp;would make fome parts of the Hones grate andnbsp;fire againft each other; whilft other parts ofnbsp;them would be too far afunder, and by thatnbsp;means fpoil the meal in grinding.

Whenever the fpindle wears the bulh fo as to begin to lhake in t, tiie ftone muft be taken up,nbsp;and a chifel drove into feveral parts of the bufh inbsp;and when it is taken out, wooden wedges muft benbsp;driven into the holes; by which means the bufhnbsp;will be made to embrace the fpindle clofe allnbsp;around it again. In doing this, great care muftnbsp;be taken to drive equal wedges into the bufh onnbsp;oppofite Tides of the fpindle; otherv/ife it willnbsp;be thrown out of the perpendicular, and fo hinder the upper ftone from being fet parallel to thenbsp;under one, which is abfolutely neceffary for making good work. When any accident of thisnbsp;kind happens, the perpendicular pofition cf thenbsp;fpindle muft be reftored by adjufting the bridge-tree 5 T by proper wedges put between it andnbsp;the brayer ^R.

It often happens, that the rynd is a little wrenched in laying down,the upper ftone uponnbsp;it; or is made to link a little lower upon onenbsp;fide of the fpindle than on the other; and thisnbsp;will caufe one edge of the upper ftone to dragnbsp;all around upon the other, whilft the oppofitenbsp;edge will not touch. But this is eafily fet tonbsp;rights, by raifing the ftone a little with a lever,nbsp;and putting bits of paper, cards or thin chips,nbsp;between the rynd and the ftone.

The diameter of the upper ftone is generally about fix feet, the lower ftone about an inch

more : and the upper ftone when new contains about 224- cube feet, which weighs fomewhatnbsp;more than 19000 povinds. A ftone of this diameter ought never to go more than 60 timesnbsp;round in a minute; for if it turns fafter, it willnbsp;heat the meal.

The grinding furface of the under ftone is a little convex from the edge to the center, andnbsp;that of the upper ftone a little more concave: lbnbsp;that they are fartheft from one another in thenbsp;middle, and come gradually nearer towards thenbsp;edges. By this means, the corn at its firft entrance between the ftones is only bruifed; but asnbsp;it goes farther on towards the circumference ornbsp;edge, it is cut fmaller and fmaller ; and at laftnbsp;finely ground juft before it comes out from between them.

The water-wheel muft not be too large, for if it be, its motion will be too flow; nor toonbsp;little, for then it will want power. And for anbsp;mill to be in perfedlion, the floats of the wheelnbsp;ought to move with a third part of the velocitynbsp;of the water, and the ftone to turn round once innbsp;a fecond of time.

In order to conftrud a mill in this perfedt manner, obferve the following rules :

1. nbsp;nbsp;nbsp;Meafure the perpendicular height of thenbsp;fall of water, in feet, above that part of thenbsp;wheel on which the water begins to aft ,; andnbsp;call that, the height of the fall.

2. nbsp;nbsp;nbsp;Multiply this conftant number 64.2882 bynbsp;the height of the fall in feet, and the fquare rootnbsp;of the produdl fliall be the velocity of the waternbsp;at the bottom of the fall, or the number of feetnbsp;that the water there movesfecond.

3. nbsp;nbsp;nbsp;Divide the velocity of the water by 3, andnbsp;the quotient ftiall be the velocity of the float-boards of the wheel; or the number of feet they

I nbsp;nbsp;nbsp;muft

muft each go through in a fecond, when the water adts upon them To, as to have the greateftnbsp;power to turn the mill.

4. nbsp;nbsp;nbsp;Divide the circumference of the wheel innbsp;feet by the velocity of its floats in feet per fecond, and the quotient fhall be the number ofnbsp;feconds in which the wheel turns round.

5. nbsp;nbsp;nbsp;By this laft number of feconds divide 60 ;nbsp;and the quotient fhall be the number of turnsnbsp;of the wheel in a minute.

6. nbsp;nbsp;nbsp;Divide 60 (the number of revolutions thenbsp;millftof^� ought to have in a minute) by the num^nbsp;ber of turns of the wheel in a minute, and thenbsp;quotient fhall be the number of turns the mill-ftone ought to have for one turn of the wheel.

7. nbsp;nbsp;nbsp;Then, as the number of turns of the wheelnbsp;in a minute is to the number of turns of thenbsp;millftone in a minyte, fo muft the number ofnbsp;ftaves in the trundle be to the number of cogsnbsp;in the wheel, in the neareft whole numbers thatnbsp;can be found.

By thefe rules I have calculated the following table to a water wheel 18 feet diameter, whichnbsp;I apprehend may be a good fize in general.

To conftrudl: a m�l by this table, find the height of the fall of water in the firft column, andnbsp;againft that height, in the fixth column, you havenbsp;the number of cogs in the wheel,^nd ftaves in thenbsp;trundle, for caufing the millftone to make aboutnbsp;60 revolutions in a minute, as near as pofTible,nbsp;when the wheel goes with a third part of the velocity of the water. And it appears by the 7thnbsp;column, that the number of cogs in the wheel, andnbsp;ftaves in the trundle, are fo near the truth for thenbsp;required purpofe, that the leaft number of revolutions of the millftone in a minute is between 59nbsp;and 60, and the greaeft number never amountsnbsp;to 6i.

The

The MILL-WRIGHT�s TABLE.

Such

Such a mill as this, with a fall of water aboui 74- feet, will require about 32 hogfheads everynbsp;minute to turn the wheel with a third part of thenbsp;velocity with which the water falls and tonbsp;overcome the refiftance arifing from the fricflionnbsp;of the geers and attrition of the ftones in grinding the corn.

The greater fall the water has^ the lefs quantity of it will ferve to turn the mill. The water is kept up in the mill-dam, and let out by 3nbsp;fluice called the penftock, when the mill is to go.nbsp;When the penftock is drawn up by means of anbsp;lever, it opens a paflage through which the waternbsp;flows to the wheel; and when the mill is to benbsp;ftopt, the penftock is let down, which flops thenbsp;water from falling upon the wheel.

A lefs quantity of water will turn an overlhot-mill (where the wheel has buckets inftead of float-boards j than a breaft-mill where the fall ofnbsp;the water feldom exceeds half the height Jb oinbsp;the wheel. So that, where there is but a fmallnbsp;quantity of water, and a fall great enough for thenbsp;wheel to lie under it, the bucket (or overlhot)nbsp;wheel is always ufed. But where there is a largenbsp;body of water, with a little fall, the breaftor float-board wheel muft take place. Where the waternbsp;runs only upon a little declivity, it can aft butnbsp;flowly upon the under part of the wheel at b\ innbsp;which cafe, the motion of the wheel will be verynbsp;flow: and therefore, the floats ought to be verynbsp;long, though not high, that a large body of waternbsp;may aft upon them; fo that what is wanting innbsp;velocity may be made up in power; and then thenbsp;cog-wheel may have a greater number of cogs innbsp;proportion to the rounds in the trundle, in ordernbsp;to give themillftoneafufficientdegreeof velocity.nbsp;They who have read what is faid in the firft

falling freely by the power of gravity acting conftantly and uniformly upon them, may perhaps aflc, Why fliould the motion of the wheel be-equable, and not accelerated,feeingthewater aflsnbsp;conftantly and uniformly upon it ? The plainnbsp;anfwer is. That the velocity of the wheel cannbsp;never be fo great as the velocity of the waternbsp;that turns it �, for, if it (liould become fo great,nbsp;the power of the water would be quite loft uponnbsp;the wheel, and then there would he no propernbsp;force ta overcome the friftion of the geers andnbsp;attrition of the ftones. Therefore, the velocitynbsp;�with which the wheel begins to move, will in-creafe no longer than till its momentum or forcenbsp;is balanced by the refiftance of the workingnbsp;parts of the mill �, and then the wheel will gonbsp;on with an equable motion.

[If the cog-wheel D be made about i8 inches A hand-diameter, with 30 cogs, the trundle as fmall in proportion, with loftaves, and the millftones benbsp;each about two feet in diameter, and the wholenbsp;work be put into a ftrong frame of wood, as rc-prefented in the figure, the engine will be a hand-mill for grinding corn or malt in private families. And then, it may be turned by a winchnbsp;infteadof the wheel A A: the millftone makingnbsp;three revolutions for every one of the winch.

Tf a heavy fly be put upon the axle 5, near the winch, it will help to regulate the motion.]

If the cogs of the, wheel and rounds of the trundle could be put in as exactly as the teethnbsp;are cut in the wheels and pinions of a clock,nbsp;then the trundle might divide the wheel exadtly;nbsp;that is to fay, the trundle might make a givennbsp;number of revolutions for one of the wheel,nbsp;without a fraftion. But as any exaft number isnbsp;not neceflfary in mill-work, and the cogs andnbsp;rounds cannot be fet in fo truly as to make all

the intervals between them equal; a Ikilful mill-wright will always give the wheel what henbsp;calls a hunting cog; that is, one more than whatnbsp;will anlwer to an exad divifion of the wheel bynbsp;the trundle. And then, as every cog comes tonbsp;the trundle, it will take the next ftaff or roundinbsp;behind the one which it took in the former revolution : and by that means, will wear all thenbsp;parts of the cogs and rounds which work uponnbsp;one another equally, and to equal diftances fromnbsp;one another in a little time; and fo make a truenbsp;uniform motion throughout the whole work.nbsp;Thus, in the above water-mill, the trundle hasnbsp;10 ftaves, and the wheel 61 cogs.

Sometimes, where there is a fufficient quantity of water, the cog-wheel A A turns a large trundle B 5, on whofe axis C is fixed the hori-2ontal wheel D, with cogs all around its edge,nbsp;turning two trundles E and F at the fame time jnbsp;whofe axes or fpindles G and U turn two mill-ftones I and K, upon the fixed ftones L and M.nbsp;And when there is not work for them both,nbsp;either may be made to lie quiet, by taking outnbsp;one of the ftaves of its trundle, and turning thenbsp;vacant place towards the cog wheel D. Andnbsp;there may be a wheel fixt on the upper end ofnbsp;the great upright axle C for turning a couple ofnbsp;boulting-mills; and other work for drawingnbsp;up the facks, fanning and cleaning the corn,nbsp;fharpening of tools, amp;c.

If, inftead of the cog-wheel A A and trundle B B, horizontal levers be fixed into the axle C,nbsp;below the wheel D then, horfes may be put tonbsp;thefe levers for turning the mill: which is oftennbsp;done where water cannot be had for that pur-pofe.

The working parts of a wind-mill differ very little from thole of a water-mill j only'the former

Of Wind-Mills.

IS turned by the a6tion of the wind upon four fails, every one of which ought (as is generallynbsp;believed) to make an angle of 544 degrees withnbsp;a plane perpendicular to the axis on which thenbsp;arms are fixt for carrying them. It being de-monftrable, that when the fails are fet to luch annbsp;angle, and the axis turned end-ways toward thenbsp;wind, the wind has the greateft power upon thenbsp;fails. But this angle anfwers only to the cafe ofnbsp;a vane or fail juft beginning to move¹ : for,nbsp;when the vane has a certain degree of motion, itnbsp;yields to the wind �, and then that angle mull benbsp;increafed to give the wind its full effed.

Again, the increafe of this angle Ihould be different, according to the difl'erent velocitiesnbsp;from the axis to the extremity of the vane. Atnbsp;the axis it fhould be 54^ degrees, and thencenbsp;continually decreafe, giving the vane a twift, andnbsp;fo caufing all the ribs of the vane to lie in different planes.

Laftly, Thefe ribs ought to decreafe in length from the axis to the extremity, giving the vane anbsp;curvilineal form,; fo that no part of the force ofnbsp;anyone rib be fpent upon the reft, but all movenbsp;on independent of each other. All this is required to give the fails of a wind-mill their truenbsp;form : and we fee both the twift and the diminution of the ribs exemplified in the wings of birds.

It is ahnoft; incredible to think with what velocity the tips of the fails move when adednbsp;upon by a moderate gale of wind. I have fe-veral times counted the number of revolutionsnbsp;made by the fails in ten or fifteen minutes andnbsp;from the length of the arms from tip to tip,nbsp;have computed, that if a hoop of that diameternbsp;was to run upon the ground with the fame velo-

city that it would move if put upon the fail-arms, it would go upwards of 30 miles in an hour.

As the ends of the fails neareft the axis cannot move tvith the fame velocity that the tips or fartheil ends do, although the wind afts equallynbsp;ftrong upon them; perhaps a better pofitionnbsp;than that of fhretching them along the armsnbsp;dire�lly from the center of motion, might be tonbsp;have them fet perpendicularly acrofs the farthernbsp;ends of the arms, and there adjuftcd lengthwifenbsp;to the proper angle. For, in that cafe, bothnbsp;ends of the fails would move with the fame velocity ; and being farther from the center of motion, they would have fo much the m.ore power :nbsp;and then, there would be no occafion for havingnbsp;them fo large as they are generally made ; whichnbsp;would render them lighter, and confequently,nbsp;there would be fo much the lefs fridtion on thenbsp;thick neck of the axle where it turns in the wall.

A crane is an engine by which great weights are raifed to certain heights, or let down to certain depths. It confifts of wheels, axles, pul-PhteVLI. |gys^ ropes, and a gib or gibbet. When thenbsp;rope H is hooked to the weight K, a man turnsnbsp;the winch y/, on the axis whereof is the trundlenbsp;J3, which turns the wheel C, on whofe axis D isnbsp;the trundle E, which turns the wheel F with itsnbsp;upright axis G, on which the great rope HHnbsp;winds as the wheel turns; and going over anbsp;pulley I at the end of the arm d of the gib cede,nbsp;it draws up the heavy weight K which, beingnbsp;raifed to a proper height, as from a fhip to thenbsp;quay, is then brought over the quay by pullingnbsp;the wheel Z round by the handles z, z, whichnbsp;turns the gib by means of the half wheel � fixtnbsp;on the gib-poft c c, and the ftrong pinion a fixtnbsp;on the axis of the wheel Z. This wheel givesnbsp;the man that turns it an abfolute command overnbsp;3nbsp;nbsp;nbsp;nbsp;the

the gib, fo as to prevent it from talcing any unlucky fwing, fuch as often happens when it is only guided by a rope tied to its arm d; andnbsp;people are frequently hurt, fometlmes killed,nbsp;by fuch accidents.

The great rope goes between two upright rollers i and which turn upon gudgeons innbsp;the fixed beams � and g; and as the gib is turned towards either fide, the rope bends upon thenbsp;roller next that fide. Were it not for thefenbsp;rollers, the gib would be quite unmanageable;nbsp;for the moment it were turned ever fo little towards any fide, the weight K would begin tonbsp;defcend, becaufe the rope would be Ihortenednbsp;between the pulley � and axis G ; and fo the gibnbsp;would be pulled violently to that fide, and eithernbsp;be broke to pieces, or break every thing thatnbsp;came in its way. Thefe rollers mull; be placednbsp;fo, that the Tides of them, round which the ropenbsp;bends, may keep the middle of the bended partnbsp;diredly even with the center of the hole innbsp;which the upper gudgeon of the gib turns innbsp;the beam/. The truer thefe rollers are placed,nbsp;the eafier the gib is managed, and the lefs apt tonbsp;fwing either way by the force of the weight K.

A ratchet-wheel ^ is fixt upon the axis D, near the trundle E; and into this wheel the catchnbsp;or click R falls. This hinders the machinerynbsp;frorn runing back by the weight of the burdennbsp;Ki if the man who raifes it ftiould happen to benbsp;carelefs, and fo leave off working at the winchnbsp;A fooner than he ought to do.

When the weight K is raifed to its proper height from the ftiip, and brought over thenbsp;quay by turning the gib about, it is let downnbsp;gently upon the quay, or into a cart (landingnbsp;thereon, in the following manner ; A man takesnbsp;hold of the rope 11 ('which goes over the pulleynbsp;G 2nbsp;nbsp;nbsp;nbsp;v, and

and is tied to a hook at S in the catch R) arici fo difengages the catch from the ratchet-wheelnbsp;and then, the man at the winch A turns knbsp;backward, and lets down the weight K. But tfnbsp;the weight pulls too hard againft this man, another lays hold of the ftick V, and by pullingnbsp;k downward, draws the gripe U dole to thenbsp;wheel T, which, by rubbing hard againft thenbsp;gripe, hinders the too quick defcent of thenbsp;weight �, and not only fo, but even ftops it atnbsp;any time, if required. By this means, heavynbsp;goods may be either raifed or let down at plea-fure without any danger of hurting the mennbsp;who work the engine.

When part of the goods are craned up, and the rope is to be let down for more, the catch Rnbsp;is firft difengaged from the ratchet-wheel ^ bynbsp;pulling the cord t \ then the handle q is turnednbsp;half round backward, which, by the crank n nnbsp;in the piece o, pulls down the frame h betweennbsp;the suides m and m (in which it Hides in anbsp;groove) and fo difengages the trundle B fromnbsp;the wheel C: and then, the heavy hook (3 atnbsp;the end of the rope H defcends by its ownnbsp;weighquot;, and turns back the great wheel F withnbsp;its trundle E, and the wheel Cand this laftnbsp;wheel a6ts like a fly againft the wheel F andnbsp;hook |3; and fo hinders it from going down toonbsp;quick j whilft the weight X keeps up the gripenbsp;V from rubbing againft the wheel T, by meansnbsp;of a cord going from the weight, over the pulleynbsp;w to the hook F/ in the gripe; fo that the gripenbsp;never touches the wheel, unlefs it be pullednbsp;down by the handle V,

When the crane is to. be fet at work again, for drawing up another burden, the handle q isnbsp;turned half round forwards; which, by thenbsp;crank �;/, raifes up the frame h, and caufes thenbsp;8nbsp;nbsp;nbsp;nbsp;trundlo-

trundle B to lay hold of the wheel C; and then, by turning the winch A, the burden of goodsnbsp;if is drawn up as before.

The crank n n turns pretty ftiif in the inortife near e, and flops againft the farther end of itnbsp;when it has got juft a little beyond the perpendicular-, fo that it can never come back of itrnbsp;felf; and therefore, the trundle B can nevernbsp;come away from the wheel C, until the handlenbsp;be turned half round, backwards.

The great rope runs upon rollers in the lever L M, which keeps it from bending between thenbsp;axle at G and the pulley I. This lever turns uponnbsp;the axis N by means of the v/eight O, which isnbsp;juft fufficient to keep its end L up to the rope ; fonbsp;that, as the great axle turns, and the rope coilsnbsp;round it, the lever rifes with the rope, and prevents the codings from going over one another.nbsp;The power of this crane may beeftimated thus.:nbsp;fuppofe the trundle B to have 13 ftaves or rounds,nbsp;and thewheel C to have 78 fpurcogs j the trundlenbsp;E to have 14 ftaves, and the wheel F 56 cogs.nbsp;Then, by multiplying the ftaves of the trundles,nbsp;13 and 14, into one another, their product will benbsp;182 j and by multiplying the cogs of the wheels,nbsp;78 and 56, into one another, their product will benbsp;4368, and dividing 4368 by 182, the quotientnbsp;will be 24 which fbews that the winch makesnbsp;24 turns for one turn of the wheel F and itsnbsp;axle G on which the great rope or chain H IHnbsp;winds, So that, if the length or radius of thenbsp;winch A were only equal to half the diameternbsp;of the great axle G, added to half the thicknefsnbsp;of the rope //, the power of the crane would benbsp;as 24 to 1 ; but the radius of the winch beingnbsp;double the above length, it doubles the faklnbsp;power, and fo makes it as 48 to i : in whichnbsp;cafe, a man may raile 48 times as much weight

3 nbsp;nbsp;nbsp;by

by this engine as he could do by his natural ftrength without it, making proper allowancenbsp;for the fridlion of the working parts.�Twonbsp;men may work at once, by heaving anothernbsp;winch on the oppofite end of the axis of thenbsp;trundle under B ; and this will make the powernbsp;double.

If this power be thought greater than what may be generally wanted, the wheels may benbsp;made with fewer cogs in proportion to the ftavesnbsp;in the trundles; and fo the power may be ofnbsp;whatever degree is judged to be requifite. Butnbsp;if the weight be fo great as will require yet morenbsp;power to raife it (fuppofe a double quantity)nbsp;then the rope H may be put under a moveablenbsp;pulley, as and the end of it tied to a hook innbsp;the gib at s; which will give a double power tonbsp;the machine, and fo raife a double weightnbsp;hooked to the block of the moveable pulley.

When only fmall burthens are to be raifed, this may be quickly done by men puflting thenbsp;axle G round by the long fpokesy,jy,y,_y ; having firft difengaged the trundle B from the wheelnbsp;C: and then, this wheel will only a�l as a flynbsp;upon the wheel F; and the catch R will preventnbsp;its running back, if the men Ihould inadvert-ently leave off pulhing before the burthen benbsp;unhooked from (3.

Laftly, When very heavy burthens are to be raifed, which might endanger the breaking ofnbsp;the cogs in the wheel F; their force againft thefenbsp;cogs may be much abated by men pufiiing roundnbsp;the long fpokes jy, _y, j, jy, whilft the man at /fnbsp;turns the winch.

I have only Ihewn the working parts of this crane, without the whole of the beams whichnbsp;fupport them; knowing that thefe are eafily

fuppofed, and that if they had been drawn, they would have hid a great deal of thenbsp;working parts from fight, and alfo confufed thenbsp;figure.

Another very good crane is made in the fol- Another lowing manner. A A is a. great wheel turnednbsp;by men walking within it at H. On the part 2-C, of its axle B C, the great rope D is wound asnbsp;the wheel turns ; and this rope draws up goodsnbsp;in the fame way as the rope H H does in thenbsp;above-mentioned crane, the gib-work here being fuppofed to be of the fame fort. But thefenbsp;cranes are very dangerous to the men in thenbsp;wheel j for, if any of the men fhould chance tonbsp;fall, the burthen will make the wheel run backnbsp;and throw them all about within it ; whichnbsp;often breaks their limbs, and fometimes killsnbsp;them. The late ingenious Mr. Padmore of Brif-tol, (whofe contrivance the forementioned cranenbsp;is, fo far as I can remember its confl:ru6lion,nbsp;after feeing it once -about twelve years ago *,)nbsp;obferving this dangerous conftruftion, contrived a method for remedying it, by puttingnbsp;cogs all around the outfide of the wheel, andnbsp;applying a trundle E to turn it; which increafesnbsp;the power as much as the number of cogs in thenbsp;wheel is greater than the number of ftaves innbsp;the trundle : and by putting a ratchet-wheel Fnbsp;on the axis of the trundle, (as in the above-mentioned crane) with a catch to fall into ir, thenbsp;great wheel is ftopc from running back bynbsp;the force of the weight, even if all the men in

* Since the firft edition of this book was printed, I have feen the fame crane again ; and do find, that though thenbsp;working parts are much the fame as above dcfcribed, yetnbsp;the method of raifing or lowering the trundle B, and thenbsp;catch R, are better contrived than I had defcribed them.

it (hould leave off walking. And by one man working at the winch i, or two men at the op-pofite winches when needful, the men in thenbsp;wheel are much affiRed, and much greaternbsp;weights are raifed, than could be by men onlynbsp;within the wheel. Mr. Padmore put alfo anbsp;gripe-wheel G upon the axis of the trundle,nbsp;which being pinched in the fame manner as de-feribed in the former crane, heavy burthensnbsp;may be let down without the leaft danger.nbsp;And before this contrivance, the lowering ofnbsp;goods was always attended with the utmoftnbsp;danger to the men in the wheel; as every onenbsp;muft be fenfible of, who has feen fuch enginesnbsp;at work.

And it is furprifing that the mafters of wharfs and cranes Ihould be fo regardlefs of the limbs,nbsp;or even lives of their workmen, that exceptingnbsp;the late Sir fames Creed of Greenwich, andnbsp;Ibme gentlemen at Briftol, there is fcarce an in-ftance of any who has ufed this fafe contrivance.

Whiel- The ftrudlure of �wdoeel-carriages is generally carriages, fo well known, that it would be needlefs to de-feribe them. And therefore, we lhall onlynbsp;point out fome inconveniencies attending thenbsp;common method of placing the wheels, andnbsp;loading the waggons.

In coaches, and all other four-wheeled carriages, the fore-wheels are made of a lefs fize than the hind ones, both on account of turning fhort, and to avoid cutting the braces :nbsp;otherwii'e, the carriage would go much eafier ifnbsp;the fore-wheels were as high as the hind ones,nbsp;and the higher the better, becaufe they wouldnbsp;fink to lefs depths in little hollov/ings in thenbsp;roads, and be the more eafily drawn out of

them. But carriers and coachmen give another reafon for making the fore-wheels much lowernbsp;than the hind-wheels; namely, that when theynbsp;are fo, the hind-wheels help to puflr on the forenbsp;ones: which is too unphilofophical and abfurdnbsp;to deferve a refutation, and yet for their fatis-faftion we Ihall Ihew by experiment that it hasnbsp;no exiftence but in their own imaginations.

It is plain that the fmall wheels mull turn as much oftener round than the great ones, asnbsp;their circumferences are lefs. And therefore,nbsp;when the carriage is loaded equally heavy onnbsp;both axles, the fore-axle muft fuftain as muchnbsp;more fridion, and confequently wear out asnbsp;much fooner, than the hind-axle, as the fore-wheels are lefs than the hind-ones. But thenbsp;great misfortune is, that all the carriers to anbsp;man do obftinately perfift, againft the cleareftnbsp;reafon and demonftration, in putting the heaviernbsp;part of the load upon the fore-axle of the waggon; which not only makes the friftion greatefl:nbsp;where it ought to be lead, but alfo prefleth thenbsp;fore-wheels deeper into the ground than thenbsp;hind-wheels, notwithftanding the fore-wheels,nbsp;being lefs than the hind ones, are with io muchnbsp;the greater difficulty drawn out of a hole or overnbsp;an obftacle, even fuppofing the weights onnbsp;their axles were equal. For the difficulty, withnbsp;equal weights, will be as the depth of the hole Fig, 3.nbsp;or height of the obftacle is to the femidiameternbsp;of th� wheel. Thus, if we fuppofe the fmallnbsp;wheel D of the waggon AB to fall into a holenbsp;of the depth E F, which is equal to the femidiameter of the wheel, and the waggon to benbsp;drawn horizontally along ; it is evident, thatnbsp;the point E of the fmall wheel will be drawnnbsp;diredlly againft the top of the hole ; and therefore,

92 nbsp;nbsp;nbsp;Of Wheel-Carriages.

fore, all the power of horfes and men will not be able to draw it out, unlefs the ground givesnbsp;way before it. Whereas, if the hind-wheel Gnbsp;falls into fuch a hole, it finks not near fo deepnbsp;in proportion to its femidiameter; and therefore, the point G of the large wheel will not benbsp;drawn direftly, but obliquely, againlt the topnbsp;of the hole; and fo will be eafily got out of it.nbsp;Add to this, that as a fmall wheel will oftennbsp;fink to the bottom of a hole, in which a greatnbsp;wheel will go but a very little way, the fmallnbsp;wheels ought in all reafon to be loaded with lefsnbsp;weight than the great ones : and then the heaviernbsp;part of the load would be lefs jolted upward andnbsp;downward, and the horfes tired fo much thenbsp;lefs, as their draught raifed the load to lefsnbsp;heights.

It is true, that when the waggon-road is much up-hill, there may be danger in loadingnbsp;the hind part much heavier than the fore part;nbsp;for then the weight would overhang the hind-axle, efpecially if the load be high, and endanger tilting up the fore-wheels from the ground.nbsp;In this cafe, the fafeft way would be to load itnbsp;equally heavy on both axles ; and then, as muchnbsp;more of the weight would be thrown upon thenbsp;hind-axle than upon the fore one, as the groundnbsp;rifes from a level below the carriage. But as thisnbsp;feldom happens, and when it does, a fmall temporary weight laid upon the pole between thenbsp;horfes would overbalance the danger ; and thisnbsp;weight might be thrown into the waggon whennbsp;it comes to level ground ; it is ftrange that annbsp;advantage fo plain and obvious as would arifenbsp;from loading the hind-wheels heavieft, ftiouldnbsp;not be laid hold of, by complying with thisnbsp;method.

cord, and it will be found to move along with the fame velocity as at firft; whichnbsp;that the power required to draw thenbsp;is all the fame, whether the great or fmallnbsp;wheels are foremoft; and therefore the greatnbsp;wheels do not help in the leaft to puilt on thenbsp;fmall wheels in the road.

, Hang the fcale to the fore-cord, -and place the fore-wheels (which are the fmall ones) innbsp;two holes, cut three eight parts of an inchnbsp;deep into the board ; then put a weight of 32nbsp;ounces into the carriage, over the fore-axle,nbsp;and an equal weight over the hind one : thisnbsp;done, put 44 ounces into the fcale, which willnbsp;be juft fufficient to draw out the fore-wheels :nbsp;but if this weight be taken out of the fcale, andnbsp;one of 16 ounces put into its place, if the hind-wheels are placed in the holes, the 16 ouncenbsp;weight will draw them out; which is little morenbsp;than a third part of what was neceflary to drawnbsp;out the fore-wheels. This fnews, that the larger the wheels are, the lefs power v;ill draw thenbsp;carriage, efpecially on rough ground.

Put 64 ounces over the axle of the hind-wheels, and 32 over the axle of the fore-ones, in the carriage-, and place the fore wheels innbsp;the holes: then, put 38 ounces into the fcale,nbsp;which will juft draw out the fore-wheels ; andnbsp;when the hind ones come to the hole, they willnbsp;find but very little refiftance, becaufe they finknbsp;but a little way into it.

But Ihift the weights in the carriage, by putting the 32 ounces upon the hind-axle, and the 64 ounces upon the fore one; and place thenbsp;fore-wheels in the holes : then, if 76 ounces benbsp;put into the fcale, it will be found no more thannbsp;fufficient to draw out thefe wheels; which isnbsp;double the power required to draw them out,nbsp;when the lighter part of the load was put uponnbsp;them: which is a plain demonftration of the ab-furdity of putting the heavieft part of the loadnbsp;in the fore-part of the waggon.

Every one knows what an out-cry was made by the generality, if not the whole body, of thenbsp;carriers, againft the broad-wheel a�l; and hownbsp;�hard it was to perfuade them to comply with it,nbsp;even though the government allowed them tonbsp;draw with more horfes, and carry greater loads,nbsp;than ufual. Their principal objedion was, thatnbsp;as a broad wheel mull touch the ground in a greatnbsp;many more points than a narrow wheel, the friction muft of courfe be juft fo much the greater ;nbsp;and confequently, there muft be fo many morenbsp;horfes than ufual, to draw the waggon. 1 believenbsp;that the majority of people were of the famenbsp;opinion, not confidering, that if the whole weightnbsp;of the waggon and load in it bears upon anbsp;great many points, each fuftains a propor-tionably lefs degree of weight and friction, thannbsp;when it bears only upon a few points; fo that

what is wanting in one, is hiade up in the other; and therefore will be juft equal under equal degrees of weight, as msf be fhewn by the following plain and eafy experiment.

Let one end of a piece of packthread be fattened to a brick, and the other end to a common fcale for holding weights: then, havingnbsp;laid the brick edgewife on a table, and let thenbsp;fcale hang under the edge of the table, put asnbsp;much weight into the fcale as will juft draw thenbsp;brick along the table. Then taking back thenbsp;brick to its former place, lay it fiat on the table,nbsp;and leave it to be aded upon by the fame weightnbsp;in the fcale as before, which will draw it alongnbsp;with the fame eafe as when it lay upon its edge.nbsp;In the former cafe, the brick may be confiderednbsp;as a narrow wheel on the ground ; and in thenbsp;latter as a broad wheel. And fince the brick isnbsp;drawn along with equal eafe, whether its broadnbsp;fide or narrow edge touches the table, it Ihewsnbsp;that a broad wheel might be drawn along thenbsp;ground with the fame eafe as a narrow one (fup-pofing them equally heavy) even though theynbsp;fhould drag, and not roll, as they go along.

As narrow wheels are always finking into the ground, efpecially when the heavieft part of thenbsp;load lies upon them, they muft be confidered asnbsp;going conftantly up hill, even on level ground.nbsp;And their fides muft fuftain a great deal of fridtionnbsp;by rubbing againft the ruts made by them. Butnbsp;both thefe inconveniencies are avoided by broadnbsp;wheels j which, inftead of cutting and ploughing up the roads, roll them fmooth, and hardennbsp;th' tm ; as experience teftifies in places wherenbsp;they have been ufed, efpecially either on wettidinbsp;or fandy ground; though after all it muft be con-felTed, that they v^'ill not do in ftiff clayey crofs

roads becaufe they would foon gather up as much clay as would be almoft equal to thenbsp;weight of an ordinary load.

If the wheels were always to go upon fmooth and level ground, the beft way would be to makenbsp;the fpokes perpendicular to the naves; that is,nbsp;to ftand at right angles to the axles; becaufenbsp;they would then bear the weight of the loadnbsp;perpendicularly, which is the ftrongeft way fornbsp;wood. But becaufe the ground is generally uneven, one wheel often falls into a cavity or rutnbsp;when the other does not �, and then it bears muchnbsp;more of the weight than the other does: innbsp;which cafe, concave or difhing wheels are beft,nbsp;becaule when one falls into a rut, and the othernbsp;keeps upon high ground, the fpokes become perpendicular in the rut, and therefore have thenbsp;greateft ftrength when the obliquity of tiie loadnbsp;throws moft of its weight upon them whilftnbsp;thofe on the high ground have lefs weight to bear,nbsp;and therefore need not be at their full ftrength.nbsp;So that the ufual way of making the wheels concave is by much the beft.

The axles of the wheels ought to be perfedly ftraight, that the rim of the wheels may benbsp;parallel to each other; for then they will movenbsp;eafieft, becaufe they will be at liberty to go onnbsp;ftraight forwards. But in the ufual way of practice, the axles are bent downward at their ends ;nbsp;which brings the fides of the wheels next thenbsp;ground nearer to one another than their oppofitenbsp;or higher fides are: and this not only makes thenbsp;wheels to drag fidewife as they go along, andnbsp;gives the load as much greater power of crulhingnbsp;them than when they are parallel to each other,nbsp;but alfo endangers the over-turning of the carriage when any wheel falls into a hole or rut; or

when the carriage goes in a, road which has one fide lower than the other, as along the fide of anbsp;hill. Thus (in the hind view of a waggon ornbsp;cart) let J E and B F be the great wheels parallel to each other, on their ftraight axle K, and Fig.

HC / the carriage loaded with heavy goods from C to G. Then, as the carriage goes on in thenbsp;oblique road JaB, the center of gravity of thenbsp;whole machine and load will be at C*; and the * Sppnbsp;line of dire�lion C d D falling within the wheel page 13.nbsp;B F, the carriage will not overfer. But if thenbsp;wheels be inclined to each other on the ground. Fig. 5�nbsp;as A E and B F are, and the machine be loadednbsp;as before,quot; from C to G, the line of diredionnbsp;CdD falls without the wheel B F, and the wholenbsp;machine tumbles over. When it is loaded withnbsp;heavy goods (fuch as lead or iron) which lie low. Fig. 4.nbsp;it may travel fafely upon an oblique road fo longnbsp;as the center of gravity is at C, and the line of di-redion C d falls within the wheels ; but if it benbsp;loaded high with lighter goods (fuch as wool-packs) from C to Lf the center of gravity is raifed Fig. 6.nbsp;from C to K, which throws the line of diredionnbsp;K k without the lowed edge of the wheel B F,nbsp;and then the load overfets the waggon.

If there be fome advantage from fmall forewheels, on account of the carriage turning more eafily and flaort than it can be made to do whennbsp;they are large; there is at lead as great a difad-vantage attending them, which is, that as theirnbsp;axle is below the level of the horfes breads, thenbsp;horfes not only have the loaded carriage tonbsp;draw along, but alfo part of its weight to bear;nbsp;which tires them fooner, and makes themnbsp;grow much differ in their hams, than theynbsp;would be if they drew on a level with the foreaxle. And for this reafon, we find coach horfes

foot! become unfit for riding. So that on all 3(gt; counts it is plain, that the fore-wheels of all carriages ought to be fo high, as to have their axlesnbsp;even with the breaft of the horfes ; which wouldnbsp;not only give the horfes a fair draught, but like-wife keep them longer fit for drawing the carriage.

We {hall conclude this ledlure with adefcrip-tion of Mr. Vauloue�s curious engine, which was made ufe of for driving the piles of Weflminfler-bridge: and the reader may caft his eyes uponnbsp;the firft and iecond figures of the plate, in whichnbsp;the fame letters of reference are annexed to thenbsp;fame parts, in order to explain thofe in the fe-cond, which are either partly or wholly hid innbsp;the firft.

The pile- A is the great upright (haf^t or axle, on which engine. are the great wheel B and drum C, turned bynbsp;hotfes joined to the bars S, S. The wheel B turnsnbsp;the trundle X, on the top of whofe axis is thenbsp;fly O, which ferves to regulate the motion, and.nbsp;alfo to aft againft the horfes, and keep themnbsp;from falling when the heavy ram ^is difchargednbsp;to drive the pile P down into the mud in thenbsp;bottom of the river. The drum C is loofe uponnbsp;the (haft A, but is locked to the wheel B by thenbsp;bolt T. On this drum the great rope H H \snbsp;wound 5 one end of the rope being fixed to thenbsp;drum, and the other to the follower G, to whichnbsp;it is conveyed over the pulleys / and K. In thenbsp;follower G is contained the tongs F (fee Fig.nbsp;3.) that takes hold of the ram ^by the ftaple Rnbsp;for drawing it up. Z) is a fpiral or fufy fixt tonbsp;the drum, on which is wound the fmall rope Tnbsp;that goes over the pulley U, under the pulley F,nbsp;and is fattened to the top of the frame at 7. Tonbsp;the pulley block F is hung the counterpoife

which hinders the follower from accelerating as it goes down to take hold of the ram : for, asnbsp;the follower tends to acquire velocity in its de-feent, the line 'P winds downwards upon th�nbsp;fufy, on a larger and larger radius, by whichnbsp;means the counterpoife ff' ads ftronger andnbsp;lironger againft it j and fo allows it to comenbsp;down with only a moderate and uniform velocity. The bolt T locks the drum to the greatnbsp;wheel, being puflied upward by the fmali levernbsp;2, which goes through a mortile in the fhaft A,nbsp;turns upon a pin in the bar 3 fixt to the greatnbsp;wheel 5, and has a weight 4, which always tendsnbsp;to pulli up the bolt T through the wheel intonbsp;the drum. L is the great lever turning on thenbsp;axis m, and refting upon the forcing bar 5, 5,nbsp;which goes down through a hollow in the lliafcnbsp;A, and bears up the little levef 2.

By the: horfes going round, the gfcai rope H is wound about the drum C, and the ram ^ isnbsp;drawn up by the tongs F in the follower G, untilnbsp;the tongs comes between the inclined planes E;nbsp;which, by Ihutting the tongs at the top, opens itnbsp;at the foot, and difeharges the ram, Which fallsnbsp;down between the guides b b upon the pile P,nbsp;and drives it by a few ftrokes as far into the mudnbsp;as it can go; after which, the top part is fawednbsp;off clofe to the mud, by an engine for that pur-pofe. Imrhediately after the ram is difeharged,nbsp;the piece 6 upon the follower G takes hold of thenbsp;iopes 0, which raife the end, of the levef P, andnbsp;caufe its end iV to defeend and prefs down thenbsp;forcing bar 5 upon the little lever 2, which bynbsp;pulling down the bolt T, unlocks the drum Cnbsp;from the great wheel B ; and then, the follower,nbsp;being at liberty, comes down by its own weightnbsp;to the ram; and the low'er ends of the tongs flipnbsp;Hnbsp;nbsp;nbsp;nbsp;ov�r

over the ftaple R, and the weight of their'heads caufes them to fall outward, and fhuts uponnbsp;it. Then the weight 4 puflies up the bolt T into the drum, which locks it to the great wheel,nbsp;and fo the ram is drawn up as before.

As the follower comes down, it caufes the drum to turn backward, and unwinds the ropenbsp;from it, whilft the horfes, great wheel, trundlenbsp;and fly, go on with an uninterrupted motion :nbsp;and as the drum is turning backward, the coun-terpolfe is drawn up, and its rope 2quot; woundnbsp;upon the fpiral fufy D.

There are feveral holes in the under fide of the drum, and the bolt T always takes the firftnbsp;one that it finds when the drum flops by thenbsp;falling of the follower upon the ram ; until whichnbsp;ftoppage, the bolt has not time to flip into anynbsp;of the holes.

This engine was placed upon a barge on the water, and fo was eafily conveyed to any placenbsp;defired.�I never had the good fortune to fee it,nbsp;but drew this figure from a model which I madenbsp;from a print of it; being not quite fatisfied withnbsp;the view which the print gives. I have beennbsp;told that the ram was a ton weight, and that thenbsp;guides b between which jt was drawn up andnbsp;let fall down, were 30 feet high. I fuppofe thenbsp;great wheel may have had 100 cogs, and thenbsp;trundle 10 ftaves or rounds; fo that the flynbsp;would make 10 revolutions for one of the greatnbsp;wheel.

LECT.

L E C T. V.

Th E fcience of hydrojlalics treats of the nature, gravity, prefiure, and motion of

A fluid is a body that yields to the leaft pref- Defim-fure or difference of preflures. Its particles are fo fmall, that they cannot be difcerned by thenbsp;beft microfcopes ; they are hard, fince no fluid,nbsp;except air or fteam, can be preffed into a lefsnbsp;fpace than it naturally poffefles'; and they muftnbsp;be round and fmooth, feeming they are lb eafilynbsp;moved among one another.

All bodies, both fluid and folid, prefs downwards by the force of gravity : but fluids have this wonderful property, that their preffure upwards and fidewife is equal to their preflTurenbsp;downwards-, and this is always in proportion tonbsp;their perpendicular height, without any regardnbsp;to their quantity ; for, as each particle is quitenbsp;free to move, it will move towards that part ornbsp;fide on which the preflTure is leaft. And hence,nbsp;no particle or quantity of a fluid can be at reft,nbsp;till it is every way equally prefled.

To fhew by experiment that fluids prefs up- Plate X. ward as well as downward, let be a long F'g. i.nbsp;upright tube filled with water near to its top ;nbsp;and C D a fmall tube open at both ends, and much up-immerfed into the water in the large one -, if the ward a/nbsp;immerfion be quick, you will fee the water rife down-in the fmall tube to the fame height that it ftandsnbsp;in the great one, or until the furfaces of thenbsp;H 2nbsp;nbsp;nbsp;nbsp;water

water in both are on the fame level: which fliews that the water is prefled upward into the fmallnbsp;' tube by the weight of what is in the greatnbsp;one ; otherwife it could never rife therein, contrary to its natural gravity ; unlefs the diameternbsp;of the bore were fo fmall, that the attradlion ofnbsp;the tube would raife the water; which will never happen, if the tube be as wide as that in anbsp;common barometer. And, as the water rifes nonbsp;higher in the fmall tube than till its furface been a level with the furface of the water in thenbsp;great one, this (hews that the preflure is not innbsp;proportion to the quantity of water in the greatnbsp;tube, but in proportion to its perpendicularnbsp;height therein : for there is much more waternbsp;in the great tube all around the fmall one, thannbsp;what is raifed to the fame height in the fmall one,nbsp;as it ftands within the great.

Take out the fmall tube, and let the water run out of it �, then it will be filled with air.nbsp;Stop its upper end with the cork C, and it willnbsp;be full of air all below the cork: this done,nbsp;plunge it again to the bottom of the water in thenbsp;great tube, and you will fee the water rife up innbsp;it only to the height B; which fhews that the airnbsp;is a body, otherwife it could not hinder the waternbsp;from rifing up to the fame height as it did before, namely, to A and in fo doing, it drovenbsp;the air out at the top; but now the air is confined by the cork C: and it alfo fhews that thenbsp;air is a compreffible body, for if it were not fo,nbsp;a drop of water could not enter into the tube.

The preflfure of fluids being equal in all di-redtions, it follows that the fides of a veffel are as rnuch prelTed by a fluid in if, all around in anynbsp;given ring of points, as the fluid below that ringnbsp;is preffed by the weight of all that ftands above

it. Hence the preffure upon every point in the fides, immediately above the bottom, is equal tonbsp;the preffure upon every point of the bottom. Tonbsp;Ihew this by experiment, let a hole be made at Fig. 2,nbsp;e in the fide of the tube A B clofe by the bottom ; and another hole of the fame fize in thenbsp;bottom at C; then pour water into the tube,nbsp;keeping it full as long as you choofe the holesnbsp;fhould run, and have two bafons ready to receivenbsp;the water that runs through the two holes, untilnbsp;you think there is enough in each bafon ; andnbsp;you will find by meafuring the quantities, thatnbsp;they are equal; which fhews that the water runnbsp;with equal fpeed through both holes: which itnbsp;could not have done, if it had not been equallynbsp;preffed through them both. For, if a hole ofnbsp;the fame fize be made in the fide of the rube, asnbsp;about �, and if all three are permitted to runnbsp;together, you will find that the quantity runnbsp;through the hole at � is much lefs than what hasnbsp;run in the fame time through either of the holesnbsp;C or e.

In the fame figure, let a tube be turned up from the bottom at C into the fliape D E-, andnbsp;the hole at C be ftopt with a cork. Then, pournbsp;water into the tube to any height, as Ag, and itnbsp;will fpout up in a jet E FG, nearly as high as itnbsp;is kept in the tube A B, by continuing to pournbsp;in as much there as runs through the hole Enbsp;which will be the cafe whilft the furface Ag keepsnbsp;at the fame height. And if a little ball of corknbsp;G be laid upon the top of the jet, it will be fup-ported thereby, and dance upon it. The reafonnbsp;why the jet rifes not quite fo high as the furfacenbsp;of the water Ag^ is owing to the refiftanceit meetsnbsp;with in the open air : for, if a tube, either greatnbsp;or fmall, was fcrewed upon the pipe at E, thenbsp;H 3nbsp;nbsp;nbsp;nbsp;water

water would rife in it until the furface of the water in both tubes were on the fame level ; asnbsp;will be fhewn by the next experiment.

Any quantity of a fluid, how fmall foever, may be made to balance and fupport any quantity, how great foever. This is defervedlynbsp;termed the hydrojlatical paradox., which we lha1lnbsp;firft fliew by an experiment, and then account fornbsp;it upon the principle above mentioned; namely,nbsp;th^tthe prejfure of fluids is diredlly as their perpendicular height, without any regard to their quantity.

Let a fmall glafs tube DCG, open throughout, and bended at B, be joined to the end of a greatnbsp;one A1 zt c d, where the great one is alfo open ;nbsp;fo that thefe tubes in their openings may freelynbsp;communicate with each other. Then pour water through a fmall necked funnel into the fmallnbsp;tube at H; this water will run through the joining of the tubes at c d, and rife up into the greatnbsp;tube ; and if you continue pouring until the fur-face of the water comes to any part, as A, in thenbsp;great tube, and then leave off, you will fee thatnbsp;the furface of the water in the fmall tube will benbsp;juft as high, at D; fo that the perpendicularnbsp;height of the water will be the fame in bothnbsp;tubes, however fmall the one be in proportion tonbsp;the other. This ftiews, that the fmall columnnbsp;D C G balances and fupports the great columnnbsp;A c d: which it could not do if their preffuresnbsp;were not equal againft one another in the recurved bottom at B.�If the fmall tube be madenbsp;longer, and inclined in the fituation G E F, thenbsp;furface of the water in it will ftand at F, on thenbsp;fame level with the furface A in the great tube ;nbsp;that is, the water will have the fame perpendicularnbsp;height in both tubes, although the column in thenbsp;fmall tube is longer than that in the great one ;

Since then the prefllire of fluids is diredly as their perpendicular heights, without any regardnbsp;to their quantities, it appears that whatever thenbsp;fiaure or fize of veflels be, if they are of equalnbsp;heights, and if the areas of their bottoms arenbsp;equal, the prefllires of equal heights of water arenbsp;equal upon the bottoms of thefe vclTels; evennbsp;though the one Ihould hold a thouland or tennbsp;thouland times as much water as vrould fill thenbsp;other. To confirm this part of the hydroftatical fig*nbsp;paradox by an experiment, let two vedels benbsp;prepared of equal heights but very unequalnbsp;contents, fuch as A B in Fig. 4. and AB in Fig.

5. Let each veflel be open at both ends, and their bottoms D d, Z) i be of equal v/idths. Letnbsp;a brafs bottom CC be exactly fitted to each vef-fel, not to go into it, but for it to ftand upon ;nbsp;and let a piece of wet leather be put betweennbsp;each velTel and its brafs bottom, for the fake ofnbsp;, clofenefs. Join each bottom to its veffel by anbsp;hinge D, fo that it may open like the lid of anbsp;box; and let each bottom be kept up to itsnbsp;velTel by equal weights E and E hung to linesnbsp;which go over the pulleys F and F (wbofc blocksnbsp;are fixed to the Tides of the velTels at/) and thenbsp;lines tied to hooks at d and d, fixed in the brafsnbsp;bottoms oppofite to the hinges D and D. Thingsnbsp;being thus prepared and fitted, hold the veffelnbsp;AB (Fig. 5.) upright in your hands over a bafonnbsp;on a table, and caufe water to be poured into thenbsp;veffel flowly, till the preffure of the water bearsnbsp;down its bottom at the fide d, and raifes thenbsp;weight E j and then part of the water will runnbsp;out at d. Mark the height at which the furfacenbsp;H of the water ffood in the veffel, when the bot-H 4nbsp;nbsp;nbsp;nbsp;tom

tom began to give way at d-, and then, holding op the other veffel A B (Fig. 4,) in the famenbsp;manner, caufe water to be poured into it atnbsp;and you will fee that vyhen the water rifes to Anbsp;in this veffel, juft as high as it did in the former,nbsp;its bottom will alfo give way at d, and it willnbsp;lofe part of the \yater.

The natpral reafon of this furprifing phenomenon is, that fince all parts of a fluid at equal depths belovy the furface are equally preffed innbsp;all manner of diredlions, the water immediatelynbsp;below the fixed part B f (Fig. 4.) will be preffednbsp;as much upvyard againft its lower furface withirinbsp;the veffel, by the adion of the column Ag^ asnbsp;it would be by a column of the fame height, andnbsp;of any diameter whatever; (as was evident bynbsp;the experiment with the tube. Fig. 3.) and therefore, fince adion and readion are equal andnbsp;contrary to each other, the \yater immediatelynbsp;below the furface B f will be preffed as muchnbsp;downward by it, as if it was immediately touched and preffed by a column of the height^ A^nbsp;and of the diameter B f: and therefore, thenbsp;water in the cavity B D df will be preffed asnbsp;much downward upon its bottom C C, as thenbsp;bottom of the other veffel (Fig. 5.) is preffed bynbsp;all the water above it.

To illuftrate this a little farther, let a hole be made at � in the fixed top B �, and let a tube Gnbsp;be put into it �, then, if wder be poured into thenbsp;tube A, it will (after filling the cavity B d) rifenbsp;up into the tube G, until it comes to a level withnbsp;that in the tube A^ which is manifeftly owing tonbsp;the preffure of the water in the tube A, uponnbsp;that in the cavity of the veffel below it. Con-lequently, that part of the top B f, in which thenbsp;hole is now made, would, if corked up, be

preffed

preffed upward with a force equal to the weight of all the water which is fupported in the tube G:nbsp;and the fame thing would hold at g, if a holenbsp;were made there. And fo if the whole cover ornbsp;top B � were full of holes, and had tubes as highnbsp;as the middle one Ag put into them, the waternbsp;in each tube would rife to the fame height as it isnbsp;kept into the tube A, by pouring more into it,nbsp;to make up the deficiency that it fuftains by fup-plying the others, until they are all full: andnbsp;then the water in the tube A would fupportnbsp;equal heights of water in all the reft of the tubes.

Or, if all the tubes except A, or any other one, were taken away, and a large tube equal in diameter to the whole top ,B� were placed upon it,nbsp;and cemented to it, and then if water werenbsp;poured into the tube that was left in either ofnbsp;the holes, it would afeend through all the reft ofnbsp;the holes, until it filled the large tube to thenbsp;fame height that it ftands in the fmall one, afternbsp;a fufficient quantity had been poured into it:nbsp;which fhews, that the top Bf was prefled upward by the water under it, and before anynbsp;hole was made in it, with a force equal to thatnbsp;wherewith it is now preffed downward by thenbsp;weight of all the water above it in the greatnbsp;tube. And therefore, the reaftion of the fixednbsp;top Bf muft be as great, in prefling the waternbsp;downward upon the bottom C C, as the wholenbsp;prefiiire of the water in the great tube wouldnbsp;have been, if the top had been taken away, andnbsp;the water in that tube left to prefs diredlly uponnbsp;the water in the cavity B Ddf.

Perhaps the beft machine in the world for Fig. 6. demonftrating the upward prefllire of fluids, is The hy.nbsp;the hydroftatic bellows A j which confifts of twonbsp;thick oval boards, each about i6 inches broad,nbsp;and 18 inches long, covered with leather, tonbsp;5nbsp;nbsp;nbsp;nbsp;open

open and (hut like a common bellows, but without valves; only a pipe 5, about three feet high, is fixed into the bellows at e. Let fomenbsp;water be poured into the pipe at c, which willnbsp;run into the bellows, and feparate the boards anbsp;little. Then lay three weights b, c, d, each weighing loo pounds, upon the upper board , andnbsp;pour more water into the pipe B, which will runnbsp;into the bellows, and raife up the board with allnbsp;the weights upon it; and if the pipe be keptnbsp;full, until the weights are raifed as high as thenbsp;leather which covers the bellows will allow them,nbsp;the water will remain in the pipe, and fupportnbsp;all the weights, even though it ihould weigh nonbsp;' more than a quarter of a pound, and they 300nbsp;pounds: nor will all their force be able to caufenbsp;them to defcend and force the water out at thenbsp;top of the pipe.

The reafon of this will be made evident, by confidering what has been already faid of thenbsp;refult of the prelTure of fluids of equal heightsnbsp;without any regard to the quantities. For, if anbsp;hole be made in the upper board, and a tube benbsp;put into it, the water will rife in the tube to thenbsp;fame height that it does in the pipe ; and wouldnbsp;rife as high (by lupplying the pipej in as manynbsp;tubes as the board could contain holes. Now,nbsp;fuppofe only one hole to be made in any part ofnbsp;the board, of an equal diameter with the bore ofnbsp;the pipe B j and that the pipe holds juft a quarter of a pound of water; if a perlon claps hisnbsp;finger upon the hole, and the pipe be filled withnbsp;water, he will find his linger to be prelTed upward with a force equal to a t]uarter of a pound.nbsp;And as the fame preffure is equal upon all equalnbsp;parts of the board, each part whofe area is equalnbsp;to the area of the hole, will be prefled upv/ardwithnbsp;a force equal to that of a quarter of a pound : the

fum of all which preflures againft the under fide of an oval board 16 inches broad, and 18 inchesnbsp;long, will amount to 300 pounds; and thereforenbsp;fo much weight will be railed up and fupportednbsp;by a quarter of a pound of water in the pipe.

Hence, if a man ftands upon the upper board. How a and blows into the bellows through the pipe 5, man maybe will raife himfelf upward upon the board :nbsp;and the fmaller the bore of the pipe is, the eafiernbsp;he will be able to raife himfelf. And then, by hisnbsp;clapping his finger upon the top of the pipe, he breath,nbsp;can fupport himfelf as long as he pleafes ; provided the bellows be air-tight fo as not to lofenbsp;what is blown into it.

This figure, I confefs, ought to have been much larger than any other upon the plate j butnbsp;it was not thought of, until all the reft werenbsp;drawn and it could not fo properly come intonbsp;any other plate.

Upon this principle of the upward prefiure of how foiid fluids, a piece of lead may be made to fwim in lead maynbsp;water, by immerfing it to a proper depth, and b^madetonbsp;keeping the water from getting above it. Letnbsp;C D be a glafs tube, open throughout, andnbsp;EFG a fiat piece of lead, exadly fitted to the p;g,nbsp;lower end of the tube, not to go within it, butnbsp;for it to ftand upon ; with a wet leather betweennbsp;the lead and the tube to make clofe work. Letnbsp;this leaden bottom be half an inch thick, andnbsp;held clofe to the tube by pulling the packthreadnbsp;JHL upward at L with one hand, whilft thenbsp;tube is held in the other by the upper end C.

In this fituation, let the tube be immerfed in water in the glafs veflel ^ B, to the depth of fixnbsp;inches below the furface of the water at K andnbsp;then, the leaden bottom EFG will be plungednbsp;to the depth of fomewhat more than eleven times

its own thicknefs : holding the tube at that depth, you may let go the thread at L; andnbsp;the lead will not fall from the tube, but will benbsp;kept to it by the upward prelTure of the waternbsp;below it, occafioned by the height of the waternbsp;at K above the level of the lead. For as lead isnbsp;11,33 times as heavy as its bulk of water, and isnbsp;in this experiment immerfed to a depth fome-what more than �i.33 times its thicknefs, andnbsp;no water getting into the tube between it andnbsp;the lead, the column of water Eabc G below thenbsp;lead is prelTed upward againft it by the waternbsp;K D E G L all around the tube ; which waternbsp;being a little more than 11.33 as high asnbsp;the lead is thick, is fufficient to balance and fup-port the lead at the depth K E. If a little waternbsp;be poured into the tube upon the lead, it willnbsp;increafe the weight upon the column of waternbsp;under the lead, and caufe the lead to fall fromnbsp;the tube to the bottom of the glafs veflel, wherenbsp;it will lie in the fituation b d. Or, if the tube benbsp;raifed a little in the water, the lead will fall by itsnbsp;own weight, which will then be too great for thenbsp;prelTure of the water around the tube upon thenbsp;column of water below it.

How light Let two piecesof wood be plained quite flat, fo wood may as no water may get in between them when theynbsp;be made ^j-e put together: let one of the pieces, as b d,nbsp;be cemented to the bottom of the veflel ji Bnbsp;(Fig. 7.) and the other piece be laid flat and clofenbsp;upon it, and held down to it by a flick, whilftnbsp;water is poured into the veflel; then removenbsp;the flick, and the upper piece of wood will notnbsp;rife from the lower one: for, as the upper one isnbsp;preflTed down both by its own weight and thenbsp;weight of all the water over it, whilft the contrary prelTure of the water is kept off by the

wood under it, it will lie as ftill as a ftone would do in its place. But if it be raifed ever fo littlenbsp;at any edge� fome water will then get under it;nbsp;which being aded upon by the water above, willnbsp;immediately prefs it upward and as it is lighternbsp;than its bulk of water, it will rife, and float uponnbsp;the furface of the water.

All fluids weigh juft as much in their own elements as they do in open air. To provenbsp;this by experiment, let as much fhot be put intonbsp;a phial, as, when corked, will make it fink innbsp;water: and being thus charged, let it benbsp;weighed, firft in air, and then in water, andnbsp;the weights in both cafes wrote down. Then,nbsp;as the phial hangs fufpended in water, andnbsp;counterpoifed, pull out the cork, that water maynbsp;run into it, and it will defeend, and pull downnbsp;that end of the beam. This done, put as muchnbsp;weight into the oppofite fcale as will reftore thenbsp;equipoife; which weight will be found to anfwernbsp;cxaftly to the additional weight of the phial whennbsp;it is ag^n weighed in air, with the water in it.

The velocity with which water fpouts out at a jjjg hole in the fide or bottom of a veflel, is as the city ofnbsp;* fquare root of the depth or diftance of the fpowingnbsp;hole below the furface of the water. For, innbsp;order to make double the quantity of a fluidnbsp;run through one hole as through another of thenbsp;fame fize, it will require four times the preflurenbsp;of the other, and therefore muft be four timesnbsp;the depth of the other below the furface of thenbsp;water: and for the lame realbn, three times thenbsp;quantity running in an equal time through the

* The fquare root of any number is that which being multiplied by itfelf produces the faid number. Thus, 2 isnbsp;the fquare root of 4, and 3 is the fquare root of g: for anbsp;multiplied by 2 produces 4, and 3 multiplied by 2 produces 9, amp;c.

fame fort of hole, muft run with three times the velocity, which will require nine times thenbsp;preffure; and confequently muft be nine timesnbsp;as deep below the furface of the fluid : and fonbsp;on.�To prove this by an experiment, let tv/onbsp;pipes, as C and of equal fized bores, benbsp;fixed into the fide of the veffel A B the pipenbsp;g being four times as deep below the furface ofnbsp;the water at ^ in the veffel as the pipe C is: andnbsp;whilft thefe pipes run, let water be conftantlynbsp;poured into the veffel, to keep the furface ftillnbsp;at the fame height. Then, if a cup that holdsnbsp;a pint be fo placed as to receive the water thatnbsp;fpouts from the pipe C, and at the fame momentnbsp;a cup that holds a quart be fo placed as to receivenbsp;the water that fpouts from the pipe^quot;, both cupsnbsp;will be filled at the fame time by their refpec-tive pipes.

The horizontal diftance, to which a fluid will fpout from a horizontal pipe, in any part of thenbsp;fide of an upright veffel below the furface of thenbsp;fluid, is equal to twice the length of a perpendicular to the fide of the veffel, drawn from thenbsp;mouth of the pipe to a femicircle defcribed uponnbsp;the altitude of the fluid: and therefore, thenbsp;fluid will fpout to the greateft diftance poffiblenbsp;from a pipe, whofe mouth is at the center ofnbsp;the femicircle; becaufe a perpendicular to itsnbsp;diameter (fuppofed parallel to the fide of thenbsp;veffel) drawn from that point, is the longeft thatnbsp;can poffibly be drawn from any part of thenbsp;diameter to the circumference of the femicircle.

Fig. 8. Thus, if the veffel A B he full of water, the horizontal pipe D be in the middle of its fide,nbsp;and the femicircle N d c bhe defcribed upon Z)nbsp;as a center, with the radius or femidiameternbsp;D g N, or D fby the perpendicular D d to thenbsp;diameter N D bh the longeft that can be drawn

from any part of the diameter to the circumference H d c b. And if the velTel be-kept full, the jet G will fpout from the pipe Z), to thenbsp;horizontal diftance iV M, which is double thenbsp;length of the perpendicular D d. If two othernbsp;pipes, as C and E, be 6xed into the fide of thenbsp;veflel at equal diftances above and below thenbsp;pipe D, the perpendiculars C c and E e, fromnbsp;thefe pipes to the femicircle, will be equal �, andnbsp;the jets F and H fpouting from them will eachnbsp;go to the horizontal diftance NK-, which isnbsp;double the length of either of the equal perpendiculars C c ox E H.

Fluids by their preffure may be conveyed over How wa-hills and vallies in bended pipes, to any height not greater than the level of the fpring fromnbsp;whence they flow. But when they are defigned overhilisnbsp;to be raifed higher than the fprings, forcing en- ^�nd vai-gines mull be ufed i which lhall be defcribednbsp;when we come to treat of pumps.

A fyphon, generally ufed for decanting liquors, is a bended pipe, whofe legs are of unequal lengths ; and the fiiorteft leg muft always be put into the liquor intended to be decanted,nbsp;that the perpendicular altitude of the column ofnbsp;liquor in the other leg may be longer than thenbsp;column in the immerfed leg, efpecially abovenbsp;the furface of the water. For, if both columnsnbsp;were equally high in that refpeft, the atmo-fphere, which prefTes as much upward as downward, and therefore afts as much upwardnbsp;againft the column in the leg that hangs withoutnbsp;the velTel, as it afts downward upon the fur-face of the liquor in the velTel, would hindernbsp;the running of the liquor through the fyphon,nbsp;even though it were brought over the bendednbsp;part by fuftion. So that there is nothing left tonbsp;3nbsp;nbsp;nbsp;nbsp;caufe

caufe the motion of the liquor, but the fuperlof weight of the column, in the longer leg, onnbsp;account of its having the greater perpendicularnbsp;height.

F'g- 9* Let D be a cup filled with water to C, and ABCs, fyphon, whofe Ihorter leg B C F is im-merled in the water from C to F. If the end ofnbsp;the other leg were no lower than the line AC,nbsp;which is level with the furface of the water, thenbsp;fyphon would not run, even though the airnbsp;Ihould be drawn out of it at the mouth A. Fornbsp;although the fuiStion would draw fome water atnbsp;firft, yet the water would flop at the momentnbsp;the fuclion ceafed; becaufe the air would aft asnbsp;much upward againft the water at A, as it aflednbsp;downward for it by prefling on the furface at C.nbsp;But if the leg A B comes down to G, and thenbsp;air be drawn out at G by fuflion, the water willnbsp;immediately follow, and continue to run, untilnbsp;the furface of the water in the cup comes downnbsp;to F-, becaufe, till then, the perpendicularnbsp;height of the column BAG will be greater thannbsp;that of the column CB ; and confequently, itsnbsp;weight will be greater, until the furface comesnbsp;down to F �, and then the fyphon will Hop,nbsp;though the leg C F Ihould reach to the bottomnbsp;of the cup. For which realbn, the leg thatnbsp;hangs without the cup is always made longnbsp;enough to reach below the level of its bottomnbsp;as from dxo E: and then, when the fyphon isnbsp;emptied of air by fuflion at E, the water immediately follows, and by its continuity bringsnbsp;away the whole from the cup �, juft as pullingnbsp;one end of a thread will make the whole cluenbsp;follow.

If the perpendicular height of a fyphon, from the furface of the water to its bended top at B,

be more than 33 feet, it will draw no water, even though the other leg were much longer,nbsp;and the fyphon quite emptied of air; becaufenbsp;the weight of a column of water 3^ feet highnbsp;is equal to the weight of as thick a column ofnbsp;air, reaching from the furface of the earth tonbsp;the top of the atmofphere; fo that there willnbsp;then be an equilibrium, and confequently,nbsp;though there would be weight enough of airnbsp;upon the furface C to make the water afeend innbsp;the leg C B almoft to the heiglit B, if the fyphon were emptied of air, yet that weight wouldnbsp;not be fufficient to force the water over thenbsp;bend ; and therefore, it could never be broughtnbsp;over into the leg B AG.

Let a hole be made quite through the bottom Fig. 10. of the cup A., and the longer leg of the bended Tantalus'snbsp;fyphon D � B G be cemented into the hole, fonbsp;that the end � of the Ihortcr leg Z) E may al-moft touch the bottom of the cup within.

Then, if water be poured into this cup, it will rife in the fliorter leg by its upward prelfure,nbsp;driving out the air all the way before it throughnbsp;the longer leg: and when the cup is filled abovenbsp;the bend of the fyphon at �, the preflure ofnbsp;the water in the cup will force it over the bendnbsp;of the fyphon; and it will defeend in the longernbsp;leg C S G, and run through the bottom, untilnbsp;the cup be emptied.

This is generally called �Tantalus's cup^ and the legs of the fyphon in it are almoft clofe together ; and a little hollow ftarue, or figure ofnbsp;a man, is fometimes put over the fyphon to conceal it �, the bend E being within the neck ofnbsp;the figure as high as the chin. So that poornbsp;thirfty Tantalus ftands up to the chin in water,nbsp;imagining it will rife a little higher, and henbsp;Inbsp;nbsp;nbsp;nbsp;may

may drink ; but inftead of that, when the watei* comes up to his chin, it immediately begins tonbsp;defcend, and fo, as he cannot Hoop to follownbsp;it, he is left as much pained with third asnbsp;ever.

The device called the fountain at command afts upon the fame principle with the fyphon innbsp;the cup. Let two veflels A and B be joinednbsp;together by the pipe C which opens into themnbsp;both. Let A be open at top, B clofe both atnbsp;top and bottom (fave only a fmall hole at h tonbsp;let the air get out of the veflTel B) and A be ofnbsp;fuch a fize, as to hold about fix times as muchnbsp;water as B. Let a fyphon D E Fhc foldered tonbsp;the veflel X), fo that the part D Ee may benbsp;within the velTel, and F without it; the end Dnbsp;almoft touching the bottom of the velTel, andnbsp;the end F below the level of D: the veflel Bnbsp;hanging to A by the pipe C (foldered into both)nbsp;and the whole fupported by the pillars G and Hnbsp;upon the ftand L The bore of the pipe multnbsp;be confiderably lefs than the bore of the fyphon.

The whole being thus conftrudled, let the velTel A be filled with water, which will runnbsp;through the pipe C, and fill the veflel B. Whennbsp;B is filled above the top of the fyphon at E, thenbsp;water will run through the fyphon, and be dif-charged at F. But as the bore of the fyphonnbsp;is larger than the bore of the pipe, the fyphonnbsp;will run fafter than the pipe, and will foonnbsp;empty the velTel B-, upon which the water willnbsp;ceafe from running through the fyphon at F,nbsp;until the pipe C re-fills the velTel B, and then itnbsp;will begin to run as before. And thus the fyphon will continue to run and flop alternately,nbsp;until all the water in the veflel A has run

through the pipe C�So that after a fe\v trials, one may eafily guefs about what time the fy-phon will flop, and when it will begin to run :nbsp;and then, to amufe others, he may call cutnbsp;or run, accordingly.

Upon this principle, we may eafily account for intermitting or reciprocating fprings. L,ec/�^

J J be part of a hill, within which there is z,^prings. cavity EB-, and from this cavity a vein or t^ig. 2.nbsp;channel running in the diredion BCVE. Thenbsp;rain that falls u^on the fide of the hill will finknbsp;and ftrain through the fmall pores and craniesnbsp;G, G, G, G; and fill the cavity with water K.

When the water rifes to the level HH C, the vein BCDE will be filled to C, and the waternbsp;will run through CDF as through a fyphon ;nbsp;which running will continue until the cavity benbsp;emptied, and then it will ftop until the cavitynbsp;be filled again.

The common pump (improperly called the fuck- The coming pump), with,which we draw water out oimonpump. wells, is an engine both pneumatic and hydraulic.

It confifts of a pipe open at both ends, in which is a moveable pifton or bucket, as big as thenbsp;bore of the pipe in that part wherein it works ;nbsp;and is leathered round, fo as to fit the borenbsp;exadly ; and may be moved up and down, without fuffering any air to come between it and thenbsp;pipe or pump barrel.

We fliall explain the conftrudion both of this and the forcing-pump by pictures of glafsnbsp;models, in which both the adion of the piftonsnbsp;and motion of the valves are leen.

Hold the model DCBL upright in the veffel of water K, the water being deep enough tonbsp;rife at lead; as high as from A to L. The valvenbsp;a on the moveable bucket G, and the valve bnbsp;I 2nbsp;nbsp;nbsp;nbsp;on

on the fixed box //, (which box quite fills the bore of the pipe or barrel at H) will each lienbsp;clofe, by its own weight, upon the hole in thenbsp;bucket and box, until the engine begins tonbsp;work. The valves are made of brafs, andnbsp;lined underneath with leather for covering thenbsp;holes the more clofely: and the bucket G is inbsp;raifed and deprefied alternately by the handle E 'nbsp;and rod D d, the bucket being fuppofcd at Bnbsp;before the v/orking begins.

Take hold of the handle E, and thereby draw up the bucket from B to C, which willnbsp;make room for the air in the pump all the waynbsp;below the bucket to dilate itfelf, by which itsnbsp;fpring is weakened, and then its force is notnbsp;equivalent to the weight or prefllire of the out-wat4 -air upon the water in the veflel K: andnbsp;therefore, at the fir ft ftroke, the outward airnbsp;wifi prefs up the water through the notchednbsp;fbot A, into the lower pipe, about as far as e:nbsp;this will condenfe the rarefied air in the pipenbsp;between e and C to the fame ftate it was in before �, and then, as its fpring within the pipenbsp;is equal to the force or preffure of the outwardnbsp;air, the water will rife no higher by the firftnbsp;ftroke i and the valve lgt;, which was raifed anbsp;little by the dilatation of the air in the pipe, willnbsp;fall, and ftop the hole in the box H; and thenbsp;furface of the water will ftand at e. Then,nbsp;deprefs the pifton or bucket from C to B, andnbsp;as the air in the part B cannot get back againnbsp;through the valve it will (as the bucket de-fcends) raife the valve a, and fo rhake its waynbsp;through the upper part of the barrel d into thenbsp;open air. But upon raifing the bucket G a fe-cond time, the air between it and the water innbsp;the lower pipe at a will be again left at liberty to

fill a larger fpace; and fo its fpring being again weakened, the preffure of the outward air onnbsp;the water in the velTel K will force more waternbsp;up into the lower pipe from e to and whennbsp;the bucket is at its greateft height C, the lowernbsp;valve h will fall, and ftop the hole in the boxnbsp;U as before. At the next ftroke of the bucketnbsp;or pifton, the water will rife through the boxnbsp;H towards 5, and then the valve b, which wasnbsp;raifed by it, will fall when the bucket G is atnbsp;its greateft height. Upon depreffing the bucketnbsp;again, the water cannot be pulhed back throughnbsp;the valve I, which keeps clofe upon the holenbsp;whilft the pifton delcends. And upon railingnbsp;the pifton again, the outward preffure of the airnbsp;will force the water up through �/, where it willnbsp;raife the valve, and follow the bucket tonbsp;C. Upon the next depreffion of the bucketnbsp;G, it will go down into the water in the barrelnbsp;B; and as the water cannot be driven backnbsp;through the now dole valve it will raife thenbsp;valve a as the bucket defcends, and will benbsp;lifted up by the bucket when it is next raifed.nbsp;And now, the whole fpace below the bucketnbsp;being full, the water above it cannot fink w'hennbsp;it is next depreffed; but upon its deprclfion,nbsp;the valve a will rife to let the bucket go down ;nbsp;and when it is quite down, the valve a will fallnbsp;by its weight, and ftop the hole in the bucket.nbsp;quot;When the bucket is next raifed, all the waternbsp;above it will be lifted up, and begin to run offnbsp;by the pipe F. And thus, by raifing andnbsp;depreffing the bucket alternately, there is ftillnbsp;more water raifed by it �, which getting abovenbsp;the pipe F, into the wide top Z, will fupplynbsp;the pipe, and make it run cvith a continuednbsp;ftream.

So, at every time the bucket is raifed, the valve b riles, and the valve falls; and at everynbsp;time the bucket is deprefled, the valve b falls,nbsp;and a riles.

As it is the preflure of the air or atmofphere which caiifes the water to rife, and follow thenbsp;pifton or bucket G as it is drawn up; and fincenbsp;a column of water 33 feet high is of equalnbsp;weight with as thick a column of the atmofphere, from the earth to the very top of the air;nbsp;therefore, the perpendicular height of the piftonnbsp;or bucket from the furface of the water in thenbsp;well muft always be lei's than 33 feet; otherwifenbsp;the water will never get above the bucket.nbsp;But, when the height is lefs, the prefture of thenbsp;atmofphere will be greater than the weight ofnbsp;the water in the pump, and will therefore raifenbsp;it above the bucket: and when the water hasnbsp;once got above the bucket, it may be liftednbsp;thereby to any height, if the rod D be madenbsp;long enough, and a fufficienr degree of ftrengthnbsp;be employed, to raife it with the weight of thenbsp;water above the bucket.

The force required to work a pump, will be as the height to which the water is raifed, andnbsp;as the fquare of the diameter of the pump-bore,nbsp;in that part where the pifton works. So that,nbsp;if two pumps be of equal heights, and one ofnbsp;them be twice as wide in the bore as the other,nbsp;the wideft will raife four times as much waternbsp;as the narroweft; and will therefore require fournbsp;times as much ftrength to work it.

The widenefs or narrownefs of the pump, in any other part befides that in which the piftonnbsp;works, does not make the pump either more ornbsp;lefs difficult to work, except what differencenbsp;may arife from the fridion of the water in the

bore j which is always greater in a narrow bore than in a wide one, becaufe of the greaternbsp;velocity of the water.

The pump-rod is never raifcd direftly by fuch a handle as E at the top, but by means of anbsp;lever, whofe longer arm (at the end of whichnbsp;the power is applied) generally exceeds thenbsp;length of the fliorter arm five or fix times; and,nbsp;by that means, it gives five or fix times as muchnbsp;advantage to the power. Upon thefe principles,nbsp;it will be eafy to find the dimenfions of a pumpnbsp;that Ihall work with a given force, and drawnbsp;water from any given depth. But, as thefenbsp;calculations have been generally negledted bynbsp;pump-makers (either for want of fkill or in-duftry) the following table was calculated by thenbsp;late ingenious Mr. Booth for their benefit*.nbsp;In this calculation, he fuppofed the handle ofnbsp;the pump to be a lever increafing the powernbsp;five times; and had often found that a man cannbsp;work a pump four inches diameter, and 30 feetnbsp;high, and difcharge 274- gallons of water (Eng-lilh wine meafure) in a minute. Now, if it benbsp;required to find the diameter of a pump, thatnbsp;Ihall raife water with the fame eafe from anynbsp;other height above the furface of the well-, looknbsp;for that height in the firft column, and over-againft it in the fecond you have the diameter ornbsp;width of the pump; and in the third, you findnbsp;the quantity of water which a man pf ordinarynbsp;ftrength can difcharge in a minute.

� I have taken the liberty to make 3 few alterations in Mr. Booth�i numbers in the table, and to lengthen it outnbsp;from 80 feet to too.

water through the box H when the plunger g was drawn up) falls down and flops the hole innbsp;H, the moment that the plunger is raifed to itsnbsp;greatefl height. Therefore, as the water between the plunger g and box H can neither getnbsp;through the plunger upon its defcent, nor backnbsp;a�ain into the lower part of the pump L e, butnbsp;has a free paffage by the cavity around H intonbsp;the pipe MM, which opens info the air-veflelnbsp;KK a.t P-, the water is forced through the pipenbsp;MM by the defcent of the plunger, and drivennbsp;into the air-veflel; and in running up throughnbsp;the pipe at P, it opens the valve a ; which fhucsnbsp;at the moment the plunger begins to be raif�d,nbsp;becaufe the a�lion of the water againft the undernbsp;fide of the valve then .ceafes.

The water, being thus forced into the air-veflel KK by repeated ftrokes of the plunger, gets above the lower end of the pipe G H /,nbsp;and then begins to condenfe the air in the veffelnbsp;K K. . For, as the pipe GH is fixed air-tightnbsp;into the vefTel below F, and the air has no waynbsp;to get out of the veffel but through tne mouthnbsp;of the pipe at �, and cannot get out when thenbsp;mouth 1 is covered with water, and is morenbsp;and more condenled as rhe water rifes uponnbsp;the pipe, the air then begins to aft forcibly bynbsp;its fpring againfl; the furface of the water at H:nbsp;and this aftion drives the water up through thenbsp;pipe IH G F, from whence it fpouts in a jet 5nbsp;to a great height; and is fl.ipplied by akerna'tclynbsp;raifing and depreifing of the plungerj-, whichnbsp;conftantly forces the water that it raifes throughnbsp;the valve H, along the pipe MM, into the air-veflTel K K.

The higher that the furface of the water H is raifed in the air-veffel, the lefs fpace will the

air be condenfed into, which before filled that veflel; and therefore the force of its fpring willnbsp;be fo much the ftronger upon the water, andnbsp;will drive it with the greater force through thenbsp;pipe at F: and as the fpring of the air continues vvhilft the plunger g is rifing, the ftrearnnbsp;or jet 5 will be uniform, as long as the aflionnbsp;of the plunger continues : and when the valve bnbsp;opens, to let the water follow the plunger upward, the valve � Ihuts, to hinder the water,nbsp;which is forced into the air veflel, from runningnbsp;back by the pipe M M. into the barrel of thenbsp;pump.

If there was no air-velTel to this engine, the pipe G/^/would be joined to the pipe MMNnbsp;at P j and then, the jet S would flop everynbsp;time the plunger is raifed, and run only whennbsp;the plunger is depreffed.

Mr. Newfiam's water-engine, for extinguifh-ing fire, confifts of two forcing-pumps, which alternately drive water into a clofe velTel of air ^nbsp;and by forcing the water into that veflTel, thenbsp;air in it is thereby condenfed, and compreiTesnbsp;the water fo ftrongly, that it rulhes out withnbsp;great impetuofity and force through a pipe thatnbsp;comes down into it j and makes a continuednbsp;uniform ftrearn by the condenfation of the airnbsp;upon its furface in the veflTel.

By means of forcing-pumps, water may be raifed to any height above the level of a rivernbsp;or fpring; and machines may be contrivednbsp;to work thefe pumps, either by a runningnbsp;ftrearn, a fall of water, or by horles. Annbsp;inftance in each fort will be fufficient to Ihewnbsp;the method.

Firft,

Firfl, by 3 running ftream, or a fall of wa- Plate XII. ter. Let AAhez wheel, turned by the fall ^�8- ��nbsp;of water BB-, and haye any number of cranksnbsp;(fuppofe fix) as C, A A A G, H, on its axis,nbsp;according to the ftrength of the fall of water,nbsp;and the height to which the water is intended tonbsp;be raifed by the engine. As the wheel turnsnbsp;round, thefe cranks move the levers c, d, e,f,gj h A pumpnbsp;up and down, by the iron rods /, I, m, n, o-, engine tonbsp;which alternately raife and deprefs the piftons bynbsp;the other iron rods /gt;, q, r, f /, �, x, jy, innbsp;twelve pumps �, nine whereof, as Z-, M, Ny 0, P,

P, S, Ty appear in the plate; the other three being hid behind the work at V. And as pipesnbsp;may go from all thefe pumps, to convey thenbsp;water (drawn up by them to a fmall height) intonbsp;a clofe cittern, from which the main pipe goesnbsp;off, the water will be forced into this citternnbsp;�by the deiceht of the piftons. And as eachnbsp;pipe, going from its refpedive pump into thenbsp;cittern, has a valve at its end in the cittern,nbsp;thefe valves will hinder the return of the waternbsp;by the pipes ; and therefore, when the citternnbsp;is once full, each pifton upon its defcent willnbsp;force the water (conveyed into the cittern by anbsp;former ftroke) up the main pipe, to thenbsp;height the engine was intended to raife it:nbsp;which height depends upon the quantity raifed, �nbsp;and the power that turns the wheel. Whennbsp;the power upon, the wheel is leflTened by anynbsp;dcfeft of the quantity of water turning it, anbsp;proportionable number of the pumps may benbsp;fet afide, by difengaging their rods from thenbsp;vibrating levers.

This figure is a reprefentation of the engine eredbed at Blenheim for the Duke of Marlboroughynbsp;by the late ingenious Mx, Alderfea, The water-Inbsp;nbsp;nbsp;nbsp;wheel

wheel is feet in diameter, according to Mr, Switzer's account in his Hydraulics,

When fuch a machine is placed in a ftream that runs upon a fmall declivity, the motion ofnbsp;the levers and adion of the pumps will be butnbsp;flow �, fince the wheel muft go once round fornbsp;each ftroke of the pumps. Bur, when there is anbsp;large body of flow running water, a cog or fpur-wheel may be placed upon each fide of thenbsp;water-wheel A A., upon its axis, to turn a trundlenbsp;upon each fide; the cranks being upon the axisnbsp;of the trundle. And by proportioning the cogwheels to the trundles, the motion of the pumpsnbsp;may be made quicker, according to the quantitynbsp;and ftrength of the water upon the firft wheel jnbsp;which may be as great as the workman pleafes jnbsp;according to the length and breadth of the float-boards or wings of the wheel. In this manner,nbsp;the engine for raifing water at London-Bride isnbsp;conftrudled ; in which, the water-wheel is 20nbsp;feet diameter, and the floats 14 feet long.

engine t� and gentlemen want to have water raifed, and goquot;bynbsp;nbsp;nbsp;nbsp;brought to their houfes from a rivulet or fpring;

three forcing pumps which ftand in a refervoir filled by the fpring or rivulet: the piftons beingnbsp;moved up and down in the pumps by means of anbsp;triple crank ABC, w'hich, as it is turned roundnbsp;by the trundle G, raifes and deprelTes the rodsnbsp;D,E,F. The trundle may be turned by fuch anbsp;wheel as Fin Fig. i. of Plate VIII, having leversnbsp;y,y,y,y, on its upright axle, to which horfes maynbsp;be joined for working the engine.- And if thenbsp;wheel has three times as many cogs as thenbsp;trundle has ftaves or rounds, the trundle andnbsp;cranks will make three revolutions for every one

�f

of the wheel: and as each crank will fetch a ftroke in the time it goes round, the three cranksnbsp;will make nine ftrokes for every turn of the greatnbsp;wheel.

The cranks fliould be made of call iron, be-caufe that will not bend; and they fliould each make an angle of 120 with both of the others,nbsp;as atnbsp;nbsp;nbsp;nbsp;which is (as it were) a view of their piajg xil.

ro.dii�, in looking endwife at the axis: and then Fig. 2. there will be always one or other of them goingnbsp;downward, which will pufli the water forwardnbsp;with a continued ftream into the main pipe.

For, when b is almoft at its lowed; pofiion, and is therefore juft beginning to lofe its aftion uponnbsp;the pifton which it moves, c is beginning to movenbsp;downward, which will by its pifton continue thenbsp;propelling force upon the water; and when c isnbsp;come down to the pofition of b^ a will be in thenbsp;pofition of c.

The more perpendicularly the pifton rods move up and down in the pumps, the freer andnbsp;better will their ftrokes be: but a little deviation from the perpendicular will not be material.nbsp;Therefore, when the pump-rods D, F, and Fnbsp;go down into a deep well, they may be movednbsp;diredtly by the cranks, as is done in a very goodnbsp;horfe-engine of this fort at the late Sir famesnbsp;Creed�s, at Greenwich^ which forces up water aboutnbsp;64 feet from a well under ground, to a refervoirnbsp;on the top of his houfe. But when the cranksnbsp;are only at a Imall height above the pumps, thenbsp;piftons muft be moved by vibrating levers, as innbsp;the above engine at Blenheim: and the longernbsp;the levers are, the nearer will the ftrokes be to

Let us fuppofe, that in fuch an engine as Sir a calcu-fames Creed�s., the great wheel is 12 feet diame- la'ioquot; ter, the trundle 4 feet, and the radius or length

water that of each crank 9 inches, working a pifton in its way be pump. Let ther be three pumps in all, and thenbsp;bore of each piimp be four inches diameter.nbsp;Then, if the great wheel has three times as manynbsp;cogs as the trundle has ftaves, the trundle andnbsp;cranks will go three times round for each revolution of the horfes and wheel, and the threenbsp;cranks will make nine ftrokes of the pumps iiinbsp;that time, each ftroke being 18 inches (or doublenbsp;the length of the crank) in a four-inch bore. Letnbsp;the diameter of the horfe-walk be 18 feet, andnbsp;the perpendicular height to which the water isnbsp;raifed above the furface of the well be 64 feet.

If the horfes go at the rate of two miles an hour (which is very moderate walking) they willnbsp;turn the great wheel 187 times round in annbsp;hour.

In each turn of the wheel the piftons make 9 ftrokes in the pumps, which amount to 1683nbsp;an hour.

Each ftroke raifes a column of water 18 inches long, and four inches thick, in the pump-barrels ; which column, upon the defcent of thenbsp;pifton, is forced into the main pipe, whofe perpendicular altitude above the furface of the wellnbsp;is �4 feet.

Now, fince a column of water 18 inches long, and 4 inches thick, contains 226.18 cubic inches,nbsp;this nun bcr multiplied by 1683 (the ftrokes innbsp;an hour gi cs 380061 for the number of cubicnbsp;inches of vater raifed in an hour.

A gallon, in wine meafure, contains 231 cubic inches, by which divide 380661, and it quotesnbsp;1468 in round numbers, for the number of gallons raifed in an hour; which, divided by 63,nbsp;gives 26f hogfiieads. �if the horfes go fafter,nbsp;the quaniuy railed will be fo much the greater.

is wafted by the engine. But as no forcing engine can be fuppofed to loie lefs than a fifthnbsp;part of the calculated quantity of water, betweennbsp;the piftons and barrels, and by the opening andnbsp;(hutting of the valves, the hoffes ought to walknbsp;altnoft 2i- miles per hour, to fetch up this lofs,

A column of water 4 inches thick, and 64 feet high, weighs 349-i-�-s-pounds avoirdupoife, ornbsp;424x-5-pounds troy i and thisweight together withnbsp;the friftion of the engine, is the refiftance thatnbsp;muft be overcome by the ftrength of the horfes.

The horfe-tackle (hould be fo contrived, that the horfes may rather pulh on than drag thenbsp;levers after them. For if they draw, in goingnbsp;round the walk, the outfide leather (traps willnbsp;rub againft their Tides and hams ; which willnbsp;hinder them from drawing at right angles to thenbsp;levers, and fo make them pull at a diladvantage.nbsp;But if they pulh the levers before their breafts,nbsp;inftead of dragging them, they can always walknbsp;at right angles to thefe levers.

It is no ways material what the diameter or the main or condufl pipe be; for the wholenbsp;refiftance of the water therein, againft the horfesnbsp;will be according to the height to which it isnbsp;raifed, and the diameter of that part of the pumpnbsp;in which the pifton works, as we have alreadynbsp;obferved. So that by the fame pump, an equalnbsp;quantity of water may be raifed in (and confe-quently made to run from) a pipe of a foot diameter, with the fame eafe as in a pipe of five ornbsp;fix inches : or rather with more eafe, becaufe itsnbsp;velocity in a large pipe will be lefs than in anbsp;fmall one �, and therefore its friftion againft thenbsp;fides of the pipe will be lefs alfo.

And the force required to raife water depends not upon the length of the pipe, but upon thenbsp;perpendicular height to which it is raifed therein

above the level of the fpring. So that the fam� force, which would taife water to the height ABnbsp;in the upright pipe Aiklmnop g Bi will raife itnbsp;to the fame height or level B I H m the obliquenbsp;pipe AEFGH. For the preflure of the water atnbsp;the end A of the latter, is no more that its pref-fure againft the end A of the former.

The weight or preflure of water at the lower end of the pipe, is always as the fine of thenbsp;angle to which the pipe is elevated above thenbsp;level parallel to the horizon. For, although thenbsp;water in the upright pipe A B would require anbsp;force applied immediately to the lower end Anbsp;equal to the weight of all the water in it, to fup-port the water, and a little more to drive it up,nbsp;and out pf the pipe-, yet, if that pipe be inclinednbsp;from its upright pofition to an artgle of 80 degrees (as in A 80) the force required to fupportnbsp;or to raife the fame cylinder of water will thennbsp;be as much lefs, as the fine 80 h is lefs than thenbsp;radius AB\ or as the fine of 80 degrees is lefsnbsp;than the fine of 90. And fo, decreafing as thenbsp;fine of the angle of elevation leflens, until it arrives at its level AC or place of reft, where thenbsp;force of the water is nothing at either end of thenbsp;pipe. For, although the abfolute weight of thenbsp;water is the fame in all potitions, yet its pref-fure at the lower end decreafes, as the fine of thenbsp;angle of elevation decreafes; as will appear plainly by a farther confideration of the figure.

Let two pipes, A B and AC, of equal lengths and bores, join each other at A; and let thenbsp;pipe A B he divided into 100 equal parts, asnbsp;the fcale S is; whofe length is equal to thenbsp;length of the pipe.�Upon this length, as anbsp;radius, defcribe the quadrant BCD, and dividenbsp;it into qo equal parts or degrees.

upon the quadrant, and filled with Water j then, part of the water that is in it will rife innbsp;the pipe HB, and if it be kept full of water, itnbsp;will raife the water in the pipe AB from Ax.oi-,nbsp;that is, to a level i lo with the mouth of thenbsp;pipe at lo: and the upright line a lo, equal tonbsp;Ai, will be the fine of lo degrees elevation ^nbsp;which being meafured upon the fcale 5, will benbsp;about 17.4 of fuch parts as the pipe containsnbsp;100 in length: and therefore, the force or pref-fure of the water at A, in the pipe A 10, willnbsp;be to the force or prefiTure at A in the pipenbsp;A B, as 17.4 to 100.

Let the fame pipe be elevated to 20 degrees in the quadrant, and if it be kept full of water,nbsp;part of that water will run into the pipe AB,nbsp;and rife therein to the height Ak, which isnbsp;equal to the length of the upright line b 20, ornbsp;to the fine of 20 degrees elevation; which, being meafured upon the fcale 5, will be 34.2 ofnbsp;fuch parts as the pipe contains 100 in length.nbsp;And therefore, the preffure of the water at A,nbsp;in the full pipe ^20, will be to its preflure, ifnbsp;that pipe were raifed to the perpendicular fitua-tion AB^ as 34.2 to 100.

Elevate the pipe to the pofition A 30 on the quadrant, and if it be fupplied with water, thenbsp;water will rife from it, into the pipe AB^ tonbsp;the height A /, or to the fame level w'ith thenbsp;mouth of the pipe at 30. The fine of this elevation, or of the angle of 30 degrees, is r 30;nbsp;which is juft equal to half the length of the pipe,nbsp;or to 50 of Inch parts of the fcale, as the lengthnbsp;of the pipe contains leo. Therefore, the preffure of the 'water at A^ in a pipe elevated 30nbsp;degrees above the horizontal level, will be equalnbsp;to one half of what it would be, if the famenbsp;pipe flood upright in the lituation AB.

Of Hydraulic Engines.

And thus, by elevating the pipe to 40, 50, 60, 70, and 80 degrees on the quadrant, thenbsp;fines of thefe elevations will be d 40, e 50,/60,nbsp;g 70, and b 80; which will be equal to thenbsp;heights Jm, Jn, Jo, Jp, and Jq: and thefe

Sine of	Parti	Sine of	Parts	Sine of	Par s
D,i	17	D.31	515	D.61	875
2	35	32	530	62	883
3	52	33	545	63	891
4	70	34	559	64	899
5	87	35	573	65	906
6	104	3�	588	66	9�3
7	122	37	602	67	920
8	139	38	616	68	927
9	156	39	629	69	934
10	174	40	643	70	940
11	191	41	656	7'	945
12	208	42	669	72	95 �
13	225	43	682	73	95�
H	242	44	695	74	961
15	259	45	707	75	966
16	276	46	719	76	970
^7	292	47	73 ^	77	974
18	309	48	743	78	978
19	325	49	755	79	982
20	342	50	y6B	80	985
21	358	51	777	81	988
22	375	52	788	82	990
23	391	53	799	83	992
24	407	54	809	84	994
25	423	55	819	85	996
26	438	56	829	80	997
27	454	57	839	8.7	998
28	469	58	848	88	999
29	485	59	857	89	1000
30	500	�0	866	90	1000

heights meafured upon the fcale S Will be 64.3, 76.6, 86.6, 94-0, and 98.5 �, whichnbsp;exprefs the prelTures at in all rhefe elevations,nbsp;confidering the preffure in the upright pipe ABnbsp;as 100.

Becaufe it may be of ufe to have the lengths of all the fines of a quadrant from o degreesnbsp;to 90, we have given the foregoing table, (hewing the length of the fine of every degree innbsp;fuch parts as the whole pipe (equal to the radiusnbsp;of the quadrant) contains 1000. Then the finesnbsp;will be integral or whole parts in length. Butnbsp;if you fuppofe the length of the pipe to be divided only into too equal parts, the laft figurenbsp;of each part or fine muft be cut off as a decimal;nbsp;and then thofe which remain at the left handnbsp;of this reparation will be integral or wholenbsp;parts.

Thus, if the radius of the quadrant (fup-pofed to be equal to the length of the pipe AC) be divided into 1000 equal parts; and the elevation be 45 degrees, the fine of that elevationnbsp;will be equal to 707 of thefe parts: but if thenbsp;radius be divided only into 100 equal parts, thenbsp;fame fine will be only 70,7 or 70-iV of thefenbsp;parts. For, as 1000 is to 707, fo is ico tonbsp;70.7.

As it is of great importance to all engine-makers, to know what quantity and weight of water will be contained in an upright, roundnbsp;pipe of a given diameter and height; fo as bynbsp;knowing what weight is to be raifed, they maynbsp;proportion their engines to the force whichnbsp;they can afford to work them; we fiiall fubjoinnbsp;tables Ihewing the number of cubic inches ofnbsp;Water contained in an upright pipe of a roundnbsp;bore, of any diameter from one inch to fix andnbsp;K 2nbsp;nbsp;nbsp;nbsp;a half s

a half; and of any height from one foot to two hundred : together with the weight of the faidnbsp;number of cubic inches, both in troy and avoir-dupoife ounces. The number of cubic inchesnbsp;divided by 231, will reduce the water to gallons in wine meafure; and divided by 282, willnbsp;reduce it to the meafure of ale gallons. Allb,nbsp;the troy ounces divided by 12, will reduce thenbsp;weight to troy pounds; and the avoirdupoifenbsp;ounces divided by 16, will reduce the weightnbsp;to avoirdupoife pounds.

And here I muft repeat it again, that the weight or preffure of the water adting againftnbsp;the power that works the engine, muft alwaysnbsp;be eftimated according to the perpendicularnbsp;height to which it is to be raifed, without anynbsp;regard to the length of the condu6l-pipe, whennbsp;it has an oblique pofition; and as if the diameter of that pipe were juft equal to the diameternbsp;of that part of the pump in �which the piftonnbsp;works. Thus, by the following tables, thenbsp;preffure of the water, againft an engine whofenbsp;pump is of a inch bore, and the perpendicular height of the water in the conduct-pipe isnbsp;80 feet, will be equal to 8057.5 troy ounces,nbsp;and to 8848.2 avoirdupoife ounces �, whichnbsp;makes 671.4 troy pounds, and 553 avoirdu-pofe.

For any bore whofe diameter exceeds S-inches, multiply the numbers on the following page, againft any height, (belonging to i inchnbsp;diameter) by the fquare of the diameter of thenbsp;given bore, and the products will be the number of cubic inches, troy ounces, and avoirdupoife ounces of water, that the given bore willnbsp;contain.

Hydrcftatical �Tables.

I Inch diameter.
r� rD	Quantity	Weight	In avoir-
	in cubic	in troy	dupoife
f	inches.	ounces.	ounces.
I	9.42	4-97	5.46
2	11.85	9-95	10.92
3	28,27	14.92	16.38
4	37-70	19.89	21.85
5	47.12	24.87	27.31
6	56.55	29.84	32-77
7	65.97	34.82	38.23
8	75-40	39-79	43-69
9	84.82	44-76	49.16
10	94-25	49 74	54-62
20	188.49	99.48	109.24
30	282.74	149.21	163.86
40	376.99	198.95	218.47
50	471-24	248,69	273.09
60	565.49	298.43	327-71
70	659-73	348-17	382.23
80	753-98	397-90	436-95
90	848.23	447.64	4.91.57
100	942.48	497-38	546.19
200	1884.96	994.76	1092.38

Example, Required the number of cubic inches, and the �weight of the �water, in an upright pipe 2-.'b, feet high, andnbsp;\\ inch diameter ?nbsp;nbsp;nbsp;nbsp;e e, j-r / Jnbsp;nbsp;nbsp;nbsp;s

200�4241.1 -2238.2--Z457.3 70-�484.4- 783.3- 860.2nbsp;8- 1696-nbsp;nbsp;nbsp;nbsp;895-nbsp;nbsp;nbsp;nbsp;98.3

Thefe tables were at firfl: calculated to fix decimal places for the fake of exadnefs ; butnbsp;in tranfcnbing them there are no more thannbsp;two decimal figures taken into the account, andnbsp;fometimes but one-, becaufe there is no neceffity

Hydrojiatical Talles.

for computing to hundredth parts of an inch or of an ounce in pradtice. And as they nevernbsp;appeared in print before, it may not be amiisnbsp;to give the reader an account of the principlesnbsp;vTpon which they were conftriiaed.

The

Hydrojiatical tables.

The folidity of cylinders are found by multiplying the areas of their bafes by their altitudes. And Archimedes gives the following proportion for finding the area of a circle, andnbsp;the folidity of a cylinder raifed upon that circle;

Hydrcftatical �Tables.

As I is to 0.78535^, fo is the fquare of the diameter to the area of the circle. And as i isnbsp;to 0.785399, fo is the fquare of the diameternbsp;multiplied by the height to the folidiry of thenbsp;cylinder. By this analogy the folid inches and

parts of an inch in the tables are calculated to a cylinder 200 feet high, of any diameter from inbsp;inch to 64, and may be continued at pleafure.

And as to the weight of a cubic foot of running water, it has been often found upon trial, by

Hydrojiaiical �Tables.

quently, if the number of cubic inches contained in any given cylinder, be divided by 1.8949, it will give the weight in troy ounces;nbsp;and divided by 1.72556, will give the weight

Hydroftatical �Tables.

in avoirdupoife ounces. By this method, the weights fhevvn in the tables were calculated ;nbsp;and are near enough for any common praftice.

The fire-engine comes next in order to be ex- The/n plained; but as it would be difficult, even by engint.

the

Hydroftatical �Tables'^

the beft plates, to give a particular defcription of its feveral parts, fo as to make the wholenbsp;intelligible, I fliall only explain the principlesnbsp;upon which it is conftruifted.

Hydrojiatical �Tables'.

1. Whatever weight of water is to be raifed, the pump-rod muft be loaded with weights fuf-ficient for that purpofe, if it be done by anbsp;forcins-pump, as is generally the cafe; and the

power

Hydroj�atical Tall�S^

power of the engine muft be fufficient for the weight of the rod, in order to bring it up.

2. It is known, that the atmoiphere prefles upon the furface of the earth with a force equalnbsp;to 15 pounds upon every fquare inch.

3. When

3. nbsp;nbsp;nbsp;When water is heated to a certain degree^nbsp;the particles thereof repel one another, and con-ftitute an elattic fluid, which is generally callednbsp;ft earn or vapour.

4. nbsp;nbsp;nbsp;Hot fleam is very elaftic and when it isnbsp;cooled by any means, particularly by its beingnbsp;mixed with cold water, its elafticity is deftroyednbsp;immediately, and it is reduced to water again.

5. nbsp;nbsp;nbsp;If a veffel be filled with hot fteam, andnbsp;then clofed, fu as to keep out the external air,nbsp;and all other fluids; when that fteam is by anynbsp;means condenfed, cooled, or reduced to water,nbsp;that water will fall to the bottom of the veiTe!;nbsp;and the cavity of the veflTel will be almoft a per-fe�l vacuum.

6. nbsp;nbsp;nbsp;Whenever a vacuum is made in any veffel,nbsp;the air by its weight will endeavour to ruflr intonbsp;the veffel, or to drive in any other body thatnbsp;will give way to its preffure; as may be eafilynbsp;feen by a common iyringe. For, if you flopnbsp;the bottom of a fyringe, and then draw up thenbsp;pifton, if it be fo tight as to drive out all thenbsp;air before it, and leave a vacuum within thenbsp;fyringe, the piflon being let go will be drivennbsp;down with a great force.

7. nbsp;nbsp;nbsp;The force with which the pifton is drivennbsp;down, when there is a vacuum under it, will benbsp;as the fquare of the diameter of the bore in thenbsp;Iyringe. That is to fay, it will be driven downnbsp;with four times as much force in a fyringe of anbsp;twodnch bore, as in a fyringe of one inch : fornbsp;the areas of circles are always as the fquares ofnbsp;their diameters.

8. nbsp;nbsp;nbsp;The preffure of the atmofphere beingnbsp;equal to 15 pounds upon a fquare inch, itnbsp;will be almoft equal to 12 pounds upon a circular inch. So that if the bore of the fyringe

be round, and one inch in diameter, the pifton^ will be preft down into it by a force nearly equalnbsp;to 12 pounds; but if the bore be two inchesnbsp;diameter, the pifton will be preft down v/ithnbsp;four times that force.

And hence it is eafy to find with what force the atmofphcre preffes upon any given numbernbsp;either of iquare or circular inches.

Thefe being the principles upon which this engine is conftrudled, we fnall next deferibe thenbsp;chief working parts of it: which are, i. Anbsp;boiler. 2. A cylinder and pifton. 3. A beamnbsp;or lever.

The hikr is a large veflel made of iron or copper; and commonly fo big as to containnbsp;about 2000 gallons.

The cylinder is about 40 inches diameter, bored fo fmooth, and its leathered pifton fittingnbsp;fo clofe, that little or no water can get betweennbsp;the pifton and Tides of the cylinder.

Things being thus prepared, the cylinder is placed upright, and the Ihank of the pifton isnbsp;fixed to one end of the beam, which turns on anbsp;center like a common balance.

' The boiler is placed under the cylinder, with a communication between them, which can benbsp;opened and ftiut occafionally.

The boiler is filled about half full of water, and a ftrong fire is placed under it: then, if thenbsp;communication between the boiler and the cylinder be opened, the cylinder will be filled withnbsp;hot fteam ; which would drive the pifton quitenbsp;out at the top of it. But there is a contrivancenbsp;by which the beam, when the pifton is near thenbsp;top of the cylinder, Ihuts the communication atnbsp;the top of the boiler within.

This is no fooncr fliut, than another is opened by which a little cold water is thrown upwardsnbsp;in a jet into the cylinder, which tnixing with thenbsp;hot fleam, condenfes it innnediately ; by whichnbsp;means a vacuum js made in the cylinder, andnbsp;the pifton is prefled down by the weight of thenbsp;atmofphere j and lb lifts up the loaded pump-rod at the other end of the beam.

If the cylinder be 42 inches in diameter, the pifton will be prefled down with a force greaternbsp;than 20000 pounds, and will confequently liftnbsp;up that weight at the oppofice end of the beam:nbsp;and as the pump-rod with its plunger is fixednbsp;to that end, if the bore where the plunger worksnbsp;were 10 inches diameter, the water would benbsp;forced up through a pipe of 180 yards perpendicular height.

But, as the parrts of this engine have a good deal of fridion, and muft work with a confi-derable velocity, and there is no fuch thing asnbsp;making a perfed vacuum in the cylinder, it isnbsp;found that no more than 8 pounds of prefllirenbsp;muft be allowed for, on every circular inch ofnbsp;the pifton in the cylinder, that it may makenbsp;about 16 ftrokes in a minute, about 6 feetnbsp;each.

Where the boiler is very large, the pifton will make between 20 and 25 ftrokes in a minute, and each ftroke 7 or 8 feet; which, in anbsp;pump of 9 inches bore, will raife upwards ofnbsp;300 hogftieads of water in an hour.

It is found by experience that a cylinder, 40 inches diameter, will work a pump 10 inchesnbsp;diameter, and 100 yards long: and hence wenbsp;can find the diameter and length of a pump,nbsp;that can be worked by any other Cylinder.

For

For the convenience of thofe who would make ufe of this engine for raifing water, wenbsp;lhal! fubjoin part of a table calculated by Mr.nbsp;Beighton, firevving how any given quantity ofnbsp;water may be raifcd in an hour, from 48 to 440nbsp;hoglheads; at any given depth, from 15 tonbsp;ICO yards; the machine working at the ratenbsp;of 16 ftrokcs/gt;er minute, and each ftroke beingnbsp;6 feet long.

One example cf the ufe of this table will make the whole plain. Suppofe it were requirednbsp;to draw 150 hogflieads per hour, at 90 yardsnbsp;depth -, in the fecond column from the rightnbsp;hand, I find the neareft number, viz. 149 hogf-heads 40 gallons, againft which, on the rightnbsp;hand, � find the diameter of the bore of the pumpnbsp;mull be 7 inches; and in the fame collateral line,nbsp;under the given depth 90,1 find 27 inches, thenbsp;diameter of the cylinder fit for that purpofe.�nbsp;And fo for any other.

Hydraulic ^ahle.

This table is c.Mcu'aied to the meafure of ale gallons, at 282 Cubic inches per gallon.

Water

Water may be railed by means of a ftream JB turning a wheel QBE, according to thenbsp;order of the letters, with buckets a, a, a, a, amp;c.nbsp;hung upon the wl;'eel by ftrong pins b, b, b, b,nbsp;amp;c. fixed in the ride of the rim : bur the wheelnbsp;mull be made as high ds the water is intendednbsp;to be railed above the level of that part of thenbsp;ftream in which the v/beel is placed. As thenbsp;wheel turns, the buckets on th^ right-hand gonbsp;down into the water, and aoquot; h'lied therewith, andnbsp;go up full on the left- land, until they ccme tonbsp;the top at K-, where they lirike againft the endnbsp;ft of the fixed trough M, and are thereby over-fet, and empty the water into the trough �, fromnbsp;which it may be conveyed in pipes to the placenbsp;which it is defigned for : and as each bucketnbsp;gets over the trough, it falis into a perpendicular pofition again, and goes down empty,nbsp;until it comes to the water at where it i.nbsp;filled as before. On each bucket is a fpring -,nbsp;which going over the top or crown of the bar mnbsp;(fixed to the trough M) raifes the bottom of thenbsp;bucket above the level of its mouth, and fonbsp;caufes it to empty all its water into the trough.

Sometimes this wheel is made to raife water no higher than its axle ; and then, inftead ofnbsp;buckets hung upon it, its fpokes C, d, e, �, g, ,nbsp;are made of a bent form, and hollow within ;nbsp;thefe hollows opening into the holes C, D, E, Ftnbsp;jn the oiitfide of the wheel, and alfo into thofenbsp;at 0 in the box N upon the axle. So that, asnbsp;the holes C, D, amp;c. dip into the water, it runsnbsp;into them ; and as the wheel turns, the waternbsp;rifts in the hollow fpokes, c, d, amp;c. and runsnbsp;out in a ftream P from the holes at O, and fallsnbsp;into the trough ^ from whence it is conveyednbsp;by pipes. And this is a very eafy way of raifing

The art of weighing different bodies in water, o'quot; ffe and thereby finding their fyecific gravities, or Cptcificnbsp;weights, bulk for bulk, was invented by Archimedes; of which we have the followingnbsp;account:

Hiero king of Syracufe, having employed a goldfmith to make a crown, and given him anbsp;mals of pure gold for that purpole, lufpeftednbsp;that the workman had kept back part of thenbsp;gold for liis own ufe, and made up the weightnbsp;by allaying the crown with copper. But thenbsp;king not knov.'ing how to find out the truth ofnbsp;that matter, referred it to /Irchitnedes �, whonbsp;having ftudied a long time in vain, found it outnbsp;at laft by chance. For, going into a bathing-tub of water, and obferving that he therebynbsp;raifed the water higher in the tub than it wasnbsp;before, he concluded inftantly that he had raifednbsp;is juft as high as any thing die could have done,nbsp;that was exaftly of his bulk : and confideringnbsp;that any otlier body of equal weight, and of Icfsnbsp;bulk than himfelf, could not have raifed thenbsp;water fo high as he did ; he immediately toldnbsp;the king, that he had found a method by whichnbsp;he could difcover whether there were any cheatnbsp;in the crown. For, fince gold is the heavieftnbsp;of all known metals, it mult be of lefs bulk,nbsp;according to its weight, than any other metal.

And therefore he defired that a mafs of pure gold, equally heavy with the crown whennbsp;weighed in air, Ihoiild be weighed againftnbsp;it in water; and if the crown was not allayed,nbsp;it would counterpoile the mafs of gold whennbsp;they were both immerfed in water, as well as itnbsp;did when they were weighed in air. But uponnbsp;L 4nbsp;nbsp;nbsp;nbsp;making

making the trial, he found that the mafs of gold weighed much heavier in water than thenbsp;crown did'. And not only fo, but that, whennbsp;the mafs and crown were immerl�d feparatelynbsp;in one vdiel of v/ater, the crown railed thenbsp;water much higher than the mafs did ; whichnbsp;fhewed it to be allayed v/ith fome ligher metalnbsp;that increafed its bulk. And fo, by makingnbsp;trials with different metals, all equally heavynbsp;with the crown when weighed in air, he foundnbsp;out the quantity of alloy in tire crow:..

The fpccihc gravities of bodies are as their weights, bulk for bulk; thus a body is faid tonbsp;have two or three times the fpeeific gravity ofnbsp;another, when it contains two or three times asnbsp;much matter in the fame fpace.

A body immerfed in a fluid will fink to the bottom, if it be heavier than its bulk of thenbsp;fluid. If it be fufpended therein, it will lofenbsp;as much of what it weighed in air, as its bulknbsp;of the fluid weighs. Hence, all bodies of equalnbsp;bulks, which would fink in fluids, lofe equalnbsp;weights when fufpended therein. And unequalnbsp;bodies lofe in proportion to their bulks.

The hydrojiatic balance differs very little from a common balance that is nicely made :nbsp;only it has a hook at the bottom of each fcale,nbsp;on which fmall weights may be hung by hoi'fe-hairs, or by filk threads. So that a body, fufpended by the hair or thread, may be immerfednbsp;in water without wetting the fcale from whichnbsp;it hangs.

If the body thus fufpended under the fcale, at one end of the balance, be firft counterpoifednbsp;^in air by weights in the oppofite fcale, and then

eravify Of- nbsp;nbsp;nbsp;amp;nbsp;nbsp;nbsp;nbsp;, r'r ,nbsp;nbsp;nbsp;nbsp;�

be put into the fcale from which the body hangs, as will reftore the equilibrium (without alteringnbsp;the weights in the oppofite fcale) that weight,nbsp;which reftores the equilibrium, will be equal tonbsp;the weight of a quantity of water as big as thenbsp;immerfed body. And if the weight of the bodynbsp;in air be divided by what it lofes in water, thenbsp;quotient will fliew how much that body is heavier than its bulk of water. Thus, if a guineanbsp;fufpended in air, be counterbalanced by 129nbsp;grains in the oppofite fcale of the balance; andnbsp;then, upon its being immerfed in water, it becomes fo much lighter, as to require y-J grainsnbsp;put into the fcale over it, to reftore the equilibrium, it Ihews that a quantity of water, ofnbsp;equal bulk with the guinea, weighs yf grains,nbsp;or y.25 ; by which divide 129 (the weight ofnbsp;the guinea in air) and the quotient will benbsp;iy.793 ; which fnews that the guinea is 17-79^nbsp;times as heavy as its bulk of water. And thus,nbsp;any piece of gold may be tried, by weighing itnbsp;firft in air, and then in water; and if uponnbsp;dividing the weight in air by the Jofs in water,nbsp;the quotient comes out to be 17.793, the gold .nbsp;is good; if the quotient be 18, or between 18nbsp;and 19, the gold is very fine ; but if it be lefsnbsp;than ly, the gold is too much allayed,.by beingnbsp;mixed with Tome other metal.

If filver be tried in this manner and found to be II times as heavy as water, it is verynbsp;fine; if it be lot times as heavy, it is ftand-ard ; but if it be of any lefs weight comparednbsp;with water, it is mixed with fome lighter metal, fuch as tin.

By this method, the fpecific gravities of all bodies that will fink in water, may be found.nbsp;But as to thofe which are lighter thaq water, as

moft

moft forts of wood are, the following method may be taken, to (hew how much lighter theynbsp;are than their refpedive bulks of water.

Let an upright ftud be fixed into a thick flat piece of brafs, and in this ftud let a fmall lever,nbsp;whofe arms are equally long, turn upon a finenbsp;pin as an axis. Let the thread which hangsnbsp;from the fcale of the balance be tied to one endnbsp;of the lever, and a thread from the body to benbsp;�weighed, tied to the other end. This done,nbsp;put the brafs and lever into a vefTel; then pournbsp;water into the veflTel, and the body will rife andnbsp;float upon it, and draw down the end of thenbsp;balance from which it hangs: then, put as muchnbsp;weight in the oppofite fcale as will raife that endnbsp;of the balance, fo as to puli the body down intonbsp;the water by means of the lever ; and thisnbsp;weight in the fcale will (hew how much the bodynbsp;is lighter than its bulk of water.

There are fome things which cannot be weighed in this manner, fuch as quickfilver,nbsp;fragments of diamonds, amp;c. becaufe they cannot be fufpended in threads; and muft thereforenbsp;be put into a glafs bucket, hanging by a threadnbsp;from the hook of one fcale, and counterpoifcdnbsp;by weights put into the oppofite fcale. Thus,nbsp;fuppofe you want to know the fpecific gravitynbsp;of quickfilver, with refpedt to that of water; letnbsp;the empty bucket be firft counterpoifcd in air,nbsp;and then the quickfilver put into it and weighed.nbsp;Write down the weight of the bucket, and alfonbsp;of the quickfilver; which done, empty thenbsp;bucket, and let it be immerfed in wafer as itnbsp;hangs by the thread, and counterpoifed thereinnbsp;by weights in the oppofite fcale : then, pournbsp;the quickfilver into the bucket in the water,nbsp;which will caufe it to preponderate ; and put as

much weight into the oppofite fcale as will re-ftore the balance to an equipoife ; and this weight will be the weight of a quantity of waternbsp;equal in bulk to the quickfilver. Laftly, divide the weight of the quickfilver in air, by thenbsp;weight of its bulk of water, and the quotientnbsp;v/ill fliew how much the quickfilver is heaviernbsp;than its bulk of water.

If a piece of brafs, glafs, lead, or filver, be immerfed and fufpended in different forts ofnbsp;fluids, the different Ioffes of weight therein willnbsp;Ihew how much it is heavier than its bulk of thenbsp;fluid-; the fluid being lighteft in which the immerfed body lofes leaft of its aerial weight. Anbsp;folid bubble of glafs is generally ufed for findingnbsp;the fpecific gravities of fluids.

Hence we have an eafy method of finding the fpecific gravities both of folids and fluids, withnbsp;regard to their fpecific bulks of commonnbsp;pump water, which is generally made a ffand-ard for comparing all others by,

Jn conflructing tables of fpecific gravities with accuracy, the gravity of water muff be repre-fented by unity or i.ooo, where three cyphersnbsp;are added, to give room for expreflang the ratiosnbsp;of other gravities in decimal parts, as in thenbsp;following table.

N. B. Although guinea gold has been generally reckoned 17.798 times as heavy as its bulk of water, yet, by many repeated trials, Inbsp;cannot fay that I have found it to be more thannbsp;j 7.200 (or i7t-5-) as heavy.

158 nbsp;nbsp;nbsp;Of the fpecifx Grfivities of Bodies.

A Table of the fpecific gravities of feveral folid and fluid bodies.

The

\0f the fpecific Gravities of Bodies. The Table concluded.

Take away the decimal points from the numbers in the right-hand column, or (which is the fame) multiply them by 1000, and they willnbsp;fhew how many avoirdupoife ounces are contained in a cubic foot of each body.

The ufe of the table of fpecific gravities will How to beft appear by an example. Suppofe a body to find oatnbsp;be compounded of gold and filver, and it is re-'!�� quan-quired to find the quantity of each metal innbsp;the compound.nbsp;nbsp;nbsp;nbsp;tion ia

Firft find the fpecific gravity of the com-matals. pound, by weighing it in air anti in water, andnbsp;dividing its aerial weight by what it lofes thereof in water, the quotient will ft^ew its fpecific

gravity, or how many times it is heavier than its bulk of water. Then, fubtrad the fpecificnbsp;gravity of filver (found in the table) from thatnbsp;of the compound, and the fpecific gravity of thenbsp;compound from that of gold; the firft remainedernbsp;fhews the bulk of gold, and the latter the bulknbsp;of filver, in the whole compound : and if thefenbsp;remainders be multiplied by the refpedive fpecific gravities, the produds will fhew the proportion of weights of each metal in the body.nbsp;Example.

Suppofe the fpecific gravity of the compounded body be 13 that of ftandard filver, (by the table) is 10.5, and that of gold 19.63: thereforenbsp;10.5 from 13, remains 2.5, the proportionalnbsp;bulk of the gold; and 13 from 19.63, remainsnbsp;6.63 the proportional bulk of filver in the compound. Then, the firft remainder 2.5, multiplied by 19.63, the fpecific gravity of gold,nbsp;produces 49.075 for the proportional weight ofnbsp;gold ; and the laft remainder 6.63 multipliednbsp;by 10.5, the fpecific gravity of filver producesnbsp;69.615nbsp;nbsp;nbsp;nbsp;proportional weight of filver in

the whole body. So that for every 49.07 ounces or pounds of gold, there are 69.6 pounds ornbsp;ounces of filver in the body.

Hence it is eafy to know whether any fufped;-ed metal be genuine,, or allayed, or counterfeit; by finding how much it is heavier than its bulknbsp;of water, and comparing the fame with thenbsp;table : if they agree, the metal is good; if theynbsp;differ, it is allayed or counterfeited.

A cubical inch of good brandy, rum, or other proof fpirits, weighs 235.7 grains: therefore, ifnbsp;a true inch cube of any metal weighs 235.7nbsp;grains lefs in fpirits than in air, it ftiews thenbsp;fpirits are proof. If it lofes lefs of its aerial

weight in fpirits, they are above proof; if it lofei more, they are under. For, the better thenbsp;fpirits are, they are the lighter; and the worlb,nbsp;the heavier. All bodies expand with heat andnbsp;contract with cold, but fome more and fome iefsnbsp;than others. And therefore the fpecific gravitiesnbsp;of bodies are not precifely the fame in lummernbsp;as in winter. It has been found, that a cubicnbsp;inch of good brandy is ten grains heavier in winter than in fummer; as much fpirit of nitre, 20nbsp;grains; vinegar 6 grains, and fpring-water 3.

Hence it is mod profitable to buy fpirits in winter, and fell them in fummer, fince they arenbsp;always bought and fold by meafure. It hasnbsp;been found, that 32 gallons of fpirits in winternbsp;will make 33 in fummer.

The expanfion of all fluids is proportionable to the degree of heat; that is, with a double ornbsp;triple heat a fluid will expand two or three timesnbsp;as much.

Upon thefe principles depends the conftruc- The ther tion of the thermometer, in which the globe ornbsp;bulb, and part of the tube, are filled with anbsp;fluid, which, when joined to the barometer, isnbsp;fpirits of wine tinged, that it may be more eafilynbsp;feen in the tube. But when thermometers are

In the thermometer, a fcale is fitted to the tube, to Ihew the expanfion of the quickfilver,nbsp;and confequently the degree of heat. And, asnbsp;Fahrenheit's fcale is moft in efteern at prefent, Inbsp;fhall explain the conftrudtion and graduation ofnbsp;thermometers according to that fcale.

Firft, Let the globe or bulb, and part of the tube, be filled with a fluid; then immerfe thenbsp;bulb in water juft freezing, or fnow juft thawing;

ing,; and even with that part in the fcale where the fluid then hands in the tube, place the number 32, to denote the freezing point: then putnbsp;the bulb under your arm-pit, when your body isnbsp;of a moderate degree of heat, fo that it maynbsp;acquire the fame degree of heat with your fltin inbsp;and when the fluid has rifen as far as it can bynbsp;that hear, there place the number 97 : thennbsp;divide the fpace between thefe numbers into 65nbsp;equal parts, and continue thofe divifions bothnbsp;above 97 and below 32, and number them accordingly.

This may be done in any part of the world j for it is found that the freezing point is alwaysnbsp;the fame in all places, and the heat of the humannbsp;body differs but very little ; fo that the thermometers made in this manner will agree with onenbsp;another ; and the heat of feveral bodies will benbsp;fliewn by them, and exprelTed by the numbersnbsp;upon the fcale, thus.

Air, in fevere cold w'eather, in our climate, from 15 to 25. Air in winter, from 26 to 42,nbsp;Air in fpring and autumm, from 43 to 53. Airnbsp;at midfummer, from 65 to 68. Extreme heatnbsp;of the fummer fun, from 86 to 100. Butternbsp;juft melting, 95. Alcohol boils with 174 ornbsp;175. Brandy with 190. Water 212. Oil ofnbsp;turpentine 550. Tin melts with 498, and leadnbsp;with 540. Milk freezes about 30, vinegar 38,nbsp;and blood 27.

A body fpecifically lighter than a fluid will fwim upon its furface, in fuch a manner, that anbsp;quantity of the fluid equal in bulk with thenbsp;immerfed part of the body, will be as heavy asnbsp;the w'hole body. Hence, the lighter a fluid is,nbsp;the deeper a body will fink in it; upon which

From this we can eafily find the weight of a How the fhip, or any other body that floats in water, wfight ofnbsp;For, if we multiply the number of cubic feet �nbsp;which are under the furface, by 62.5, the number git^ated.nbsp;of pounds in one cubic foot of frelh water; or bynbsp;64.4, the number of pounds in a cubic foot ofnbsp;fait water; the prodiidl will be the weight ofnbsp;the fhip, and all that is in it For, fince it isnbsp;the weight of the fhip that difplaces the water,nbsp;it muft continue to fink until it has removed asnbsp;much water as is equal to it in weight; andnbsp;therefore the part immerfed rnuft be equal innbsp;bulk to fuch a portion of the water as is equalnbsp;to the weight of the whole fhip.

To prove this by experiment, let a ball of fome light wood, iiich as fir or pear-tree, benbsp;put into water contained in a glafs veffel; andnbsp;let the velTel be put into a fcale at one end of anbsp;balance, and counterpoifed by weights in thenbsp;oppofite fcale: then, marking the height of thenbsp;water in the veflel, take out the ball; and fillnbsp;up the veffel with water to the fame height thatnbsp;it flood at when the ball was in it; and the famenbsp;weight will counterpoife it as before.

From the veffel�s being filled up to the fame height at which the water flood when the ballnbsp;was in it, it is evident that the quantity pourednbsp;in is equal in magnitude to the immerfed partnbsp;of the ball; and from the fame weight coun-terpoifing, it is plain that the water poured in,nbsp;is equal in weight to the whole ball.

In troy weight, 24 grains make a pennyweight, 20 pennyweights make an ounce, and 12 ounces a pound. In avoirdupoife weight,

pound. The troy pound contains 5760 grains, and the avoirdupoife pound 7000 ; quot;and hence,nbsp;the avoirdupoite dram weighs 27.34375 grains,nbsp;and the avoirdupoife ounce 437-5.

Becaufe it is often of ufe to know how much any given quantity of goods in troy weight donbsp;make in avoirdupoife weight, and the reverfe ;nbsp;we {hall here annex two tables for convertingnbsp;thefe weights into one another. Thofe fromnbsp;page 135 to page 146 are near enough for common hydraulic purpofes; but the two followingnbsp;are better, where accuracy is required in comparing the weights with one another : and Inbsp;find, by trial, that 175 troy ounces are precifelynbsp;equal to 192 avoirdupoife ounces, and 175 troynbsp;pounds are equal to 144 avoirdupoife. Andnbsp;although there are feveral leffer integral numbers, which come very near to agree together,nbsp;yet I have found none lefs than the above tonbsp;agree exaftly. Indeed 4.1 troy ounces are fonbsp;nearly equal to 45 avoirdupoife ounces, that thenbsp;latter contains only, 74 grains more than the former : and 45 troy pounds weigh only 7-V dramsnbsp;more than 37 avoirdupoife.

1 have lately made a fcale for comparing thefe weights with one another, and (hewing thenbsp;weight of pump-water, proof fpirits, pure fpi-rits, and guinea gold, taken in cubic inches,nbsp;to any quantity lefs than a pound, both in troynbsp;and avoirdupoife; only by Aiding one fide of anbsp;fquare along the Icaie, and the other fide crof-ling it.

A Tabl�

The two following examples will be fufficient to explain thefe two tables, and Ihew their agreement.

Ex. I, 6835 Troy pounds 6 ounces 9 pennyweights 6 grains^ How much Avoirdupoife. weight? (See page 165.)

Ex. II. In 5624 pounds 10 ounces 12 drams Avoirdupoife, ^i. How much Troy weight ?nbsp;(See page 166.)

L E C T. VI.

This fcience treats of the nature, weight, prefTure, and fpring of the air, and thenbsp;effefts ariiing therefrom.

The pro- Tiic air is that thin tranfparent fluid body in parties of which we live and breathe. It encompafl�s thenbsp;whole earth to a confiderable height; and, together with the clouds and vapours that float innbsp;it, it is-called the atmofphere. The air is juftlynbsp;reckoned among the number of fluids, becaufenbsp;it has ail the properties by which a fluid is dif-tinguiflhed. For, it yields to the leafl; forcenbsp;imprefied, its parts are eafily moved among onenbsp;another, it prefl�s according to its perpendicular height, and its preflure is every way equal.

That the air is a fluid, conlifting of fuch particles as have no cohefion betwixt them, butnbsp;eafily glide over one another, and yield to thenbsp;flighteft imprefllon, appears from that eafe andnbsp;freedom with which animals breathe in it, andnbsp;move through it without any difficulty or fen-fible refiftance.

But it differs from all other fluids in the four following particulars, i. It can be compreffednbsp;into a much lefs fpace than what it naturallynbsp;polTeflech, which no other fluid can. 2. It cannotnbsp;be congealed or fixed, as other fluids may. 3. Itnbsp;is of a different denfity in every part, upwardnbsp;from the earth�s furface, decreafing in its weight,nbsp;bulk for bulk, the higher it rifes; and thereforenbsp;mull; allb decreafe in denfity. 4. It is of an

That air is a body, is evident from its excluding all other bodies out of the fpace it pof-feffes : for, if a glafs jar be plunged with its mouth downward into a velTel of water, therenbsp;will but very little water get into the jar, becaufenbsp;the air of which it is full keeps the water out.

As air is a body, it muft needs have gravity or weight: and that it is weighty, is demon-ftrated by experiment. For, let the air benbsp;taken out of a veffel by means of the air-pump,nbsp;then, having weighed the veflel, let in the airnbsp;again, and upon weighing it when re-filled withnbsp;air, it will be found confiderably heavier. Thus,nbsp;a bottle that holds a wine quart, being emptiednbsp;of air and weighed, is found to be about 16'nbsp;grains lighter than when the air is let into itnbsp;again ; which fliews that a quart of air weighsnbsp;16 grains. But a quart of water weighs 14621nbsp;grains; this divided by 16, quotes 914 in roundnbsp;numbers; which firews, that water is 914 timesnbsp;as heavy as air near the furface of the earth.

As the air rifes above the earth�s furface, it grows rarer, and confequently lighter, bulk fornbsp;bulk. For, becaufe it is of an elaftic or fpringynbsp;nature, and its lowermoft parts are prcfied withnbsp;the weight of all that is above them, it is plainnbsp;that the air muft be more denfe or compadl atnbsp;the earth�s furface, than at any height above it;nbsp;and gradually rarer the higher up. For, thenbsp;denfity of the air is always as the force thatnbsp;comprefleth it; and therefore, the air towardsnbsp;the upper parts of the atmofphere being lefs,nbsp;prefled than that which is near the earth, it willnbsp;expand itfelf, and thereby become thinner thaanbsp;at the earth�s furface.

M 4 nbsp;nbsp;nbsp;Otv

Dr. Cctes ha.s demonftrated, that if altitudes in the air be taken in arithmetical proportion,nbsp;the rarity of the air will be in geometrical proportion. Iquot;or inltancc,

And hence it is eafy to prove by calculation, that a cubic inch of fuch air as we breathe,nbsp;would be fo much rareSed at the altitude of 500nbsp;miles, that it would fill a hollow fphere equal innbsp;diameter to the orbit of Saturn.

The weight or preflTure of the air is exaflly determined by the following experiment.

Take a glafs tube about three feet long, and open at one end; fill it with quickfilver, andnbsp;putting, your finger upon the open cud, turnnbsp;that end downward, and immerfe it into a fmall

Of Pneumatics.

veH�l of quickfilver, without letting in any air: then take away your finger; and the quickfilvernbsp;will remain fufpended in the tube 294^ inchesnbsp;above its furface in the veflfel; fometimes more,nbsp;and at other times lefs, as the weight of thenbsp;air is varied by winds and other caufes. Thatnbsp;the quickfilver is kept up in the tube by thenbsp;preflfure of the atmofphere upon that in the ba-fon, is evident; for, if the bafon and tube benbsp;put under a glafs, and the air be then taken outnbsp;of the glafs, all the quickfilver in the tube willnbsp;fall down into the bafon; and if the air be let innbsp;again, the quickfilver will fife to the famenbsp;height as before. Therefore the air�s preffurenbsp;on the furface of the earth, is equal to thenbsp;weight of 294 inches depth of quickfilver allnbsp;over the earth�s furface, at a mean rate.

A fquare column of quickfilver, 294 inches high, and one inch thick, weighs juft 15nbsp;pounds, which is equal to the prelTure of airnbsp;upon every fquare inch of the earth�s furface;nbsp;and 144. times as much, or 2! 60 pounds, uponnbsp;every fquare foot; becaufe a fquare foot contains 144 fquare inches. At this rate, a middle-fized man, whofc furface may be about 14 fquarenbsp;feet, fuftains a prelTure of 30240 pounds,nbsp;when the air is of a mean gravity: a prelTurenbsp;which would be infupportabie, and even fatalnbsp;to us, were it not equal on every part, andnbsp;counterbalanced by the fpri.ng of the air withinnbsp;us, which is diffufed through the w'lole body ;nbsp;and re-a6ts with an equal force againft the outward prelTure.

Now, fince the earth�s furface contains (in round numbers) 200,000,000 fquare miles,nbsp;and every fquare mile 27,878,400 Iquare feet,nbsp;there muft be 5,575,680,000,000,000 fquare

feet on the earth�s furface; which multiplied by 2160 pounds (the preflure on each fquare foot)nbsp;gives I 2,043,468,800,000,000,000 pounds fornbsp;the preflure or weight of the whole atmo-fphere.

When the end of a pipe is immerfed in water, and the air is taken out of the pipe, the waternbsp;will rife in it to the height of 33 feet abovenbsp;the furface of the water in which it is immerfed jnbsp;but will go no higher: for it is found, that anbsp;common pump will draw water no higher thannbsp;33 feet above the furface of the well: and unlefsnbsp;the bucket goes within that diftance from thenbsp;well, the water will never get above it. Now,nbsp;as it is the preflfure of the atmofphere, on thenbsp;furface of the water in the well, that caufes thenbsp;water to afcend in the pump, and follow thenbsp;pifton or bucket, when the air above it is liftednbsp;up; it is evident, that a column of water 33nbsp;feet high, is equal in weight to a column ofnbsp;quickfilver of the fame diameter, 29^ inchesnbsp;high ; and to as thick a column of air, reaching from the earth�s furface to the top of thenbsp;atmofphere.

In ferene calm weather, the air has weight enough to fupport a column of quickfilver 31nbsp;inches high ; but in tempeftuous ftormy weather, not above 28 inches. The quickfilver,nbsp;thus fupported in a glafs tube, is found to be anbsp;nice counterbalance to the v/eight or prelTure ofnbsp;the air, and to Ihew its alterations at differentnbsp;times. And being now generally ufed to denote the changes in the weight of the air, andnbsp;of the weather confequent upon them, it isnbsp;called the barometer., or weather-glals.

The prefTure of the air being equal on all Tides of a body expofed to it, the fofteft bodies

fuftain

fuftain this preffure without fufFering any change in their figure; and fo do the moft brittle bodiesnbsp;without being broke.

The air is rarefied, or made to fwell with heat; and of this property, wind is a necefTary -fhe caufenbsp;confequence. For, when any part of the air is ofW�*.nbsp;heated by the fun, or otherwife, it will fwel!,nbsp;and thereby affedl the adjacent air: and fo, by-various degrees of heat in different places, therenbsp;will arife various winds.

When the air is much heated, it will afcend towards the upper part of the atmofphere, andnbsp;the adjacent air will rufh in to fupply its place ;nbsp;and therefore, there will be a ftream or currentnbsp;of air from all parts towards the place wherenbsp;the heat is. And hence we fee the reafon whynbsp;the air rufhes with fuch force into a glafs-houfe,nbsp;or towards any place where a great fire is made.

And alfo, why fmoke is carried up a chimney, and why the air rufhes in at the key-hole of thenbsp;door, or any fmall chink, when there is a firenbsp;in the room. So we may take it in general, thatnbsp;the air will prefs towards that part of the worldnbsp;where it is moft heated.

Upon this principle, we can eafily account for The the trade-winds, which blow conftantly from eaft^''quot;*-to weft about the equator. For, when the fun'nbsp;fiiines perpendicularly on any part of the earth,nbsp;it will heat the air very much in that part, whichnbsp;air will therefore rife upward, and when the funnbsp;withdraws, the adjacent air will rufh in to fill itsnbsp;place ; and confequently will caufe a ftream ornbsp;current of air from all parts towards that whichnbsp;is moft heated by the fun. But as the fun, withnbsp;refpeft to the earth, moves from eaft to weft,nbsp;the common courfe of the air will be that waynbsp;�00; continually preffing after the fun : and

therefore, at the equator, where the fun ftiines ftrongly, there will be a continual wind fromnbsp;the eaft; but, on the north fide, it will inclinenbsp;a little to the north, and on the fouth-fide, tonbsp;the fouth.

This general courfe of the wind about the equator, is changed in feveral places, andnbsp;upon feveral accounts-, as, i. By exhalationsnbsp;that rife out of the earth at certain times, andnbsp;from certain places in earthquakes, and fromnbsp;volcanos. 2. By the failing of great quantities of rain, caufing thereby a fudden conden-fation or contraftion of the air. 3. By burning fands, that often retain the folar heat to anbsp;degree incredible to thofe who have not felt it,nbsp;caufing a more than ordinary rarefaftion of thenbsp;air contiguous to them. 4. By high mountains, which alter the dire�fion of the windsnbsp;in ftriking againft them. 5. By the declination of the fun towards the north or fouth,nbsp;heating the air on the north or fouth fide of thenbsp;equator.

. To thefe and fuch like caufes is owing, 1. The irregularity and uncertainty of winds in climatesnbsp;dillant from the equator, as in moft parts ofnbsp;Europe. 2. Thofe periodical winds, callednbsp;monfconsy which in the Indian feas blow half anbsp;year one way, and the other half another,nbsp;3. Thofe winds which, on the coaft of Guiney^nbsp;and on the weftern coafts of America^ blow always from weft to eaft. 4. The fea-breezes,nbsp;which, in hot countries, blow generally fromnbsp;fea to land, in the day time; and the land-breezes, which blow in the night; and, in fhort,nbsp;all thofe ftorms, hurricanes, whirlwinds, andnbsp;irregularities, which happen at different timesnbsp;and places.

All

All common air is impregnated vvith a cer tain kind of 'vivifying f^irit or quality, which \%fy��g-�-neceflary to continue the lives of animals : andnbsp;this, in a gallon of air, is fufficient for one mannbsp;during the fpace of a minute, and not muchnbsp;longer-

This fpirit in air is deftroyed by pafllng through the lungs of animals ; and hence it is,nbsp;that an animal dies foon, after being put undernbsp;a veflel which admits no frelh air to come to it.

This fpirit is alfo in the air which is in water ; for fifh die when they are excluded from frcflinbsp;air, as in a pond that is clofely frozen over.

And the little eggs of infeds, flopped up in a glafs, do not produce their young, thoughnbsp;aflifted by a kindly warmth. The feeds alfo ofnbsp;plants mixed with good earth, and inclofed innbsp;a glafs, will not grow.

This enlivening quality in air, is alfo deftroyed by the air�s pafling through fire; particularly charcoal fire, or the flame of fulphur.

Hence, fmoking chimneys muft be very un-wholefome, efpecially if the rooms they are in be fmall and clofe.

Air is alfo vitiated, by remaining clofely pent up in any place for a confiderable time;nbsp;or perhaps, by being mixed with malignantnbsp;fleams and particles flowing from the neighbouring bodies : or laflly, by the corruption of thenbsp;vivifying fpirit; as in the holds of fliips, innbsp;oil-ciflerns, or wine-cellars, which have beennbsp;fhut for a confiderable time. The air in any ofnbsp;them is fometimes fo much vitiated, as to be immediate death to any animal that comes into it.

Air that has loft its vivifying fpirit, is called dampy not only becaufe it is filled with humidnbsp;or moifl vapours, but becaufe it deadens fire,

extinguiflies flame, and deftroys life. The dreadful elFeds of damps are fufiiciently knownnbsp;to fuch as work in mines.

If part of the vivifying fpirit of air in any country begins to putrefy, the inhabitants of thatnbsp;country will be fubjeft to an epidemical difeafe,nbsp;which will continue until the putrefaction isnbsp;over. And as the putrefying fpirit occafionsnbsp;the difeafe, fo it the difeafed body contributesnbsp;towards the putrefying of the air, then the difeafe will not only be epidemical, but peftiientialnbsp;and contagious.

The atmofphere is the common receptacle of all the effluvia or vapours arifing from differentnbsp;bodies; Oi the fleams and fmoke of things burntnbsp;or melted ; the fogs or vapours proceeding fromnbsp;damp watery places; and of the effluvia fromnbsp;fulphureous, nitrous, acid, and alkaline bodies.nbsp;In fliort, whatever may be called volatile, rifesnbsp;in the air to greater or lefs heights, accordingnbsp;to its fpecific gravity.

When the effluvia, which arife from acid and alkaline bodies, meet each other in the air,nbsp;there will be a ftrong conflidl: or fermentation between them j which will fometimes be fo great,nbsp;as to produce a fire ; then if the effluvia benbsp;combuftible, the fire will run from one partnbsp;to another, juft as the inflammable matter happens to lie.

Any one may be convinced of this, by mixing an acid and an alkaline fluid together, as thenbsp;fpirit of nitre and oil of cloves; upon the doingnbsp;of which, a fudden ferment, with a fine flame,nbsp;will arife; and if the ingredients be very purenbsp;and ftrong, there will be a fudden explofion.

Whoever confiders the effedts of fermentation, cannot be at a lofs to account for the

dreadful effects of thunder and lightning: for the effluvia of fulphureous and nitrous bodies, andnbsp;others that may rife into the atmofphere, willnbsp;ferment with each other, and take fire very oftennbsp;of themfelves; fometimes by the affiftance of thonbsp;fun�s heat.

If the inflammable matter be thin and light, it will rife to the upper part of the atmofphere,

�where it will flalh without doing any harm: but if it be denfe, it will lie near the fur-face of the earth, where Staking fire, it will explode with a furprifing force; and by its heatnbsp;rarefy and drive away the air, kill men andnbsp;cattle, fplit trees, walls, rocks, amp;c. and be accompanied with terrible claps of thunder.

The heat of lightning appears to be quite different from that of other fires; for it hasnbsp;been known to run through wood, leather,nbsp;cloth, amp;c. without hurting them, while it hasnbsp;broken and melted iron, lleel, filver, gold, andnbsp;other hard bodies. Thus it has melted or burntnbsp;afunder a fword, without hurting the fcabbard;nbsp;and money in a man�s pocket, without hurtingnbsp;his cloaths: the reafon of this feems to be, thatnbsp;the particles of that fire are fo fine, as to palsnbsp;through foft loofe bodies without dil��lvingnbsp;them ; whiift they fpend their whole force uponnbsp;the hard ones.

It is remarkable, that knives and forks which have been ftruck with lightning have a verynbsp;ftrong magnetical virtue for feveral years after ;nbsp;and 1 have heard that lightning ftriking uponnbsp;the mariner�s compafs, will fometimes turn itnbsp;round ; and often make it Hand the contrarynbsp;W'ay; or with the north-pole towards the fouth.

Much of the fame kind with lightning, are thofe explofions, called fulminating or fire-damps, damps.

which fometimes happen in mines; and are occafioned by fulphureous and nitrous, or rather oleaginous particles, rifing from the mine,nbsp;and mixing with the air, where they will takenbsp;fire by the lights which the workmen are obligednbsp;to make ufe of. The fire being kindled willnbsp;run from one part of the mine to another, likenbsp;a train of gunpowder, as the combufiible mattei*nbsp;happens to lie. And as the elafticity of the airnbsp;is increafed by heat, that in the mine will con-fequently fwell very much, and fo, for want ofnbsp;room, will explode with a greater or lefs degreenbsp;of force, according to the denfity of the com-buftible vapours. It is fometimes fo ftrong, asnbsp;to blow up the mine ; and at other times fonbsp;weak, that when it has taken fire at the flamenbsp;of a candle, it is eafily blown out.

Air that will take fire at the flame of a candle may be produced thus. Having exhaufted anbsp;receiver of the air-pump, let the air run into itnbsp;through the flame of the oil of turpentine thennbsp;remove the cover of the receiver, and holding anbsp;candle to that air, it will take fire, and burnnbsp;quicker or flower, according to the denfity ofnbsp;the oleaginous vapour.

When fuch combuftible matter, as is above-mentioned, kindles in the bov/els of the earth, where there is little or no vent, it producesnbsp;earthquakes, and violent ftorms or hurricanes ofnbsp;wind when it breaks forth into the air.

An artificial earthquake may be made thus. Take lO or 15 pounds of fulphur, and as muchnbsp;of the filings of iron, and knead them withnbsp;common water into the confiftency of a pafte :nbsp;this being buried in the ground, will, in 8 ornbsp;10 hours time, buft out in flames, and caufenbsp;1nbsp;nbsp;nbsp;nbsp;the

From this experiment we have a very natural account of tlie fires of mount Astna, Vefuvius^nbsp;and other volcanos, they being probably feenbsp;or fire at firft by the mixture of fuch metallinenbsp;and fulphureous particles.

The air pump being conflrufted the fame way pjatexrv, as the water-pump, v/hoever underftands the Fig. i.nbsp;one, will be at no lofs to underftand the other.

Having put a wet leather on the plate Z-TThea/r-of the air-pump, place the glafs receiver upon the leather, fo that the hole i in the platenbsp;may be within the glafs. Then, turning thenbsp;handle F backward and forward, the air will benbsp;pumped out of the receiver; which will thennbsp;be held down to the plate by the prefTure of thenbsp;external air, or atmofphere. For, as the handlenbsp;F(Fig. 2.) is turned backwards, it raifes thenbsp;pifton de \n the barrel B K, by means of thenbsp;wheel E and rack Dd: and, as the pifton is leathered fo tight as to fit the barrel exadtly, nonbsp;air can get between the pifton and barrel; andnbsp;therefore, all the air above d in the barrel isnbsp;lifted up towards B, and a vacuum is made innbsp;the barrel from b to e-, upon which, part of thenbsp;air in the receiver M (Fig. i.) by its fpring,

Tulhes through the hole i, in the brafs plate L L, along the pipe GCG (which communicates with both barrels by the hollow trunk IHKnbsp;(Fig. 2.) and pulbing up the valve b, entersnbsp;into the vacant place be of the barrel BK. For,nbsp;wherever the refiftance or prefllire is taken off,nbsp;the air will run to that place, if it can find anbsp;paflage.�Then, if the handle F be turnednbsp;forward, the pifton d e will be deprefled in thenbsp;barrelj and, as the air which had got into thenbsp;Nnbsp;nbsp;nbsp;nbsp;barrel

barrel cannot be pufhed back through the valve h, it will afcend through a hole in the pifton,nbsp;and efcape through a valve at d; and be hindered by that valve from returning into the barrel, when the pifton is again railed. At thenbsp;next railing of the pifton, a vacuum is againnbsp;made in the fame manner as before, between bnbsp;and e ; upon which, more of the air that wasnbsp;left in the receiver M, gets out thence by itsnbsp;fpring, and runs into the barrel B K, throughnbsp;the valve B. The fame thing is to be under-ftood with regard to the other barrel AI; andnbsp;as the handle F is turned backwards and forwards, it alternately raifes and deprefles the pif-tons in their barrels ; always raifing one whilfl;nbsp;it deprefles the other. And, as there is a vacuum made in each barrel when its pifton isnbsp;raifed, the particles of air in the receiver Mnbsp;pulh out another by their fpring or elafticity,nbsp;through the hole r, and pipe G G into the barrels; until at laft the air in the receiver comes tonbsp;be fo much dilated, and its fpring fo far weakened, that it can no longer get through thenbsp;valves ; and then no more can be taken out.nbsp;Hence, there is no fuch thing as making a perfect vacuum in the receiver; for the quantity ofnbsp;air taken out at any one ftroke, will always be asnbsp;the denfity thereof in the receiver: and therefore it is impoffible to take it all out, becaufe,nbsp;fuppofing the receiver and barrels of equal capacity, there will be always as much left as wasnbsp;taken out at the laft turn of the handle.

There is a cock k below the pump plate, which being turned, lets the air into the receivernbsp;again; and then the receiver becomes loofe, andnbsp;may be taken off the plate. The barrels arenbsp;fixed to the frame Ee e hy two Icrew-nuts ��,

Vvhich prefs down the top piece � upon the bar-J'els : and the hollow trunk //(in Fig. 2.} is covered by a box, as G// in Fig, i.

There is a glafs tube I m m m n open at both ends, and about 34 inches long; the upper endnbsp;communicating with the hole in the pump-plate,nbsp;and the lower end immerfed in cjuickfilver at nnbsp;in the veffel iV. To this tube is ihtted a woodennbsp;ruler mm, called the^^?^^, which is divided intonbsp;inches and parts of an inch, from the bottom atnbsp;n (where it is even with the furface of the quick-filver) and continued up to the top, a littlenbsp;below /, to 30 or 31 inches.

As the air is pumped outof the receiver Mf\x.\% likewife pumped out of the glafs tube Imn, be-caufe that tube opens into the receiver throughnbsp;the pump-plate ; and as the tube is gradually-emptied of air, the quckfilver in the veflel iVisnbsp;forced up into the tube by the prelTure of thenbsp;atmofphere. And if the receiver could be per-feftly exhaufted of air, the quickfilver wouldnbsp;Hand as high in the tube as it does at that timenbsp;in the barometer ; for it is fupported by thenbsp;fame power or weight of the atmofphere innbsp;both.

The quantity of air exhaufted out of the receiver on each turn of the handle, is always proportionable to the afcent of the quickfilver on that turn ; and the quantity of air remaining innbsp;the receiver, is proportionable to the defe/t ofnbsp;the height of the quickfilver in the gage, fromnbsp;what it is at that time in the barometer.

I fhall now give an account of the experiments made with the air-pump in my lectures; ftiew-ing the refiftance, weight, and elafticity of thenbsp;air.

iSz nbsp;nbsp;nbsp;Of the Air-Vtimp.

T. There is a little machine, confifting of two Fig. 3. mills, a and b, which are of equal weights, independent of each other, and turn equally freenbsp;on their axes in the frame. Each mill has fournbsp;thin arms or fails, fixed into the axis : thofe ofnbsp;the mill a have their planes at right angles to itsnbsp;axis, and thofe of h have their planes parallel tonbsp;it. Therefore, as the mill a turns round in common air, it is but little refifted thereby, becaufenbsp;it�s fails cut the air with their thin edges: butnbsp;the mill b is much refilled, becaufe the broadnbsp;fides of it�s fails move againft the air when itnbsp;turns round. In each axle is a pin near thenbsp;middle of the frame, which goes quite through ,nbsp;the axle, and Hands out a little on each fide of it:nbsp;upon thefepins, the flider d may be made to bear,nbsp;and fo hinder the mills from going, when thenbsp;ftrong fpring c is fet on bend againll the oppofitenbsp;ends of the pins.

Having fet this machine upon the pump-plate L L (Fig. I.) draw up the flider d to the pins on one fide, and fee the fpring c at bendnbsp;upon the oppofite ends of the pins : then pulhnbsp;down the flider d, and the fpring afting equallynbsp;ftrong upon each mill, will fet them both agoingnbsp;with equal forces and velocities: but the mill anbsp;will run much longer than the mill b, becaufe thenbsp;air makes much lefs refiftance againft the edgesnbsp;of its fails, than againft the fides of the failsnbsp;of b.

Draw up the flider again, and fet the fpring upon the pins as before ; then cover the machine with the receiver M upon the pump-, plate, and having exhaufted the receivec of air,

pufli down the wire P P (through the colier of leathers in the neck q) upon the Aider; whichnbsp;will difengage it from the pins, and allow thenbsp;mills to turn round by the impulfe of the fpring:nbsp;and as there is no air in the receiver to make anynbsp;fenfible refiltance againft them, they will bothnbsp;move a confiderable time longer than , they didnbsp;in the open air; and the moment that one hops,nbsp;the other will do fo too.�This Ihews that airnbsp;refills bodies in motion, and that equal bodiesnbsp;meet with different degrees of refiftance, according as they prefent greater or lefs furfaces to thenbsp;air, in the planes of their motions.

2, Take off the receiver M, and the mills; and having put the guinea a and feather b uponnbsp;the brafs flap c, turn up the flap, and fliut it intonbsp;the notch d. Then, putting a wet leather overnbsp;the top of the tall receiver being open bothnbsp;at top and battom) cover it with the plate C,nbsp;from which the guinea and feather tongs ed willnbsp;then hang within the receiver. This done, pumpnbsp;the air out of the receiver; and then draw upnbsp;the wire � a little, which by a fquare piece on itsnbsp;lower end will open the tongs e d\ and the flapnbsp;falling down as at r, the guinea and feather willnbsp;defcend with equal velocities in the receiver;nbsp;and both will fall upon the pump-plate at thenbsp;fame inftant. N. B. In this experiment, thenbsp;obfervers ought not to look at the top, but at thenbsp;bottom of the receiver; in order to fee the guinea and feather fall upon the plate : othcrwife,nbsp;on account of the quicknefs of their motion, theynbsp;will efcape the fight of the beholders. �

I. Having fitted a brafs cap, with a valve tied over it, to the mouth of a thin bottle ornbsp;Florence flaflc, whofe contents are exa(5tly known,nbsp;fcrew the neck of this cap into the hole i of thenbsp;pump-plate : then, having exhaufted the air outnbsp;of the flalk, and taken it off from the pump, letnbsp;it be fufpended at one end of a balance, and nicelynbsp;counterpoifed by weights in the fcale at the othernbsp;end : this done, raife up the valve with a pin, andnbsp;the air will rufh into the fiaik with an audiblenbsp;noife : during which time, the flaflc will defcend,nbsp;and pull down that end of the beam. When thenbsp;noife is over, put as many grains into the fcale atnbsp;the other end as will reftore the equilibrium -,nbsp;and they will Ihew exactly the weight of thenbsp;quantity of air which has got into the flalk, andnbsp;filled it. If the flalk holds an exadl quart, itnbsp;will be found, that 16 grains will reftore thenbsp;equipoife of the balance, when the quickfilvernbsp;ftands at 29T inches in the barometer: whichnbsp;fhews, that when the air is at a mean rate of den-fity, a quart of it weighs 16 grains : it weighsnbsp;more when the quickfilver ftands higher; andnbsp;lefs when it ftands lower.

2. Place the ftnall receiver O (Fig. i.) over the hole i in the pump-piate, and upon exhauftingnbsp;the air, the receiver will be fixed down to thenbsp;plate by the preflure of the air on its outfide,nbsp;which is left to a�t alone, without any air in thenbsp;receiver to aift: againft it: and this prefTure willnbsp;be equal to as many times 15 pounds, as therenbsp;are fquare inches in that pare of the plate whichnbsp;the receiver covers which will hold down thenbsp;receiver fo fall, that it cannot be got off, untilnbsp;5nbsp;nbsp;nbsp;nbsp;the

Of the Air-Pump.

3. nbsp;nbsp;nbsp;Set the little glafs A B (which is open at Fig. 5.nbsp;both ends) over the hole i upon the pump-plate

L L, and put your hand c'ofe upon the top of it at B: then, upon exhaulling the air out of thenbsp;glafs, you will find your hand prefled down withnbsp;a great weight upon it: fo that you can hardlynbsp;releafe it, until the air be re-admitted into thenbsp;glafs by turning the cock k which air, by a�l-ing as ftrongly upward againll the hand as thenbsp;external air a�ed in prefling it downward, willnbsp;releafe the hand from its confinement.

4. nbsp;nbsp;nbsp;Having tied a piece of wet bladder b over Fig. 6.nbsp;the open top of the glafs A (which is alfo open atnbsp;bottom) fet it to dry, and then the blatlder will

be tight like a drum. I'lien place the open end A upon the pump-placc, over the hole /, andnbsp;begin to exhauft the air out of the glafs. Asnbsp;the air is exliaufting, its fpring in the glafs willnbsp;be weakened, and give way to the prefiure of thenbsp;outward air on the bladder, which, as it is pref-fed down, will put on a fpherical concave figure,nbsp;which will grow deeper and deeper, until thenbsp;flirength of the bladder be overcome by thenbsp;weight of the air; and then it will break with anbsp;report as loud as that of a gun.�If a flat piecenbsp;of glafs be laid upon the open top of this receiver, and joined to it by a flat ring of wetnbsp;leather between them; upon pumping the airnbsp;out of the receiver, the prelfure of the outwardnbsp;air upon the flat glafs will break it all tonbsp;pieces.

5. nbsp;nbsp;nbsp;Immerfe the neck c of the hollow glafs Fig; 7;nbsp;biWeb in water, contained in the phial aa-, then

fet it upon the pamp-plate, and cover it and the hole i with the dole receiver A-, and then begin

to pump out the air. As the air goes out of the receiver by its fpring, it will alfo by the famenbsp;means go out of the hollow ball eb, through thenbsp;neck dc, and rife up in bubbles to the furface ofnbsp;the water in the phial; from whence it will makenbsp;its way, with the reft of the air in the receiver,

the open air. When it has done bubbling in the phial, the ball is fufficiently exhaufted; andnbsp;then, upon turning the cock k, the air will getnbsp;into the receiver, and prefs fo upon the furfacenbsp;of the water in the phial, as to force the waternbsp;up into the ball in a jet, through the neck c d;nbsp;and will fill the ball almoft full of Water. Thenbsp;reafon why the ball is not quite filled, is becaufenbsp;all the air could not be taken out of it; and thenbsp;fmall quantity that was left in, and had expandednbsp;itfelf fo as to fill the whole ball, is now condenfednbsp;into the fame ftate as the outward air, and remains in a fmall bubble at the top of the ball;nbsp;and fo keeps the water from filling that part ofnbsp;the ball.

fet it on the pump-plate near the hole /; then fet on the tall open receiver AB, fo as to be overnbsp;the jar and hole-, and cover the receiver with thanbsp;brafs plate C. Screw the open glafs tube fgnbsp;(which has a brafs top on it at ^j into the fyringanbsp;H, and putting the tube through a hole in thenbsp;middle of the plate, fo as to immerfe the lowernbsp;end of the tube e in the quickfilyer at D, fcrewnbsp;the end h of the fyringe into the plate. Thisnbsp;done, draw up the pifton in the fyringe by thenbsp;ring/, which will make a vacuum in the fyringe,nbsp;below the pifton; and as the upper end of thenbsp;tube opens into the fyringe, the air will be dilated in the tube, becaufe part of it, by its fpring,

Of the Air-Pump.

gets up into the fyringe j and the fpring of the un-dilated air in the receiver afting upon thenbsp;furface of the quickfilver in the jar^ will forcenbsp;part of it up into the tube : for the quickfilvernbsp;will follow the pifton in the, fyringe, in the famenbsp;way, and for the fame reafon, that water followsnbsp;the pifton of a common pump when it is raifednbsp;in the pump-barrel; and this, according to feme,nbsp;is done by fuction. But to refute that erroneousnbsp;notion, let the air be pumped out of the receivernbsp;AB, and then all the quickfilver in the tube willnbsp;fall down by its own weight into the jar; and cannot be again raifed one hair�s breadth in the tubenbsp;by working the fyringe: which Ihews that fuction had no hand in raifing the quickfilver; and,nbsp;to prove that it is done by prelTure, let the airnbsp;into the receiver by the cock k (Fig. i.) and itsnbsp;adtion upon the furface of the quickfilver in thenbsp;jar will raife it up into the tube, although thenbsp;pifton of the fyringe continues motionleis.�Ifnbsp;the tube be about 32 or 33 inches high, thenbsp;quickfilver will rife in it very near as high as itnbsp;ftands at that time in the barometer. And, ifnbsp;the fyringe has a fmall hole, as ?�, near the topnbsp;of it, and the pifton be drawn up above that hole,nbsp;the air will rufti through the hole into the fyringe and tube, and the quickfilver will immediately fall down into the jar. If this part of thenbsp;apparatus be air-tight, the quickfilver may benbsp;pumped up into the tube to the fame height thatnbsp;it ftands in the barometer; but it will go nonbsp;higher, becaufe then the weight of the column innbsp;the tube is the fame as the weight of a column ofnbsp;air of the fame thicknefs with the quickfilver,nbsp;and reaching from the earth to the top of thenbsp;atmofphere.^

7. Having

filver in it, on the pump-plate, as in the laft experiment, cover it with the receiver B ; thennbsp;pufli the open end of the glafs tube d e throughnbsp;the collar of leathers in the brafs neck C (whichnbsp;it fits fo as to be air-tight) almoft down to thenbsp;quickfilver in the jar. Then exhauft the airnbsp;out of the receiver, and it will alfo come out ofnbsp;the tube, becaufe the tube is clofe at top. Whennbsp;the gauge m m fhews that the receiver is wellnbsp;exhaufted, pulh down the tube, fo as to immerfenbsp;its lower end into the quickfilver in the jar.nbsp;Now, although the tube be exhaufted of air,nbsp;none of the quickfilver will rife into it, becaufenbsp;there is no air left in the receiver to prefs uponnbsp;its furface in the jar. But let the air into thenbsp;receiver by the cock k, and the quickfilver willnbsp;� immediately rife in the tube and ftand as highnbsp;in it, as it was pumped up in the laft experiment.

Both thefe experiments (hew, that the quickfilver is fupported in the barometer by the pref-fure of the air on its furface in the box, in which the open end of the tube is placed. And thatnbsp;the more denfe and heavy the air is, the highernbsp;does the quickfilver rife; and, on the contrary,nbsp;the thinner and lighter the air is, the more willnbsp;the quickfilver fall. For if the handle F benbsp;turned ever fo little, it takes fome air out of thenbsp;receiver, by raifing one or other of the piftons innbsp;its barrel; and confequently, that which remainsnbsp;in the receiver is fo much the rarer, and has fonbsp;much the lefs fpring and weight; and thereupon,nbsp;the quickfilver falls a little in the tube : butnbsp;upon turning the cock, and re-admitting the airnbsp;into the receiver, it becomes as weighty as before, and the quickfilver rifes again to the fame

height.�Thns we fee the reafon why the quick-filver in the barometer falls before rain or fnow, and rifes before fair weather; for, in the formernbsp;cafe, the air is too thin and light to bear up thenbsp;vapours, and in the latter, too denfe and heavynbsp;to ler them fall.

N. B. In all mercurial experiments with the air-pump, a Ihort pipe muft be fcrewed into thenbsp;hole z, fo as to rife about an inch above the plate,nbsp;to prevent the quickfilver from getting into thenbsp;air-pipe and barrels, in cafe any of it fhould benbsp;accidentally fpilt over the jar; for if it once getsnbsp;into the pipes or barrels, it fpoils them, bynbsp;loofening the folder, and corroding the brafs.

8. nbsp;nbsp;nbsp;Take the tube out of the receiver, and putnbsp;one end of a bit of dry hazel branch, about annbsp;inch long, tight into the hole, and the other endnbsp;tight into a hole quite through the bottom of anbsp;fmall wooden cup ; then pour fome quickfilvernbsp;into the cup, and exhauft the receiver of air, andnbsp;the preffure of the outward air, on the furfacenbsp;of the quickfilver, will force it through the poresnbsp;of the hazel, from whence it will delcend in anbsp;beautiful fhower into a glafs cup placed undernbsp;the receiver to catch it.

9. nbsp;nbsp;nbsp;Put a wire through the collar of leathers innbsp;the top of the receiver, and fix a bit of dry woodnbsp;on the end of the wire within the receiver -, thennbsp;exhauft the air, and pulh the wire down, fo as tonbsp;immerfe the wood into a jar of quickfilver on thenbsp;pump-plate; this done, let in the ^ir, and uponnbsp;taking the wood out of the jar, and fplitting it,nbsp;its pores will be found full of quickfilver, whichnbsp;the force of the air, upon being let into the receiver, drove into the wood.

10. nbsp;nbsp;nbsp;Join the two brafs hemifpherical cups^fand Fig. le.nbsp;T together, v/ith a wet leather between them, hay-

ing a hole in the middle of it; then fcrew the end D of the pipe C D into the plate of thenbsp;pump at i, and turn the cock E, fo as the pipenbsp;may be open all the way into the cavity of thenbsp;hemifpheres : then exhauft the air out of them,nbsp;and turn the cock a quarter round, which willnbsp;fliut the pipe C D, and keep out the air. Thisnbsp;done, unfcrew the pipe at D from the pump ;nbsp;and Icrcw the pjcce F h upon it at D; and letnbsp;two ftrong men try to pull the hemifpheres afun-der by the rings g and h, which they will findnbsp;hard to do : for if the diameter of the hemigt;nbsp;fpheres be four inches, they will be prefled together by the external air with a force equal tonbsp;190 pounds. And to fhew that it is the prelTurenbsp;of the air that keeps them together, hang themnbsp;by either of the rings upon the hook P of thenbsp;wire in the receiver M (Fig. i.) and upon ex-haufting the air out of the receiver, they will fallnbsp;afunder of themfelves.

II, Place a Imail receiver 0 (Fig. i.) near the hole i on the pump-plate, and cover both it andnbsp;the hole with the receiver M-, and turn thenbsp;�wire fo by the top P, that its hook may takenbsp;hold of the little receiver by a ring at its top,nbsp;allowing that receiver to ftand with its ownnbsp;weight on the plate. Then, upon working thenbsp;pump, the air will come out of both receivers;nbsp;but the large one M will be forcibly held downnbsp;to the pump by thepreffure of the external air;nbsp;whilft I he fmali one 0, having no air to prefs upon it, will continue loofe, and may be drawn upnbsp;and let down at pleafure, by the wire P P. Bur,nbsp;upon letting it quite down to the plate, and admitting the air into the receiver M, by the cocknbsp;k, the air will prefs fo ftrongly upon the fmalinbsp;receiver O, as to fix it down to the plate; and atnbsp;4nbsp;nbsp;nbsp;nbsp;the

the fame time, by counterbalancing the outward preffure on the large receiver Af, it will becomenbsp;loofe. This experiment evidently fliews, thatnbsp;the receivers are held down by preffure, andnbsp;not by fuflion, for the internal receiver continued loofe whilftthe operator was pumping, andnbsp;the external one was held down; but the formernbsp;became fall: immediately by letting in the airnbsp;upon it.

12. Screw the end A of the brafs pipe AB ^ 2\g. n. into the hole of the pump-plate, and turn thenbsp;cock e until the pipe be open; then put a wetnbsp;leather upon the plate cdy which is fixed on thenbsp;pipe, and cover it with the tall receiver G Hynbsp;which is clofe at top : then exhauft the air outnbsp;of the receiver, and turn the cock e to keep itnbsp;out; which done, unfcrew th e pipe from thenbsp;pump, and fet its end A into a bafon of water,nbsp;and turn the cock e to open the pipe; on which,nbsp;as there is no air in the receiver, the preffure ofnbsp;the atmofphere on the water in the bafon willnbsp;drive the water forcibly through the pipe, andnbsp;make it play up in a jet to the top of the receiver.

13. Set the fquare phial A (Fig. 14.) upon the pump-plate, and having covered it with the wirenbsp;cage B, put a clofe receiver over it, and exhauftnbsp;the air out of the receiver; in doing of which,nbsp;the air will alfo make its way out of the phialnbsp;through a fmall hole in its neck under the valvenbsp;h. When the air is exhaufted, turn the cocknbsp;below the plate, to re-admit the air into thenbsp;receiver; and as it cannot get into the phialnbsp;again, becaufe of the valve, the phial will benbsp;broke into fome thoufands of pieces by the preffure of the air upon it. Had the phial beennbsp;of a round form, it would have fuftained this

14. nbsp;nbsp;nbsp;Tie up a very fmall quantity of air in anbsp;bladder, and put it under a receiver; then exhauftnbsp;the air out of the receiver; and the fmall quantity which is confined in the bladder (having nothing to aft againft it) will expand itfelf fo bynbsp;the force of its fpring, as to fill the bladder asnbsp;full as it could be blown of common air. Butnbsp;upon letting the air into the receiver again, itnbsp;will overpower the air in the bladder, and prefsnbsp;its fides aimoft clofe together.

15. nbsp;nbsp;nbsp;If the bladder fo tied up be put into anbsp;wooden box, and have 20 or 30 pound weightnbsp;of lead put upon it in the box, and the box benbsp;covered with a clofe receiver ; upon exhauftingnbsp;the air out of the receiver, that air which is confined in the bladder will expand itfelf fo, as toraifsnbsp;up all the lead by the force of its fpring.

16. nbsp;nbsp;nbsp;Take the glafs ball mentioned in the fifthnbsp;experiment, which was left full of water all butnbsp;a fmall bubble of air at top, and having fee itnbsp;with its neck downward into the empty phial aa,nbsp;and covered it with a clofe receiver, exhauft thenbsp;air out of the receiver, and the fmall bubble ofnbsp;air in the top of the ball will expand itfelf, fo asnbsp;to force all the water out of the ball into thenbsp;phial.

17. nbsp;nbsp;nbsp;Screw the pipe AB into the pump-plate,nbsp;place the tall receiver GH upon the plate ri, asnbsp;in the twelfth experiment, and exhauft the airnbsp;out of the receiver ; then, turn the cock e tonbsp;keep out the air, unferew the pipe from thenbsp;pump, and ferew it into the mouth of the copper

veffel CC (Fig. 15.) the veflel having firft been about half filled with water. Then open thenbsp;cock e (Fig. 11-) the fpringof the air whichnbsp;is confined in the copper veffel will force thenbsp;water up through the pipe JB in a jet into thenbsp;exhaufted receiver, as ftrongly as it did by itsnbsp;preffure on the furface of the water in a bafon, innbsp;the twelfth experiment.

18. nbsp;nbsp;nbsp;If a fowl, a cat, rat, moufe, or bird, benbsp;put under a receiver, and the air be exhaufted,nbsp;the animal will be at firft oppreffed as with anbsp;great weight, then grow convulfed, and at laftnbsp;expire in all the agonies of a moft bitter andnbsp;cruel death. But as this experiment is toonbsp;Ihocking to every fpeftator who has the leall degree of humanity, we fubftitute a machine callednbsp;the lungs-glafs in place of the animal.

19. nbsp;nbsp;nbsp;If a butterfly be fufpended in a receiver,nbsp;by a fine thread tied to one of its horns, it will flynbsp;about in the receiver, as long as the receivernbsp;continues full of air; but if the air be exhaufted,nbsp;though the animal will not die, and will continuenbsp;to flutter its wings, it cannot remove itfelf fromnbsp;the place where it hangs in the middle of the receiver, until the air be let in again, and then thenbsp;animal will fly about as before.

into the brafs neck b of the bottle, and the lower end of the tube will be immerfed into the quickfilver, fo that the air above the quickfilver in thenbsp;bottle will be confined there, becaufe it cannotnbsp;get out about the joinings, nor can it be drawnnbsp;out through the quickfilver into the tube. Thisnbsp;tube is alfo open at top, and is to be covered withnbsp;the receiver G and large tube E F, which tube isnbsp;fixed by brafs collars to the receiver, and is dole

�at the top. This preparation being made, ex-hauft the air both out of the receiver and its tube ; and the air will by the fame meansnbsp;be exhaufted out of the inner tube 56�, throughnbsp;its open top at C; and as the receiver and tubesnbsp;are exhaufting, the air that is confined in the glafsnbsp;bottle A will prefs fo by its fpring upon thenbsp;furface of the quickfilver, as to force it up in thenbsp;inner tube as high as it was railed in the ninthnbsp;experiment by the preflure of the atmofphere :nbsp;which demonftrates that the fpring of the air isnbsp;equivalent to its weight.

hole of the pump-plate, and turn all the three cocks G, and H, fo as to open the communications between all the three pipes E, F, D C,nbsp;and the hollow trunk A B. Then, cover thenbsp;plates g and h with wet leathers, which havenbsp;holes in their middle where the pipes open intonbsp;the plates; and place the clofe receiver I uponnbsp;the plate this done, fhut the pipe F by turning the cock //, and exhauft the air out of thenbsp;receiver 1. Then, turn the cock d to fhut outnbsp;the air, unferew the machine from the pump,nbsp;and having ferewed it to the w�ooden foot L, putnbsp;the receiver K upon the plate h; this receivernbsp;will continue loofe on the plate as long as itnbsp;keeps full of air; which it will do until the cocknbsp;H be turned to open the communication betweennbsp;the pipes 5 and �, through the trunk AB-, andnbsp;then the air in the receiver K, having nothing tonbsp;,a6l againft its fpring, will run from K into /, until it be fo divided between thefe receivers, as tonbsp;be of equal denfity in both ; and then they willnbsp;be held down with equal forces to their plates bynbsp;the preffure of the atmofphere; though eachnbsp;receiver will then be kept down but with one

half of preffure upon it, that the receiver / had, when it was exhauftedof air; becaufe it has nownbsp;one half of the common air in it which fillednbsp;the receiver K when it was fet upon the platenbsp;and therefore, a force equal to half the force ofnbsp;the 1'pring of common air, will ad within thenbsp;receivers againft the whole preffure of the common air upon their outfides. This is callednbsp;transferring the air out of one veffel into another.

22. nbsp;nbsp;nbsp;Put a cork into the fquare phial yf, and Fig.nbsp;fix it in with wax or cement; put the phial uponnbsp;the pump-plate with the wire cage B over it,nbsp;and cover the cage with a clofe receiver. Then,nbsp;exhauft the air out of the receiver, and the airnbsp;that was corked up in the phial will break thenbsp;phial outwards by the force of its fpring, becaufenbsp;there is no air left on the outfide of the phial tonbsp;ad againft the air within it.

23. nbsp;nbsp;nbsp;Put a fhrivelled apple under a clofe receiver, and exhauft the air ; then the fpring ofnbsp;the air within the apple will plump it out, fo asnbsp;to caufe all the wrinkles difappear; but uponnbsp;letting the air into the receiver again, to prefsnbsp;upon the apple, it will inftantly return to itsnbsp;former decayed and ffrivelled ftate.

24. nbsp;nbsp;nbsp;Take a frefh egg, and cut off a little ofnbsp;the Ihell and film from its fmalleft end, then putnbsp;the egg under a receiver, and pump out the air �,nbsp;upon which, all the contents in the egg will benbsp;forced out into the receiver, by iheexpanfion ofnbsp;a fmall bubble of air contained in the great end,nbsp;between the ftiell and film,

25. nbsp;nbsp;nbsp;Put fome warm beer into a glafs, and having fet it on the pump, cover it with a clofe receiver, and then exhauft the air. Whilft this isnbsp;doing, and thereby the preffure more and more

taken off from the beer in the glafs, the air there-in will expand itfelf, and rife up in innumerable bubbles to the furface of the beer; and fromnbsp;thence it will be taken away with the other air innbsp;the receiver. When the receiver is nearly ex-haufted, the air in the beer, which could notnbsp;difentangle itfelf quick enough to get oft' withnbsp;the reft, will now expand itfelf fo, as to caufenbsp;the beer to have all the appearance of boiling ;nbsp;and the greateft part of it will go over thenbsp;glafs.

26. nbsp;nbsp;nbsp;Put fome warm water into a glafs, and putnbsp;a bit of dry wainfcot or other wood into thenbsp;water. Then, cover the glafs with a clofe receiver, and exhauft the air; upon which, the airnbsp;in the wood having liberty to expand itfelf, willnbsp;come out plentifully, and make all the water tonbsp;bubble about the wood, efpecially about thenbsp;ends, becaufe the pores lie lengthwife. A cubicnbsp;inch of dry wainfcot has fo much air in it, thatnbsp;it will continue bubbling for near half an hournbsp;together.

27. nbsp;nbsp;nbsp;Screw the fyringe H (Fig. 8.) to a piecenbsp;of lead that weighs one pound at leaft j and,nbsp;holding the lead in one hand, pull up the piftonnbsp;in the fyringe with the other; then, quitting

' hold of the lead, the air will pulh it upward, .and drive back the fyringe upon the pifton.nbsp;The reafon of this is, that the drawing up of thenbsp;pifton makes a vacuum in the fyringe, and thenbsp;air, which preffes every way equally, havingnbsp;nothing to refill: its preffure upward, the lead isnbsp;thereby prelTed upward, contrary to its naturalnbsp;tendency by gravity. If the fyringe, fo loaded,

be hung in a receiver, and the air be exhauftedj the fyringe and lead will defcend upon the pifton*nbsp;rod by their natural gravity ; and, upon admitting the air into the receiver, they will be drovenbsp;upward again, until the pifton be at the verynbsp;bottom of the fyringe.

28. nbsp;nbsp;nbsp;Leta'large piece of cork be fufpendednbsp;by a thread at one end of a balance, and coun-terpoifed by a leaden weight, fufpended in thenbsp;fame manner, at the other. Let this balance benbsp;hung to the in fide of the top of a large receiver;nbsp;which being fet on the pump, and the air ex-haufted, the cork will preponderate, and fhewnbsp;itfelf to be heavier than the lead ; but uponnbsp;letting in the air again, the equilibrium will benbsp;reftored. The reafon of this is, that fince thenbsp;air is a fluid, and all bodies lofe as much of theirnbsp;abfolute weight in it, as is equal to the weightnbsp;of their bulk of the fluid, the cork being thenbsp;larger body, lofes more of its real weight thannbsp;the lead does �, and therefore muft in fa�l benbsp;heavier, to balance it under the difadvantage ofnbsp;lofing fome of its weight: which difadvantagenbsp;being taken off by removing the air, the bodiesnbsp;then gravitate according to their real quantitiesnbsp;of matter, and the cork, which balanced thenbsp;lead in air, fliews itfelf to be heavier when innbsp;vacuo.

29. nbsp;nbsp;nbsp;Set a lighted candle upon the pump, andnbsp;cover it with a tall receiver. If the receivernbsp;holds a gallon, the candle will burn a minutenbsp;and then, after having gradually decayed fromnbsp;the firft inftant, it will go out: which fliews, thatnbsp;a conftant fupply of frelh air is necelTary to feednbsp;flame �, and fo it alfo is for animal life. For anbsp;bird kept under a clofe receiver will foon die,nbsp;although no air be pumped out j and it is

found that, in the diving-bell, a gallon of air is fufficient only for one minute for a man tonbsp;breathe in.

The moment when the candle goes out, the fmoke will be feen to afcend to the top of thenbsp;receiver, and there it will form a fort of cloud :nbsp;but upon exhaufting the air, the fmoke will fallnbsp;down to the bottom of the receiver, and leave itnbsp;as clear at the top as it was before it was fet uponnbsp;the pump. This (hews, that fmoke does notnbsp;afcend on account of its being pofitively light,nbsp;but becaufe it is lighter than air �, and its fallingnbsp;to the bottom wl:en the air is taken away,nbsp;lliews, that it is not deftitute of weight. Sonbsp;moft forts of wood afcend or fwim in water; andnbsp;yet there are none who doubt of the wood�snbsp;having gravity or weight.

30. nbsp;nbsp;nbsp;Set a receiver, which is open at top, uponnbsp;the air-pump, and cover it with a brafs plate,nbsp;and wet leather; and having exhaufted it of air,nbsp;let the air in again at top through an iron pipe,nbsp;making it pafs through a charcoal flame at thenbsp;end of the pipe ; and when the receiver is fullnbsp;of that air, lift up the cover, and let down anbsp;moufe or bird into the receiver, and the burntnbsp;air will immediately kill it. If a candle be letnbsp;down into that air, it will go out dire�lly ; bur,nbsp;by letting it down gently, it will purify the air fonbsp;far as it goes; and fo, by letting it down morenbsp;and more, the flame will drive out the bad air,nbsp;and good air will get in.

31. nbsp;nbsp;nbsp;Set a bell upon a cufliion on the pump-plate, and cover it with a receiver; then fhakenbsp;the pump to make the clapper ftrike againft thenbsp;bell, and the found will be very well heard : but,nbsp;exhaufl; the receiver of air, and then, if thenbsp;clapper be made to ftrike ever fo hard againft

the bell, it will make no found at all �, which ^ews, that air is abfolutely necelTary for thenbsp;propagation of found.

32. Let a candle be placed on one fide of a receiver, and viewed through the receiver atnbsp;fome diftance; then, as foon as the air begins tonbsp;be exhaufted, the receiver will be filled with vapours which rife from the wet leather, by thenbsp;fpring of the air in it �, and the light of thenbsp;candle being refradled through that medium ofnbsp;vapours, will have the appearance of circles ofnbsp;various colours, of a faint refemblance to thofenbsp;in the rain-bow.

The air-pump was invented by Otho Guerick of Magdeburg, but was much improved by Mr.nbsp;Boyle, to whom we are indebted for our greateftnbsp;part of the knowledge of the wonderful properties of the air, demonftratcd in the above experiments.

The elaftic air which is contained in many bodies, and is kept in them by the weight of thenbsp;atmofphere, may be got out of them either bynbsp;boiling, or by the air-pump, as fhewn in thenbsp;25th experiment: but the fixed air, which is bynbsp;niuch the greater quantity, cannot be got outnbsp;but by diftillation, fermentation, or putrefaction.

If fixed air did not come out of bodies with difficulty, and fpend fome time in extricatingnbsp;itfelf from them, it would tear them to pieces.nbsp;Trees would be rent by the change of air fromnbsp;a fixt, to an elaftic ftate, and animals would benbsp;burit in pieces by the explofion of air in theirnbsp;food.

Dr, Hales found by experiment, that the air in apples is fo much condenfed, that if it werenbsp;let out into the common air, it would fill a fpacenbsp;O 3nbsp;nbsp;nbsp;nbsp;4g

48 times as great as the bulk of the apples them-: ielves; fo that its preflure outwards was equalnbsp;to 117761b. and, in a cubic inch of oak, tqnbsp;198601b. againft its Tides. So that if the airnbsp;was let looTe at once in thefe fubftances, theynbsp;would tear every thing to pieces about therrinbsp;with a force fuperior to that of gunpowder.nbsp;Hence, in eating apples, it is well that they partnbsp;with the air by degrees, as they are chewed, andnbsp;ferment in the ftomach, otherwife an applenbsp;would be immediate death to him who eats it.

The mixing of fome fubftances with others will releale the air from them, all of a fudden,nbsp;which may be attended with very great danger.nbsp;Of this we have a remarkable inftance in an experiment made by Dr. Slare \ who having putnbsp;half a dram of oil of carraway-feeds into one glafs,nbsp;and a dram of compound fpirit of nitre in another, covered them both on the air-pump with anbsp;receiver fix inches wide, and eight inches deep,nbsp;and then exhaufted the air, and continued pumping until all that could poflibly be got both outnbsp;of the receiver, and out of the two fluids, wasnbsp;extricated : then, by a particular contrivancenbsp;from the top of the receiver, he mixed thenbsp;fluids together �, upon which they producednbsp;juch a prodigious quantity of air, as inftantlynbsp;blew up the receiver, although it was preflTednbsp;down by the atmofphere with upwards of 400nbsp;pound weight.

'N. B. In the 28th Experiment, the cork mull be covered all over with a piece of thin wetnbsp;bladder glued to it, and not ufed until it benbsp;thoroughly dry.

LEC T,

Of optics.

L E C T. Vill.

Light confifts of an inconceivably great number of particles flowing from a luminous body in all manner of direftions; and thefenbsp;particles are fo fmall, as to furpafs all humannbsp;comprehenfion.

That the number of particles of light is inconceivably great, appears from the light of a candle; which, if there be no obftacle in thenbsp;way to obftruLl; the paflage of its rays, will fillnbsp;all the fpace within two miles of the candle everynbsp;way, with luminous particles, before it has lollnbsp;the leaft fenfible part of its fubftance.

A ray of light is a continued ftream of thefe particles, flowing from any vifible body in anbsp;ftraight line : and that the particles themfelvesnbsp;are incomprehenfibly fmall, is manifeft from thenbsp;following experiment. Make a fmall pin-holenbsp;in a piece of black paper, and hold the papernbsp;upright on a table facing a row of candles Handing by one another; then place a (beet of pafte-board at a little diftance behind the paper, andnbsp;fome of the rays which flow from all the candlesnbsp;through the hole in the paper, will form as manynbsp;fpecks of light on the pafteboard, as there arenbsp;candles on the table before the plate: each fpeck The ama-being as diftindl and clear, as if there was only �quot;Snbsp;one fpeck from one Angle candle: which fhews ofnbsp;that the particles of light are exceedingly fmall, partidesnbsp;otherwife they could not pafs through the hole of light,nbsp;from fo many different candles without confu-fion.�Dr. Niewentyt has computed, that therenbsp;flows more than 6,000,000,000,000 times asnbsp;O 4nbsp;nbsp;nbsp;nbsp;many

many particles of light from a candle in one feconcl of time, as there are grains of fand in thenbsp;whole earth, fuppofing each cubic inch of it tonbsp;contain i,ooo,coo.

Thefe particles, by falling direftly upon our eyes, excite in our minds the idea of light.nbsp;And when they fall upon bodies, and are therebynbsp;refleded to our eyes, they excite in us the ideasnbsp;of thefe bodies. And as every point of a vifiblenbsp;body refleds the rays of light in all manner ofnbsp;diredions, every point will be vifible in everynbsp;part to which the light i? refleded from it.nbsp;Plats XV, Thus the objed AC B is vifible to an eye in anynbsp;part where the rays A a, Ah, Ac^ Ad, A e, B a,nbsp;Bh,B c, B d. Be, and C a, Ch, C c, C d, C e,nbsp;come. Here we have Ihewn the rays as if theynbsp;were only refleded from the ends A and B, andnbsp;from the middle point C of the objed -, everynbsp;other point being iuppofed to refled rays in thenbsp;Refleaed fame manner. So that wherever a fpedator isnbsp;light. placed with regard to the body, every point ofnbsp;that part of the furface which is towards him willnbsp;be vifible, when no intervening objed flops thenbsp;paflTage of the light.

As no objed can be feen through the bore of a bended pipe, it is evident that the rays ofnbsp;light move in ftraight lines, whilft there is nothing to refrad or turn them out of their redi-- lineal courfe.

While the rays of light continue in any * medium of an uniform denfity, they are flraight; but when they pafs obliquely out of one mediumnbsp;into another, which is either more denfe or more

* Any thing through which the rays of light can pafs, is called a medium; -as air, water, glafs, diamond, or erennbsp;a vacuum.

rare, they are refrafted towards the denfer medium : and this refraflion is more or lefs, as the rays fall more or lefs obliquely on the refractingnbsp;furface which divides the mediums.

To prove this by experiment, fet the empty Fig- 2. veflel JBCD into any place where the fun fhincsnbsp;obliquely, and obferve the part where thenbsp;lhadow of the edge B C falls on the bottom ofnbsp;the veffel at E-, then fill the velTel with water,nbsp;and the lliadow will reach no farther than e jnbsp;which Ihews, that the ray a B E, which camenbsp;ftraight in the open air, juft over the edge of thenbsp;veflel at B to its bottom at E, is refradled bynbsp;falling obliquely on the furface of the water at Refrsaednbsp;B ; and inftead of going on in the relt;5tilineal di- ��S'�-'*nbsp;redlion a B E, it is bent downward in the waternbsp;from B to e-, the whole bend being at the furfacenbsp;of the water: and fo of all the other raysnbsp;a h c.

If a ftick be laid over the velTel, and the fun�s rays be reflefted from a glafs perpendicularlynbsp;into the veflel, the fhadow of the flick will fallnbsp;upon the fame part of the bottom, whether thenbsp;veflel be empty or full, which Ihews, that thenbsp;rays of light are not refradled when they fallnbsp;perpendicularly on the furface of any medium.

The rays of light are as much refracted by paffing out of water into air, as by pafling out ofnbsp;air into water. Thus, if a ray of light flowsnbsp;from the point underwater, in the directionnbsp;e B; when it comes to the furface of the water atnbsp;B, it will not go on thence in the redtilinealnbsp;courfe B d, but will be refraded into the line Ba.nbsp;Therefore,

To an eye at e looking through a plane glafs in the bottom of the empty veflel, the point anbsp;cannot be feen, becaufe the fide Be of the veflel

interpofes; and the point will juft be fecnover the edge oftthe veflel at B. But if the v^flel benbsp;filled with water, the point a will be feen from e ;nbsp;and will appear as at elevated in the dire�lionnbsp;of the ray e B¹.

The time of fun-rifing or fetting, fuppofing its rays fuffered no refratftion, is eafily found bynbsp;calculation. But obfervation proves that thenbsp;fun rifes fooner, and fets later every day than thenbsp;calculated time; the reafon of which is plain,nbsp;from what was faid immediately above. For,nbsp;though the fun�s rays do not come part of thenbsp;way to us through water, yet they do through thenbsp;air or atmofphere, which being a grofler mediumnbsp;than the free fpace between the fun and the topnbsp;of the atmofphere, the rays, by entering obliquely into the atmofphere, are there refrafted,nbsp;and thence bent down to the earth. And although there are many places of the earth tonbsp;v/hich the fun is vertical at noon, and confe-quently his rays can fuffer no refraflion at thatnbsp;time, becaufe they come perpendicularly throughnbsp;the atmofphere : yet there is no place to whichnbsp;the fun�s rays do not fall obliquely on the top ofnbsp;the atmofphere, at his rifing and fetting; andnbsp;confequently, no clear day in which the fun willnbsp;not be vifible before he rifes in the horizon, andnbsp;after he fets in it: and the longer or Ihorter, asnbsp;the atmofphere is more or lefs replete with va-Fig. 3. pours. For, let 5 C be part of the earth�snbsp;furface, D E F the atmofphere that covers it,

Hence a piece of money lying at e, in the bottom of an empty veliel, cannot be feen by an eye at a, becaufe the edgenbsp;of the veffel intervenes ; but let the veflel be filled withnbsp;water, and the ray e a being tlien refrafled at B, will flrikenbsp;the eye at a, and fo render the money vifible, which willnbsp;� appear as if it were raifed up to f in the line a Bf,

snd EB G H the fenfible horizon of an obferver at B. As every point of the fun�s furface fendsnbsp;out rays of light in all manner of direftions,nbsp;feme of his rays will conftantly fall upon, andnbsp;enligliten, fome half of the atmofphere; andnbsp;therefore, when the fun is at 7, below the horizon H, thofe rays which go on in the free fpacenbsp;I k K preferve a reftilineal cotirfe until they fallnbsp;upon the top of the atmofphere and thofenbsp;which fall fo about K, are refradted at theirnbsp;entrance into the atmofphere, and bent downnbsp;in the line Km B, to the obferver�s place at B :nbsp;and therefore, to him, the fun will appear at Z.,nbsp;in the diredlion of the ray B m K, above the horizon B G H, when he is really below it at 7.

The angle contained between a ray of light, and a perpendicular to the refrafting furface, isnbsp;called the angle of incidence ; and the angle con� Angle ofnbsp;tained between the fame perpendicular, and the incidence.nbsp;fame ray after refradlion, is called the angle ofnbsp;refrahlion. Thus, let 7- 5 M be the refrading pig. 4.nbsp;furface of a medium (fuppofe water) and ABC Angle ofnbsp;a perpendicular to that iurface ; let D S be a refraaton.nbsp;ray of light, going out of air into water at 5,nbsp;and therein refraded in the line B H ; the anglenbsp;AB D, is the angle of incidence, of Which D Fnbsp;is the fine ; and the angle K B H Is the angle ofnbsp;refradion, whofe fine is K 7.

When the refrading medium is water, the fine of the angle of incidence is to the fine ofnbsp;the angle of refrad�X)n, as 4 to 3 ; which is confirmed by the following experiment, taken fromnbsp;Dodor Smith�s Optics.

Defcribe the circle B A EC on z plane fquare board, and crofs it at right angles with thenbsp;ftraight lines ABC, and L 5 M-, then, fromnbsp;the interfedion, A, with any opening of the com-

Of opties.

paffes, fet off the equal arcs A B and A and draw the right line D F E: then, taking Fanbsp;which is three quarters of the length F E, fromnbsp;the point a, draw a I parallel to A B K, andnbsp;join K �, parallel to B M: fo K I will be equalnbsp;to three quarters oi FE or of D F. This done,nbsp;fix the board upright upon the leaden pedeftalnbsp;O, and flick three pins perpendicularly into thenbsp;board, at the points Z),-j8, and I: then fet thenbsp;board upright into the veffel VU F, and fill upnbsp;the veffel with water to the line L B M. Whennbsp;the water has fettled, look along the line D B,nbsp;fo as you may fee the head of the pin 5 over thenbsp;head of the pin D; and the pin / will appear innbsp;the fame right line produced to G, for its headnbsp;will be feen juft over the head of the pin at B:nbsp;which (hews that the ray IB, coming from thenbsp;pin at /, is fo refra�led at B, as to proceed fromnbsp;thence in the line B D to the eye of the obferver;nbsp;the fame as it would do from any point G in thenbsp;right line DBG, if there were no water in thenbsp;veffel; and .alfo fiiews that K /, the fine of re-fradlion in water, is to D F, the fine of incidence in air, as 3 to 4 *

Hence, if D B H were a crooked flick put obliquely into the water, it would appear anbsp;flraight one, zs D B G. Therefore, as the linenbsp;B H appears at B G, fo the line B G will appearnbsp;at B g-, and confequently, a flraight flick B B Gnbsp;put obliquely into water, will feem bent at thenbsp;lurfate of the water in B, and crooked, asnbsp;BBg.

When a ray of light paffes out of air into glafs, the fine of incidence is to the fine of re-

Cf optics.

Glafs may be ground into eight different S-flaapes at leaft, for optical purpofcs, viz.

1. nbsp;nbsp;nbsp;Ps plane glafs, which is flat on both fides,nbsp;and of equal thicknefs in all its parts, as A.

2. nbsp;nbsp;nbsp;A piano convex, which is flat on one fide, Lenfcs.nbsp;and convex on the other, as B.

4. nbsp;nbsp;nbsp;A plano-concave which is flat on one fide,nbsp;and concave on the other, as D.

6. nbsp;nbsp;nbsp;A menifcus, which is concave on one fide,nbsp;and convex on the other, as F.

7. nbsp;nbsp;nbsp;A flat plano-convex, whofe convex fide isnbsp;ground into feveral little flat furfaces, as G.

8. nbsp;nbsp;nbsp;A prifm, which has three fiat fides, andnbsp;when viewed endwife, appears like an equilateralnbsp;triangle, as H.

A right line L IK, going perpendicularly through the middle of a lens, is called the axisnbsp;of the lens.

A ray of light G h, falling perpendicularly on a plane glafs E F, will pafs through the glafs Fig, 6.nbsp;in the fame diredlion h i, and go out of it intonbsp;the air in the fame right courfe i H.

A ray of light A B, falling obliquely on a plane glafs, will go out of the glafs in the famenbsp;dire�lion, but not in the fame right line ; for innbsp;touching the glafs, it will be refrafted in thenbsp;line B C, and in leaving the glafs, it will be re-frafted in the line C D.

A ray of light C D, falling obliquely pn the middle of a convex glafs, will go forward in thenbsp;fame dire�tion D E, as if it had fallen with th�nbsp;fame degree of obliquity on a plane glafs; andnbsp;will go out of the glafs in the fame direftiorinbsp;with which it entered ; for ic will be equally re-frafled at the points D and E, as if it had paffednbsp;through a plane furface. But the rays C G andnbsp;C I wiil be fo refra�led, as to meet again at thenbsp;point F. Therefore, all the rays which flownbsp;from the point C, fo as to go through the glafs,nbsp;will meet again at F \ and if they go farthernbsp;onward, as to Z, they crofs at T, and go forward on the oppofite fides of the middle raynbsp;CB E F, to what they were in approaching it innbsp;the direflioiis H F and K F.

When parallel rays, as ABC., fall direiflly upon aplano-convex glafs D E, and pafs throughnbsp;it, they will be fo refrafted, as to unite in anbsp;point � behind it: and this point is called thenbsp;principal focus: the diftance of which, from thenbsp;middle of the glafs, is called the fecal diftance jnbsp;which is equal to twice the radius of the fpherenbsp;of the glaf�s convexity. And,

upon a glafs D E, which is equally convex on both fides, and pafs through it; they will be fonbsp;refradted, as to meet in a point or principal focusnbsp;�, whofe diftance is equal to the radius or femi-diameter of the fphere �f the glafs�s convexity.nbsp;But if a glafs be more convex on one fide thannbsp;on the other, the rule for finding the focalnbsp;diftance is this; as the fum of the femidiametersnbsp;of both convexities is to the femidiameter ofnbsp;either, fo is double the femidiameter of thenbsp;other to the diftance of the focus. Or, divide

Of optics.

the double produft of the radii by their futUi and the quotient will be the diftance fought.

Since all thofe rays of the fun which pafs through a convex glafs are colledted togethernbsp;in its focus, the force of all their heat is col-leded into that part; and is in proportion tonbsp;the common heat of the fun, as the area of thenbsp;glafs is to the area of the focus. Hence we feenbsp;the reafon why a convex glafs caufes the fun�snbsp;rays to burn after pafling through it.

All thefe rays crofs the middle ray in the focus �, and then diverge from it, to the contrary lides, in the fame manner FfG, as they converged in the fpace DfEin coming to it.

If another glafs F G, of the fame convexity as D �, be placed in the rays at the fame distance from the focus, it will refraft them fo,nbsp;as that after going out of it, they will be allnbsp;parallel, as a b e; and go on in the lame manner as they came to the firft glafs Z) �, throughnbsp;the fpace ABC-, but on the contrary fides ofnbsp;the middle ray B f b: for the ray A D � will gonbsp;on from � in the direction f G and the raynbsp;C � � in the direftion f F c �, and fo of the reft.

The rays diverge from any radiant point, as from a principal focus: therefore, if a candlenbsp;be placed at �, in the focus of the convex glafsnbsp;F G, the diverging rays in the fpace FfG willnbsp;be fo refradled by the glafs, as, that after goingnbsp;out of it, they will become parallel, as fhewnnbsp;in the fpace c b a.

If the candle be placed nearer the glafs than its focal diftanc�, the rays will diverge afternbsp;palling through the glafs, more or lefs, as thenbsp;candle is more or lefs diftant from the focus.

If the candle be placed farther from the glafs than its focal diftance, the rays will converge

after pafflng through the glafs, and meet in a point which will be more or lefs diftant from thenbsp;glafs, as the candle is nearer to, or farther fromnbsp;its focus i and where the rays meet, they willnbsp;form an inverted image of the flame of thenbsp;candle; which may be feen on a paper placednbsp;in the meeting of the rays.

Hence, if any object ABC he placed beyond the focus F �f the convex glafs d e f, fome ofnbsp;the rays which flow from every point of thenbsp;object, on the fide next the glafs, will fall uponnbsp;it, and after paffing through it, they will benbsp;converged into as many points on the oppofitenbsp;fide of the glafs, where the image of every pointnbsp;will be formed : and confequently, the imagenbsp;of the whole objefl:, which will be inverted.nbsp;Thus, the rays Ad, Ae, Af, flowing from thenbsp;point A, will converge in the fpace d af, and bynbsp;meeting at a, will there form the image of thenbsp;point A. The rays Bd. Be, Bf, flowing fromnbsp;the point B, will be united at b by the refraction of the glafs, and will there form the imagenbsp;of the point B. And the rays C d, C e, C f,nbsp;flowing from the point C, will be united at c,nbsp;where they will form the image of the point C.nbsp;And fo of all the other intermediate points between A and C. The rays which flow fromnbsp;every particular point of the objeft, and arenbsp;united again by the glafs, are called pencils ofnbsp;rays.

If the objedt AB Champ; brought nearer to the glafs, the pidure a b c will be removed to anbsp;greater diftance. For then, more rays flowingnbsp;from every Angle point, will fall more divergingnbsp;upon the glafs ; and therefore cannot be fo Toonnbsp;colleded into the correfponding points behindnbsp;it. Confequentlv, if the diftance of the objedt

ABC

vf � C be equal to the diftance e B of the focus of the glafs, the rays of each pencil will be fonbsp;refracted by pafDng through the glafs, that theynbsp;�will go out of it parallel to each other; as i /,nbsp;c ff, f h, from the point C; d G, e K, f D,nbsp;from the point 5; and d K, e E., f L, from thenbsp;point A: and therefore, there will be no picture formed behind the glafs.

If the focal diftance of the glafs, and the diftance of the objeft from the glafs, be known,nbsp;the diftance of the pidture from the glafs maynbsp;be found by this rule, viz. multiply the diftancenbsp;of the focus by the diftance of the objecl, andnbsp;divide the produdl by their difference} thenbsp;quotient will be the diftance of the pifture.

The picture will be as much bigger or lefs *� than the objeCt, as its diftance from the glafs isnbsp;greater or lefs than the diftance of the objeCt.

For, as is to ^ fo is AC to r a. So that if ABC be the objeft, da will be the pidure*,nbsp;or, if f ^ � be the objeCt, ABC will be thenbsp;picture.

Having defcribed how the rays of light, The man-flowing from objects and paffing through con-vex glaffes, are collected into points, and form the images of the objeCls ; it will be eafy to un-derftand how the rays are affeCtcd by pallingnbsp;through the humours of the eye, and are thereby collected into innumerable points on the bottom of the eye, and thereon form the images ofnbsp;the objects which they flow from. For, thenbsp;different humours of the eye, and particularlynbsp;the chryftalline humour, are to be confiderednbsp;as a convex glafs; and the rays in paffingnbsp;through them to be affeCled in the fame mannernbsp;as in paffing through a convex glafs.

plateXVI. The eye is nearly globular. It conOfts of F'g* :� three coats and three humours. The partnbsp;D H H G of the outer coat, is called the fcle-rctica, the reft D E FG the cornea. Next within this coat is that called the chorcideSy whichnbsp;ferves as it were for a lining to the ocher, andnbsp;joins with the iris m n, m n. The iris is com-pofed of two fets of mufcular fibres ; the one ofnbsp;a circular form, which contrafts the hole in thenbsp;middle called the pupil, when the light wouldnbsp;The eye otherwife be too ftrong for the eye j and thenbsp;defcribed, Other of radial fibres, tending every where fromnbsp;the circumference of the iris towards the middlenbsp;of the pupil; which fibres, by their contraftion,nbsp;dilate and enlarge the pupil when the light isnbsp;weak, in order to let in the more of its rays.nbsp;The third coat is only a fine expanfion of thenbsp;optic nerve L, which fpreads like net-work allnbsp;over the infide of the choroides, and is thereforenbsp;called the retina �, upon which are painted (as itnbsp;were) the images of all vifible objedls, by thenbsp;rays of light which either flow or are refleftednbsp;from them.

Under the cornea is a fine tranfparent fluid like water, which is therefore called the aqueousnbsp;humour. It gives a protuberant figure to thenbsp;cornea, fills the two cavities m m and n n, whichnbsp;communicate by the pupil P, and has the famenbsp;limpidity, fpecific gravity, and refraftive powernbsp;as water. At the back of this,lies the chryjlallinenbsp;humour I /, which is fnaped like a double convex glafs; and is a little more convex on thenbsp;back than the fore-part. It converges the rays,nbsp;which pafs through jt from every vifible objedlnbsp;to its focus at the bottom of the eye. Thisnbsp;humour is tranfparent like chryftal, is much ofnbsp;the confiftence of hard jelly, and exceeds the

Of optici.

fpccific grivity of water in the proportion of II to 10. It is inclofed in a fine tranfparentnbsp;membrane, from which proceed radial fibresnbsp;0 0, called the ligamentum ciliare, all around itsnbsp;edge; and join to the circumference of the iris,nbsp;Thefe fibres have a power of contrading andnbsp;dilating occafionally, by which means they alternbsp;the fhape or convexity of the chryftalline humour, and alfo Ibift it a little backward or forward in the eye, fo as to adapt its focal diftancenbsp;at the bottom of the eye to the different diftancesnbsp;of objeds ; Vv'ithout which provifion, we couldnbsp;only fee thofe objefts diftindly, that were all atnbsp;one diftance from the eye.

and is largeft of all in quantity, filling the whole orb of the eye, and giving it a globular fhape.nbsp;It is much of a confiftence with the white of annbsp;egg, and very little exceeds the fpecific gravitynbsp;and refractive power of water.

As every point of an objed ABC fends out rays in all diredions, fome rays, from everynbsp;point on the fide next the eye, will fall uponnbsp;the cornea between E and F-, and by paffitig onnbsp;through the humours and pupil of the eye^nbsp;they will be converged .to as many points onnbsp;the retina or bottom of the eye, and v/ill thereonnbsp;form a diftind inverted pidure c h a oi the ob-jed;. Thus, the pencil of rays q^r s that flowsnbsp;from the point A of the objed, will be converged to the point a on thg retina ; thofe fromnbsp;the point 5 will be converged to the pointnbsp;thofe from the point C will be converged to thenbsp;point c ; and fo of all the intermediai;e points: bynbsp;, which means the whole image a b c formed,nbsp;and the objecl made vifible 5 although it muftnbsp;P 2nbsp;nbsp;nbsp;nbsp;be

be owned, that the method by which this fenfa-tion is carried from the eye by the optic nerve to the common fenfory in the brain, and therenbsp;difcerned, is above the reach of our comprc-henfion.

But that vifion is effeiSled in this manner, may be demonftrated experimentally. Take anbsp;bullock�s eye whilft it is frelh, and having cutnbsp;off the three coats from the back part, quitenbsp;to the vitreous humour, put a piece of whitenbsp;paper over that part, and hold the eye towardsnbsp;any bright objeft, and you will fee an invertednbsp;pifture of the object upon the paper.

Seeing the image is inverted, many have Wondered why the objeft appears upright. Butnbsp;we are to confider, i. That inverted is only anbsp;relative term ; and 2. That there is a very greatnbsp;difference between the real objefl and the meansnbsp;or image by which we perceive it. When allnbsp;the parts of a diftant profpeft are painted uponnbsp;the retina, they are all right with refpeft to onenbsp;another, as well as the parts of the profpedtnbsp;itfelf; and we can only judge of an object�snbsp;being inverted, when it is turned reverfe to itsnbsp;natural pofition, with refpedl to other objeflsnbsp;which we fee and compare it with.�If we laynbsp;hold of an upright ftick in the dark, we can tellnbsp;which is the upper or lower part of it, by moving our hand upward or downward; ancl knownbsp;very well that we cannot feel the upper end bynbsp;moving our hand downward. Juft fo we findnbsp;by experience, that upon diretfting our eyesnbsp;towards a tall objeff, we cannot fee its top bynbsp;turning our eyes downward, nor its foot bynbsp;turning our eyes upward; but muft trace thenbsp;objedt the fame way by the eye to fee it fromnbsp;head to foot, as we do by the hand to feel it *,nbsp;6nbsp;nbsp;nbsp;nbsp;and

Of optici.

and as the judgment is informed by the motion of the hand in one cafe, fo it is alfo by the motion of the eye in the other.

In Fig. 4. is exhibited the manner of feeing pjg_ the fame obje�l A B by both the eyes D andnbsp;E at once.

quot;When any part of the image c b a falls upon the optic nerve L, the correfponding part ofnbsp;the objed; becomes invifible. On which account nature has wifely placed the optic nervenbsp;of each eye, not in the middle of the bottom ofnbsp;the eye, but towards the fide next the nofe ; fonbsp;that whatever part of the image falls upon thenbsp;optic nerve of one eye, may not fall upon thenbsp;optic nerve of the other. Thus the point a ofnbsp;the image c b a falls upon the optic nerve of thenbsp;eye D, but not of the eye E-, and the point enbsp;falls upon the optic nerve of the eye �, but notnbsp;of the eye D ; and therefore to both eyes takennbsp;together, the whole objed A B C 'iamp; vilible.

The nearer that any objed is to the eye, the pja^ larger is the angle under which it it feen, and XVII.nbsp;the magnitude under which it appears. Thus gt;�nbsp;to the eye I), the objed A B C feen under thenbsp;angle A P C\ and its image c b a very largenbsp;upon the retina : but to the eye E, at a doublenbsp;diftance, the fame objed is feen under the anglenbsp;Ape, which is equal only to half the anglenbsp;A P C, z5 is evident by the figure. The imagenbsp;c b likewife twice as large in the eye D, asnbsp;the other image c b a h in the eye E. In bothnbsp;thefe reprefentations, a part of the image fallsnbsp;on the optic nerve, and the objed in the corre-Iponding part is invifible.

As the fenfe of feeing is allowed to be occa-fioned by the impulfe of the rays from the vilible objed upon the retina of the eye, and formingnbsp;P 3nbsp;nbsp;nbsp;nbsp;the

Of Opties.

diftance, becaufe thjsy cannot appear under any fenfible angle. The method of viewing fuchnbsp;minute objecls is by a microfeope, of which therenbsp;are three forts, viz. the fingle, the double., andnbsp;the folar.

The Jingle microfeope, is only a fmall convex glafs, as c d, having the objedl a b placed in itsnbsp;focus, and the eye at the fame diftance on thenbsp;other fide -, fo that the rays of each pencil, flowing from every point of the objetft on the fidenbsp;next the glafs, may go on parallel in the fpaccnbsp;between the eye and the glafs ; and then, bynbsp;entering the eye at C, they will be convergednbsp;to as many different points on the retina, andnbsp;form a large inverted piiffure A B upon ir, asnbsp;in the ffgure.

To find how much this glafs magnifies, divide the leaft diftance (which is about fix inches) at which an objeft can be feen diftiniftly withnbsp;the bare eye, by the focal diftance of the glafs ;nbsp;and the quotient will fliew how much the glafsnbsp;magnifies the diameter of the objeft.

The double or compound microfeope, confifls of an objed-glafs c d, and an eye glafs e f. Thenbsp;fmall objeef a b \s placed at a little greater diftance from the glais c d than its principal focus,nbsp;fo that the pencils of rays flowing from the different points of the objefl, and palfing throughnbsp;the glafs, may be made to converge and unitenbsp;in as many points between g and b, where thenbsp;image of the objed will be formed; whichnbsp;image is viewed by the eye through the eye-glafs e f. For the eye-glafs being fo placed,nbsp;that the image ^ h may be in its focus, and thenbsp;eye much about the fame diftance on the othernbsp;fide, the rays of each pencil will be parallel,nbsp;after going out of the eye-glafs, as at e and /,

Of optics.

till they come to the eye at ky where they will begin to eonverge by the refradive power ofnbsp;the humours; and after having croffed eachnbsp;Other in the pupil, and pafled through the chryf-talline and vitreous humours they will be col-Jefled into points on the retina, and form thenbsp;large inverted image A B thereon.

The magnifying power of this microfeope is as follows. Suppofe the image ^ to be fixnbsp;times the diftance of the object a b from thenbsp;objecl-glafs c d; then will the image be fix timesnbsp;the length of the objed: but fince the imagenbsp;could not be feen diflindly by the bare eye atnbsp;a lefs diftance than fix inches, if it be viewednbsp;by an eye-glafs e f, of one inch focus, it willnbsp;thereby be brought fix times nearer the eye inbsp;and confequently viewed under an angle fix timesnbsp;as large as before �, fo that it will be again magnified fix times; that is, fix times by the objed-glafs, and fix times by the eye-glafs, which multiplied into one another, makes 36 times; andnbsp;fo much is the objed magnified in diameter morenbsp;than what it appears to the bare eye; and confequently 36 times 36, or 1296 times in furface.

But becaufe the extent or field of view is very fmall in this microfeope, there are generally two eye-glafles placed fometimes clofenbsp;together, and fometimes an inch afundeti bynbsp;which means, although the objed appears lefsnbsp;magnified, yet the vifible area is much enlargednbsp;jby the interpofition of a fecond eye-glafs; andnbsp;confequently a much pleafanter view is obtained.

The folar microfeope, invented by Dr. Lie- Fig. 7. hrkhun, is conftruded in the following manner. Thegt;/arnbsp;Having procured a very dark room, let a roundnbsp;hole be made in the window-lhutcer, about three

inches diameter, through which the fun may caft a cylinder of rays A A into the room. In thisnbsp;hole, place the end of a tube, containing twonbsp;convex glafles and an objeft, viz. i. A convexnbsp;glafs a a, of about two inches diameter, andnbsp;three inches focal diftance, is to be placed innbsp;that end of the tube which is put into the hole.nbsp;2. The objeft b b, being put between twoglaffesnbsp;(which muft be concave to hold it at liberty) isnbsp;placed about two inches and a half from the glafsnbsp;a a. 3. A little more than a quarter of an inchnbsp;from the object is placed the fmall convex glafsnbsp;C c, whofe focal diftance is a quarter of an inch.

The tube may be fo placed, when the fun is low, that his rays A A may enter direftly intonbsp;it; but when he is high, his rays B B muft benbsp;refleded into the tube by the plane mirrour ornbsp;looking-glafs C C.

Things being thus prepared, the rays that enter the tube will be conveyed by the glafs a anbsp;towards the objed b b, by which means it willnbsp;* be ftrongly illuminated; and the rays �? whichnbsp;flow from it, through tlae magnifying glafs c c,nbsp;v'ill make a large inverted pidure of the objednbsp;at D D, which, being received on a white paper,nbsp;will reprefent the objed magnified in length, innbsp;proportion of the diftance of the pidure fromnbsp;the glafs c c, to the diftance of the objed: fromnbsp;the lame glafs. Thus, fuppole the diftance of thenbsp;objed: fro.m the glafs to be ^ parts of an inch,nbsp;and the diftance of the diftind pidure to be 12nbsp;feet or 144 inches, in which there are 1440 tenthsnbsp;of an inch; and this number divided by 3 tenths,nbsp;gives 480 ; which is the number of times thenbsp;pidure is longer or broader than the objed ; andnbsp;the length multiplied by the breadth, Ihews hownbsp;much the whole furface is magnified.

Of optics. nbsp;nbsp;nbsp;22�

Before we enter upon the defcription of tele- Tek/copes. fcopes, it will be proper to fliew how the raysnbsp;of light are affefted bv paffing through concavenbsp;glafles, and alfo by falling upon concave mir- .nbsp;rours.

When parallel rays, as a � c d e f g h, pafs Plate, direftly through a glafs A B, which is equally XVin.nbsp;concave on both fides, they will diverge afternbsp;paffing through the glafs, as if they had comenbsp;from a radiant point C, in the center of thenbsp;glafs�s concavity ; which point is called the negative or virtual focus of the glafs. Thus thenbsp;ray a, after paffing through the glafs A B, willnbsp;go on in the diredtion k /, as if it had proceedednbsp;from the point C, and no glafs been in the way.

The ray b will go on in the diredion m n; the ray c in the diredion op, amp;c.�The ray C,nbsp;that falls diredly upon the middle of the glafs,nbsp;fuffers no refradion in paffing through it; butnbsp;goes on in the fame redilineal diredion, as ifnbsp;no glafs had been in its way.

If the glafs had been concave only on one fide, and the other fide quite plane, the raysnbsp;would have diverged, after paffing through it,nbsp;as if they had come from a radiant point atnbsp;double the diftance of C from the glafs -, that is,nbsp;as if the radiant had been at the diftance of anbsp;whole diameter of the glafs�s concavity.

If rays come more converging to fuch a glafs, than parallel rays diverge after paffing throughnbsp;it, they will continue to converge after paffingnbsp;through it �, but will not meet fo foon as if nonbsp;glafs had been in the way; and will inclinenbsp;towards the fame fide to which they would havenbsp;diverged, if they had come parallel to the glafs.

Thus the rays � and h, going in a converging ftate towards the edge of the glafs at B, and

con-

converging more in their way to it than me parallel rays diverge after paffing through it, they will go on converging after they pafs throughnbsp;it, though in a lefs degree than they did before,nbsp;and will meet at I: but if no glafs had been innbsp;their way, they would have met at i.nbsp;iTig. 2. When the parallel rays, i f a, C m b, e I e,nbsp;fall upon a concave mirror A B (which is notnbsp;tranfparent, but has only the furfaee A b B o�nbsp;a clear polilh) they will be refiefted back fromnbsp;that mirror, and meet in a point m, at half thenbsp;diftance of the furfaee of the mirror from C,nbsp;the center of its concavity : for they will benbsp;reflefted at as great an angle from the perpendicular to the furfaee of the mirror, as they fellnbsp;upon it, with regard to that perpendicular ; butnbsp;on the other fide thereof. Thus, let C be thenbsp;center of concavity of the mirror A b B, andnbsp;let the parallel rays if a, C m b, and e / r, fallnbsp;upon it at the points a b, and c. Draw thenbsp;lines C i a, C mb, and Che, from the center Cnbsp;to ihefe points and all thefe lines will be perpendicular to the furfaee of the mirror, becaufenbsp;they proceed thereto like fo many radii or fpokesnbsp;from its center. Make the angle C a ^ equalnbsp;to the angle d a C, and draw the line a m h,nbsp;which will be the diredtion of the ray df a, afternbsp;it is refiedted from the point a of the mirror:nbsp;fo that the angle of incidence d a C, is equal tonbsp;the angle of refledtion C ah-, the rays makingnbsp;equal angles with the perpendicular Ci a on itsnbsp;oppofite fides.

Draw alfothe perpendicular C h c to the point (, where the x2Ly e I c touches the mirror; and,nbsp;having made the angle C c i, equal to the anglenbsp;C c e, draw the line c m i, which will be the

courf#

Of optics.

The ray C m b pafles through the center of concavity of the mirror, and falls upon it, atnbsp;b, the perpendicular to it; and is therefore rc-fiefted back from it in the fame line b m C.

AU thefe refiefted rays meet in the point m; and in that point the image of the body whichnbsp;emits the parallel rays da, C b, and e c, will benbsp;formed : which point is diftant from the mirror equal to half the radius b m C oi its concavity.

The rays which proceed from any celeftiai objeft may be efteemed parallel at the earthsnbsp;and therefore, the images of that objedf will benbsp;formed at m, when the reflecting furface of thenbsp;concave mirror is turned diredly towards thenbsp;objed. Hence, the focus m of parallel raysnbsp;is not in the center of the mirror�s concavity,nbsp;but half way between the mirror and thatnbsp;center.

The rays which proceed from any remote terreftrial objedt, are nearly parallel at the mirror �, not ftridlly fo, but come diverging to it,nbsp;in feparate pencils, or, as it were, bundles ofnbsp;rays, from each point of the fide of the objednbsp;next the. mirror: and therefore they will notnbsp;be converged to a point, at the diftance of halfnbsp;the radius of the mirror�s concavity from itsnbsp;refledling furface j but into feparate points at anbsp;little greater diftance from the mirror. Andnbsp;the nearer the objeft is to the mirror, the farther thefe points will be from it; and an inverted image of the objeeft will be formed innbsp;them, which will feem to hang pendent in thenbsp;air; and will be feen by an eye placed beyondnbsp;it (with regard to the mirror) in all rclpedls

Of Opics'\

Let A c B'ot the reflefting furface of a mirror, whofe center of concavity is at C; and let the upright obje�t D � be placed beyond thenbsp;center C, and fend out a conical pencil of diverging rays from its upper extremity D, tonbsp;every point of the concave furface of the mirror A c B. But to avoid confufion, we onlynbsp;draw three rays of that pencil, D A, D r,nbsp;D B.

From the center of concavity C, draw the three right-lines C A^ C c, C B, touching thenbsp;mirror in the fame points where the forefaidnbsp;rays touch it �, and all thefe lines will be perpendicular to the furface of the mirror. Makenbsp;the angle C A d equal to the angle D A C, andnbsp;draw the right line Ad for the courfe of thenbsp;refledled ray D A\ make the angle C c d equalnbsp;to the angle D c C, and draw the right line c dnbsp;for the courfe of the reflefted ray D d: makenbsp;alfo the angle C B d equal to the angle D B C,nbsp;and draw the right line B d for the courfe of thenbsp;reflefted ray D B. All thefe reflefted rays willnbsp;meet in the point d, where they will form thenbsp;extremity d of the inverted image e d, fimilar tonbsp;the extremity D of the upright object D E.

If the pencils of rays A �, Eg, Eh be alfo continued to the mirror, and their angles of re-fleftion from it be made equal to their angles ofnbsp;incidence upon it, as in the former pencil frontnbsp;D, they will all meet at the point e by refletlion,nbsp;and form the extremity e of the image e d, fimilar to the extremity E of the objeft D E,

And as each intermediate point af the objedt, between D and E, fends out a pencil of rays innbsp;like manner to every part of the mirror, the

rays of each pencil will be reflefted back from it� and meet in all the intermediate points be-*�nbsp;tween the extremities e and d of the image �, andnbsp;fo the v/hole image will be formed, not atnbsp;half the diftance of the mirror from its centernbsp;of concavity C; but at a greater diftance, between 2 and the objeft D E �, and the image willnbsp;be inverted with refpedt to the objeft.

This being well underftood, the reader will ealily fee how the image is formed by the largenbsp;concave mirror of the reflefting telefcope,nbsp;when he comes to the defcription of that in-ftrument.

When the objeft is more remote from the mirror than its center of concavity C, thenbsp;image vvill be lefs than the obie(51', and betweennbsp;the objeft and mirror : when the objedl is nearernbsp;than the center of concavity, the image will benbsp;more remote and bigger than the objedl: thus,nbsp;if D � be the objeft, e d will be its image �, for,nbsp;as the objeft recedes from the mirror, thenbsp;image approaches nearer to it; and as the ob-jedl approaches nearer to the mirror, the imagenbsp;recedes farther from it on account of the leffernbsp;or greater divergency of the pencils of raysnbsp;which proceed from the objedl-, for, the lefsnbsp;they diverge, the fooner they are converged tonbsp;points by refle�tion; and the more they diverge, the farther they muft be reflefled beforenbsp;they meet.

If the radius of the mirror�s concavity and the diftance of the objedt from it be known, thenbsp;diftance of the image from the mirror is foundnbsp;by this rule : divide the produdt of. the diftance and radius by double the diftance madenbsp;lefs by the radius, and the quotient is the diftance required.

It the objelt;5b be in the center of the mirror�s concavity^ the image and obje�l: will be coincident, and equal in bulk.

If a man places himlelf diredly before a large concave mirror, but farther from it than itsnbsp;center of concavity, he will fee an invertednbsp;image of himfelf in the air, between him andnbsp;the mirror, of a lefs fize than himfelf. Andnbsp;if he holds out his hand towards the mirror,nbsp;the hand of the image will come out towardsnbsp;his hand, and coincide with it, of an equalnbsp;bulk, when his hand is in the center of concavity ; and he will imagine he may fhake handsnbsp;with his image. If he reaches his hand farther,nbsp;the hand of the image will pafs by his hand, andnbsp;come between his hand and his body : and if henbsp;moves his hand towards either fide, the hand ofnbsp;the image will move towards the other ; fo thatnbsp;whatever way the objedl moves, the image willnbsp;move the contrary way.

All the while a by-ftander will fee nothing of the image, becaufe none of the refleded raysnbsp;that form it enter his eyes.

If a fire be made in a large room, and a fmooth mahogany table be placed at a goodnbsp;diftance near the wall, before a large concavenbsp;mirror, fo placed, that the light of the firenbsp;may be refledled from the mirror to its focusnbsp;upon the table ; if a perfon ftands by the table,nbsp;he will fee nothing upon it but a longilh beamnbsp;of light; but if he ftands at a diftance towardsnbsp;the fire, not diredly between the fire and mirror, he will fee an image of the fire upon thenbsp;table, large and ereft. And if another perfon, who knows nothing of this matter beforehand, Ihould chance to come into the room,nbsp;and ihould look from the fire towards the table,

Of op tic f, nbsp;nbsp;nbsp;227

he would be ftartled at the appearance; for the Plate table would feem to be on fire, and by beingnbsp;near the wainfcot, to endanger the whole houfe.

In this experiment, there flionld be no light in the room but what proceeds from the fire ;nbsp;and the mirror ought to be at leaft fifteennbsp;inches in diameter.

If the fire be darkened by a fcreen, and a large candle be placed at the back of the fcreen ;nbsp;a perfon ftanding by the candle will fee thenbsp;appearance of a fine large ftar, or rather planet,nbsp;upon the table, as bright as Venus or Jupiter.

And if a fmall wax taper (whofe flame is much lefs than the flame of the candle) be placed nearnbsp;the candle, a fatellite to the planet will appearnbsp;on the table; and if the taper be moved roundnbsp;the candle, the fatellite will go round the planet.

For thefe two pleafing experiments, I am indebted to the lace reverend Dr. Long, Lowndes's profeflbr of aftronomy at Cambridge, who favoured me with the fight of them, and manynbsp;more of his curious inventions.

In a refradling telefcope, the glafs which is The re-neareft the objeft in viewing it, is called the/'�^%

Fig. 4.

g h i, flowing from the upper extremity J of the remote objeft A B, will be fo refrafted by paflTingnbsp;through the glafs, as to converge and meet innbsp;the point �; whilfl; the pencil of rays klm flowing from the lower extremity 5, of the fame ob-jed J B, and pafling through the glafs, will converge and meet in the point e: and the imagesnbsp;of the points A and B, vvill be formed in thenbsp;points � and e. And as all the intermediatenbsp;points of the objedf, between A and B, fend outnbsp;pencils of rays in the fame manner, a fufHcientnbsp;number of thefe pencils will pafs through thenbsp;objeft glafs c d, and converge to as many intermediate points between e and and fo will formnbsp;the whole inverted image e E f of the diftinftnbsp;objed. But beraufe this image is fmall, a concave glafs � 0 is fo placed in the end of the tubenbsp;next the- eye, that its virtual focus may be at F.nbsp;And as the rays of the pencils pafs convergingnbsp;through the concave glafs, but converge lefs afternbsp;palling through it than before, they go on further, as to b and a, before they meet v and thenbsp;pencils themfelves being made to diverge bynbsp;paffing through the concave glafs, they enter thenbsp;eye, and form the large pilt;5tiire a b upon thenbsp;retina, whereon it is magnified under the anglenbsp;b F a.

But this telefcope has one inconveniency which renders it unfit fur moft purpofes, which is, thatnbsp;the pencils of rays being made to diverge bynbsp;pafling through the concave glafs n o, very fewnbsp;of them can enter the pupil of the eye ; andnbsp;therefore the field of view is but very fmall, asnbsp;is evident by the figure. For none of the pencils which flow either from the top or bottom ofnbsp;the obje�l A B can enter the pupil of the eye atnbsp;C, but are all ftopt by falling upon the iris

above and below the pupil: and therefore, only the middle part of the objedi: can be feen whennbsp;the telefcope lies direftly towards it, by meansnbsp;of thofe rays which proceed from the middle ofnbsp;the objedl. So that to fee the whole of it, thenbsp;telefcope muft be moved upwards and downwards, unlefs the objcdl be very remote-, andnbsp;then it is never feen diflinflly.

This inconvenience is remedied by fubftitut- Fig. 5. ing a convex eye-glafs, as g h, in place of thenbsp;concave one ; and fixing it fo in the tube, thatnbsp;its focus may be coincident with the focus of thenbsp;objeft-glafs c d, as at E. For then, the raysnbsp;of the pencils flowing from the objeft A B, andnbsp;pairing through the objefl glafs c d, will meet innbsp;its focus, and form the inverted image m E p :nbsp;and as the image is formed in the focus of thenbsp;eye-glafs g h, the rays of each pencil will be parallel, after pafling through that glafs but thenbsp;pencils themfelves will crofs in its focus, on thenbsp;other fide, as at e: and the pupil of the eyenbsp;being in this focus, the image will be viewednbsp;through the glafs, under the angle g e h �, andnbsp;being at �, it will appear magnified, fo as to fillnbsp;the whole fpace C m ep D.

But, as this telefcope inverts the image wifh refpe�f to the obje�t, it gives an unpleafant viewnbsp;of terreftriai objedls -, and is only fit for viewingnbsp;the heavenly bodies, in which we regard not theirnbsp;pofition, becaufe their being inverted does notnbsp;appear, on account of their being round. Butnbsp;whatever way the objecl; feems to move, this telefcope muft be moved the contrary way, in ordernbsp;to keep fight of it; for, fince the objed: is inverted, its motion wdll be fo too.

The magnifying power of this telefcope is, as the focal diftance of the obje�t-glafs to the

focal diftance of the eye-glafs. Therefore, if the forrner be divided by the latter, the quotientnbsp;will exprefs the magnifying power.

When we fpeak of magnifying bp a tele* fcope or microfcope, it is only meant with regardnbsp;to the diameter, not to the area or folidity of thenbsp;objedl. But as the inftrument magnifies the vertical diameter, as much as it does the horizontal,nbsp;it is eafy to find how much the whole vifible areanbsp;or furface is magnified : for, if the diameters benbsp;multiplied into one another, the produdt willnbsp;exprefs the magnification of the whole vifiblenbsp;area. Thus, fuppofe the focal diftance of thenbsp;objedt-glafs be ten times as great as the focalnbsp;diftance of the eye-glafs; then, the objeft willnbsp;be magnified ten times, both in length andnbsp;breadth: and lO multiplied by lo, producesnbsp;ICO; which fliews, that the area of the objedtnbsp;will appear too times as big when feen throughnbsp;fuch a telefcope, as it does to the bare eye.

Hence it appears, that if the focal diftance of the eye-glafs, were equal to the focal diftance ofnbsp;the objcdl-glafs, the magnifying power of thenbsp;telefcope would be nothing.

This telefcope may be made to magnify in any given degree, provided it be of a fufficientnbsp;length. For, the greater the focal diftance ofnbsp;the objedt-glafs, the lefs may be the focal diftance of the eye-glafs; though not direftly innbsp;proportion. Thus, an objed-glafs, of lo feetnbsp;focal diftance, will admit of an eye glafs whofenbsp;focal diftance is little more than zf inches;nbsp;which will magnify near 48 times ; but an ob-jedl-glafs, of 100 feet focus, will require an eye-glafs fomewhat more than 6 inches; and willnbsp;therefore magnify almoft 200 times,

A telefcope for viewing terreftrial obje(5ts,fliould be fo conftrudted, as to ftiew them in their natural

Of optics. nbsp;nbsp;nbsp;231

pofture. And this is done by one objeamp;-g1afs Fig. 6. c d, and three eye-glaffes ef,gh, i k, fo placed,nbsp;that the diftance between any two, which arenbsp;neareft to each other, may be equal to the fumnbsp;of their focal diftances; as in the figure, wherenbsp;the focus of the glaffes c d and e f meet at A,nbsp;thofe of the glafles lt;?� and^ h, meet at /, and ofnbsp;g h and i at �2; the eye being at in or nearnbsp;the focus of the eye-glafs i k, on the other fide.

Then, it is plain, that thefe pencils of rays, which flow from the objedl: A B, and pafs throughnbsp;the objedt-glafs c d, will meet and form an inverted image C F D \n the focus of that glafs �,nbsp;and the image being alfo in the. focus of the glafsnbsp;e f the rays of the pencils will become parallel,nbsp;after paflang through that glafs, and crofs at /,nbsp;in the focus of the glafs e /; from whence theynbsp;pafs on to the next glafs g h, and by goingnbsp;through it they are converged to points in itsnbsp;other focus, where they form an ere�t imagenbsp;E m F, of the obje(5i: A B : and as this image isnbsp;alfo in the focus of the eye-glafs i k, and the eyenbsp;on the oppofite fide of the fame glafs; the imagenbsp;is viewed through the eye-glais in this telefcopc,nbsp;in the fame manner as through the eye-glafs innbsp;the former one; only in a contrary pofition,nbsp;that is, in the fame pofition with the objeft.

The three glafles next the eye, have all their focal diftances equal: and the magnifying powernbsp;of this telefcope is found the fame way as thatnbsp;of the laft above; viz. by dividing the focalnbsp;diftance of the obje�l-glafs c d, by the focalnbsp;diftance of the eye-glafs i k, or g h, or ef fincenbsp;all thefe three are equal.

When the rays of light are feparated by re-fraftion, they become coloured, and if they be united again, they will be a perfect white. But

Of optics'.

thofe rays which pafs through a convex glafs, near its edges are more unequally refra�ed thannbsp;thofe which are nearer the middle of the glals.nbsp;And when the rays of any pencil are unequallynbsp;refradled by the glafs, they do not all meetnbsp;again in one and the fame point, but in feparatenbsp;points-, which makes the image indiftinft, an�dnbsp;coloured, about its edges. The remedy is, tonbsp;have a plate with a fmall round hole in its middle, fixed in the tube at�t, parallel to the glafles.nbsp;For, the wandering rays about the edges of thenbsp;glafles will be ftopr, by the plate, from comingnbsp;to the eye ; and none admitted but thofe whichnbsp;come through the middle of the glafs, or at leaftnbsp;at a good diftance 'from its edges, and pafsnbsp;through the hole in the middle of the plate. Butnbsp;this circumfcribes the image, and leflens thenbsp;field of view, which would be much larger ifnbsp;the plate could be difpenfed with.

The great inconvenience attending the management of long telefcopes of this kind, has brought them much into difufe ever fince thenbsp;reflecting telefcope was invented. For one of thisnbsp;fort, fix feet in length, magnifies as much as onenbsp;of the other an hundred. It was invented bynbsp;Sir Ifaac Newton, but has r�ceiv�d confiderablenbsp;improvements fince his time ; and is now generally conftru�led in the following manner, whichnbsp;was firft propofed by Dr. Grego'^y.

At the bottom of the great tube T T TT is placed the large concave mirror DUFF, whofenbsp;principal focus is at m ; and in its middle is anbsp;round hole P, oppofue to which is placed thenbsp;fmall mirror L, concave toward the great

Of optics.

outfide of the tube, keeping its axis ftill in the fame line P m n with that of the great one.�nbsp;Now, fince in viewing a very remote objed, wenbsp;can fcarce fee a point of it but what is at leafl: asnbsp;broad as the great mirror, we may confider thenbsp;rays of each pencil, which flow from every pointnbsp;of the objed, to be parallel to each other, andnbsp;to cover the whole refleding furface DUFF.nbsp;But to avoid confufion in the figure, we fl'.allnbsp;only draw two rays of a pencil flowing from eachnbsp;extremity of the objed into the great tube, andnbsp;trace their progrefs, through all their refledionsnbsp;and refradions, to the eye �, at the end of thenbsp;fmall tube t /, which is joined to the great one.

Let us then fuppofe the objed 5 to he at fuch a diftance, that the rays C tnay flow fromnbsp;its lower extremity B, and the rays E from itsnbsp;upper extremity A. Then the rays C fallingnbsp;parallel upon the great mirror at D, will benbsp;thence refleded, converging in the diieclionnbsp;D G and by crofling at I ih the principal focusnbsp;of the mirror, they will forrii the upper extremity � of the inverted image I K, fimilar to thenbsp;lower extremity B of the objed A B � and paf-fing on to the concave mirror L (whofe focusnbsp;is at n) they will fall upon it at and be thencenbsp;refleded converging, inthediredion^g- Ny becaufenbsp;^ is longer than g n ; and palflng through thenbsp;hole P in the large mirror, they would meetnbsp;fomewhere about r, and form the lower extremitynbsp;d of the ered image a d, fimilar to the lowerex-tremity B of the objed A B. But by pafflngnbsp;through the plano-convex-glafs R in their vvay,nbsp;they form that extremity of the image at Enbsp;In like manner, the rays E, which come from thenbsp;top of the objf A A B, and fall parallel upon thenbsp;great mirror at F, are thence refleded eonverg-

ing to its focus, where they form the lower extremity K of the inverted image / K, fimilar to the upper extremity A of the objeft A B ; andnbsp;thence palling on to the fmall mirror andnbsp;falling upon it at h, they are thence reflected innbsp;the converging ftate h O and going on throughnbsp;the hole P of the great mirror, they will meetnbsp;fomewhere about q, and form there the uppernbsp;extremity a of the ereft image a d, fimilar to thenbsp;upper extremity A of the obje6t A B ; but bynbsp;palling through the convex glafs R in their way,nbsp;they meet and crofs fooner, as at a, where thatnbsp;point of the ereft image is formed.�The likenbsp;being underftood of all thofe rays which flownbsp;from'the intermediate points of the objeft, between A and B, and enter the tube P T; all thenbsp;intermediate points of the,image between a andnbsp;b will be formed : and the rays palTing on fromnbsp;the image through the eye-glafs S, and throughnbsp;a fmall hole e in the end of the lelTer tube t t,nbsp;they enter the eye �, which fees the image a dnbsp;(by means of the eye-glafs) under the largenbsp;angle c e d, and magnified in length, under thatnbsp;angle from c to d.

In the beft refle�fing telefcopes, the focus of the fmall mirror is never coincident with thenbsp;focus m of the great one, where the firfl; imagenbsp;IK is formed, but a little beyond it (with refpe�lnbsp;to the eye) as at n: the confequence of which is,nbsp;that the rays of the pencils will not be parallelnbsp;after refledion from the fmall mirror, bur converge fo as to meet in points about q, e, r ; wherenbsp;they will form a larger upright image than a d,nbsp;if the glafs R was not in their way : and thisnbsp;image might be viewed by means of a Anglenbsp;eye-glafs properly placed between the imagenbsp;and the ?ye ; but then the fi:eld of view would be

Of optics.

lefs, and confequently not fopleafant; for which reafon, the glafs R is ftill retained, to enlargenbsp;the fcope or area of the field.

To find the magnifying power of this tele-fcope, multiply the focal diftance of the great mirror by the diftance of the ftnall mirror fromnbsp;the image next the eye, and multiply the focalnbsp;diftance of the fmall mirror by the focal diftance of the eye-glafs : then, divide the pro-dufl: of the former multiplication by the product of the latter, and the quotient will exprefsnbsp;the magnifying power.

I lhall here fet down the dimenfions of one of Mr. Short's reflefting telefcopes, as defcribed innbsp;Dr. Smith's Optics.

The focal diftance of the great mirror g.6 inches, its breadth 2.3 the focal diftance of thenbsp;fmall mirror 1.5, its breadth 0.6: the breadthnbsp;of the hole in the great mirror 0.5 �, the diftancenbsp;between the fmall mirror and the next eye-glafsnbsp;14.2 the diftance between the two eye-glaffesnbsp;2.4 the focal diftance of the eye-glafs next thenbsp;metals 3.8 �, and the focal diftance of the eye-glafs next the eye i.i.

One great advantage of the refledling tele-fcope is, that it will admit of an eye-glafs of a much fttorter focal diftance than a refraftingnbsp;telefcope will and, confequently, it will magnify fo much the more : for the rays are notnbsp;coloured by refledlion from a concave mirror,nbsp;if it be ground to a true figure, as they are bynbsp;paffing through a convex-glafs, let it be groundnbsp;ever fo true.

The adjufting fcrew on the outfide of the great tube fits this telefcope to all forts of eyes,nbsp;by bringing the fmall mirror either' nearer tonbsp;the eye, or removing it farther: by which

236 nbsp;nbsp;nbsp;Of optics.

means, the rays are made to diverge a little for ftiort-figbted eyes, or to converge for thofe of anbsp;long fight.

The nearer an objeft is to the telefcope, the more its pencils of rays will diverge before theynbsp;fall upon the great mirror, and therefore theynbsp;will be the longer of meeting in points after re-fledion; fo that the firft image 1 K will benbsp;formed at a greater d'ftance from the large mirror, when the objed is near the telefcope, thannbsp;when it is very remote. But as this image muftnbsp;be formed farther from the fmall mirror thannbsp;its principal focus �, this mirror muft be alwaysnbsp;fet at a greater diftance from the large one, innbsp;viewing near objeds, than in viewing remotenbsp;ones. And this is done by turning the f rew onnbsp;the outfide of the tube, until the fmall mirrornbsp;be fo adjufted, that the objed (or rather itsnbsp;image) appears, perfed.

In looking through any telefcope towards an objed, we never fee the objed itfelf, but onlynbsp;that image of it which is formed next the eye innbsp;the telefcope. For, if a man holds his finger or anbsp;flick between his bare eye and an objed, it willnbsp;hide part (if not the whole) of the objed fromnbsp;his view. But if he ties a ftick acrofs the mouthnbsp;of a telefcope, before the objed-glafs, it w ill hidenbsp;no part of the imaginary objed he faw throughnbsp;the telefcope before, unlefs it covers the wholenbsp;mouth of the tube; for, all the effed will be, tonbsp;make the objed appear dimmer, becaufe it intercepts part of the rays. Whereas, if he putsnbsp;only a piece of wire acrofs the infide of the tube,nbsp;between the eye-glafs and his eye, it will hidenbsp;part of the objed which he thinks he fees: whichnbsp;proves that he fees not the real objed, but itsnbsp;This is alfo confirmed by means of the

fmall

Of optics. nbsp;nbsp;nbsp;25^

fmall mirror L, in the reflefting telefcope, which is made of opake metal, and ftands dire�tly between the eye and the obj^^�l towards which thenbsp;teleP-ope is turned ; and will hide the whole ob-jeft from the eye at e, if the two glaflcs R andnbsp;S are taken out of the tube.

The multiplying glafs is made by grinding pjateXIX. down the round fid^e h i k of a convex glafs ^ B Fig, i.nbsp;into feveral flat i'urfaces, amp;s h b, bld^ dk. An ob- Tue W-jecl C will not appear magnifi�d, when feennbsp;through this glafs, by the eye at H-, but it will*nbsp;appear multiplied into as many different objeftsnbsp;as the glais contains plane furfaces. For, fincenbsp;rays will flow from the objedl C to all parts ofnbsp;the glafs, and each plane furface will refra�l thel�nbsp;rays to the eye, the fame objeft will appear tonbsp;the eye, in the direflion of the rays which enternbsp;it through each furface. Thus, a ray g i Hynbsp;falling perpendicularly on the middle furfacenbsp;will go through the glafs to the eye without fuf-fering any refradlion ; and will therefore fhewnbsp;the objeft in its true place at C; whilft a ray 0 ^nbsp;flowing from the fame objedt, and falling obliquely on the plane furface b h, will be refradlcdnbsp;in the diredlion b e, by pafljng through the glafs ;nbsp;and upon leaving ir, will go on to the eye in thenbsp;dirtdtion e H-, which will caufe the fame obj�clnbsp;C to appear alfo at �, in the diredtion of the raynbsp;He, produced in the right line Hen. And thenbsp;ray c d, flowing from the objeci; C, and fallingnbsp;obliqvK'ly on :heplane furface d k, will be refradf-ed (by pafTing through the glafs and leaving itnbsp;ttf) to the eye at H which will caufe the fatlienbsp;objedl to appear at D, in thediredlion Hf m.�

If the glafs be turned round the line g I H, as an axis, the objedl C will keep its place, becaufenbsp;the furface b I d \% not removed; but all the

Other objeds will feem to go round C, becaufe the oblique planes, on which the a b, c dnbsp;fall. Will go round by the turning of the glafs.

The camera ohfcura is made by a convex glafs C D, placed in a hole of a window-lhutter.nbsp;Then, if the room be darkened fo as no lightnbsp;can enter but what comes through the glafs, thenbsp;pictures of all the obje�ls (as fields, trees, buildings, men, cattle, amp;c.) on the outfide, will benbsp;Ihewn in an inverted order, on a white papernbsp;placed at G H in the focus of the glafs; andnbsp;will afford a molt beautiful and perfetl piece ofnbsp;perfpedfive or landfcape of whatever is beforenbsp;the glafs; efpecially if the fun fhines upon thenbsp;objeds.

If the convex glafs C D be placed in a tube in the fide of a fquare box, within which is thenbsp;plane mirror E F, reclining backwards in annbsp;angle of 45 degrees from the perpendicular k q,nbsp;the pencils of rays flowing from the outward ob-jefls, and paffing through the convex glafs tonbsp;the plane mirror, will be rcfle�ted upwards fromnbsp;it, and meet in points, as / and K (at the famenbsp;diftance that they would have meet at H andnbsp;G, if the mirror had not been in the way) andnbsp;will form the aforefaid images on an oiled papernbsp;ftretched horizontally in the diredfion IK-, onnbsp;which paper, the out-lines of the images maynbsp;be eafily drawn with a black lead pencil andnbsp;then copied on a clean flieet, and coloured bynbsp;art, as the objedls themfelves are by nature,�nbsp;Ip this machine, it is ufual to place a plane glafs,nbsp;unpolifhed, in the horizontal fituation IK, whichnbsp;glafs receives the images of the outward objedts;nbsp;and their outlines may be traced upon it by anbsp;black-lead pencil.

3 nbsp;nbsp;nbsp;B.

N. B. The tube in which the convex glafs C D is fixed, muft be made to draw out, or pu(hnbsp;in, fo as to adjuft the diftance of that glafs fromnbsp;the plane mirror, in proportion to the diftancenbsp;of the outward objects; which the operator does,nbsp;until he fees their images diftindly painted onnbsp;the horizontal glafs at / K.

The forming a horizontal image, as IK, of an upright object JB, depends upon the angles ofnbsp;incidence of the rays upon the plane mirror E F,nbsp;being equal to their angles of refledtion fromnbsp;it. For, if a perpendicular be fuppofed to benbsp;drawn to the furface of the plane mirror at e,nbsp;where the ray A aC e falls upon it, that ray willnbsp;be refledted upwards in an equal angle with thenbsp;other fide of the perpendicular, in the line e d I.nbsp;Again, if a perpendicular be drawn to the mirror from the point �, where the ray A b f fallsnbsp;upon it, that ray will be refledled in an equalnbsp;angle from the other fide of the perpendicular, innbsp;the line f b I. And if a perpendicular be drawnnbsp;from the point where the ray A eg falls uponnbsp;the mirror, that ray will be refledted in an equalnbsp;angle from the other fide of the perpendicular,nbsp;in the line g i 1. So that all the rays of the pencilnbsp;ah flowing from the upper extremity of thenbsp;objedl A By and pafllng through the convex gl'afsnbsp;C i), to the plane mirror E F, will be refleftednbsp;from the mirror and meet at /, where they willnbsp;form the extremity I of the image IK, fimilarnbsp;to the extremity A of the object A B. 7'lienbsp;like is to be underftood of the pencil qr s, flowing from the lower extremity of the objedt A Bynbsp;and meeting at K (after refledlion from the planenbsp;mirror) the rays form the extremity K of thenbsp;image, fimilar to the extremity B of the objedt;nbsp;and fo of all the pencils that flow from the intermediate

�f opticf,

If a convex glafs, of a fhort focal diftance, be placed near the plane mirror, in the end of anbsp;fhort tube, and a convex glafs be placed in anbsp;hole in the fide of the tube, fo as the image maynbsp;be formed between the laft mentioned convexnbsp;glafs, and the plane mirror, the image beingnbsp;vievved through this glafs will appear magnified.nbsp;�In this manner the opera-glares are contlruft-ed ; with which a gentleman may look at anynbsp;lady at a diftance in the company, and the ladynbsp;know nothing of it.

The image of any objeft that is placed before � a plane mirror, appears as big to the eye as thenbsp;object itfelf �, and is eredt, diftindt, and feeming-ly as far behind the mirrotj as the objedl is before it: and that part or the mirror, whichnbsp;refledts the image of the objedt to the eye (thenbsp;eye being fuppofed equally diftant from the glafsnbsp;with the objedt) is juft half as long and half asnbsp;broad as the objedt itfelf. Let 5 be an objedt placed before the refledting furface g h i o�nbsp;the plane mirror C D; and let the eye be at 0.nbsp;Let /h be a ray of liahc flowing from the topnbsp;A of the object, and falling upon the mirror atnbsp;h : and /h �; be a perpendicular to the furface ofnbsp;the mirror at ^, the ray A h will be refledtednbsp;from the mirror to the eye at 0, making annbsp;angle m h 0 equal to the angle Ah m : then willnbsp;the top of the image E appear to the eye in thenbsp;diredtion of the refledted ray 0 h produced to 5�,nbsp;where the right line Ap E, from the top of thenbsp;objedt, cuts the right line 0 h E^ ?ii E. Let B inbsp;be a ray of light proceeding from the toot of thenbsp;objedl at B to the mirror at ;, and �fa perpendicular to the mirror from the point ?,

Of optics.

where the ray B i falls upon it: this ray will be reflefted in the line i making an angle n i 0,nbsp;equal to the angle B i n, with that perpendicular, and entering the eye at 0 : then will thenbsp;foot F of the image appear in the direflion ofnbsp;the reflefted ray 0 2, produced to F, where thenbsp;right line B F cuts the reflefted ray produced tonbsp;F. All the ocher rays that flow from the intermediate points of the objed A and fall uponnbsp;the mirror betw�een h and i, will be refledted tonbsp;the eye at 0; and all the intermediate points ofnbsp;the image E F will appear to the eye in the di-re6tion-line of thefe refledled rays produced.

But all the rays that flow from the objecb, and fall upon the mirror above h, will be refleftednbsp;back above the eye at 0 ; and all the rays thatnbsp;flow from the objeft, and fall upon the mirrornbsp;below r, will be refledled back below the eye atnbsp;0: fo that none of the rays that fall above h, ornbsp;below 2, can be refledled to the eye at 0; andnbsp;the diftance between h and 2 is equal to half thenbsp;length of the objedl A B.

Hence it appears, that if a man fee his whole A man image in a plane looking-glafs, the part of the will feenbsp;glafs that refledls his image muft be juft half asnbsp;long and half as broad as hinilelf, let him ftand lookLg-'nbsp;at any diftance from it whatever; and that his glafs, thatnbsp;image muft appear juft as far behind the glafs as i� .nbsp;he is before it. Thus, the man A B viewingnbsp;bimfelf in the plane .mirror C D, which is juft pig^.nbsp;half as long as himfelf, fees his whole image asnbsp;at E F, behind the glafs, exadlly equal to hisnbsp;own fize. .For, a ray A C proceeding from hisnbsp;eye at A, and falling perpendicularly upon thenbsp;furface of the glafs at C, is refledled back to hisnbsp;eye in the fame line CA-, and the eye of hisnbsp;image will appear at F, in the fame line produced

duced to E, beyond the glafs. And a ray B Di flowing from his foot, and falling obliquely onnbsp;the glafs at D, will be reflefted as obliquely onnbsp;the other fide of the perpendicular a b D,m thenbsp;direclion D A; and the foot of his image willnbsp;appear at F, in the diredlion of the refiefted ray

D, produced to F, where it is cut by the right line B G F, drawn parallel to the right line ACE.nbsp;Juft the fame as if the glafs were taken away,nbsp;and a real man flood at F, equal in fize to thenbsp;man ftanding at B : for to his eye at A, the eyenbsp;of the other man at E would be feen in the di-redtion of the line ACE-, and the foot of thenbsp;man at F would be feen by the eye A, in thenbsp;diredion of the line AD F.

If the glafs be brought nearer the man A B^ as fuppofe to c b, he will fee his image as atnbsp;C D G : for the reflefled ray C A (being perpendicular to the glafs) will Ihew the eye of thenbsp;image as at C-, and the incident ray B b, beingnbsp;refle�led in the line b A, will fliew the foot of hisnbsp;image as at G; the angle of refledion ab A beingnbsp;always equal to the angle of incidence B b a;nbsp;and fo of all the intermediate rays from A to B.nbsp;Hence, if the man A B advances towards thenbsp;glafs C D, his image will approach towards it jnbsp;and if he recedes from the glafs, his image willnbsp;aifo recede from it.

Having already Ihewn, that the rays of light are refraded when they pafs obliquely throughnbsp;different mediums, we come now to prove thatnbsp;fome rays are more refrangible than others; andnbsp;that, as they are differently refracted, they excite in our minds the ideas of different colours.nbsp;This will account for the colours feen about thenbsp;edges of the images of thofe objedts which arenbsp;viewed through fome telefcopes.

of optics.

Let the fun fliine into a dark room through a Fig. 5. fmair hole, as at e f, in a window-fluittcr andnbsp;place a triangular j rifm BC \n the beam of raysnbsp;A, in fuch a nsanner, that the '.earn may fall obliquely on one of the Tides abC oi the gt;rifm.

The rays will fuffer different refradtions by paf- The fing through the prifm, fo that inftead of goingnbsp;all out of it on the fide dcC, in one dircdlion,nbsp;they will go on from it in the different diredionsnbsp;reprefented by the lines �, g, h, i, k, I, m, n-, andnbsp;falling upon the oppofite fide of the room, ornbsp;on white paper placed as at p 11 to receive them,nbsp;they will paint upon it a feries of moll beautifulnbsp;lively colours 'not to be equalled by art) in this The reorder, viz. thofe rays which areleaft refra�led bynbsp;the prifm, and will therefore go on between che^ ^nbsp;lines n and ?�, will be of a very bright intenfenbsp;red at �, degenerating from thence graduallynbsp;into an orange colour, as they are nearer the linenbsp;m : the next will be of a fine orange colour atnbsp;and from thence degenerate into a yellow colour towards h at I they will be of a fine yellow,

�which will incline towards a green, more and more, as they are nearer and nearer k: atk theynbsp;will be a pure green, but from thence towards inbsp;they will incline gradually to a blue ; at i theynbsp;�will be a perfed blue, inclining to an indigo colour from thence towards h; at h they will benbsp;quite the colour of indigo, which will graduallynbsp;change towards a violet, the nearer they are tonbsp;g: and at ^ they will be of a fine violet colour,nbsp;which will incline gradually to a red as theynbsp;come nearer to �, where the coloured imagenbsp;ends.

There is not an equal quantity qfjrays in each of thefe colours j for, if the oblong image f gnbsp;be divided into 360 equal parts, the red fp'accnbsp;Rnbsp;nbsp;nbsp;nbsp;K will

R will take up 45 of thefe parts: the orange �, 27; the yellow 2quot;, 48; the green G, 60; thenbsp;blue 5, 60; the indigo �, 40 ; and the violet K,nbsp;80; all which fpaces are as nearly proportioned innbsp;the figure as the fmall fpace would admit of.

If ail thefe colours be blended together again, they will make a pure white �, as is proved thus.nbsp;Take away the paper on which the colours^ jnbsp;fell, and place a large convex glafs D in the raysnbsp;h, amp;c. which will refradt them fo, as to makenbsp;them unite and crofs each other at^: where, if anbsp;white paper be placed to receive them, they willnbsp;excite the idea of a ftrong lively white. But ifnbsp;the paper be placed farther from the glafs, as atnbsp;rsy the different colours will appear again uponnbsp;it, in an inverted order, occafioned by the raysnbsp;croffing at /F.

As white is a compofuion of all colours, fo black is a privation of them all, and, therefore,nbsp;properly no colour.

Let two concentric circles be drawn on a fmooth round board A B C D E F G, and thenbsp;outermoft of them divided into 360 equal partsnbsp;or degrees; then, draw feven right lines, as o A^nbsp;G 5, amp;c. from the center to the outermoft circle;nbsp;making the lines � A and o B include 80 degrees of that circle ; the lines G B and O C 40nbsp;degrees; G C and � D 60; O Z) and O � 60;nbsp;��and O F4S'; 0 Fand � G27; � G and O ^nbsp;45. Then, between thefe two circles, paint thenbsp;fpace AG red, inclining to orange near GG Fnbsp;orange, inclining to yellow near F-, F E yellow,nbsp;inclining to green near E-, ED green, incliningnbsp;to blue near D �, D C blue, inclining to indigonbsp;near C', CB indigo. Inclining to violet near B;nbsp;and B A violet, inclining to a foft red near A.nbsp;This done, paint all that part of the board blacknbsp;6nbsp;nbsp;nbsp;nbsp;which

Of optics.

which lies within the inner circle j and putting an axis through the center of the board, let itnbsp;be turned very fwiftly round that axis, fo as thenbsp;rays proceeding from the above colours, may benbsp;all blended and mixed together in coming tonbsp;the eye; and then, the whole coloured part willnbsp;appear like a white ring, a little greyi�', notnbsp;perfedtly white, becaiife no colours prepared bynbsp;art are perfcdt.

Any of thefe colours, except red and violet, may be made by mixing together the two. contiguous prifmatic colours. Thus, yellow is madenbsp;by mixing together a due proportion of orangenbsp;and green ; and green may be made by a mixture of yellow and blue.

All bodies appear of that colour, whofe rays they refleft moll; as a body appears red whennbsp;it refledls molf of the red-making rays, and ab-forbs the reft.

Any two or more colours that are quite tranf-parent by themfelves, become opake when put together. Thus, if water or fpirits of wine benbsp;tinged red, and put in a phial, every objed feennbsp;through it will appear red ; becaul'e it lets onlynbsp;the red rays pafs through it, and ftops all thenbsp;reft. If water or fpirits be tinged blue, and putnbsp;in a phial, all objeds feen through it will appearnbsp;blue, becaufe it tranfmits only the blue rays, andnbsp;ftops all the reft. But if thefe tw'o phials arcnbsp;held clofe together, fo as both of them may benbsp;between the eye and objedt, the objtdl will nonbsp;more be feen through them than through a platenbsp;of metal; for whatever rays are tranfmitcednbsp;through the fluid in the phial next the objedf,nbsp;are flopped by that in the phial next the eye.nbsp;In this experiment, the phials ought not to benbsp;round, but fquare; becaufe nothing but thenbsp;R 2nbsp;nbsp;nbsp;nbsp;light

246 nbsp;nbsp;nbsp;Of optics.

As the rays of light fufFer different degrees of refradion by paffing obliquely through anbsp;prifm, or through a convex glafs, and are therebynbsp;ieparated into all the feven original or primarynbsp;colours �, 10 they alfo fuffer different degrees ofnbsp;refradion by paffing through drops of fallingnbsp;rain; and then, being refleded towards the eye,nbsp;from the Tides of thefe drops which are fartheftnbsp;from the eye, and again refraded by paffing outnbsp;of thefe drops into the air, in which refradednbsp;diredions they come to the eye ; they make allnbsp;the colours to appear in the form of a fine archnbsp;in the heavens, which is called the rain-bow.

There are always two rain-bows feen together, the interior of which is formed by the rays a b,nbsp;which falling upon the upper part of the dropnbsp;Fig' 7- bed, are refracted into the line ^c as they enternbsp;the drop, and are refleded from the back of it atnbsp;c, in the line c d, and then, by paffing out of thenbsp;drop into air,they are again refraded at d-, andnbsp;from thence they pafs on to the eye at e: fo thatnbsp;to form the interior bow, the rays fuffer two re-fradions, as at b and d and one refledion, asnbsp;at c.

The exterior bow is formed by rays which fuffer two refiedions, and two refradions jnbsp;which is the occafion of its being lefs vivid thannbsp;the interior, and alfo of its colours being inverted with refped; to thofe of the interior. For,nbsp;when a ray a ^ falls upon the lower part of thenbsp;Fig. 8. drop b c de, it is refraded into the diredion benbsp;by entering the drop; and paffing on to thenbsp;back of the drop at c, it is thence refleded in thenbsp;line c d, in which diredion it is impoffible for itnbsp;to enter the eye at/: but by being again refleded

fletfled from the point d of the drop, it goes on in the drop to e, where it paffes out of the drop intonbsp;the air, and is there refracted downward to thenbsp;eye, in the diredion ef.

TF a map of the world be accurately delineated **� on a fpherical ball, the furface thereof willnbsp;reprefent the furface of the earth; for the higheftnbsp;hills are fo inconfiderable with refped to the bulknbsp;of the earth, that they take off no more from itsnbsp;roundnefs, than grains of fand do from thenbsp;roundnefs of a common globe-, for the diameternbsp;of the earth is 8000 miles in round numbers,nbsp;and no known hill upon it is three miles in perpendicular height.

That the earth is fpherical, or round like a globe, appears, i. From its calling a roundnbsp;Ihadow upon the moon, whatever fide be turnednbsp;towards her when the is eclipfed. 2. From itsnbsp;having been failed round by feveral perfons.nbsp;3. From our feeing the farther, the higher wenbsp;ftand. 4, From our feeing the mafts of a fiiip,nbsp;whilft the hull is hid by the convexity of thenbsp;water.

The attradlive power of the earth draws all terreftrial bodies towards its center; as is evident from the defcent of bodies in lines perpendicular to the earth�s furface, at the placesnbsp;whereon they fall; even when they are thrownnbsp;off from the earth on oppofite fides, and con-fequently, in oppofite diredions. So that thenbsp;R 3nbsp;nbsp;nbsp;nbsp;earth

earth may be compared to a great magnet rolled in filings of fteel, which attrads and keeps themnbsp;equally fail to its furface on all fides. Hence,nbsp;as all terreftrial bodies are attraded toward thenbsp;earth�s center, they can be in no danger of falling from any fide of the earth, more than fromnbsp;any other.

The heaven or Iky furrounds the whole earth: and when we fpeak of up or down^ we meannbsp;only with regard to ourfelves �, for no point,nbsp;either in the heaven, or on the furface of thenbsp;earth, is above or below, but only with refped:nbsp;to ourfelves. And let us be upon what part ofnbsp;the earth we will, we ftand with our feet towards its center, and our heads tow'ards the fky :nbsp;and fo we fay, it is up towards the Iky, and downnbsp;toward the center of the earth.

To an obferver placed any where in the indefinite fpace, where there is nothing to limit his view, all remote objeds appear equallynbsp;dittant from him-, and feem to be placed in anbsp;vaft concave fphere, of which his eye is thenbsp;center. Every aftronomer can demonftrate,nbsp;that the .moon is njuch nearer to us than the funnbsp;is that fome of the planets are fometimesnbsp;nearer to us, and fometimes farther from us,nbsp;than the fun that others (T them never come fonbsp;near us as the fun always is; that the retnoteftnbsp;planet in our lyftem, is beyond comparifonnbsp;nearer to us than any of the fixed liars are; andnbsp;that it is highly probable forne ftars are, in anbsp;manner, infinitely more diftant from us thannbsp;others ; and yet all thefe celeftial objedis appear equally dilfant from us. Therefore, if wenbsp;imagine a large hollow fphe.quot;e of glafs to havenbsp;as many bright ftuds fixed to its infide, asnbsp;there are ftars vifible in the heaven, and thefe

ftuds to be of different magnitudes, and placed reprefent-at the fame angular diftances from each other ? as the ftars are the fphere will be a true re-prefentation of the ftarry heaven, to an eye fup-pofed to be in its center, and viewing it allnbsp;around. And if a fmall globe, with a map ofnbsp;the earth upon it, be placed on an axis in thenbsp;center of this ftarry fphere, and the fphere benbsp;made to turn round on this axis, it will repre-fent the apparent motion of the heavens roundnbsp;the earth.

If a great circle be fo drawp upon this fphere, as to divide it into two equal parts, or hemi-fpheres, and the plane of the circle be perpendicular to the axis of the fphere, this circle willnbsp;reprefent the equincSiial, which divides the hea- The equi-ven into two equal parts, called the northern andnbsp;the fouthern hemifpheres and every point of thatnbsp;circle will be equally diftant from the poles, orThe/o/�.nbsp;ends of the axis in the fphere. That pole whichnbsp;is in the middle of the northern hemifpherc,nbsp;will be called the north pole of the fphere, andnbsp;that which is in the middle of the fouthern hemi-fphere, the South pole.

If another great circle be drawn upon the fphere, in fuch a manner as to cut the equinoctial at an angle of 23-5: degrees in two oppofjtenbsp;points, it will reprefent the ecliptic, or circle of The erZ/y-thc fun�s apparent annual motion: one half of''^*nbsp;which is on the north fide of the equinodtial,nbsp;and the other half on the fouth.

If a large ftud be made to move eaftward in this ecliptic, in fuch a manner as to go quitenbsp;round it, in the time that the fphere is turnednbsp;round weftward 366 times upon its axis �, thisnbsp;ftud will reprefent the fun, changing his place Thegt;�.nbsp;every day a 365th part of the ecliptic; andnbsp;R 4nbsp;nbsp;nbsp;nbsp;going

going round weftward, the fame way as the ftars do ; but with a motion fo much flower thannbsp;the motion of the ftars, that they will make q66nbsp;revolutions about the axis of the fphere, in thenbsp;time that the fun makes only 365. , During onenbsp;half of thefe revolution?, the fun will be on thenbsp;north fide of the equinodial; during the othernbsp;half, on the fouth : and at the end of each half,nbsp;in the equinoftial.

Theear/h. If we fuppofe the terreftrial globe in this machine to be about one inch in diameter, and the diameter of the ftarry fphere to be about fivenbsp;or fix feet, a fmall infedt on the globe would feenbsp;only a very little portion of its furface �, but itnbsp;would fee one half of the ftarry fphere; the con-vexity of the globe hiding the other half from itsnbsp;� �P' view. If the fphere be turned weftward roundnbsp;motion of globe, and the infedt could judge of the ap-the hea- pearances which arife from that motion, it wouldnbsp;yens, fee fome ftars rifing to its view in the eafternnbsp;fide of the fphere, whilft others were fetting onnbsp;the weftern : but as all the ftars are fixed to thenbsp;fphere, the fame ftars would always rife in thenbsp;fame points of view on the eaft fide, and fet innbsp;the fame points of view on the weft fide. Withnbsp;the fun it would be otherwife, becaufe the funnbsp;is not fixed to any point of the fphere, butnbsp;moves flowly along an oblique circle in it. Andnbsp;if the infedt (hould look towards the fouth, andnbsp;call that point of the globe, where the equi-nodlial in the fphere feems to cut it on the leftnbsp;fide, the eaf point; and where it cuts the globenbsp;on the right fide, the wefi point; the little animal would fee the fun rife north of the eaft, andnbsp;fet north of the weft, for 1824- revolutions;nbsp;after which, for as many more, the fun wouldnbsp;rife fouth of the eaft, and fet fouth of the

Of the Heavens and the Earth. nbsp;nbsp;nbsp;251

weft. And in the vvhole 365 revolutions, the fun would rife only twice in the eaft point, andnbsp;fet twice in the weft. All thefe appearancesnbsp;would be the fame, if the ftarry fphere ftoodnbsp;ftill (the fun only moving in the ecliptic) andnbsp;the earthly globe were turned round the axis ofnbsp;the fphere eaftward. For, as the infed wouldnbsp;be carried round with the globe, he would benbsp;quite infenfible of its motion ; and the fun andnbsp;ftars would appear to move weftward.

We are but very fmall beings when compared with our earthly globe, and the globe itfelfis butnbsp;a dimenfionlefs point compared with the magnitude of the ftarry heavens. Whether thenbsp;earth be at reft, and the heaven turns round it,nbsp;or the heaven be at reft, and the earth turnsnbsp;round, the appearance to us will be exadly thenbsp;fame. And becaufe the heaven is fo immenfelynbsp;large, in comparifon of the earth, we fee onenbsp;half of the heaven as well from the earth�s fur-face, as we could do from its center, if thenbsp;limits of our view are not intercepted bynbsp;hills.

We may imagine as many circles defcribed upon the earth as we pleafe �, and we may thefphtrt.nbsp;imagine the plane of any circle defcribed uponnbsp;the earth to be continued, until it marks a circlenbsp;in the concave fphere of the heavens.

The horizon is either fenfible or rational. The The^n-fenfihle horizon is that circle, which a man ftand-�quot;quot;� ing upon a large plane, obferves to terminatenbsp;his view all around, where the heaven and earthnbsp;feem to meet. The plane of our fenfible horizon continued to the heaven, divides it into twonbsp;hemifperes j one vifible to us, the other hid bynbsp;th? convexity of the earth.

The

The plane of the rational horizon, is fuppofcd parallel to the plane of the fenfible; to pafsnbsp;through the center of the earth, and to benbsp;continued to the heavens. And although thenbsp;plane of the fenfible horizon touches the earthnbsp;in the place of the obferver, yet this plane,nbsp;and that of the rational horizon, will feem tonbsp;coincide in the heaven, becaufe the whole earthnbsp;is but a point compared to the fphere of thenbsp;heaven.

The earth being a fpherical body, the hori* zon, or limit of our view, muft change as wenbsp;change our place.

Tht poles of the earth, are thofe two points on its furface in which its axis terminates. Thenbsp;one is called the north pole, and the other thenbsp;fouth pole.

The poles of the heaven, are thofe two points in which the earth�s axis produced terminates innbsp;the heaven ; fo that the north pole of the heavennbsp;is direclly over the north pole of the earth ; andnbsp;the fouth pole of the heaven is direftly over thenbsp;fouth pole of the earth.

The equator is a great circle upon the earth, every part of which is equally diftant fromnbsp;either of the poles. It divides the earth intonbsp;two equal parts, called the northern and fouthernnbsp;bemifpheres. If we fuppofe the plane of thisnbsp;circle to be extended to the heaven, it willnbsp;mark the equinohiial therein, and will divide thenbsp;heaven into two equal parts, called the northernnbsp;and fouthern hemiipheres of the heaven.

I he meridian of any place is a great circle pafling through that place and the poles of thenbsp;earth. We may imagine as many fuch meridians as we pleafe, becaufe any place that is

ever fo little to the eaft or weft of any other place, has a different meridian from that place;nbsp;for no one circle can pafs through any two fuchnbsp;places and the poles of the earth.

The meridian of any place is divided by the poles, into two femicircles: that which paffesnbsp;through the place is called the geographical, ornbsp;�upper meridian; and that which paffes throughnbsp;the oppofite place, is called the lower meridian.

When the rotation ot the earth brings the Nian and plane of the geographical meridian to the fun, rnid-night,nbsp;it is noon or mid-day to that place ; and whennbsp;our lower meridian comes to the fun, it is midnight.

All places lying under the fame geographical meridian, have their noon at the fame time, andnbsp;confequently all the other hours. All thpfenbsp;places are faid to have the fame longitude, becaufcnbsp;no one of them lies either eaftward or weftwardnbsp;from any of the reft.

If we imagine 24 femicircles, one of which ^0�' eiu� is the geographical meridian of a given place,nbsp;to meet at the poles, and to divide the equatornbsp;into 24 equal parts ; each of thefe meridiansnbsp;will come round to the fun in 24 hours, by thenbsp;earth�s equable motion round its axis in thatnbsp;time. And, as the etpator contains 360 degrees, there will be 15 degrees contained between any two of thefe meridians which arenbsp;neareft to one another: for 24 times 15 is 360.

And as the earth�s motion is eaftward, the fun�s apparent motion will be weftward, at the ratenbsp;of 15 degrees each hour. Therefore,

They whofc geographical meridian is 15 de- Ungituie. grees eaftward from us, have noon, and everynbsp;other hour, an hour fooner than we have. Theynbsp;whofe meridian is fifteen degrees weftward from

us, have noon, and every other hour, an hour later than we have: and fo on in proportion,nbsp;reckoining one hour for every fifteen degrees.

As the earth turns round its axis once in 24 hours, and fhews itfelf all round to the fun innbsp;that time ; fo it goes round the fun crice a year.nbsp;Ecliptic, in a great circle called the ecliptic, which croffesnbsp;the equinodial in two oppofite points, makingnbsp;an angle of 23-�- degrees with the equinodial onnbsp;each fide. So that one half of the ecliptic is innbsp;the northern heniifphere, and the other in rhenbsp;fouthern. It concains 360 equal parts, callednbsp;degrees (as all other circles do, whether greatnbsp;or fmall) and as the eartii goes once round itnbsp;every year, the fun will appear to do the fame,nbsp;changing his place almoft a degree, at a meannbsp;rate, every 24 hours. So that whatever place,nbsp;or degree of the ecliptic, the earth is in at anynbsp;time, the fun will then appear in the oppofite.nbsp;And as one half of the eel ptic is on the northnbsp;fide of the equinodial, and the other half on thenbsp;fouth ; the fun, as fetn from the earth, will benbsp;half a year on the fouth fide of the equinocial,nbsp;and half a year on the north: and twice a yearnbsp;in the equinodial itfelf.

Signs scad. The ecliptic is divided by aftronomers into degrees. 12 equal parts, callednbsp;nbsp;nbsp;nbsp;each fign into 30

degrees, and each degree into 6o minutes: but in ufing the globes, we fe]do(n want the fun�snbsp;place nearer than half a degree of the truth.

The names and charadcis of the 12 figns are as follow beginning at that point of the ecliptic where it croffes the equinodial to the northward, and reckoning eaftward round to thenbsp;fame point again. And the days of the monthsnbsp;on which the fun now enters the figns, are fetnbsp;down below them.

Sagittarius^ Capricornus, Aquarius, Pifces, tnbsp;nbsp;nbsp;nbsp;Jcfnbsp;nbsp;nbsp;nbsp;X

By remembering on what day the fun enters any particular fign, we may eafily find hisnbsp;place any day afterward, whilft he is in thatnbsp;fign, by reckoning a degree for each day �,nbsp;which will occafion no error of confequence innbsp;ufing the globes.

When the fun is at the beginning of Aries, he is in the equinoftial ; and from that time benbsp;declines northward every day, until he comesnbsp;to the begnning of Cancer, which is 23^ degrees from the equinoftial: from thence he recedes fouthward every day, for half a year; innbsp;the middle of which half, he crofles the equi-no6tial at the beginning of Libra, and at thenbsp;end of that half year, he is at his greateft fouthnbsp;declination, in the beginning of Capricorn, whichnbsp;is alfo degrees from the equinodial. Then,nbsp;he returns northward from Capricorn every day,nbsp;for half a year; in the middle of which half, henbsp;crofles the equinoftial at the beginning of Aries-,nbsp;and at the end of it he arrives at Cancer.

The

The fun�s motion in the ecliptic is not pef-feftly equable, for he continues eight days longer in the northern half of the ecliptic, thannbsp;in the fouthern: fo that the fummer half year,nbsp;in the northern hemifphere, is eight days longernbsp;than the winter half year j and the contrary innbsp;the fouthern hemifphere;

Tropics. The tropics are lefler circles in the heaven, parallel to the equInotSial; one on each fide ofnbsp;it, touching the ecliptic in the points of itsnbsp;greateft declination ; fo that each tropic isnbsp;degrees from the equinodtial, one on the northnbsp;fide of it, and the other on the fouth. Thenbsp;northern tropic touches the ecliptic at the beginning of Cancer., the fouthern at the beginningnbsp;of Capricorn -, for which reafon the former isnbsp;called the tropic of Cancer, and the latter thenbsp;tropic of Capricorn.

Tolarcir- xhc poloT circks in the heaven, are each degrees from the poles, all around. Thatnbsp;which goes round the north pole, is called thenbsp;ar Stic circle, fromnbsp;nbsp;nbsp;nbsp;which fignifies a hear-,

there being a colle�tion or groupe of ftars near the north pole, which goes by that name. Thenbsp;fouth polar circle, is called the antarElic circle,nbsp;from its being oppofite to the arctic.

The ecliptic, tropics, and polar circles, are drawn upon the terreftrial globe, as well asnbsp;upon the celeftial. Bgt the ecliptic, being anbsp;great fixed circle in the heavens, cannot properly be faid to belong to the terreftrial globe �,nbsp;and is laid down upon it only for the conveniencynbsp;of folving fome problems. So that, if thisnbsp;circle on the terreftrial globe was properly divided into the months and days of the year, itnbsp;would not only fuit the globe better, but wouldnbsp;alfo naake .the problems thereon much eafier.

In order to form a true idea of the earth�s motion round its axis every 24 hours, which isnbsp;the caufe of day and night; and of its motionnbsp;in the ecliptic round the fun every year, whichnbsp;is the caufe of the different lengths of days andnbsp;nights, and of the viciffitude of feafons; takenbsp;the following method, which will be both eafynbsp;and pleafant.

Let a fmall terreftrial globe, of about three An idea inches diameter, be fufpended by a long thread of thenbsp;of twifted filk, fixt to its north pole ; then hav-ing placed a lighted candle on a table, to repre-fent the fun, in the center of a hoop of a largenbsp;cafk, which may reprefent the ecliptic, the hoopnbsp;making an angle of degrees with the planenbsp;of the table ; hang the globe within the hoopnbsp;near to it ; and if the table be level, the equator of the globe will be parallel to the table,nbsp;and the plane of the hoop will cut the equatornbsp;at an angle of 234- degrees *, fo that one half ofnbsp;the equator will be above the hoop, and thenbsp;other half below it: and the candle will enlighten one half of the globe, as the funnbsp;enlightens one half of the eai^ch, whilfl: thenbsp;other half is in the dark.

Things being thus prepared, twift the thread towards the left hand, that it may turn thenbsp;globe the fame way by untwifting-, that is, fromnbsp;weft, by foutb, to eaft. As the globe turnsnbsp;round its axis or thread, the diamp;rent places ofnbsp;its furface will go regularly through the lightnbsp;and d^rk; and have, as it were, an alternatenbsp;return of day and night in each rotation. Asnbsp;the globe continues to turn round, and to Ihewnbsp;itfelf all around to the candle, carry it flowlynbsp;round the hoop by the thread, from weft, bynbsp;fouth, to eaft j which is the way that the earth

moves round the fun, once a year, in the ecliptic: and you will fee, that whilft the globenbsp;continues in the lower part of the hoop, the candle (being then north of the equator) will con-ftantly Ihine round the north pole ; and all thenbsp;northern places which go through any part ofnbsp;the dark, will go through a lefs portion of it thannbsp;they do of the light �, and the more fo, the farther they are from the equator: confequently,nbsp;their days are then longer than their nights.nbsp;When the globe comes to a point in the hoop,nbsp;mid-way between the higheft and loweft points,nbsp;the candle will be direftly over the equator, andnbsp;will enlighten the globe juft from pole to pole;nbsp;and then every place on the globe will gonbsp;through equal portions of light and darknefs,nbsp;as it runs round its axis and confequently, thenbsp;day and night will be of equal length at allnbsp;places upan it. As the globe advances thenceforward, towards the higheft part of the hoop,nbsp;the candle will be on the fouth fide of the equator, Alining farther and farther round the fouthnbsp;pole, as the globe rifes higher and higher in thenbsp;hoop ; leaving the north pole as much in darknefs, as the fouth pole is then in the light, andnbsp;making long days and Aiort nights on the fouthnbsp;fide of the equator, and the contrary on thenbsp;north fide, whilft the globe continues in thenbsp;nothern or higher fide of the hoop ; and whennbsp;it comes to the higheft point, the days will be atnbsp;the longeft, and the nights at the Aiorteft, in thenbsp;fouthern hemifphere; and the reverfe in thenbsp;northern. As the globe advances and defcendsnbsp;in the hoop, the light will gradually recede fromnbsp;the fouth pole, and approach towards the northnbsp;pole, which will caufe the northern days tonbsp;lengthen, and the fouthern days to Ihorten innbsp;3nbsp;nbsp;nbsp;nbsp;the

the fame proportion. When the globe comes to the middle point, between the higheft and lowed:nbsp;points of the hoop, the candle will be over thenbsp;equator, enlightening the globe juft from polenbsp;to pole, when every place of the earth (exceptnbsp;the poles) will go through equal portions ofnbsp;light and darknefs ; and confequently, the daynbsp;and night will be then equal, all over the globe.

And thus, at a very fmall expence, one may-have a delightful and demonftrative view of the caufe of days and nights, with their gradualnbsp;increafe and decreafe in length, through thenbsp;whole year together, with the viciffitudes ofnbsp;fpring, fummer, autumn, and winter, in eachnbsp;annual courfe of the earth round the fun.

If the hoop be divided into 12 equal parts, and the figns be marked in order upon it, beginning with Cancer at the higheft point of thenbsp;hoop, and reckoning eaftward for contrary tonbsp;the apparent motion of the fun) you will feenbsp;how the fun appears to change his place everynbsp;day in the ecliptic, as the globe advances eaftward along the hoop, and turns round its ownnbsp;axis : and that when the earth is in a low fign,nbsp;as at Capricorn, the fun muft appear in a highnbsp;fign, as at Cancer, oppofite to the earth�s realnbsp;place and that whilft the earth is in thenbsp;fouthern half of the ecliptic, the fun appears innbsp;the northern half, and vice verfd : that the farther any place is from the equator, between itnbsp;and the polar circle, the greater is the dilFerenrenbsp;between the longeft and Ihorteft day at thatnbsp;place-, and that the poles have but one day andnbsp;one night in the whole year.

Thefe things premifed, we fnall proceed to the defeription and ufe of the terreftrial globe,

This globe has the boundaries of land and water laid down upon it, the countries andnbsp;kingdoms divided by dots, and coloured tonbsp;diftinguilh them, the iflands properly fituated,nbsp;the rivers and principal towns inferted, as theynbsp;have been afcertained upon the earth by mea-fiirement and obfervation.

The equator, ecliptic, tropics, polar circles, and meridians, are laid dowti upon the globe innbsp;the manner already defcribed. The ecliptic isnbsp;divided into 12 figns, and each fign into 30nbsp;degrees, which are generally fubdivided intonbsp;halves, and into quarters if the globe is large.nbsp;Each tropic is 23-5: degrees from the equator,nbsp;and each polar circle 234- degrees from itsnbsp;refpeftive pole. Circles are drawn parallel tonbsp;the equator, at every ten degrees diftance fromnbsp;it on each fide to the poles; thefe circles arenbsp;called parallels of latitude. On large globesnbsp;there are circles drawn perpendicularly throughnbsp;every tenth degree of the equator, interferingnbsp;each other at the poles: but on globes of ornbsp;under a foot diameter, they are only drawnnbsp;through every fifteenth degree of the equator .�nbsp;thefe circles are generally called meridians, fomc-times circles of longitude, and at other times hour-circles,

1 he globe is hung in a brafs ring, called the hrafen meridian ; and turris upon a wire in eachnbsp;pole funk half its thicknefs into one fide of thenbsp;meridian ring �, by which means, that fide ofnbsp;the ring divides the globe into two equal parts,nbsp;called the eaflern and wejlern hemifpheres ; as thenbsp;equator divides it into two equal parts, called thenbsp;northern and foutbern hemifpheres. This ring isnbsp;4nbsp;nbsp;nbsp;nbsp;divided

divided into 360 equal parts or degrees, on the fide wherein the axis of the globe turns. Onenbsp;half of thefe degrees are numbered, and reckoned, from the equator to the poles, where theynbsp;end at 90 : their ufe is to Ihew the latitudes ofnbsp;places. The degrees on the other half of thenbsp;meridian ring, are numbered from the poles tonbsp;the equator, where they end at 90 : their ufe isnbsp;to (hew how to elevate either the north or fouthnbsp;pole above the horizon, according to the latitude of any given place, as it is north or fouthnbsp;of the equator.

The brafen meridian is let into two notches made in a broad flat ring, called the woodennbsp;horizon^ the upper furface of which divides thenbsp;globe into two equal parts, called the upper andnbsp;lower hemifpberes. One notch is in the northnbsp;point of the horizon, and the other in the fouth.nbsp;On this horizon are feveral concentric circles,nbsp;which contain the months and days of the year,nbsp;the figns and degrees anfwering to the fun�snbsp;place for each month and day, and the 32 pointsnbsp;of the compals.�The graduated fide of thenbsp;brafs meridian lies towards the eaft fide of thenbsp;horizon, and (hould be generally kept towardnbsp;the perfon who works problems by the globes.

There is a fmall horary circle^ fo fixed to the north part of the brafen meridian, that the wirenbsp;in the north pole of the globe is in the centernbsp;of that circle-, and on the wire is an index,nbsp;which goes over all the 24 hours of the circle,nbsp;as the globe is turned round its axis. Sometimes there are two horary circles, one betweennbsp;each pole of the globe and the brafen meridian jnbsp;which is the contrivance of the late ingenious Mr.nbsp;Jofeph Harris, mailer of the alTay-office in thenbsp;Tower of London ; and makes it very conve-

nient for putting the poles of the globe through the horizon, and for elevating the pole to fmallnbsp;latitudes, and declinations of the fun; v/hich cannot be done where there is only one horary circle fixed to the outer edge of the brafen meridian.

There is a thin flip of brafs, called the q^ua-drant of altitude^ which is divided into 90 equal parts or degrees, anfwering exactly to fo manynbsp;degrees of the equator. It is occafionally fixednbsp;to the uppermoft point of the brafen meridiannbsp;by a nut and ferew. The divifions end at thenbsp;nut, and the quadrant is turned round upon it.

As the globe has been feen by moft people, and upon the figure of which, in a plate, neither the circles nor countries can be properlynbsp;expreflfed, we judge it would fignify very littlenbsp;to refer to a figure of it; and fhall thereforenbsp;only give fome directions how to choofe a globe,nbsp;and then deferibe its ufe.

Direftions I. See that the papers be well and neatly forchoof- pafted on the globes, which you may know, ifnbsp;ing ofnbsp;nbsp;nbsp;nbsp;jjpgg anj circles thereon meet exaftly, and

continue all the way even and whole; the circles not breaking into fevera) arches, nor the papers either coming Ihorr, or lapping over onenbsp;another.

2. See that the colours be tranfparent, and not laid too thick upon the globe to hide thenbsp;names of places.

g. See that the globe hang evenly between the brafen meridian and the wooden horizon ;nbsp;not inclining either to one fide or to thenbsp;other.

4. See that the globe be as clofe to the horizon and meridian as it conveniently may ; other-wife, you will be too much puzzled to find

5. nbsp;nbsp;nbsp;See that the equinoftial line be even withnbsp;the horizon all around, with the north or fouthnbsp;pole is elevated 90 degrees above the horizon.

6. nbsp;nbsp;nbsp;See that the equinocftial line cuts the horizon in the eaft and weft points, in all elevationsnbsp;of the pole from o to 90 degrees.

7. nbsp;nbsp;nbsp;See that the degree of the brafen meridiannbsp;marked with o, be exaftly over the equinoilialnbsp;line of the globe.

8. nbsp;nbsp;nbsp;See that there be exaftly half of the brafennbsp;meridian above the horizon ; which you maynbsp;know, if you bring any of the decimal divifionsnbsp;on the meridian to the north point of the horizon, and find their complement to 90 in thenbsp;fouth point.

9. nbsp;nbsp;nbsp;See that when the quadrant of altitude isnbsp;placed as far from the equator, on the brafennbsp;meridian, as the pole is elevated above the horizon, the beginning of the degrees of the quadrant reaches juft to the plane furface of thenbsp;horizon.

10. nbsp;nbsp;nbsp;See that whilft the index of the hour-circle (by the motion of the globe) pafles fromnbsp;one hour to another, 15 degrees of, the equatornbsp;pafs under the graduated edge of the brafennbsp;meridian.

11. nbsp;nbsp;nbsp;See that the wooden horizon be madenbsp;fubftantial and ftrong: it being generally ob-ferved, that in moft globes, the horizon is thenbsp;firft part that fails, on account of its havingnbsp;been made too flight.

In ufing the globes, keep the caft fide of the Dire�ioBs horizon towards you (unlefs your problem re- for ufingnbsp;quires the turning of it) which fide you maynbsp;know by the word Eaft upon the horizon ; fornbsp;S 3nbsp;nbsp;nbsp;nbsp;then

then you have the graduated fide of the meridian towards yon, the quadrant of altitude before you, and the globle divided exaftly into twonbsp;equal parts, by the graduated fide of the meridian.

In working fome problems, it will be necef-fary to turn the whole globe and horizon about, that you may look on the weft fide thereof;nbsp;which turning will be apt to jog the ball fo, asnbsp;to fifift away that degree of the globe whichnbsp;was before fet to the horizon or meridian: tonbsp;avoid which inconvenience, you may thruft innbsp;the feather-end of a quill between the ball ofnbsp;the globe and the brafen meridian ; which, without hurting the ball, will keep it from turningnbsp;in the meridian, whilft you turn the weft fide ofnbsp;the horizon towards you.

Turn the globe on its axis, until the given place comes exadly under that graduated fide ofnbsp;the brafen meridian, on which the degrees are

numbered

The latitude of a place is its diftance from the equator, and is north or fouth, as the place is north or fouth of thenbsp;equator. Thofe who live at the equator have no latitude,nbsp;becaufe it is there that the latitude begins.

-j- The longitude of a place is the number of degrees (reckoned upon the equator) that the meridian of the faidnbsp;place is dillant from the meridian of any other place fromnbsp;which we reckon, either eaftward or weft ward, for 180 degrees, or half round the globe. The Britifti reckon thenbsp;longitude from the meridian of London, and the Frenchnbsp;now reckon it from the meridian of Paris. The meridiannbsp;of that place, from which the longitude is reckoned, is

numbered from the equator ; and obferve what degree of the meridian the place then lies under ;nbsp;which is its latitude, north or fouth, as the placenbsp;is north or fouth of the equator.

The globe remaining in this pofition, the degree of the equator, which is under the brafen meridian, is the longitude of the place, (fromnbsp;the meridian of London on the Englijh globes)nbsp;which is eaft or weft, as the place lies on thenbsp;caft or weft fide of the firft meridian of thenbsp;globe.�All the Atlantic Ocean, and America,nbsp;is on the weft fide of the meridian of London;nbsp;and the greateft part of Europe, and of Africa,nbsp;together with all Afta, is on the eaft fide of thenbsp;meridian of London, which is reckoned the firftnbsp;meridian of the globe by the Britijh geographersnbsp;and aftronomers.

PROBLEM II.

^he longitude and latitude of a place being given, ts find that place on the globe.

� Look for the given longitude in the equator (counting it eaftward or weftward from the firftnbsp;meridian, as it is mentioned to be eaft or weft;)nbsp;and bring the point of longtude in the equatornbsp;to the brafen meridian, on that fide which isnbsp;above the fouth point of the horizon : thennbsp;count from the equator, on the brafen meridian,nbsp;to'the degree of the given latitude, towards thenbsp;north or fouth pole, according as the latitude isnbsp;north or fouth; and under that degree of latitude on the meridian, you will have the placenbsp;required.

called the firjl meridian. The places upon this meridian have no longitude, becaufe it is there that the longitudenbsp;begins.

PROBLEM III.

To find the dijfieretice of longitude, or difference of latitude, between any two given flaces.

Bring each of thefe places to�the brafen meridian, and fee what its latitude is : the leffer latitude fubtracled from the greater, if bothnbsp;places are on the fame fide of the equator, ornbsp;both latitudes added together, if they are onnbsp;different fides of it, is the difference of latitudenbsp;required. And the number of degrees containednbsp;between thefe places, reckoned on the equator,nbsp;when they are brought feparately under thenbsp;brafen meridian, is their difference of longitude ;nbsp;if it be lefs than 18o : but if more, let it be fub-traded from 360, and the remainder is the difference of longitude required. Or,nbsp;i Having brought one of the places to thenbsp;brafen meridian, and fet the hour-index to XII,nbsp;i turn the globe until the other place comes to thenbsp;' brafen meridian, and the number of hours andnbsp;� parts of an hour, paft over by the index, willnbsp;give the longitude in time; which may be eafilynbsp;reduced to degrees, by allowing 15 degrees fornbsp;I every hour, and one degree for every four minutes.

N. B. When we fpeak of bringing any place to the brafen meridian, it is the graduated fidenbsp;of the meridian that is meant.

P R 0 B-

Any place heing given^ to find all thofe places that have the fame longitude or latitude with it.

Bring the given place to the brafen meridian, then all thofe places which lie under that fide ofnbsp;the meridian, from pole to pole, have the famenbsp;longitude with the given place. Turn the globenbsp;round its axis, and all thofe places which pafsnbsp;under the fame degree of the meridian that thenbsp;given place does, have the fame latitude withnbsp;that place, ,

Since all latitudes are reckoned from the equator, and all longitudes are reckoned fromnbsp;the firft meridian, it is evident, that the point ofnbsp;the equator which is cut by the firft meridian, hasnbsp;neither latitude nor longitude.�The greateftnbsp;latitude is 90 degrees, bccaufe no place is morenbsp;than 90 degrees from the equator. And thenbsp;greateft longitude is 180 degrees, becaufe nonbsp;place is more than 180 degrees from the firftnbsp;meridian.

Bring the given place to the brafen meridian, and having found its latitude, keep the globe innbsp;that fituation, and count the fame number of

� The anteeci are thofe people who live on the fame meridian, and in equal latitudes, on different fides of the equator. Being on the fame meridian, they have the fame hours ; that is, when it is noon to the one, it is alfo noon to thenbsp;other; and when it is mid-night to the one, it is tdfo midnight to the other, Hz, Being on different fides of the equator

268 nbsp;nbsp;nbsp;�The Ufe of the Terreftrial Globe.

degrees of latitude from the equator towards the contrary pole, and where the reckoning ends,nbsp;you have the ajjtceci of the given place upon thenbsp;globe. Thofe who live at the equator have nonbsp;antosci.

The globe remaining in the fame pofitiori, fet the hour-index to the upper XII. on the horarynbsp;circle, and turn the globe until the index comesnbsp;to the lower XII; then, the place which liesnbsp;under the meridian, in the fame latitude withnbsp;the given place, is thenbsp;nbsp;nbsp;nbsp;required. Thofe

As the globe now ftands (with the index at the lower XII.) the antipodes of the given placenbsp;will be under the fame point of the brafen meridian where its ant(�ci ilood before. Everynbsp;place upon the globe has its antipodes.

tor, they have dilFerent or oppofite feafons at the fame time ; the length of any day to the one is equal to the length of thenbsp;night of that day to the other; and they have equal elevations of the different poles.

-j- The periaci are thofe people who live on the fame parallel of latitude, but on oppofite meridians: fo that though their latitude be the fame, their longitude differs i8o degrees, By being in the fame latitude, they have equal elevations of the fame pole (for the elevation of the pole isnbsp;always equal to the latitude of the place) the fame length ofnbsp;Hays or nights, and the fame feafoos. But being on oppofite meridians, when it is noon to the one, it is mid-nightnbsp;to the other.

J The antipodes are thofe who live diametrically oppo-fite to one another upon the globe. Handing with feet towards feet, on oppofite meridians and parallels. Being onnbsp;oppofite fides of the equator, they have oppofite featons,nbsp;winter to one, when it is fumnier to the other; being equallynbsp;diftant from the equator, they have their contrary poles equallynbsp;. elevated above the horizon ; being on oppofite meridians,nbsp;when it is noon to the one, it muftbe mid-night to the other;nbsp;and as the fun recedes from the one when be approaches tonbsp;the other, the length of the day to one muft be equal to thenbsp;length of the night at the fame time to the other.

l'he Uj� of the �T�errefirial Globe.

PROBLEM VI.

'�o find the diflance between any two places on the

Lay the graduated edge of the quadrant of altitude over both the places, and count thenbsp;number of degrees intercepted between them onnbsp;the quadrant; then multiply thefe degrees bynbsp;60, and the produfi: will give the diftance innbsp;geographical miles: but to find the diftance innbsp;Englifh miles, multiply the degrees by 69^, andnbsp;the produdl will by the number of miles required.

Or, take the diftance betwixt any two places with a pair of compafles, and apply that extentnbsp;to the equator; the number of degrees, intercepted between the points of the compafles, isnbsp;the diftance in degrees of a great circle *; whichnbsp;may be reduced either to geographical miles, ornbsp;to Englifli miles, as above.

* Any circle that divides the globe into two equal parts, Great is called a great circle, as the equator or meridian. Any drcle.nbsp;circle that divides the globe into two unequal parts (whichnbsp;every parallel of latitude does) is called a lejir circle. Now, LeJJernbsp;as every circle, whether great or fmall, contains 360 degrees, circle,nbsp;and a degree upon the equator or meridian contains 60 geographical miles, it is evident, that a degree of longitude uponnbsp;the equator, is longer than a degree of longitude upon anynbsp;parallel of latitude, and mull: therefore contain a greaternbsp;number of miles. So that, although all the degrees of latitude are equally long upon an artificial globe (though notnbsp;precifely fo upon the earth itfelf) yet the degrees of longitude decreafe in length, as the latitude increafes, but not innbsp;the fame proportion. The following table thews the lengthnbsp;of a degree of longitude, in geographical miles, and hundredth parts of a mile, for every degree of latitude, fromnbsp;the equator to the poles: a degree on the equator being 60nbsp;geographical miles,

PR O B-

A place on the globe being given, and its dijlance from any other place, to find all the other placesnbsp;npon the globe which are at the fame difiance fromnbsp;the given place.

Bring the given place to the brafen meridian, and fcrew the quadrant of altitude to the meridian, diredly over that place; then keeping thenbsp;globe in that pofition, turn the quadrant quitenbsp;round upon it, and the degree^of the quadrantnbsp;that touches the fecond place, will pafs over allnbsp;the other places which are equally diftant with itnbsp;from the given place.

This is the fame as if one foot of a pair of compafTes was fet in the given place, and thenbsp;other foot extended to the fecond place, whofenbsp;diftance is known; for if the compafles be thennbsp;turned round the firft place as a center, thenbsp;moving foot will go over all thofe places whichnbsp;are at the fame diftance with the fecond fromnbsp;it.

stable Jhewing the number of miles in a degree of longitude, in any given degree of latitude^

PROB-

PROBLEM Vlir.

^he hour of the day at any place being given, to find all thofe places where it is noon at that time.

Bring the given place to the brafen meridian, and fet the index to the given hour; this done,nbsp;turn the globe until the index points to the uppernbsp;XII, and then, all the places that lie under thenbsp;brafen meridian have noon at that time.

N. B. The upper XII always ftands for noon j and when the bringing of any place to the brafennbsp;meridian is mentioned, the fide of that meridiannbsp;on which the degrees are reckoned from thenbsp;equator is meant, unlefs the contrary fide benbsp;mentioned.

�The hour of the day at any place being given to find what o'clock it then is at any other place.

Bring the given place to the brafen meridian, and fet the index to the given hour; then turnnbsp;the globe, until the place where the hour is required comes to the brafen meridian, and the index will point out the hour at that place.

'To find the funds place in the ecliptic, and his * declination, for any given day of the year.

Look on the horizon for the given day, and right againft it you have the degree of the fignnbsp;in which the fun is (or his place) on that day

* The fun�s declination is his diflance from the equinoflial in degrees, and is north or fouth, as the fun is between thenbsp;cquinoftial and the north or fouth pole.

at noon, Find the fame degree of that fign in the ecliptic line upon the globe, and havingnbsp;brought it to the brafen meridian, obferve whatnbsp;degree of the meridian Hands over it for thatnbsp;is the fun�s declination, reckoned from thenbsp;equator.

The day of the month being given, to find all thofe places of the earth over which the fun will pafsnbsp;vertically on that day.

Find the fun�s place in the ecliptic for the given day, and having brought it to the brafennbsp;meridian, obferve what point of the meridian isnbsp;over it ; then turning the globe round its axis;nbsp;all thofe places which pafs under that point ofnbsp;the meridian are the places required -, for asnbsp;their latitude is equal, in degrees and parts of anbsp;degree, to the fun�s declination, the fun muftbenbsp;dire�lly over head to each of them at its refpec-tive noon.

A place being given in the¹ torrid zone, to find thofe two days of the year, on which the fun pall benbsp;vertical to that place.

Bring the given place to the brafen meridian, and mark the degree of latitude that is cxaftly

The globe is divided into five zones; one torrid, two temperate, and two frigid. The torrid zone lies between the twonbsp;tropics, and is 47 degrees in breadth, or 23I on each fide ofnbsp;the equator : the temperate zones lie between the iropics andnbsp;poiar circles, or from 235 degrees of latitude, to 66|:, oti

over it on the meridian; then turn the globe round its axis, and obferve the two degrees ofnbsp;the ecliptic which pafs exadlly under that degreenbsp;of latitude: Laftly, find on the wooden horizonnbsp;the two days of the year on which the fun is innbsp;thofe degrees of the ecliptic, and they are thenbsp;days required : for on them, and none elfe, thenbsp;fun�s declination is equal to the latitude of thenbsp;given place �, and confequently, he will then benbsp;vertical to it at noon.

fTo find all thofe places of the north frigid �zone, where the fun begins to floine confiantly withoutnbsp;fetting, on any given day, from the zoth of March,nbsp;to the 2^d of September.

On thefe two days, the fun is in the equinoctial, and enlightens the globe exadly from pol^; to pole: therefore, as the earth turns round itsnbsp;axis, which terminates in the poles, every placenbsp;upon it will go equally tl\rough the light and thenbsp;dark, and fo make the day and night equal to allnbsp;places of the earth. But as the fun declinesnbsp;from the equator, towards either pole, he willnbsp;fhine juft as many degrees round that pole, asnbsp;are equal to his declination from the equator;nbsp;fo that no place within that diftance of the polenbsp;will then go through any part of the dark, andnbsp;confequently the fun will not fet to it. Now, as

each fide of the equator; and are each 43 degrees in breadth: the frigid zones are the fpaces included within the polarnbsp;ciicles, which being each 234 degrees from their refpeftivenbsp;poles, the breadth of each of thefe zones is 47 degrees. Asnbsp;the fun never goes without the tropics, he muft every moment be vertical to fome place or other in the torrid zone.

the fun�s declination is northward, from the 21ft of March to the 23d of September, he muft con-ftantly fhine round the north pole all that time jnbsp;and on the day that he is in the northern tropic,nbsp;he Ihines upon the whole north frigid zone ; fonbsp;that no place within the north polar circle goesnbsp;through any part of the dark on that day.nbsp;Therefore,

Having brought the fun�s place for the given day to the brafen meridian, and found his declination (by Prob. IX.) count as many degreesnbsp;on the meridian, from the north pole, as arenbsp;equal to the fun�s declination from the equator,nbsp;and mark that degree from the pole where thenbsp;reckoning ends : then, turning the globe roundnbsp;its axis, obferve what places in the north frigidnbsp;zone pafs diredtly under that mark; for theynbsp;are the places required.

The like may be done for the fouth frigid zone, from the 23d of September to the 21ft ofnbsp;March, during which time the fun fhines con-ftantly on the fouth pole.

Having found the fun�s declination for the given day (by Prob. IX.) mark it with a chalknbsp;on the brafen meridian : then bring the placenbsp;where you are (fuppofe London) to the brafennbsp;meridian, and fet the index to the given hour ;nbsp;which done, turn the globe on its axis, until thenbsp;index points to XII at noon ; and the place onnbsp;the globe, which is then directly under the pointnbsp;Tnbsp;nbsp;nbsp;nbsp;of

of the fun�s declination marked upon the meridian, has the fun that moment in the zenith* ck diredlly overhead.

problem XV.

The day and hour at any place being given, to find all thofe places where the fun is then rifing, ornbsp;felting, or on the meridian: confequently, all thofenbsp;tlaces which are enlightened at that time, andnbsp;thofe which are in the dark.

This problem cannot be folved by any globe fitted up in the common way, with the hournbsp;circle fixed upon the brafs meridian ; unlefs thenbsp;fun be on or near fome of the tropics on thenbsp;given day. But by a globe fitted up accordingnbsp;to Mr. Jofeph Harris�s invention (already mentioned) where the hour-circle lies on the furfacenbsp;of the globe, below the meridian, it may be folvednbsp;for, any day in the year, according to his method -, which is as follows.

Having found the place to which the fun is vertical at the given hour, if the place be in thenbsp;northern hemifphere, elevate the north pole asnbsp;many degrees above the horizon, as are equal tonbsp;the latitude of that place ; if the place be in thenbsp;Ibuthern hemifphere, elevate the fouth pole accordingly -, and bring the faid place to the brafennbsp;meridian. Then, all thofe places which are innbsp;the weftern femicircle of the horizon, have thenbsp;fun rifing to them at that time ; and thofe in thenbsp;eaftern femicircle have it fetting : to thofe undernbsp;the upper femicircle of the brafs meridian, it isnbsp;noon i and to thofe under the lower femicircle,nbsp;it is midnight. All thofe places which arenbsp;above the horizon, are enlightened by the fun,

�nd have the fun juft as many degrees high to them, as they themfelves are above the horizon :nbsp;and this height may be known, by fixing thenbsp;quadrant of altitude on the brafen meridian overnbsp;the place to which the fun is vertical; and then,nbsp;laying it over any other place, obferve whatnbsp;numb^er of degrees on the quadrant are intercepted between the faid place and the horizon.nbsp;In all thofe places that are 18 degrees below thenbsp;weftern femicircle of the horizon, the morningnbsp;twilight is juft beginning ; in all thofe places thatnbsp;are i8 degrees below the eaftern femicircle ofnbsp;the horizon, the evening twilight is ending �, andnbsp;all thofe places that are lower than i8 degrees,nbsp;have dark night.

If any place be brought to the upper femicircle of the brafen meridian, and the hour index be fet to the upper XII or noon, and then thenbsp;globe be turned round eaftward on its axis;nbsp;when the place comes to the weftern femicirclenbsp;of the horizon, the index will Ihew the time ofnbsp;fun-rifing at that place-, and when the famenbsp;place comes to the eaftern femicircle of the horizon, the index will fhew the time of fun-fet.

To thofe places which do not go under the horizon, the fun fets not on that day: and tonbsp;thofe which do not come above it, the lun docsnbsp;not rife.

The day and hour of a lunar ecUf fe being given ; to find all thofe places of the earth to which it willnbsp;be viftble.

The moon is never eclipfed but when fhe is full, and fo diredly oppofite to the fun, that thenbsp;T 2nbsp;nbsp;nbsp;nbsp;earth�s

earth�s fhadow falls upon her. Therefore, whatever place of the earth the fun is vertical to at that time, the moon muft be vertical to the antipodes of that place ; fo that the fun will be thennbsp;vifible to one half of the earth, and the moonnbsp;to the other.

Find the place to which the fun is vertical at the given hour (by Prob. XIV.) elevate the polenbsp;to the latitude of that place, and bring the placenbsp;to the upper part of the brafen meridian, as innbsp;the former problem: then, as the fun will benbsp;vifible to all thofe parts of the globe which arenbsp;above the horizon, the moon will be vifible to allnbsp;thofe parts of the globe which are below it, atnbsp;the time of her greatefl: obfcuration.

But with regard to an eclipfe of the fun, there is no fuch thing as fhewing to what places itnbsp;will be vifible, with any degree of certainty, bynbsp;a common globe; becaufe the moon�s fhadownbsp;covers but a fmall portion of the earth�s furfacenbsp;and her latitude, or declination from the ecliptic, throws her fhadow fo varioufly upon thenbsp;earth, that to determine the places on which itnbsp;falls, recourfe muft be had to long calculations.

Find the latitude of the place (by Prob. I.)andif the place be in the northern hemilphere, raife thenbsp;north pole above the north point of the horizon,

* The zenith, in this fenfe, is the higheft point of the brafen meridian above the horizon ; but in the proper fenfe it is that point of the heaven which is direftly vertical tonbsp;any given place, at any given inftant of time.

as many degrees (counted from the pole upon the brafen meridian) as are equal to the latitudenbsp;of the place. If the place be in the fouthernnbsp;hemifphere, raife the fouth pole above the fouthnbsp;point of the horizon, as many degrees as are equalnbsp;to the latitude. Then, turn the globe till thenbsp;place comes under its latitude on the brafennbsp;meridian, and fallen the quadrant of altitude fo,nbsp;that the chamfered edge of its nut (which isnbsp;even with the graduated edge) may be joinednbsp;to the zenith, or point of latitude. This done,nbsp;bring the fun�s place in the ecliptic for the givennbsp;day, (found by Prob. X.) to the graduated fidenbsp;of the brafen meridian, and fet the hour-index tonbsp;XII. at noon, which is the uppcrmoft XI� on thenbsp;hour-circle ; and the globe will be rectified.

The latitude of any place is equal to the ele- Remark, vation of the neareft pole of the heaven abovenbsp;the horizon of that place; and the poles ofnbsp;the heaven are diredly over the poles of thenbsp;earth, each 90 degrees from the equinoctial line. Let us be upon what place of thenbsp;earth we will, if the limits of our view be notnbsp;intercepted by hills, we fliall fee one half of thenbsp;heaven, or 90 degrees every way round, fromnbsp;that point which is over our heads. Therefore,nbsp;if we were upon the equator, the poles of thenbsp;heaven would lie in our horizon, or limit of ournbsp;view : if we go from the equator, towards eithernbsp;pole of the earth, we lhall fee the correfpondingnbsp;pole of the heaven rifing gradually above ournbsp;horizon, jull as many degrees as vve have gonenbsp;from the equator: and if we were at either ofnbsp;the earth�s poles, the correfponding pole of thenbsp;heaven would be diredtly over our head. Con-fequently, the elevation or height of the pole innbsp;T 3nbsp;nbsp;nbsp;nbsp;degrees

degrees above the horizon, is equal to the number of degrees that the place is from thenbsp;equator.

PROBLEM XVIII.

�the latitude of any place, not exceeding *664. degrees, and the day of the month, being given; to find the time of fun-rifing and fetting, and ccnfe-qiiently the length of the day and night.

Having reftified the globe for the latitude, and for the fun�s place on the given day (as di-redted in the preceding problem) bring the fun�snbsp;place in the ecliptic to the eaftern fide of the horizon, and the hour-index will Ihew the time ofnbsp;fun-rifing; then turn the globe on its axis, untilnbsp;the fun�s place comes to the weftern fide of thenbsp;horizon, and the index will Ihew the time of fun-fetting.

1'he hour of fun-fetting doubled, gives the length of the day ; and the hour of fun-rifingnbsp;doubled gives the length of the night,

PROBLEM XIX.

the latitude of any place, and the day of the month, being given % to find when the morning twilightnbsp;begins, and the evening twilight ends, at thatnbsp;place.

This ploblem is often limited ; for, when the fun does not go 18 degrees beiow the horizoij,nbsp;the twilight continues the whole night �, and for

* All places whofe latitucle is more than 664 degrees, are in the frigid zones; and to thole places the fun doss notnbsp;fet in fummer, for a certain number of diurnal revolutions,nbsp;which occafions this limitation of ladtude.

feveral nights together in fummer, between 49 and 66f degrees of latitude : and the nearernbsp;to 66 '-, the greater is the number of thefe nights.nbsp;But when it does begin and end, the foUow-ing method will llaew the time for any givennbsp;day.

Reftify the globe, and bring the fun�s place in the ecliptic to the eaftern fide of the horizon;nbsp;then mark that point of the ecliptic with a chalknbsp;which is in the vveftern fide of the horizon, it being the point oppofite to the fun�s place : thisnbsp;done, lay the quadrant of altitude over the faidnbsp;point, and turn the globe eaftward, keeping thenbsp;quadrant at the chalk-mark, until it is juft 18nbsp;degrees high on the quadrant; and the indexnbsp;will point out the time when the morning twilight begins : for the fun�s place will then be 18nbsp;degrees below the eaftern fide of the horizon.nbsp;To find the time when the evening twilightnbsp;ends, bring the fun�s place to the weftern fidenbsp;of the horizon, and the point oppofite to it,nbsp;which was marked with the chalk, will be rilingnbsp;in the eaft : then, bring the quadrant over thatnbsp;point, and keeping it thereon, turn the globenbsp;weftward, until the faid point be 18 degreesnbsp;above the horizon on the quadrant, and the index will Ihew the time when the evening twilight �nds ; the fun�s place being then 18 degreesnbsp;below' the weftern fide of the horizon.

PRO-

to find on what day of the year the fun begins to fhine conftantly without Jetting^ on any givennbsp;place in the north frigid zone and how long henbsp;continues to do fo.

Refbify the globe to the latitude of the place, and turn it about until fome point of the ecliptic, between, Aries and Cancer^ coincides withnbsp;the north point of the horizon where the brafennbsp;meridian cuts it: then find, on the woodennbsp;horizon, what day of the year the fun is in thatnbsp;point of the ecliptic; for that is the day onnbsp;which the fun begins to fliine conftantly on thenbsp;given place, without fetting. This done, turnnbsp;the globe until fome point of the ecliptic, between Cancer and Libra, coincides with thenbsp;north point of the horizon, where the brafennbsp;meridian cuts it; and find, on the woodennbsp;horizon, on what day the fun is in that point ofnbsp;the ecliptic; which is the day that the fun leavesnbsp;off conftantly fhining on the faid place, and rifesnbsp;and fets to it as to other places on the globe.nbsp;The number of natural days, or complete revolutions of the fun about the earth, betweennbsp;the two days above found, is the time that thenbsp;fun keeps conftantly above the horizon withoutnbsp;fetting ; for all the portion of the ecliptic, thatnbsp;lies between the two points which interfedi: thenbsp;horizon in the very north, never fets below it:nbsp;and there is juft as much of the oppofite part ofnbsp;the ecliptic that never rifes; therefore, the funnbsp;will keep as long conftantly below the horizonnbsp;in winter, as above it in fummer.

2 nbsp;nbsp;nbsp;Whoever

Whoever confiders the globe, will find, that all places of the earth do equally enjoy the benefit of the fun, in refpe�t of time, and are equallynbsp;deprived of it. For, the days and nights arenbsp;always equally long at the equator: and in allnbsp;places that have latitude, the days at one timenbsp;of the year are exaftly equal to the nights at thenbsp;oppofite feafon.

Find a point in the ecliptic half as many de* grees from the beginning of Cancer (either towards Aries or Libra) as there are -}� natural daysnbsp;in the time given ; and bring that point to thenbsp;north fide of the brafen meridian, on which thenbsp;degrees are numbered from the pole towardsnbsp;the equator: then, keep the globe from turningnbsp;on its axis, and Aide the meridian up or down,nbsp;until the forefaid point of the ecliptic comesnbsp;to the north point of the horizon, and then, thenbsp;elevation of the pole will be equal to the latitudenbsp;required.

* nbsp;nbsp;nbsp;The reafon of this limitation is, that iSzj of our daysnbsp;and nights make half a year, which is the longeft time thatnbsp;the fun fliines without fetting, even at the poles of thenbsp;earth.

f A natural day contains the whole 24 hours: an artificial day, the time that the fun is above the horizon.

PRO-

The latitude of a place, not exceeding 664- degrees, and the day, of the month being given �, to findnbsp;the fun's amplitude, or point of the compafs onnbsp;�which he rifes or fels on that day.

Reftify the globe, and bring the fun�s place to the eaftern fide of the horizon; then obfervenbsp;what point of the compafs on the horizon ftandsnbsp;right againft the fun�s place, for that is hisnbsp;amplitude at rifing. This done, turn the globenbsp;weftward, until the fun�s place comes to thenbsp;weftern fide of the horizon, and it will cut thenbsp;point of his amplitude at fetting. Or, you maynbsp;count the rifing amplitude in degrees, from thenbsp;eaft point of the horizon, to that point wherenbsp;the fun�s place cuts it; and the fetting amplitude, from the weft point of the horizon, to thenbsp;fun�s place at fetting.

PROBLEM XXIII.

The latitude, the fun's place, and his¹ altitude, being given to find the hour of the day, and thenbsp;fun�s azimuth, or number of degrees that he isnbsp;dijiant from the meridian.

Reftify the globe, and bring the fun�s place to the given height upon the quadrant of altitude ; on the eaftern fide of the horizon, if thenbsp;time be in the forenoon ; or the weftern fide, if

The fun�s altitude, at any time, is his height in degrees above the horizon at that time,

it be in the afternoon : then, the index will fhew the hour and the number of degrees innbsp;the horizon intercepted between the quadrant ofnbsp;altitude and the fouth point, will be the fun�snbsp;true azimuth at that time.

N. B. Always when the quadrant of altitude is mentioned in working any problem, the graduated edge of it is meant.

If this be done at fea, and compared with the fun�s azimuth, as fhewn by the compafs, if theynbsp;agree, the compafs has no variation in that place;nbsp;but if they differ, the compafs does vary ; andnbsp;the variation is equal to this difference.

The latitude, hour of the day, and the fun�s flace, being given �, to find the furds altitude andnbsp;azimuth.

Reftify the globe, and turn it until the index points to the given hour; then lay the quadrant of altitude over the fun�s place in the ecliptic, and the degree of the quadrant cut bynbsp;the fun�s place is his altitude at that time abovenbsp;the horizon ; and the degree of the horizon cutnbsp;by the quadrant is thp fun�s azimuth, reckonednbsp;from the fouth.

PRO-

latitude^ the fun's altitude, and his azimuth being given; to find his place in the ecliptic, thenbsp;day of the month, and hour of the day, thoughnbsp;they had all been loft.

Re�lify the globe for the latitude and * zenith, and fet the quadrant of altitude to the givennbsp;azimuth in the horizon ; keeping it there, turnnbsp;the globe on its axis until the ecliptic cuts thenbsp;quadrant in the given altitude : that point ofnbsp;the ecliptic which cuts the quadrant there, willnbsp;be the fun�s place; and the day of the monthnbsp;anfwering thereto, will be found over the likenbsp;place of the fun on the wooden horizon. Keepnbsp;the quadrant of altitude in that pofition, andnbsp;having brought the fun�s place to the brafennbsp;meridian, and the hour index to XII at noon,nbsp;turn back the globe, until the fun�s place cutsnbsp;the quadrant of altitude again, and the indexnbsp;will ftiew the hour.

Any two points of the ecliptic which are equidiftant from the beginning of Cancer or ofnbsp;Capricorn, will have the fame altitude and azimuth at the fame hour, though the months benbsp;different -, and therefore it requires fome care innbsp;this problem, not to miftake both the month,nbsp;and the day of the month ; to avoid which ob-ferve, that from the 20th of March to the 21ftnbsp;of June, that part of the ecliptic which is be-

* By reflifying the globe for the zenith, is meant fcrevv-ing the quadrant of altitude to the given latitude on the brafs meridian.

tween the beginning of Aries and beginning of Cancer is to be ufed ; from the 21ft of June tonbsp;the 23d of September, between the beginningnbsp;of Cancer and beginning of Libra: from thenbsp;23d of September to the 21 ft of December,nbsp;between the beginning of Libra and the beginning of Capricorn; and from the 2 ift of December to the 20th of March, between the begin-nining of Capricorn and beginning of Aries. Andnbsp;as one can never be at a lofs to know in whatnbsp;quarter of the year he takes the fun�s altitudenbsp;and azimuth, the above caution with regard tonbsp;the quarters of the ecliptic, will keep him rightnbsp;as to the month and day thereof.

If the place be on the north fide of the equator, find its latitude (by Prob. 1.) and elevate the north pole to that latitude ; then, bring thenbsp;beginning of Cancer go to the brafen meridian,nbsp;and fet the hour-index to XII at noon. But ifnbsp;the given place be on the fouth fide of thenbsp;equator, elevate the fouth pole to its latitude,nbsp;and bring the beginning of Capricorn tcp to thenbsp;brais meridian, and the hour-index to Xlf.nbsp;This done, turn the globe weftward, until thenbsp;beginning of Canter or Capricorn (as the latitudenbsp;is north or fouth) comes to the horizon; andnbsp;the index will then point out the time of fun-fetting, for it will have gone over ail the afternoon hours, between ,mid-day and fun-feti

which length of time being doubled, will giv� the whole length of the day, from fun-rifing t�nbsp;fun-fecting. For, in all latitudes, the fun rifesnbsp;as long before mid day, as he fets after it.

To find in what latitude the longeft day is of any given length lefs than 24 hours.

If the latitude be north, bring the beginning of Cancer to the brafen meridian, and elevatenbsp;the north pole to about 664- degrees -, but ifnbsp;the latitude be foutn, bring the beginning ofnbsp;Capricorn to the meridian, and elevate the fouthnbsp;pole to about 664 degrees ; becaufe the longeftnbsp;day in north latitude, is when the fun is in thenbsp;firfl point of Cancer; and in fouth latitude,nbsp;when he is in the firft point of Capricorn. Thennbsp;fet the hour-index to XII at noon, and turn thenbsp;globe weftward, until the index points at, halfnbsp;the number of hours given ; which done, keepnbsp;the globe from turning on its axis, and Hide thenbsp;meridian down in the notches, until the afore-faid point of the ecliptic (viz. Cancer or Capri^nbsp;corn) comes to the horizon �, then, the elevationnbsp;of the pole will be equal to the latitude required.

PRO-

The latitude of any place^ not exceeding 66i degrees being given ; to find in what clitnate the place is.

Find the length of the longeft day at the given place by Prob. XXVI. and whatever benbsp;the number of hours whereby it exceedethnbsp;twelve, double that number, and the fum willnbsp;anfwer to the climate in which the place is.

T�he latitude, and the day of the month, beinggwen% to find the hour of the day when the fun pines.

Set the wooden honzan truly level, and the brafen meridian due north and fouth by a mariner�s compafs: then, having reftified thenbsp;globe, ftick a fmall fewing-needle into the fun�snbsp;place in the ecliptic, perpendicular to that partnbsp;of the furface of the globe: this done, turn thenbsp;globe on its axis, until the needle comes to thenbsp;brafen meridian, and fet the hour-index to XII

* A climate, from the equator to either of the polar circles, is a ttadl of the earth�s furface, included between two fuch parallels of latitude, that the length of the longeft daynbsp;in the one exceeds that in the other by half an hour; butnbsp;from the polar circles to the poles, where the fun keeps longnbsp;above the horizon without fetting, each climate differs anbsp;whole month from the one next to it. There are twenty-fnur climates between the equator and each of the polar cir.nbsp;�^les; and fix from ?ach polar circle to its refpedive pole.

at noon-, then, turn the globe on its axis, until the needle points exaftJy towards the fun (whichnbsp;it will do when it cafts no (hadow on the globe)nbsp;and the index will fhew the hour of the day.

PROBLEM XXX.

A pleafant way of Jhewing all thofe places of the earth which are enlightened by the fun^ and alfonbsp;the time of the day when the fun Jhines,

TaRe the terreftrial ball out of the wooden horizon, and alfo out of the brafen meridiannbsp;then fet it upon a pedeftal in fun*fliine, in fuchnbsp;a manner, that its north pole may point direftlynbsp;towards the north pole of the heaven, and thenbsp;meridian of the place where you are be direftlynbsp;towards the fouth. Then, the fun will Ihinenbsp;upon all the like places of the globe, that henbsp;does on the real earth, rifing to fome when henbsp;is fetting to others ; as you may perceive by thatnbsp;part where the enlightened half of the globe isnbsp;divided from the half in the lhade, by thenbsp;boundary of the light and darknefs : all thofenbsp;places, on which the fun Ihines, at any time,nbsp;having day; and all thole, on which he doesnbsp;not fhine, having night.

If a narrow flip of paper be put round the equator, and divided into 24 equal parts, beginning at the meridian of your place, and thenbsp;hours be fet to thofe diviflons in fuch a manner,nbsp;that one of the VFs may be upon your meridian ; the fun being upon that meridian at noon,nbsp;will then Ihine exadlly to the two XIPs; and atnbsp;one o�clock to the two I�s, amp;c. So that the

place, where the enlightened half of the globe is parted from the (haded half, in this circle ofnbsp;hours, will fliew the time of the day.

The principles of dialing (bail be explained farther on, by the terreftrial globe. Atprefcntnbsp;we (hall only add the following obfervationsnbsp;upon it �, and then proceed to the ufe of the ce-leftial globe.

1. nbsp;nbsp;nbsp;The latitude of any place is equal to the elevation of the pole above the horizon of that place.,nbsp;and the elevation of the equator is equal to the complement of the latitude^ that is, to what the latitudenbsp;wants of go degrees.

2. nbsp;nbsp;nbsp;Ihofe places which lie on the equator, have nonbsp;latitude, it being there that the latitude begins ; andnbsp;thofe places which lie on the firfi meridian havenbsp;no longitude, it being there that the longitude begins. Cenfequendy, that particular place of the earthnbsp;where the firjt meridian inierfedls the equator, hasnbsp;neither longitude nor latitude.

3. nbsp;nbsp;nbsp;At all 'places of the earth, except the poles,nbsp;all the points of the conpafs may be diflinguijhed innbsp;the horizon : but from the north pole, every placenbsp;is fouth ; a?rd from the fouth pole, every placenbsp;is north. Therefore, as the fun is conftantly abovenbsp;the horizon of each pole for half a year in its turn,nbsp;he cannot he faid to depart from the meridian ofnbsp;either pole for half a year together. Confequently,nbsp;at the north pole it may be faid to be noon everynbsp;moment fer half a year ; and let the winds blownbsp;from what part they will, they muft always blownbsp;from the fouth �, and at the fouth pole, from thenbsp;north.

4. nbsp;nbsp;nbsp;Becaufe one half of the ecliptic is above thenbsp;horizon of the pole, and the fun, moon, and planetsnbsp;move in {or nearly in) the ecliptic �, they will all

rife and fet to the poles. But, hecaufe the Jiars never change their declinations from the equator (atnbsp;leajl not fenfibly in one age) thofe which are oncenbsp;above the horizon of either pole, never fet below it �,nbsp;and thofe which are once below it, never rife.

p. All places of the earth do equally enjoy the benefit of the fun, in refpebi of time, and are equally deprived of it.

6. nbsp;nbsp;nbsp;All places upon the equator have their daysnbsp;and nights equally long, that is, 12 hours each, atnbsp;all times of the year. For although the fun declinesnbsp;alternately, from the equator towards the north andnbsp;towards the fouth, yet, as the horizon of the equator cuts all the parallels of latitude aftd declinationnbsp;in halves, the fun mujl always continue above thenbsp;horizon for one half a diurnal revolution about thenbsp;earth, and for the other half below it.

7. nbsp;nbsp;nbsp;IVhen the fun's declination is greater than thenbsp;latitude of any place, upon either fide of the equator,nbsp;the fun will come twice to the fame azimuth or pointnbsp;of the compafs in the forenoon, at that place, andnbsp;twice to a like azimuth in the afternoon �, that is,nbsp;be will go twice back every day, whilft his declination continues to be greater than the latitude. Thus^nbsp;fuppofe the globe reblified to the latitude of Barba-does, which is 13 degrees north ; and the fun to benbsp;any where in the ecliptic, between the middle ofnbsp;Faurus and middle of Leo if the quadrant of altitude be fet to about ¹ 18 degrees north of the eajinbsp;in the horizon, the fun's place be marked with atnbsp;chalk upon the ecliptic, aud the globe be then turnednbsp;wejlward on its axis, the faid mark will rife in thenbsp;horizon a little to the north of the quadrant, andnbsp;thence afeending, it will crofs the quadrant towards

From the middle of Gemini to the middle of Cancer, the quadrtne may be fet 20 degrees.

the fouth; but before it arrives at the meridian, it will crofs the q^uadrant again, and pafs over thenbsp;meridian northward of Barbadoes. And if thenbsp;quadrant be fet about 18 degrees north of the wefi,nbsp;the fun s place will crofs it twice, as it defends fromnbsp;the meridian towards the horizon, in the afternoon.

8. In all places of the earth between the equator and poles, the days and nights are equally long, viz.nbsp;12 hours each, when the fitn is in the equinoblial:nbsp;for, in all elevations of the pole, /hort of (^o degrees (which is the greateji) one half of the equatornbsp;or equinobiial will be above the horizon, and thenbsp;other half below it.

g. 7'ke days and nights are never of an equal length at any place between the equator and polarnbsp;circles, but when the fun enters the figns v Ariesnbsp;and �= Libra. For in every other part of thenbsp;ecliptic, the circle of the fun's daily motion is dividednbsp;into two unequal parts by the horizon.

I o. Fhe nearer that any place is to the equator, the lefs is the difference between the length of the daysnbsp;and nights in that place; and the more remote,nbsp;the contrary. Fhe circles which the fun defcribesnbsp;in the heaven every 24 hours, being cut more nearlynbsp;equal in the former cafe, and more unequally in thenbsp;latter.

11. nbsp;nbsp;nbsp;In all places lying upon any given parallelnbsp;of latitude, however long or Jhort the day or nightnbsp;be at any one of thefe places, at any time of thenbsp;year, it is then of the fame length at all the reft ;nbsp;for in turning the globe round its axis (when rebli-fied according to the fun's declination) all thefenbsp;places will keep equally long above or below thenbsp;horizon.

12. nbsp;nbsp;nbsp;fhe fun is vertical twice a year to everynbsp;place between the tropics �, to thofe under the tropics,

once a year, but never any where elfe. For, there can he no place between the tropics, hut that therenbsp;will be two points in the ecliptic, vohofe declinationnbsp;from the equator is equal to the latitude of thatnbsp;place ; and hut one point of the ecliptic which has anbsp;declination equal to the latitude of places on thenbsp;tropic which that point of the ecliptic touches �, andnbsp;as the fun never goes without the tropics, he cannbsp;never he vertical to any place that lies withoutnbsp;them,

13. nbsp;nbsp;nbsp;jT� all places in the¹ torrid zone, the dura-tion of the twilight is leaji, becaufe the funs dailynbsp;motion is the moji perpendicular to the horizon. Innbsp;the frigid f zones, great eft �, becaufe the fun�s dailynbsp;motion is nearly parallel to the horizon -, and therefore he is the longer of getting 18 degrees below itnbsp;(till vohich time the twilight always continues.)nbsp;And in the j; temperate zones it is at a medium between the two, becaufe the obliquity of the fun'snbsp;daily motion is fo.

14. nbsp;nbsp;nbsp;In all places lying exaUly under the polarnbsp;circles, the fun, when he is in the neareft tropic,nbsp;continues 24 hours above the horizon without fet-iing; becaufe no part of that tropic is below theirnbsp;horizon. And when the fun is in the fartheftnbsp;tropic, he is for the fame length of time withoutnbsp;rijing ; becaufe no part of that tropic is above theirnbsp;horizon. But, at all other times of the year, henbsp;rifes and fets there, as in other places -, becaufe allnbsp;the circles that can be drawn parallel to the equator,nbsp;between the tropics, are more or lefs cut by thenbsp;horizon, as they are farther from, or nearer to,nbsp;that tropic which is all above the horizon: and

when the fun is not in either of the tropics, his diurnal courfe muft be in one or other of thefenbsp;circles.

15. nbsp;nbsp;nbsp;To all places in the northern hemifpheye,nbsp;from the equator to the polar circle, the longejl daynbsp;and JJoorteJl night is when the fun is in the northernnbsp;tropic �, and the Jhorteft day and longejl night isnbsp;when the fun is in the fouthern tropic ; becaufe nonbsp;circle of the fun's daily motion is Jo much above thenbsp;horizon, and Jo little below it, as the northern tropic ; and none fo little above it, and fo much belownbsp;it, as the fouthern. In the fouthern hemifphere,nbsp;the contrary.

16. nbsp;nbsp;nbsp;In all places between the polar circles andnbsp;poles, the fun appears for fame number of days {ornbsp;rather diurnal revolutions) without fetting; and atnbsp;the oppofite time of the year without rijing �, becaufenbsp;Jome part of the ecliptic never fets in the formernbsp;cafe, and as much of the oppofite part never rifes innbsp;the latter. And the nearer unto, or the more remote from the pole, thefe places are, the longer ornbsp;floor ter is the Juris continuing prefence or abfence.

ly. If a fhip fets out from any port, and fails round the earth eaftward to the fame port again,nbsp;let her take what time fhe will to do it in, thenbsp;people in that fhip, in reckoning their time, willnbsp;gain one complete day at their return, or count' onenbsp;day more than thofe who reftde at the fame port �,nbsp;becaufe, by going contrary to the fun's diurnal motion,nbsp;and being forwarder every evening than they werenbsp;in the morning, their horizon will get fo much thenbsp;fooner above the fetting fun, than if they had keptnbsp;for a whole day at any particular place. And thus,nbsp;by cutting off a part proportionable to their ownnbsp;motion, from the length of every day, they willnbsp;gain a complete day of that fort at their return;nbsp;without gaining one moment of abfolule time morenbsp;f-f 3nbsp;nbsp;nbsp;nbsp;then

than is elapfed during their courfe., to the people at the port. If they fail wejlward, they will reckon one day lefs than the people do who rejide atnbsp;the Jaid port, becaufe by gradually following thenbsp;apparent diurnal motion of the Jun, they will keepnbsp;him each particular day fo much longer above theirnbsp;horizon, as anfwers to that day's courfe j and bynbsp;that means, they cut off a whole^ day in reckoning.^nbsp;at their return, without lojing one moment of ab-folute time.

Hence, if two jhips Jhculd fet out at the fame time from any port, and fail round the glebe, onenbsp;eaftward and the other weftward, fo as to meet atnbsp;the fame port on any day whatever ; they will differnbsp;two days in reckoning their time, at their return.nbsp;If they fail twice round the earth, they will differnbsp;four days j if thrice, then fix, amp; c,

FT A V I N G done for the prefent with the si terreftrial globe, we fhall proceed to thenbsp;ufe of the celeftial i firft premifing, that as thenbsp;equator, elliptic, tropics, polar circles, horizon, and brafen meridian, are exadliy alike onnbsp;both globes, all the former problems concerning the fun are folved the fame way by bothnbsp;globes. The method alfo of redtifying thenbsp;celeftial globe is the fame as redtifying the ter-reftriai, viz. Elevate the pole according to thenbsp;latitude of your place, then ferew the quadrantnbsp;of altitude to the zenith, on the brafs meridiannbsp;bring the fun�s place in the ecliptic tq thenbsp;graduated edge of the brafs meridian, on the

� nbsp;nbsp;nbsp;......... pjde

fide which is above the fouth point of the wooden horizon, and fet the hour-index to thenbsp;uppermoft XII, which ftands for noon.

N. B. The fun�s place for any day of the year ftands diredly over that day on the horizon of the celeftial globe, as it does on that ofnbsp;the terreftrial.

The latitude and longitude of the ftars, and pf Latitu�t all other celeftial phenomena, are reckoned in a andnbsp;very different manner from the latitudenbsp;longitude of places on the earth : for all terref-''^nbsp;trial latitudes are reckoned from the equator �,nbsp;and longitudes from the meridian of fome remarkable place, as of London by the Britilh,nbsp;and of Paris by the French ; though moft ofnbsp;the French maps begin their longitude at the

nomers of all nations agree in reckoning the latitudes of the moon, ftars, planets, and comets,nbsp;from the ecliftic and their longitudes from thenbsp;* equino�iial colure, in that femicircle of it whiclinbsp;cuts the ecliptic at the beginning of Aries t ;nbsp;and thence eaftward, quite round, to the famenbsp;femicircle again. Confcquenlty thofe ftars whichnbsp;lie between the equinodial and the northernnbsp;half of the ecliptic, have north declination andnbsp;fouth latitude; thofe which lie between thenbsp;equinodial and the fouthern half of the ecliptic,nbsp;have fouth declination and north latitude j and

* The great circle that paffes through the equinoStial points at the beginning of cyinbsp;nbsp;nbsp;nbsp;through the poles of

the world (which are two oppofite points, each i go degrees from the ecuinoilial) is called the equinoSiial colure: and thenbsp;great aWehhat paffes through the beginning of gs andnbsp;and alfo through the poles of the ecliptic, and poles of thenbsp;world, is called the foljiitial colure.

all

all thofe which lie between the tropics and pole?, have their declinations and latitudes of the famenbsp;denomination.

There are fix great circles on the celeftial globe, which cut the ecliptic perpendicularly,nbsp;and meet in two oppofite points in the polarnbsp;circles-, which points are each ninety degreesnbsp;f'tom the ecliptic, and are called its poles.nbsp;Thefe polar points divide thofe circles into 12nbsp;femicircles which cut the ecliptic at the beginnings of the 12 figns. They refemble fo manynbsp;meridians on the terreftrial globe ; and as allnbsp;places which lie under any particular meridiannbsp;femicircle on that globe; have the fame longitude, io all thofe points of the heaven, throughnbsp;which any one of the above femicircles arenbsp;drawn, have the fame longitude.�f\.nd as thenbsp;greateft latitudes on the earth are at the northnbsp;and fouth poles of the earth, fo the greateft latitudes in the heaven, are at the north and fouthnbsp;poles of the ecliptic.

In order to diftinguifti the ftars, with regard to their fituations and pofuions in the heaven,nbsp;the ancients divided the whole vifjble firmamentnbsp;of ftars into particular fyftems, which they callednbsp;conftellations; and digefted them into the formsnbsp;of fuch animals as are delineated upon the celeftial globe. And thofe ftars which lie betweennbsp;the figures of thofe imaginary animals, andnbsp;could not be brought within the compafs of anynbsp;of them, were called unformed ftars.

Becaufe the moon and all the planets were obferved to move in circles or orbits which crofsnbsp;the ecliptic (or line of the fun�s path) at fmallnbsp;angles, and to be on the north fide of the ecliptic for one half of their courfe round the heaven of ftars, and on the fouth fide of it for the

other half, but never to go quite 8 degrees from it on either fide, the ancients diftinguifhed thatnbsp;fpace by twoleffer circles, parallel to the eclipticnbsp;(one on each fide) at 8 degrees diftance from it.

And the fpace included between the circles, they called the zodiac, becaufe moft of the 12nbsp;conftellations placed therein refemble fome livingnbsp;creature.�Thefe conftellations are, i. Aries lt;rnbsp;the ram 2. Taurus � , the bull �, 3. Gemini nnbsp;the twins; 4. Cancer 25, the crab ; 5. Leo SInbsp;the lion; 6. Virgo �jt, the virgin : 7. Libra ===nbsp;the balance ; 8 Scorpio ni, the fcorpion ; 9, Sanbsp;gittarius ^ , the archer-, 10. Capriccrnns thenbsp;goat-, II. Aqiiarius xs, the water bearer; andnbsp;12. Pifces X , the filhes.

It is to be obfervcd, that in the infancy of Remark aftronomy, thefe twelve conftellations flrood atnbsp;or near the places of the ecliptic, where thenbsp;above charafteriftics are marked upon the globe ;nbsp;but now, each conftellation has got a whole fignnbsp;forwarder, on account of the receffion of thenbsp;equinoflial points from their former places. Sonbsp;that the conftellation of Aries, is now in thenbsp;former place of Taurus-, that of Taurus, in thenbsp;former place of Gemini; and fo on.

The ftars appear of different magnitudes to the eye ; probably becaufe they are at differentnbsp;diftances from us. Thofe which appear bright-eft and largeft, are caWtd ftars of the firft magnitude ; the next to them in fize and luftre, arenbsp;called ftars of the fecond magnitude -, and fo onnbsp;to the fixth, which are the fmalleft that can benbsp;difcerned by the bare eye.

Some of the moft remarkable ftars have names given them, as Caftor aind Pollux in the heads ofnbsp;the Twins, Sirius in the mouth of the Greatnbsp;Dog, Procyon in the fide of the Little Dog, Rigel

Thefe things being premifed, which I think are all that the young �jro need be acquaintednbsp;with, before he begins to work any problem bynbsp;this globe, we {hall now proceed to the moftnbsp;ufeful of thofe problems; omitting fcveral whichnbsp;are of little or no confequence,

Bring the fun�s place in the ecliptic to the brafen meridian, then that degree in the equi-poftial which is cut by the meridian, is the fun�snbsp;right afcenfion and that degree of the meridiannbsp;which is over the fun�s place, is his declination.nbsp;Bring any fixed ftar to the meridian, and itsnbsp;right afcenfion will be cut by the meridian in thenbsp;equinodial; and the degree of the meridian thatnbsp;ftands over it, is its declination.

So that right afcenfion and declination, on the celeftial globe, are found in the fame mannernbsp;as longitude and latitude on the terreftrial.

� The degree of the equinodlial, reckoned from the beginning of Aries, that comes to the meridian with the fun or ftar, is its right afcenfion.

f The diltance of the fun or ftar in degrees from the equi-nodlial, towards either of the poles, north or fouth, is its declination, which is north or fouth accordingly.

PROBLEM II.

If the given ftar be on the north fide of the ecliptic, place the 90th degree of the quadrantnbsp;of altitude on the north pole of the ecliptic,nbsp;where the twelve femicircles meetj which divide the ecliptic into the 12 figns : but if thenbsp;ftar be on the fouth fide of the ecliptic, placenbsp;the 90th degree of the quadrant on the fouthnbsp;pole of the ecliptic ; keeping the 90th degree ofnbsp;the quadrant on the proper pole, turn the quadrant about, until its graduated edge cuts thenbsp;ftar : then, the number of degrees in the quadrant, between the ecliptic and the ftar, is itsnbsp;latitude ; and the degree of the ecliptic cut bynbsp;the quadrant is the ftar�s longitude, reckonednbsp;according to the fign in which the quadrantnbsp;then is.

To reprefent the face of the Jiarry firmament, as feen from any given place of the earth, at anynbsp;hour of the night.

Reftify the celeftial globe for the given latitude, the zenith, and fun�s place, in every re-ipeft, as taught by the 17th problem, for the terreftrial �, and turn it about, until the indexnbsp;points to the given hour: then, the upper he-mifphere of the globe will reprefent the vifiblenbsp;half of the heaven for fchat time; all the ftars

upon the globe being then in fuch fituations, as exa�tly correfpond to thofe in the heaven. Andnbsp;if the globe be placed duly north and fouth, bynbsp;means of a fmall fea-compafs, every ftar on thenbsp;globe will point toward the like ftar in the heaven : by which means, the conftellations andnbsp;remarkable ftars may be eafily known. Allnbsp;thofe ftars which are in the eaftern fide of thenbsp;horizon, are then rifing in the eaftern fide ofnbsp;the heaven; all in the weftern, are fetting innbsp;the weftern fide; and all thofe under the uppernbsp;part of the brafen meridian, between the fouthnbsp;point of the horizon and the north pole, are atnbsp;their greateft altitude, if the latitude of thenbsp;place be north : but if the latitude be fouth,nbsp;thofe ftars which lie under the upper part of thenbsp;meridian, between the north point of the horizon and the fouth pole, are at their greateftnbsp;altitude.

'The latitude of the place, and day of the month, being given -, to find the time when any knownnbsp;ftar will rife, or he on the meridian, or fet.

Having reftified the globe, turn it about until the given ftar comes to the eaftern fide of the horizon, and the index will ftiew the time ofnbsp;the ftar�s rifing; then turn the globe weftward,nbsp;and when the ftar comes to the brafen meridian,nbsp;the index will fhew the time of the ftar�s comingnbsp;to the meridian of your place; laftly, turn on,nbsp;until the ftar comes to the weftern fide of thenbsp;horizon, and the index will Ihew the time of thenbsp;ftar�s fetting.

N, B. In northern latitudes, thofe ftars which are lefs diftant from the north pole, than [thenbsp;quantity of its elevation above the north pointnbsp;of the horizon, never fct; and thofe which arenbsp;lefs diftant from the foutb pole, than the number of degrees by which it is deprefied belownbsp;the horizon, never rife ; and vice verjd in fouth-ern latitudes.

To find at what time of the year a given far will be upon the meridian^ at a given hour of thenbsp;night.

Bring the given ftar to the upper femicircle of the brafs meridian, and fet the index tonbsp;the given hour �, then turn the globe, until thenbsp;index points to XII at noon, and the upper femicircle of the meridian will then cut the fun�snbsp;place, anfwering to the day of the year foughtnbsp;which day may be eafily found againft the likenbsp;place of the fun among the figns on the woodennbsp;horizon.

The latitude., day of the month., and* azimuth of any known ftar being given ; to find the hour ofnbsp;the night.

Having reflified the globe for the latitude, zenith, and fun�s place j lay the quadrant of

* The number of degrees that the fun, moon, or any ftar, is from the meridian, either to the eaft or weft, is called its

altitude

altitude to the given degree of azimuth in the Horizon : then turn the globe on its axis, until the ftar comes to the graduated edge of the quadrant ; and when it does, the index will pointnbsp;out the hour of the night.

The latitude of the flace, the day of th� month, and altitude * of any known far, being given;nbsp;to find the hour of the night.

Reftify the globe as in the former problem,' guefs at the hour of the night, and turn thenbsp;globe until the index points at the fuppofednbsp;hour; then lay the graduated edge of the quadrant of altitude over the known ftar, and if thenbsp;degree of the ftar�s height in the quadrant uponnbsp;the globe, anfwers exaftly to the degree of thenbsp;ftar�s obferved altitude in the heaven, you havenbsp;guefled exaftly : but if the ftar on the globe isnbsp;higher or lower than it was obferved to be in thenbsp;heaven, turn the globe backwards or forwards,nbsp;keeping the edge of the quadrant upon the ftar,nbsp;until its center comes to the obferved altitude innbsp;the quadrant; and then, the index will fhew thenbsp;true time of the night.

* The number of degrees that the Sar is above the horizon, as obferved by means of a common quadrant, is called its altitude.

PRO.

An eajy method for finding the hour of the night by any two known flars, without knowing eithernbsp;their altitude or azimuth; and then, of findingnbsp;both their altitude and azimuth, and thereby thenbsp;true meridian.

Tie one end of a thread to a common muflcet bullet; and, having reftified the globe as above,nbsp;hold the other end of the thread in your hand,nbsp;and carry it flowly round betwixt your eye andnbsp;the ftarry heaven, until you find it cuts any twonbsp;known ftars at once. Then, guelTing at thenbsp;hour of the night, turn the globe until the indexnbsp;points to the time in the hour-circle; Vv'hichnbsp;done, lay the graduated edge of the quadrantnbsp;over any one of thefe two ftars on the globe,nbsp;which the thread cut in the heaven. If the faidnbsp;edge of the quadrant cuts the other ftar alfo, younbsp;have guefled the time exadlj; but if it doesnbsp;not, turn the globe llowly oackwards or fot-wards, until the quadrant (kept upon either ftar)nbsp;cuts them both through their centers: and then,nbsp;the index will point out the exadt time of thenbsp;night; the degree of the horizon, cut by thenbsp;quadrant, will be the true azimuth of both thefenbsp;ftars from the fouth; and the ftars themfelvesnbsp;will cut their true altitudes in the quadrant. Atnbsp;which moment, if a common azimuth compafsnbsp;be fo fet upon a floor or level pavement, thatnbsp;thefe ftars in the heaven may have the famenbsp;bearing upon it (allowing for the variation ofnbsp;the needle) as the quadrant of altitude h,as in thenbsp;wooden horizon of the globe, a thread extendednbsp;over the north and fouth points of that compafsnbsp;6nbsp;nbsp;nbsp;nbsp;will

will be direftly in the plane of the meridian : and if a line be drawn upon the floor or pavement, along the courfe of the thread, and an upright wire be placed in the fouthnioftend of thenbsp;line, the fliadow of the wire will fall upon thatnbsp;line, when the fun is on the meridian, and ftiinesnbsp;upon the pavement,

2quot;^ find the place of the moon., or of any planet �, and thereby to Jhew the time of its rifing, foiithingynbsp;and fetting.

Seek in Parker's or White's Ephenieris the * geocentric place of the moon or planet in thenbsp;ecliptic, for the given day of the month, and,nbsp;according to its longitude and latitude, as Ihewnnbsp;by the Ephemeris, mark the fame with a chalknbsp;Upon the globe. Then, having redtified thenbsp;globe, turn it round its axis wellward; and asnbsp;the faid mark comes to the eaftern fide of thenbsp;horizon, to the brafen meridian, and to thenbsp;weftern fide of the horizon, the index will fhewnbsp;at what time the planet rifes, comes to the meridian, and fets, in the fame manner as it wouldnbsp;do for a fixed ftar.

PROBLEM X.

In order to do this, we mufl: premife the following things. I. That as the fun goes only

� The place of the moon or planet, as feen from the earth, is called its geocentric place.

once a year round the ecliptic, he can be but once a year in any particular point of it: andnbsp;that his motion is almoft a degree every 24nbsp;hours, at a mean rate. 2. That as the moonnbsp;goes round the ecliptic once in 27 days and 8nbsp;hours, Ihe advances 13 J degrees in it, everynbsp;day at a mean rate. 3. That as the fun goesnbsp;through part of the ecliptic in the time thenbsp;moon goes round it, the moon cannot at anytimenbsp;be either in conjunction with the fun, or oppofitenbsp;to him, in that part of the ecliptic where Ihe wasnbsp;fo the laft time before but muft travel asnbsp;much forwarder, as the fun has advanced in thenbsp;faid time : which being 294 days, makes almotl;nbsp;a whole fign. Therefore, 4. The moon can benbsp;but once a year oppofite to the fun, in anynbsp;particular part of the ecliptic. 5. That thenbsp;moon is never full but when Ihe is oppofite tonbsp;the fun, becaufe at no other time can we fee allnbsp;that half of her, which the fun enlightens. 6. Thatnbsp;when any point of the ecliptic rifes, the oppofitenbsp;point fets. Therefore, when the moon is oppofite to the fun, (he muft rife at * fun fet. 7. Thatnbsp;the different figns of the ecliptic rife at very different angles or degrees of obliquity with thenbsp;horizon, efpecially in confiderable latitudes ; andnbsp;that the fmaller this angle is, the greater is thenbsp;portion of the ecliptic that rifes in any fmaJl partnbsp;of time ; and vice verfd. 8. That, in northernnbsp;latitudes, no part of the ecliptic rifes at fo fmallnbsp;an angle with the horizon, as Pifees and juries do,nbsp;therefore, a greater portion of the ecliptic rifes in

� This is not always ftridlly true, becaufe the moon does not keep in the ecliptic, but crolTes it twice every month.nbsp;However, the difference need not be regarded in a generalnbsp;explanation of the caufe of the harveft moon,

X nbsp;nbsp;nbsp;�ne

One hour, about thefe figns, tha-n about any �f the reft. g. That the moon can never be fullnbsp;in Pifces and Arks but in our autumnal months,nbsp;for at no other time of the year is the fun in-thenbsp;oppofite figns Virgo and Libra.

'fhefe things premifed, take 15-j degrees of the ecliptic in your compaffes, and beginning atnbsp;Pifces, carry that extent all round the ecliptic,nbsp;marking the places v/ith a chalk, where thenbsp;points of the compaffes fucceffively fail. Sonbsp;you will have the moon�s daily motion markednbsp;out for one complete revolution in the eclipticnbsp;(according to � 2 of the laft paragraph.)

Reflify the globe for any confiderable northern latitude, (as fuppofe that of London) and then,nbsp;turning the globe round its axis, obferve hownbsp;much of the hour circle the index has gone over,nbsp;at the rifing of each particular mark on thenbsp;ecliptic ; and you will find that feven of thenbsp;marks (which take in as much of the ecliptic asnbsp;the moon goes through in a week) will all rifenbsp;fucceffively about Pifces and Aries in the timenbsp;that the index goes over two hours. Therefore,nbsp;whilft the moon is in Pifces and Aries, Ihe will notnbsp;differ in general above two hours in her rifingnbsp;for a whole week. But if you take notice ofnbsp;the marks on the oppofite figns, and Libra^nbsp;you will find that feven of them take nine hoursnbsp;to rife; which fliews, that when the moon is innbsp;thefe two figns, (he differs nine hours in hernbsp;rifing within the compafs of a week. And fonbsp;much later as every mark is of rifing than thenbsp;one that rofe next before it, fo much later willnbsp;the moon be of rifing on any day than fhe was onnbsp;the day before, in the correfponding part of thenbsp;heaven. 1'he marks about Cancer and Capricorn

Now, although the moon is in Pifcss and Aries every month, and therefore mult rife in thofenbsp;figns within the fpace of two hours later for anbsp;whole week, dr only about 17 minutes laternbsp;every day then fhe did on the former-, yet Ihenbsp;is never full in thefe figns, but in our autumnalnbsp;months, Auguji and September., when the fun is innbsp;Virgo and Libra. Therefore, no full moon innbsp;the year will continue to rife fo near the time ofnbsp;fun fet for a week or fo, as thefe two full moonsnbsp;do, which fall in the time of harveft.

In the winter months, the moon is in Pifces and Aries about her firft quarter and as thefenbsp;figns rife about noon in winter, the moon�s rif-ing in them paffes unobferved. In the fpringnbsp;months, the moon changes in thefe figns, andnbsp;confequetitly rifes at the fame time with the fun jnbsp;fo that it is impoffible to fee her at that time.nbsp;In the fummer months fhe is in thefe figns aboutnbsp;her third quarter, and rifes not until mid-night,nbsp;when her riling is but very little taken noticenbsp;of; efpecially as flie is on the decreafe. But innbsp;the harveft months fhe is at the full, when innbsp;thefe figns, and being oppofite to the fun, fhenbsp;rifes when the fun fets (or foon after) and fhinesnbsp;all the night.

In fouthern latitudes, Virgo and Libra rife at as fmall angles with the horizon, as Pifces and Ariesnbsp;do in the northern ; and as our fpring is at thenbsp;time of their harveft, it is plain their harveft fullnbsp;moons muft be in Virgo znd Libra-, and willnbsp;therefore rife with as little difference of timfe, asnbsp;o.urs do in Pifces and Aries.

For a fuller account of this matter, I muff refer the reader to my Aftronomy, in whkh it is

PROBLEM XL

^0 explain the eq^uation of time, or difference of time ietmeen 'well regulated clocks and true fun-dials.

Tho earth�s motion on its axis being perfedly equable, and thereby caufing an apparentnbsp;equable motion of the ftarry heaven round thenbsp;fame axis, produced to the poles of the heaven ;nbsp;it is plain that equal portions of the celeftianbsp;equator pafs over the meridian in equal parts ofnbsp;time, becaufe the axis of the world is perpendicular to the plane of the equator. And therefore, if the fun kept his annual courfe in thenbsp;celeftial equator, he would always revolve fromnbsp;the meridian to the meridian again in 24 hoursnbsp;cxadlly, as fhewn by a well-regulated clock.

But as the fun moves in the ecliptic, which is oblique both to the plane of the equator and axisnbsp;of the world, he cannot always revolve from thenbsp;meridian to tlie meridian again in 24 equalnbsp;hours but ibmetitnes a little fooner, and atnbsp;other times a little latter, becaufe equal portionsnbsp;of the ecliptic pals over the meridian in unequalnbsp;parts of time on account of its obliquity. Andnbsp;this difference is th� fame in all latitudes.

To fliew this by a globe, make chalk-marks all round the equator and ecliptic, at equalnbsp;diffances from one another (fuppofe 10 degrees)nbsp;beginning at Aries or at Libra, where thefe twonbsp;circles interfefl each other. Then turn the

globe round its axis, and you will fee that all the marks in the firft quadrant of the ecliptic, ornbsp;from the beginning o� Aries to the beginning ofnbsp;Cancer^ come fooner to the bralen meridian thannbsp;their correfponding marks do on the equator;nbsp;thofe in the fecond qviadrant, or from the beginning of Cancer to the beginning of Libra^nbsp;come later: thofe in the third quadrant, fromnbsp;Libra to Capricorn^ fooner; and thofe in thenbsp;fourth, from Capricorn to Aries, later. But thofenbsp;at the beginning of each quadrant come to thenbsp;meridian at the fame time with their correfpond-ing marks on the equator.

Therefore, whilft the fun is in the firft and third quadrants of the ecliptic, he comes foonernbsp;to the meridian every day than he would do ifnbsp;he kept in the equator; and confequently he isnbsp;fafter than a well regulated clock, which alwaysnbsp;keeps equable or equatorial time ; and whilft henbsp;is in the fecond and fourth quadrants, he comesnbsp;latter to the meridian every day than he wouldnbsp;do if he kept in the equator ; and is thereforenbsp;flower than the clock. But at the beginning ofnbsp;�each quadrant, the fun and clock are equal.

And thus, if the fun moved equably in the ecliptic, he would be equal with the clock onnbsp;four days of the year, which would have equalnbsp;intervals of time between them. But as henbsp;moves fafter at fome times than at others (beingnbsp;eight days longer in the northern half of thenbsp;ecliptic than in the fouthern) this will catife anbsp;fecond inequality; which combined with thenbsp;former, arifing from the obliquity of the eclipticnbsp;to the equator, makes up that difference, whichnbsp;is flaewn by the common equation tables to benbsp;between good clocks and true fun-dials.

Whoever has feen a common armillary fphere^ and iinderftands how to ufe it, muft be fenfiblenbsp;that the machine here referred to, is of a verynbsp;different, and much more advantageous con-ftruftion. And thofe who have feen the curiousnbsp;glafs fphere invented by Dr. Long, or the figurenbsp;of it in his Aftronomy, muft knov/ that the furniture of the terreftrial globe in this machine,nbsp;the form of the pedeftal, and the manner ofnbsp;turning either the earthly globe or the circlesnbsp;which furround it, are. all copied from thenbsp;Doflor�s glafs fphere -, and that the only difference is, a parcel of rings inftead of a.glafs celef-tial globe; and all the additions are a moonnbsp;within the fphere, and a femicircle upon thenbsp;pedeftal.

The exterior parts of this machine are a corn-pages of brafs rings, which reprefent the principaal circles of the heaven, viz. i. The equinodtial A A, which is divided into 360 degrees, (beginning at its interfedlion with the ecliptic in /iries)nbsp;for (hewing the fun�s right alcenfion in degrees;nbsp;and aifo into 24 hours, for (hewing his rightnbsp;afcenfion in time. 2. The ecliptic B B, which isnbsp;divided into j2 figns, and each fign into 30 degrees, and alfo into the months and days of thenbsp;year ; in fuch a manner, that the degree or pointnbsp;of the ecliptic in which the fun is, on any givennbsp;day, ftands over that day in the circle of months,nbsp;3. The tropic of Cancer C C, touching the eclip-tic at the beginning of Cancer in e, and thenbsp;tropic of Capricorn D D, touching the ecliptic atnbsp;phpbeginning of Capricornm �; each 23t degrees

from the equinoftial circle. 4. The arctic circle �, and the antarftic circle F, each degreesnbsp;from its refpeflive pole at N and lt;S.nbsp;nbsp;nbsp;nbsp;5. The

equinoflrial colure G G, paffing through the north and fouth poles of the heaven at N and 5,nbsp;and through the equinoctial points Aries, andnbsp;Libra in the ecliptic. 6. The folftitial colurenbsp;H H, paffing through the poles of the heaven, andnbsp;through the folftitial points Cancer and Capricorn,nbsp;in the ecliptic. Each quarter of the former ofnbsp;thefe colures is divided into 90 degrees, from thenbsp;equinoctial to the poles of the world, for Ihew-ing the declination of the fun, moon, and ftars;nbsp;and each quarter of the latter, from the eclipticnbsp;at e and �, to its poles b and d, for fliewing thenbsp;latitude of the ftars.

In the north pole of the ecliptic is a nut b, to which is fixed one end of a quadrantal wire, andnbsp;to the other end a fmall fun T, which is carriednbsp;round the ecliptic 5 B, by turning the nut: andnbsp;in the fouth-pole of the ecliptic is a pin at d, onnbsp;which is another quadrantal wire, with a fmallnbsp;moon Z upon it, which may be moved round bynbsp;hand : but there is a particular contrivance fornbsp;caufins: the moon to move in an orbit whichnbsp;crolTes the ecliptic at an angle of 5-^ degrees, innbsp;two oppofite points called the moords nodes; andnbsp;alfo for ffiifting thefe points backward in thenbsp;ecliptic, as the moon's nodes Ihift in the heaven.

Within thefe circular rings is a fmall terref-trial globe I, fixt on an axis K K, which extends from the north and fouth poles of the globe at nnbsp;and s, to thofe of the celeftial fphere at Id and S.nbsp;On this axis is fixt the flat celeftial meridian L L,nbsp;which may be fet diredly over the meridian ofnbsp;sny place on the globe, and then turned roundnbsp;with the globe, fo as to keep over the famenbsp;X 4nbsp;nbsp;nbsp;nbsp;meridian

meridian upon it. This fiat meridian dilated the fame way as the brafs meridiarT ofnbsp;a common globe, and its ufe is much the fame.nbsp;To this globe is fitted the moveable horizonnbsp;M M, fo as to turn upon two ftrong wires proceeding from its ealt and weft points to thenbsp;globe, and entering the globe at oppofite pointsnbsp;of its equator, which is a moveable brafs ring letnbsp;into the globe in a groove all around its equator.nbsp;The globe may be turned by hand within thisnbsp;ring, fo as to place any given meridian upon it,nbsp;direftly under the celeftial meridian L L. Thenbsp;horizon is divided into 360 degrees all aroundnbsp;its outermoft edge, within which are the pointsnbsp;of the compafs, for ftiewing the amplitude ofnbsp;the fun and moon, both in degrees and points.nbsp;The celeftial meridian L L pafles through twonbsp;notches in the north and fouth points of thenbsp;horizon, as in a common globe : but here, ifnbsp;the globe be turned round, the horizon andnbsp;meridian turn with it. At the fouth pole of thenbsp;fphere is a circle of 24 hours, fixt to the rings,nbsp;and on the axis is an index which goes roundnbsp;that circle, if the globe be turned round itsnbsp;axis.

' The whole fabric is fupported on a pedeftal N, and may be elevated or deprefifed upon thenbsp;joint O, to any number of degrees from o to 90,nbsp;by means of the arc P, which is fixed in thenbsp;ftrong brafs arm and Aides in the uprightnbsp;piece R, in which is a fcrew at r, to fix it at anynbsp;proper elevation.

In the box 'T are two wheels (as in Dr. Long�s fphere) and two pinions, whofe axes come outnbsp;at V and U �, either of which may be turned bynbsp;the imall winch W. When the winch is putnbsp;upon the axis P, and turned backward, the ter-

reftrial globe, with its horizon and celeftial meridian, keep at reft ; and the whole fphere of circles turns round from eaft, by fouth, to weft,nbsp;carrying the fun T, and moonZ, round the famenbsp;way, and caiiGng them to rife above and fet below the horizon. But when the winch is putnbsp;upon the axis U, and turned forward, the fpherenbsp;with the fun and moon keep at reft; and thenbsp;earth, with its horizon and meridian, turn roundnbsp;from weft, by fouth, to eaft ; and bring the famenbsp;points of the horizon to the fun and moon, tonbsp;which thefe bodies came when the earth kept atnbsp;reft, and they were carried round it; fhewingnbsp;that they rife and fet in the fame points of thenbsp;horizon, and at the fame time in the hour-circle,nbsp;whether the motion be in the earth or in thenbsp;heaven. If the earthly globe be turned, thenbsp;hour-index goes round its hour-circle; but ifnbsp;the fphere be turned, the hour-circle goes roundnbsp;below the index-

And fo, by this conftruffion, the machine is equally fitted to fhew either the real motion ofnbsp;the earth, or the apparent motion of the heaven.

To redlify the fphere for ufe, firft flacken the ferew r in the upright ftem and taking holdnbsp;of the arm move it up or down until thenbsp;given degree of latitude for any place be at thenbsp;fide of the ftem R ; and then the axis of thenbsp;fphere will be properly elevated, fo as to ftandnbsp;parallel to the axis of the world, if the machinenbsp;be fet north and fouth by a fmail compafs : thisnbsp;done, count the latitude from the north-pole,nbsp;upon the celeftial meridian L L, down towardsnbsp;the north notch of the horizon, and fet the horizon to that latitude; then, turn the nut b untilnbsp;the fun T comes to the given day of the year in

the ecliptic, and the fun will be at its proper place for that day : find the place of the moon�snbsp;afcending node, and alfo the place of tlae moon,nbsp;by an Ephemeris, and fet them right accordingly : laftiy, turn the winch IV, until either thenbsp;fun comes to the meridian L L, or until the meridian comes to the fun (according as you wantnbsp;the fphere or earth to move) and fet the hour-index to the XII, marked noon, and the whole

winch, and obferve when the fun or moon rife and fet in the horizon, and the hour-index willnbsp;fiiew the times thereof for the given day.

As thofe who underftand the ufe of the globes will be at no lofs to work many other problemsnbsp;by this fphere, it is needlefs to enlarge an^nbsp;farther upon it.

of a wire, or of the upper edge of a plate ftile, eredled perpendicularly on the plane of the dial,nbsp;may ftiew the true time of the day.

The edge of the plate by which the time of the day is found, is called the ftile of the dial,nbsp;which miift be parallel to the earth�s axis �, andnbsp;the line on which the faid plate is eredted, isnbsp;called the fubftile.

The angle included between the fubftile and ftile, is called the elevation, or height of thenbsp;ftile.

Thofe dials whofe planes are parallel to the plane of the horizon, are called horizontal dials;

and thofe dials whofe planes are perpendicular to the plane of the horizon, are called vertical,nbsp;or ereft dials.

Thofe erect dials, whofe planes direftly front the north or fouth, are called direft north ornbsp;fouth dials; and all other ere6l dials are callednbsp;decliners, becaufe their planes are turned awaynbsp;from the north or fouth.

Thofe dials whofe planes are neither parallel nor perpendicular to the plane of the horizon,nbsp;are called inclining, or reclining dials, according as their planes make acute or obtufe anglesnbsp;with the horizon ; and if their planes are alfonbsp;turned afide from facing the fouth or north,nbsp;they are called declining-inclining, or declining-reclining dials.

The interfedlion of the plane of the dial, with that of the meridian, palling through the ftile,nbsp;is called the meridian of the dial, or the hour-line of XII.

Thofe meridians, whofe planes pafs through the ftile, and make angles of 15, 30, 45, 60,nbsp;75, and 90 degrees with the meridian of thenbsp;place (which marks the hour-line of XII) arenbsp;called hour-circles; and their interfedions withnbsp;the plane of the dial, are called hour-lines.

In all declining dials, the fubftile makes an angle with the hour-line of X'll ; and this anglenbsp;is called the diftance of the fubftile from thenbsp;meridian.

The declining plane�s difference of longitude, is the angle formed at the interfedtion of thenbsp;ftile and plane of the dial, by two meridians;nbsp;one of which paffes through the hour-line of XII,nbsp;and the other through the fubftile.

This much being premifed concerning dials in general, we fhall now proceed to explain the different methods of their conftrubiion.

If the whole earth a P c p were tranfparenr, and hollow, like a fphere of glafs, and had itsnbsp;equator divided into 24 equal parts by fo manynbsp;meridian femicircles, a, h, c, d, e, f g, amp;c. onenbsp;of which is the geographical meridian of anynbsp;given place, as London (which is fuppofed tonbsp;be at the point a-,) and if the hours of XIInbsp;were marked at the equator, both upon thatnbsp;meridian and the oppofite one, and all the reftnbsp;of the hours in order on the reft of the meridians, thofe meridians would be the hour-circlesnbsp;of London : then, if the fphere had an opakenbsp;axis, as P E p, terminating in the poles P andnbsp;p, the ftiadow of the axis would fall upon everynbsp;particular meridian and hour, when the funnbsp;came to the plane of the oppofite meridian, andnbsp;would confequently fhew the time at London,nbsp;and at all other places on the meridian ofnbsp;London.

If this fphere was cut through the middle by a folid plane ABCD, in the rational horizon ofnbsp;London, one half of the axis E P would benbsp;above the plane, and the other half below it;nbsp;and if ftraight lines were drawn from the centernbsp;of the plane, to thofe points where its circum-fefence is cut by the hour-circles of the fphere,nbsp;thofe lines would be the hour-lines of a horizontal dial for London : for the fhadow of thenbsp;axis would fall upon each particular hour-linenbsp;of the dial, when it fell upon the like hour-circlenbsp;of the fphere.

If the plane which cuts the fphere be upright, as AFCG, touching the given place (London)nbsp;at and direiftly facing the meridian of London ,

don, it will then become the plane of an erect direft fouth dial: and if right lines be drawn Vertkatnbsp;from its center �, to thofe points of its circura-lt;^/�/.nbsp;ference where the hour-circles of the fphere cutnbsp;it, thefe will be the hour lines of a vertical ornbsp;diredt fouth dial for London, to which the hoursnbsp;are to be fet as in the figure (contrary to thofenbsp;on a horizontal dial) and the lower half E p oinbsp;the axis will call a lhadow on the hour of thenbsp;day in this dial, at the fame time that it wouldnbsp;fall upon the like hour-circle of the fphere, ifnbsp;the dial-plane was not in the way.

If the plane (ftill facing the meridian) inclining made to incline, or recline, by any given number and re-of degrees, the hour-circles of the fphere wiU''^(quot;'quot;.Snbsp;ftill cut the edge of the plane in thofe points tonbsp;which the hour-lines mud be drawn ftraightnbsp;from the center �, and the axis of the fphere willnbsp;caft a Ihadow on thefe lines at the refpedlivenbsp;hours. The like will ftill hold, if the plane benbsp;made to decline by any given number of degrees dials. ^nbsp;from the meridian, towards the eaft or weft:nbsp;provided the declination be lefs than 90 degrees^nbsp;or the reclination be lefs than the co-latitudenbsp;of the place: and the axis of the fphere will benbsp;a gnomon, or ftile, for the dial. But it cannotnbsp;be a gnomon, when the declination is quite 90nbsp;degrees, nor when the reclination is equal tonbsp;the co-latitude; becaufe in thefe two cafes,nbsp;the axis has no elevation above the plane of thenbsp;dial.

And thus it appears, that the plane of every dial reprefents the plane of fome great circlenbsp;upon the earth; and the gnomon the earth�snbsp;axis, whether it be a fmall wire, as in the abovenbsp;figures, or the edge of a thin plate, as in thenbsp;common horizontal dials.

The whole earth, as to its bulk, is but si point, if compared to its diftance from the fun ;nbsp;and therefore, if a fmall fphere of glafs be placednbsp;upon any part of the earth�s furfacCj fo thatnbsp;its axis be parallel to the axis of the earth, andnbsp;the fphere have fuch lines upon it, and fuchnbsp;planes within it, as above defcribed; it willnbsp;ihew the hours of the day as truly as if it werenbsp;placed at the earth�s center, and the Ihell of thenbsp;earth were as tranfparent as glafs.

Fig. 2, 3. But becaufe it is impolTible to have a hollow fphere of glafs perfeftly true, blown round anbsp;folid plane; or if it was, we could not get atnbsp;the plane within the glafs to fet it in any givennbsp;pofirion; we make ule of a wire-fphere to explain the principles of dialing, by joining 24nbsp;femicircles together at the poles, and putting anbsp;thin flat plate of brafs within it.

A common globe, of 12 inches diameter, has generally 24 meridian femicircles drawn uponnbsp;it. If fuch a globe be elevated to the latitude ofnbsp;any given place, and turned about until any onenbsp;of thefe meridians cuts the horizon in the northnbsp;point, where the hour of Xll is fuppofed tonbsp;be marked, the reft of the meridians will cutnbsp;the horizon at the refpeftive diftances of all thenbsp;other hours from XII. Then, if thefe points ofnbsp;diftance be marked on the horizon, and thenbsp;globe be taken out of the horizon, and a flatnbsp;board or plate be put into its place, even withnbsp;the furface of the horizon ; and if ftralght linesnbsp;be drawn from the center of the board, to thofenbsp;points of diftance on the horizon which werenbsp;cut by the 24 meridian femicircles, thefe linesnbsp;will be the hour-lines of a horizontal dial fornbsp;that latitude, the edge of whofe gnomon muftnbsp;be in the very fame fituation that the axis of the

globe was, before it was taken out of the horizon ; that is, the gnomon muft make an angle with the plane of the dial, equal to the latitudenbsp;of the place for which the dial is made.

If the pole of the globe be elevated to the * co-latitude of the given place, and any meridian be brought to the north point of the horizon, the reft of the meridians will cut the horizonnbsp;in the refpeflive diftances of all the hours fromnbsp;XII, for a direift fouth dial, whofe gnomon muft:nbsp;make an angle with the plane of the dial, equalnbsp;to the co-latitude of the place ; and the hoursnbsp;muft be fet the contrary way on this dial, tonbsp;what they are on the horizontal.

But if your globe have more than 24 meridian femicircles upon it, you muft take the following method for making horizontal andnbsp;fouth dials hy it.

Elevate the pole to the latitude of your place. To con-and turn the globe until any particular meridian � (fuppofe the firft) comes to the north point 01nbsp;the horizon and the oppofite meridian will cutnbsp;the horizon in the fouth. Then, fet the hour-index to theuppermoft XII on its circle ; whichnbsp;done, turn the globe weftward until 15 degreesnbsp;�f the equator pafs under the brafen meridian,nbsp;and then the hour-index will be at I, (for the funnbsp;moves 15 degrees every hour) and the firft meridian will cut the horizon in the number of degrees from the north point, that I is diftant fromnbsp;XII. Turn on, until other 15 degrees of thenbsp;equator pafs under the brafen meridian, and thenbsp;hour-index will then be at II, and the firft me-

� If the latitude be fubtra�ed from 90 degrees, the remainder is called the co-latitude, or complement of the latitude.

Of Didlin^i

ridiah vvill cut the horizon in the number of degrees that II is diftant from XII: and fo, bynbsp;making 15 degrees of the equator pafs undernbsp;the brafen meridian for every hour, the firft ttie-ridian of the globe will cut the horizon in thenbsp;diftances of all the hours from Xll to VI, whichnbsp;is juft go degrees -, and then you need go nonbsp;farther, for the diftances of XI, X, IX, VIII,nbsp;VII, and VI, in the forenoon, are the famenbsp;from XII, as the diftances of I, II, III, IV, V,nbsp;and VI, in the afternoon ; and thefe hour-linesnbsp;continued through the center, will give thenbsp;oppofite hour-lines on the other half of the dial:nbsp;but no more of thefe lines need be drawn, thannbsp;what anfwer to the fun�s continuance above thenbsp;horizon of your place on the longcftday, whichnbsp;may be eaiiiy found by the 26th problem of the

Thus, to make a horizontal dial for the latitude of London, which is 5 if degrees north, elevate the north pole of the globe 5 if degreesnbsp;above the north point of the horizon, and thennbsp;turn the globe, until the firft meridian (whichnbsp;is that of London on the Englilh terreftrialnbsp;globe) cuts the north point of the horizon, andnbsp;let the hour-index to XII at noon.

Then, turning the globe weftward until the index points fucceffively to I, II, III, IV, V,nbsp;and VI, in the afternoon; or until 15, 30, 45,nbsp;60, 75, and 90 degrees of the equator pafs undernbsp;the brafen meridian, you will find that the firftnbsp;meridian of the globe cuts the horizon in the

towards the eaft, viz. iif- 24?, 3871 53L 71 i'j, and go ; which are the refpeftive diftancesnbsp;of the above hours from XII upon the plane ofnbsp;the horizon.

To transfer thefe, and the reft of the hours, PlateXXl. to a horizontal plane, draw the parallel right f^�2* i*nbsp;lines a c and b d upon that plane, as far fromnbsp;each ocher as is equal to the intended thicknefsnbsp;of the'gnomon or ftile of the dial, and the fpacenbsp;included between them will be the meridiannbsp;or twelve o�clock line on the dial. Crofs thisnbsp;meridian at right angles with the fix o�clock linenbsp;ghy and fetting one foot of your compafies in thenbsp;interfedion a, as a center, deferibe the quadrantnbsp;g e with any convenient radius or opening of thenbsp;compafies: then, fetting one foot in the inter-fedion b^ as a center, with the fame radius deferibe the quadrant � b, and divide each quadrant into 90 equal parts or degrees, as in thenbsp;figure.

Becaufe the hour-lines are lefs diftant from each other about noon, than in any other part ofnbsp;the dial, it is beft to have the centers of thefenbsp;quadrants at a little diftance from the center ofnbsp;th� dial-plane, on the fide oppofite to XII, innbsp;order to enlarge the hour-diftances thereaboutnbsp;under the fame angles on the plane. Thus, thenbsp;center of the plane is at C, but the centers of thenbsp;quadrants at a and b.

Lay a ruler over the jioint b (and keeping it there for the center of all the afternoon hours innbsp;the quadrant f h) draw the hour-line of I,nbsp;through ri^ degrees in the quadrant; the hourline of II, through 24-^degrees; of III, throughnbsp;38-rV degrees; Iin, through 534-5 and V throughnbsp;7i~� becaufe the fun rifes about four in'nbsp;the morning, on the fongeft days at London,nbsp;continue the hour-fines of IIII and V, in thenbsp;afternoon, through the center b to the oppofitenbsp;fide of the dial.�This done, lay the ruler to thenbsp;center 0, of the quadrant e and through the

y � nbsp;nbsp;nbsp;like

like divifions or degrees of that quadrant, viz. ii4gt; 247,nbsp;nbsp;nbsp;nbsp;53i, and 7I^Vgt; draw the fore

noon hour-lines of XI, X, IX, VIII, and Vil �, and becaufe the fun fets net before eight in thenbsp;evening on the longeft days, continue the bourses of Vll.and VIII in theforenoon, through thenbsp;center a, to VII and VIII in the afternoon; andnbsp;all the hour-lines will be finifhed on this dial �,nbsp;to which the hours may be f. t, as in the figure.

Laftly, through 517 degrees of either quadrant, and from its center, draw the right line ag for the hypothenufe or axis of the gnomon agi-,nbsp;and from g, let fall the perpendicular^ i, uponnbsp;the meridian line 0/, and there will be a trianglenbsp;made, whofe fxdes are a g, g i, and i a. If anbsp;plate fimilar to this triangle be made as thick asnbsp;the diftance between the lines a c and b d, and fetnbsp;upright between them, touching at a and itsnbsp;hypothenufe ag wi;l be parallel to the axis of thenbsp;world, when the dial is truly fet-, and will caft anbsp;Ihadow on the hour of the day. ,

N. B. The trouble of dividing the two quadrants may be faved, if you have a fcale with a line of chords upon it, fuch as that on the rightnbsp;hand of the plate : for if you extend the com-paffesfrom o to 60 degrees of the line of chords,nbsp;and with that extent, as a radius, delcribe thenbsp;two quadrants upon their refpedtive centers, thenbsp;above diftances may be taken with the com-paffes upon the line, and fet off upon the quadrants.

�To make an ereSi direbl fouth dial. Elevate the pole to the CO-latitude of your place, and pro-ftrua an egej in all refpefts as above taught for the hori-2ontal dial, from VI in the morning to VI innbsp;� the afternoon, only the hours muft be reverfed,nbsp;as in the figure j and the hypothenufe ag-, of the

gnomon agf mnft make an angle with the dial-plane equal to the co-latitude of the place. As the fun can ftiine no longer on this dial, thannbsp;from fix in the morning until fix in the evening, 'nbsp;there is no occafion for having any more thannbsp;twelve hours upon it.

To make an ere�l dial, declining from the fouth To con-towards the eajl or weft. Elevate the pole to the ft^ua an latitude of your place, and fcrew the quadrantnbsp;altitude to the zenith. Then, if your dial de-dines towards the eaft (which we lhall fuppofenbsp;it to do at prefent) count in the horizon thenbsp;degrees of declination, from the eaft point towards the north, and bring the lower end of thenbsp;quadrant to that degree of declination at whichnbsp;the reckoning ends. This done, bring any particular meridian of your globe (as fuppofe thenbsp;firft meridian) diredliy under the graduated edgenbsp;of the upper part of the brafen meridian, andnbsp;fet the hour-index to XII at noon. Then, keeping the quadrant of altitude at the degree ofnbsp;declination in the horizon, turn the globe eaft-ward on its axis, and obferve the degrees cut bynbsp;the firft meridian in the quadrant of altitudenbsp;(counted from the zenith) as the hour-indexnbsp;comes to XI, X, IX, amp;:c. in the forenoon, or asnbsp;15, 30, 45, amp;c, degrees of the equator pafs undernbsp;the brafen meridian at thefe hours reipeflively;nbsp;and the degrees then cut in the qnadrant by thenbsp;firft meridian, are the refpeftive diftances of thenbsp;forenoon hours from XII on the plane of thenbsp;dial.�Then, for the afternoon hours, turn thenbsp;quadrant of altitude round the zenith until itnbsp;comes to the degree in the horizon, oppofite tpnbsp;that where it was placed before; namely, as farnbsp;from the weft point of the horizon towards thenbsp;fputh, as it was fet at fifft from the eaft point to-Y 2nbsp;nbsp;nbsp;nbsp;wards

wards the north ; and turn the globe weftward on its axis, until the firft meridian comes to thenbsp;brafen meridian again, and the hour-index tonbsp;XII : then, continue to turn the globe weft-ward, and as the index points to the afternoonnbsp;hours I, II, III, amp;c. or as 15, 30, 45i degrees of the equator pafs under the brafen meridian, the firft meridian will cut the quadrant ofnbsp;altitude in the refpedive number of degreesnbsp;from the zenith, that each of thefe hours is fromnbsp;XII on the dial.�And note, that when the firftnbsp;meridian goes off the quadrant at the horizon, innbsp;the forenoon, the hour-index Ihews the timenbsp;when the fun will come upon this dial: andnbsp;when it goes off the quadrant in the afternoon,nbsp;the index will point to the time when the funnbsp;goes oft the dial.

Having thus found all the hour-diftances from XII, lay them down upon your dial-plate, eithernbsp;by dividing a femicircle into two quadrants ofnbsp;90 degrees each (beginning at the hour-line ofnbsp;XII) or by the line of chords, as above direfted.

In all declining dials, the line on which the ftile or gnomon Hands (commonly called thenbsp;juhJt'ik-Une) makes an angle with the twelvenbsp;o�clock line, and falls among the forenoon hour-Mnes, if the dial declines towards the eaft; andnbsp;among the afternoon hour-lines, when the dial declines towards the weft; that is, to the left handnbsp;from the twelve o�clock line in the former cafe,nbsp;and to the right hand from it in the latter.

To find the diftance of the fubftile from the twelve o�clock line ; if your dial declines fromnbsp;the foufh towards the eaft, count the degreesnbsp;of that declination in the horizon from the eaftnbsp;point toward the north, and bring the lower endnbsp;of the quadrant of altitude to that degree of

declination where the reckoning ends: then, turn the globe until the firft meridian cuts thenbsp;horizon in the like number of degrees, countednbsp;from the fouth point toward the eaft; and thenbsp;quadrant and firft meridian will then crofs onenbsp;another at right angles, and the number of degrees of the quadrant, which are interceptednbsp;between the firft meridian and the zenith, isnbsp;equal to the diftance of the fubftile line from thenbsp;twelve o�clock line ; and the number of degreesnbsp;of the firft meridian, which are intercepted between the quadrant and the north pole, is equalnbsp;to the elevation of the ftile above the plane ofnbsp;the dial.

If the dial declines weftward from the fouth, count that declination from the eaft point of thenbsp;horizon towards the fouth, and bring the quadrant of altitude to the degree in the horizon atnbsp;which the reckoning ends-, both for finding thenbsp;forenoon hours, and the diftance of the fubftilenbsp;from the meridian: and for the afternoon hours,nbsp;bring the quadrant to the oppofite degree in thenbsp;horizon, namely, as far from the weft towardsnbsp;the north, and then proceed in all refpedts asnbsp;aboye.

T'hus, we have finilhed our declining dial j and in fo doing, we made four dials, viz.

I. A north dial, declining eaftward by the fame number of degrees. 2. A north dial, declining the fame number weft. 3. A fouthnbsp;dial, declining eaft. And, 4. a fouth dial declining weft. Only, placing the proper numbernbsp;of hours, and the ftile or gnomon refpedlively,nbsp;upon each plane. For (as above-mentioned)nbsp;in the fouth-weft plane, the fubftilar-line fallsnbsp;among the afternoon hours ; and in the fouth-eaft, of the fame declination among the forenoonnbsp;Y 3nbsp;nbsp;nbsp;nbsp;hours.

hour?, at equal diftances from XII, And fo, all the morning hours on the weft decliner willnbsp;be like the afternoon hours on theeaft decliner:nbsp;the fouth-eafl: decliner will produce the north-weft decliner; and the fouth-weft: decliner, thenbsp;north-eaft decliner, by only extending the hourlines, ftile and fubftile, quite through the center;nbsp;the axis of the ftile (or edge that calls the fhadownbsp;on the hour of the day) being in all dials whatever parallel to the axis of the world, and confe-quently pointing towards the north pole of thenbsp;heaven in north latitudes, and towards the fouthnbsp;pole, in fouth latitudes. See more of this in thenbsp;following leSlure.

But becaufe every one who would like to make a dial, may perhaps not be provided with a globenbsp;to affift him, and may probably not underftandnbsp;the method of doing it by logarithmic calculation ; we (hall fhew how to perform it by thenbsp;plain dialing lines, or fcale of latitudes andnbsp;hours; fuch as thofe on the right hand of Fig,nbsp;4. in Plate XXI, or at the top of Plate XXII,nbsp;and which may be had on fcales commonly foldnbsp;by the mathematical inftrument makers.

This is the eafieft of all mechanical methods, and by much the beft, when the lines are trulynbsp;divided : not only the half hours and quarter^nbsp;may be laid down by all of them, but every fifthnbsp;minute by moft, and every fingle minute bynbsp;thofe where the line of hours is a foot in length.

Flaving drawn yoqr double meridian line ab, c 4s on the plane intended for a horizontal dial,nbsp;and crofled it at right angles by the fix o�clock linenbsp;f e (as in Fig, 1.) take the latitude of your placenbsp;with the compaftes, in the fcale of latitudes, andnbsp;let that extent from c to e, and from a to �, otinbsp;fhe fix o�clock line : then, taking the whole fix

hours

hours between the points of the compafies in the fcale of hours, with that extent fet one foot in thenbsp;point e, and let the other foot fall where it willnbsp;upon the meridian line cd^ as at d. Do the famenbsp;from / to I, and draw the right lines e d and fb^nbsp;each of which will be equal in length to the wholenbsp;fcale of hours. This done, fecting one foot ofnbsp;the compalfes in the beginning of the fcale atXlI,nbsp;and extending the other to each hour on thenbsp;fcale, lay off thefe extents from d xo e for thenbsp;afternoon hours, and from h to � for thofe of thenbsp;forenoon : this will divide the lines d e and h fnbsp;in the fame manner as the hour-fcale is divided,nbsp;at I, 2, 3, 4, 5 and 6-, on which the quartersnbsp;may alfo be laid down, if required. Then, lay*nbsp;ing a ruler on the point r, draw the firft fivenbsp;hours in the afternoon, from that point, throughnbsp;the dots at the numeral figures i, 2, 3, 4gt; 5, onnbsp;the line ie\ and continue the lines of IIII and Vnbsp;through the center c to the other fide of the dial,nbsp;for the like hours of the m.orning ; which done,nbsp;lay the ruler on the point a, and draw the laftnbsp;five hours in the forenoon through the dotsnbsp;5, 4, 3, 2, I, on the line fb-, continuing thenbsp;hour-lines of VIJ and VIJI through the center/?nbsp;to the other fide uf the dial, for the like hoursnbsp;of the evening -, and fet the hours to their re-fpeftive lines as in the figure. Laftly, make thenbsp;gnomon the fame way as taught above for thenbsp;horizontal dial, and the whole will be finilhed.

To make an eredl fouth dial, take the co-latitude of your place from the fcale of latitudes, and then proceed in all refpeds for the hourlines, as in the horizontal dial; only reverfingnbsp;the hours, as in Fig. 2-, and making the anglenbsp;of the ftik�s height equal to the co-latitude.

I have

I have drawn out a fet of dialing lines upon the top of the 22d Plate, large enough for making a dial of nine inches diameter, or morenbsp;inches if required ; and have drawn them tolerably exadl for common pradice, to every quarternbsp;of an hour. This fcale may be cut off from thenbsp;plate, and palled on wood, or upon the inhde ofnbsp;one of the boards of this book; and then it willnbsp;be fomewhat more exa�l than it is on the plate,nbsp;for being rightly divided upon the copper-plate,nbsp;and printed off on wet paper, it Ihrinks as thenbsp;paper dries ; but when it is wetted again, itnbsp;llretches to the fame fize as when newly printed-,nbsp;and if palled on while wet, it will remain of thatnbsp;fize afterwards.

But lell the young dialill Ihould have neither globe nor wooden fcale, and Ihould tear ornbsp;otherwife fpoil the paper one in palling, we lhallnbsp;now ihew him how he may make a dial withoutnbsp;any of thefe helps. Only, if he has not a linenbsp;of chords, he mull divide a quadrant into 90nbsp;equal parts or degrees for taking the proper anglenbsp;of the llile�s elevation, which is eafily done.

With any opening of the compalTes, as Z Z, deferibe the two lemicircles L F k and Lnbsp;upon the centers Z and z, where the fix o�clocknbsp;line crolTes the double meridian line, and dividenbsp;each femicircle into 12 equal parts, beginning atnbsp;L (chough, llriaiy fpeaking, only the quadrantsnbsp;from L to the fix o�clock line need be divided):nbsp;then conneft the divifions which are equidillantnbsp;from Z, by the parallel lines KM, IN, HO, GP,nbsp;and Draw F Z for the hypothenufe of thenbsp;Hile, making the angle V Z E equal to the lati-titude of your place j and continue the line Z Z tonbsp;R. Draw the line R r parallel to the fix o�clocknbsp;line, and fet off the diftance a K from Z to 2~,

ihc diftance h I from Z lo X, c H from Z to W., d g from Z to T, and e F from Z to S. Thennbsp;draw the lines 6�s, Ft, Ww, Xx, and Ty, eachnbsp;parallel to R r. Set off the diftance y Tfrom anbsp;to 11, and from � to i ; the diftance x X from bnbsp;to lo, and from to 2 wW ixom c to 9, andnbsp;from ^ to 3 ; t F from d to 8, and from i tonbsp;4; j 3 from e to 7, and from n to 5. Then laying a ruler to the center Z, draw the forenoonnbsp;hour lines through the points 11, 10, 9, 8, 7;nbsp;and laying it to the center 2, draw the afternoonnbsp;lines through the points i, 2, 3, 4, 5; continuing the forenoon lines of VII and VIII throughnbsp;the center Z, to the oppofite fide of the dial, fornbsp;the like afternoon hoursj and the afternoon linesnbsp;inland V through the center 2, to the oppofitenbsp;fide, for the like morning hours. Set the hoursnbsp;to thefe lines as in the figure, and then ereftnbsp;the ftile or gnomon, and the horizontal dial willnbsp;be finiftied.

To conftrudt a fouth dial, draw the line VZ, South making an angle with the meridian Z L equal dial.nbsp;to the co-latitude of your place; and proceed innbsp;all refpefis as in the above horizontal dial for thenbsp;fame latitude, reverfing the hours as in Fig. 2.nbsp;and making the elevation of the gnomon equalnbsp;to the co-latitude.

Perhaps it may not be unacceptable to explain the method of conftrudling the dialing lines, andnbsp;fome others ; which is as follows.

With any opening of the compafi�s, as E A, p;a;e according to the intended length of the fcaic, XXir.nbsp;defcribe the circle ADCB, and crofs it at rightnbsp;angles by the diameters C E A and DEB. p;�.nbsp;Divide the quadrant A B firft into 9 equal parts, Dealingnbsp;and then each part into lo-, fofliall the quadrantnbsp;be divided into 90 equal parts or degrees. Draw

the right line AF Biox the chord of this quadrant, and fetting one foot of the compafles in the point yf, extend the other to the feveral divi-fions of the quadrant, and transfer thefe divifionsnbsp;to the line AFB by the arcs lo lo, 20 20, amp;c.nbsp;and this will be a line of chords, divided into 90nbsp;unequal parts; which, if transferred from thenbsp;line back again to the quadrant, will divide itnbsp;equally. It is plain by the figure, that the dif-tance from A to 60 in the line of chords, is juftnbsp;equal to AE, the radius of the circle from whichnbsp;that line is made �, for if the arc 60 60 be continued, of which A is the center, it goes exaftlynbsp;through the center E of the arc A B.

And therefore, in laying down any number of degrees on a circle, by the line of chords, younbsp;,muft firfl: open the compafTes fo, as to take innbsp;juft 60 degrees upon that line, as from A10 60;nbsp;and then, with that extent, as a radius, defcribenbsp;a circle which will be exaclly of the fame fizenbsp;with that from which the line was divided ;nbsp;which done, fet one foot of the compafTes in thenbsp;beginning of the chord line, as at A, and extendnbsp;the other to the number of degrees you wanenbsp;upon the line, which extent, applied to the circle,nbsp;�will include the like number of degrees upon

Divide the quadrant C D into 90 equal parts, and from each point of divifion draw right linesnbsp;as i, k, /, amp;c. to the line CE-, all perpendicularnbsp;to that line, and parallel to D E, which will divide E C into a line of fines; and although theftnbsp;are ftldom put among the dialing lines on a fcale,nbsp;yet they affift in drawing the line of latitudes.nbsp;For, if a ruler be laid upon the point D, andnbsp;over each divifion in the line of fines, it willnbsp;divide the qqadrant C into 90 unequal parts,

If the right line 5 C be drawn, fubtending this quadrant, and the neareft diftances B B b, Btynbsp;amp;c. be taken in the compafles from 5, and feenbsp;upon this line in the fame manner as direfted fornbsp;the line of chords, it will make a line of latitudesnbsp;B C, equal in length to the line of chords J B,nbsp;and of an equal number of divifions, but verynbsp;unequal as to their lengths.

Draw the right line D G fubtending the quadrant D A; and parallel to it, draw the rightnbsp;line r j, touching the quadrant DA at the numeral figure 3. Divide this quadrant into fix equalnbsp;parts, as 1,2, 3, amp;c. and through thefe points ofnbsp;divifion draw right lines from the center E tonbsp;the line r s, which will divide it at the pointsnbsp;where the fix hours are to be placed, as in thenbsp;figure. If every fixth part of the quadrant benbsp;fubdivided into four equal parts, right linesnbsp;drawn from the center through thefe points ofnbsp;divifion, and continued to the line rs, will dividenbsp;each hour upon it into quarters.

In Fig. 2. we have the reprefentation of 3. portable dial, which may be eafily drawn on A a card.nbsp;card, and carried in a pocket-book. The linesnbsp;(t d, ab and b c oi the gnomon muft be cut quitenbsp;through the card; and as the end ab of the gnomon is raifed occafionally above the plane of thenbsp;dial, it turns upon the uncut line r J as on anbsp;hinge, The line dotted AB muft be flit quitenbsp;through the card, and the thread muft be putnbsp;through the flit, and have a knot tied behind, tonbsp;keep it from being eafily drawn out. On thenbsp;other end of this thread is a fmall plummet Z),nbsp;and on the middle of it a fmall bead for Ihewingnbsp;the time of the day.

To rcftify this dial, fet the thread in the flit right againft the day of the month, and ftretchnbsp;the thread from the day of the month over thenbsp;angular point where the curve lines meet at XII jnbsp;then Ihifc the bead to that point on the thread,nbsp;and the dial will be rectified.

To find the hour of the day, raife the gnomon (no matter how much or how little) and holdnbsp;the edge of the dial next the gnomon towardsnbsp;the fun, lb as the uppermoft edge of the Ihadownbsp;of the gnomon may juft cover the Jhadow-line ;nbsp;and the bead then playing freely on the face ofnbsp;the dial, by the weight of the plummet, willnbsp;fhew the time of the day among the hour-lines,nbsp;as it is forenoon or afternoon.

To find the time of fun-rifing and fetting, move the thread among the hour-lines, until itnbsp;either covers fome one of them, or lies parallelnbsp;betwixt any two; and then it will cut the timenbsp;of fun-rifing among the forenoon hours, and ofnbsp;fun-fetting among the afternoon hours, on thatnbsp;day of the year for which the thread is fet in thenbsp;fcale of months.

To find the fun�s declination, ftretch the thread from the day of the m.onth over the angularnbsp;point at XII, and it will cut the fun�s declination, as it is north or fouth, for that day, in thenbsp;arched fcale of north and fouth declination.

To find on what days the fun enters the figns: when the bead, as above relt;ftified, movesnbsp;along any of the curve lines which have the fignsnbsp;of the zodiac marked upon them, the fun entersnbsp;thofe figns on the days pointed out by the threadnbsp;in the fcale of months.

The conftrucflion of this dial is very eafy, efpecially if the reader compares it all along

Draw the occult line A B parallel to the top of Fig. 3. the card, and crofs it at right angles with the fixnbsp;o�clock line E C D �, then upon C, as a center,nbsp;with the radius CA^ defcribe the femicircle AEL,nbsp;and divide it into 12 equal parts (beginning atnbsp;A) as Ar, As, amp;c. and from thefe points ofnbsp;divifion, draw the hour-lines r, s, t, u, v, E, w,nbsp;and X, all parallel to the fix o�clock line E C.

If each part of the femicircle be fubdivided into four equal parts, they will give the half-hournbsp;lines and quarters, as in Fig. 2. Draw the rightnbsp;line AS Do, making the angle 5 equal to thenbsp;latitude of your place. Upon the center defcribe the arch RST, and fet off upon it the arcsnbsp;S R and S E, each equal to 2 34: degrees, for thenbsp;fun�s greateft declination ; and divide them intonbsp;23t equal parts, as in Fig. 2. Through thenbsp;interfedion D of the lines BCD and A D 0,nbsp;draw the right line FD G at right angles tonbsp;A Do. Lay a ruler to the points A and R, andnbsp;draw the line ARE through 234- degrees ofnbsp;fouth declination in the arc S R ; and then laying the ruler to the points A and T, draw the linenbsp;AEG through 234^ degrees of north declinationnbsp;in the arc SE: fo fhall the lines A R F andnbsp;AEG cut the line F D G \n the proper lengthnbsp;for the fcale of months. Upon the center D,nbsp;with the radius D F, defcribe the femicirclenbsp;F 0 G -, and divide it into fix equal parts, F m,nbsp;m n, no, amp;c. and from thefe points of divifionnbsp;draw the right lines m h, n i, p k, and q I, eachnbsp;parallel to 0 D. Then fetting one foot of thenbsp;compalTes in the point F, extend the other to A,nbsp;and defcribe the arc AzH for the tropic of v :nbsp;with the fame extent, fetting one foot in G, defcribe

the line of r and =2= (where the circle touches) comes to the latitude of your place in the quadrant ; then, turn the whole meridional planenbsp;with its circle G, upon the horizontal planenbsp;if, until the edge of the fhadow of the circlenbsp;falls precifely on the day of the month in thenbsp;femicircle ; and then, the meridional plane willnbsp;be due north and fouth, the axis E F will benbsp;parallel to the axis of the world, and will call anbsp;Ihadow upon the true time of the day, amongnbsp;the hours on the circle.

N. B. As, when the inftrument is thus refli-fied, the quadrant and femicircle are in the plane of the meridian, fo the circle is then in the planenbsp;of the equinodlial. Therefore, as the fun is abovenbsp;the equinodlial in fummer (in nothern latitudes)nbsp;and below it in winter j the axis of the femicircle will call a fhadow on the hour of the day,nbsp;on the upper furface of the circle, from the 20thnbsp;of March to the 23d of September: and fromnbsp;the 23d of September, to the 20th of March,nbsp;the hour of the day will be determined by thenbsp;lhadow of the femicircle, upon the lower furfacenbsp;of the circle. In the former cafe, the lhadow ofnbsp;the circle falls upon the day of the month, onnbsp;the lower part of the diameter of the femicircle;nbsp;and in the latter cafe, on the upper part.

The method of laying down the months and figns upon the femicircle, is as follows. Drawnbsp;the right line AC equal the diameter of thenbsp;femicircle A D B, and crofs it in the middle atnbsp;right angles with the line ECD, equal in lengthnbsp;to A DB �, then E C will be the radius of thenbsp;circle FCG, which is the fame as that of thenbsp;femicircle. Upon E, as a center, defcribe thenbsp;circle FCG, on which fet off the arcs C b andnbsp;C/, each equal to degrees, and divide themnbsp;accordingly into that number, for the fun�s de-3nbsp;nbsp;nbsp;nbsp;clination.

tlination. Then, laying the edge of a ruler over the center E, and alfo over the fun�s declination for every .* fifth day of each month (as iiinbsp;the card dial) mark the points on the diameternbsp;/IB of the femicircle from a to g, which are cutnbsp;by the ruler j and there place the days of thenbsp;months accordingly, anfwering the fun�s declination. This done, fetting one foot of the com-paffes in C, and extending the other to a or g,nbsp;defcribe the femicircle abc defg\ which dividenbsp;into fix equal parts, and through the points ofnbsp;divifion draw right lines, parallel to C A for thenbsp;beginning of the fines (of which one half are onnbsp;one fide of the femicircle, and the other half onnbsp;the other fide) and fee the charaders of the fignsnbsp;to their proper lines, as in the figure.

The following table (hews the fun�s place and declination, in degrees and minutes, at the noonnbsp;of every day of the fecond year after leap-year;nbsp;which is a mean between thofe of leap-year it-felf, and the firft and third years after. It isnbsp;ufeful for inferibing the months and their daysnbsp;on fun-dials -, and alfo for finding the latitudesnbsp;of places, according to the methods preferibednbsp;after the table.

� The intermediate days may be drawn in by hand, jf the fpaces be large enough to contain (hem.

A Tabic

Hailes of the Sun's Place and Declination,

0	Sun�s	PI.	Sun�s	Dec-
	D.	M.	D.	M.
j	925	22	23 N 8:
2	10	19	23	4
3	II	16	23	0
4	12	14	22	55
5	13	11	22	49
6	14	8	22	43
7	15	5	22	37
8	16	0	22	30
9	�7	2	22	23
lO	17	57	22	16
11	x8	54	22	8
12	19	5�	22	0
13	20	49	21	52
14	21	46	21	43
15	22	43	21	33
16	23	40	21	22
�7	24	38	21	14
18	25	35	21	3
19	26	32	20	52
20	27	29	20	4�-
2 !	28	27	20	30
22	29	24	20	18
23:	OJt 21		20	6
24	I	19	19	54
25	2	16	19	41
26	3	13	'9	28
27	4	11	19	14
28	5	8	19	1
29	6	6	18	46
^0	7	3	18	32
31	8	0	18	*7

�	Sun�	s P!^	Son�s	Dec.
C/2	D.	M.	D.	INT
1	8^158		18 N 2
2	9	55	17	47
3	10	53	17	32
4	11	50	17	I�
5	12	48	17	0
6	13	45	16	43
7	14	43	16	26
8	15	41	16	9
9	1�	38	15	52
10	17	36	I s	25
11	18	33	�5	^7
12	19	3�	H	59
13	20	29	14	4�
'4	21	26	14	23
*5	22	24	14	4
i6	23	22	*3	45
17	24	20	13	26
18	25	17	�3	7
19	26	15	12	47
20	27	13	12	27
21	28	11	12	7
22	29	9	11	47
23	ot% 7		11	27
24	I	5	11	6
25	2	3	10	46
26	3	I	10	25
27	3	59	10	4
28	4	57	9	43
29	5	55	9	21
jO	6	.53	9	0
31	7	51	8	3�

A Table

'�ahles of the Sun's Place and Declinatioti.

A Table fhewing the fun�s					place and declination.
September.					Oftober.
�	Sun�s	Pi.	Sun�s	Dec.	a	Sun�s	PI.	Sun�s	Dec.
t/gt;	dTquot;	M.	D.	M.	C/3	D.	M.	D.	M.
I	8nR49		8N16		I	8^	8	3 S14
2	9	47	7	55	2	9	7	3	37
3	10	46	7	33	3	10	7	4	I
4	11	44	7	10	4	11	6	4	24
5	I2	42	6	48	5	12	5	4	47
6	�3	40	6	26	6	13	4	5	10
7	14	39	6	3	7	14	4	5	33
8	15	37	5	41	8	15	3	5	56
9	16	35	5	18	9	i5	3	6	19
10	17	34	4	55	10	17	2	6	42
11	18	32	4	32	11	18	I	7	5.
12	19	31	4	9	12	19	1	7	27
13	20	29	3	46	*3	20	0	7	5�
14	21	28	3	23	14	21	0	8	12
15	22	26	3	0	15	22	0	8	35
16	23	25	2	37	16	23	0	8	57
17	24	24	2	H	17	23	59	9	19
18	25	22	I	50	18	24	59	9	41
19	26	21	I	27	19	25	58	lO	3
20	27	20	I	4	20	26	58	10	24
2 1	28	19	0	40	21	27	58	10.	46
22	29	17	0	17	22	28	58-	11	7
23	0^16		oS 6		23	29	58	11	28
24	1	15	0	30	24	011158		11	49
25	2	M	0	53	25	1	58	12	10
26	3	13	1	�7	26	2	58	12	31
27	4	12	1	40	27	3	58	12	51
28	5	11	2	4	28	4	58	13	12
29	6	10	2	27	29	5	58	13	32
30	7	9	2	50	30	6	58	13	51
30					31	7	58	14	II

A Tabl^

The latitude of any place is equsl to the elevation of the pole above the horizon of thatnbsp;place. Therefore it is plain, that if a liar wasnbsp;fixt in the pole, there would be nothing required to find the latitude, but to take the altitude of that fiar with a good inftrument. Butnbsp;although there is no ftar in the pole, yet thenbsp;latitude may be found by taking the greateftnbsp;and leaft altitude of any ftar that never fets; fornbsp;if half the difference between thefe altitudes benbsp;added to the leaft altitude, or fubtrafted fromnbsp;the greateft, the fum or remainder will be equalnbsp;to the altitude of the pole at the place of ob-fervation.

But becaufe the length of the night muft be more than 12 hovirs, in order to have two fuchnbsp;obfervations; the fun�s meridian altitude andnbsp;declination are generally made ufe of for findingnbsp;the latitude, by means of its complement, whichnbsp;is equal to the elevation of the equinoftial abovenbsp;the horizon -, and if this complement be fub-tratfted from 90 degrees, the remainder will benbsp;the latitude: concerning which, I think, the following rules take in all the various cafes.

I. If the fun has north declination, and is on the meridian, and to the fouth of your place,nbsp;fubtradl: the declination from the meridian altitude (taken by a good quadrant) and the remainder will be the height of the equinoflial ornbsp;complement of the latitude north.

EXAM-,

- C The fun�s meridian altitude 42� 20' South �uppof'-^ And his declination, fubt. 10 15 North

2. If the fun has fouth declination, and is fouthward of your place at noon, add the declination to the meridian altitude; the fum, ifnbsp;lefs than 90 degrees, is the complement of thenbsp;latitude north: but if the fum exceeds 90 degrees, the latitude is fouth ; and if 90 be taken,nbsp;from that fum, the remainder will be the latitude.

EXAMPLES.

The fun�s meridian altitude � 65� lo' South The fun�s declination, add � 15nbsp;nbsp;nbsp;nbsp;30 South

3. If the fun has north declination, and is oa the meridian north of your place, add the declination to the north meridian altitude; the fum,nbsp;if Jefs than 90 degrees, is the complement ofnbsp;the latitude fouth: but if the fum is more thannbsp;90 degrees, fubtradl 90 from it, and thenbsp;mainder is the latitude north.

EXAMPLES.

4. If the fun has fouth declination, and is north of your place at noon, fubtradl: the declinationnbsp;from the north meridian altitude, and the remainder is the complement of the latitudenbsp;fouth.

EXAM-

EXAMPLE.

Which is north or fouth, according as the fun�s declination is north or fouth : for when the futinbsp;has fouth declination, he is never feen belownbsp;the north pole; nor is he ever feen below thenbsp;fouth pole, when his declination is north.

7. nbsp;nbsp;nbsp;if the fun be in the zenith at noon, andnbsp;at the fame time has no declination, you arcnbsp;then under the equinodial, and fo have nonbsp;latitude.

8. nbsp;nbsp;nbsp;If the fun be in the zenith at noon, andnbsp;has declination, the declination is equal to thenbsp;latitude, north or fouth. Thefe two cafes arenbsp;fo plain, that they require no examples.

Having Ihewn in the preceding Lec^ ture how to make fun-dials by the affift-ance of a good globe, or of a dialing fcale, wenbsp;Ihall now proceed to the method of conftruftingnbsp;dials arithmetically ; which will be more agreeable to thofe who have learnt the elements of

trigonometry, becaufe globes and fcales can never be fo accurate as the logarithms, in finding the angular diftances of the hours. Yet, asnbsp;a globe may be found exaft enough for fomenbsp;other requifites in dialing, we fhall take it innbsp;occafionally.

The conftrudtion of fun-dials on all planes whatever, may be included in one general rule:nbsp;intelligible, if that of a horizontal dial for anynbsp;given latitude be well underftood. For there isnbsp;no plane, however obliquely fituated with re-fpett to any given place, but what is parallelnbsp;to the horizon of fome other place �, and therefore, if we can find that other place by a problem on the terreftrial globe, or by a trigonometrical calculation, and conftrudt a horizontal dialnbsp;for it; that dial, applied to the plane where it isnbsp;to ferve,will be a true dial for that place.�Thus,nbsp;an ereft direfl: fouth dial in 51^: degrees northnbsp;latitude, would be a horizontal dial on the famenbsp;meridian, 90 degrees fouthward of 514- degreesnbsp;north latitude; which fails in with 384 degreesnbsp;of fouth latitude, but if the uptight plane declines from facing the fouth at the given place,nbsp;it would ftill be a horizontal plane 90 degreesnbsp;from that place -, but for a different longitude :nbsp;which would alter the reckoning of the hoursnbsp;accordingly.

CASE

I. Let us fuppofe that an upright plane at London declines 36 degrees weftward fromnbsp;facing the fouth ; and that it is required to findnbsp;a place on the globe, to whofe horizon the faidnbsp;plane is parallel; and alfo the difference of longitude between London and that place.

Rectify the globe to the latitude of London^ and bring London to the zenith under the brafsnbsp;meridian, then that point of the globe which liesnbsp;in the horizon at the given degree of declinationnbsp;(counted weftward from the fouth point of thenbsp;horizon) is the place at which the above-mentioned plane would be horizontal.�Now, tonbsp;find the latitude and longitude of that plac�,nbsp;keep your eye upon tJie place, and turn thenbsp;globe eaftward, until it comes under the graduated edge of the brafs meridian j then, the degree of the brafs meridian that hands directlynbsp;over the place, is its latitude ; and the numbernbsp;of degrees in the equator, which are interceptednbsp;between the meridian of London and the brafsnbsp;meridian, is the place�s difference of longitude.

Thus, as the latitude of London is 514- degrees north, and the declination of the place is 36 degrees weft; I elevate the north pole 514.nbsp;degrees above the horizon, and turn the globenbsp;until London comes to the zenith, or under thenbsp;graduated edge of the meridian; then, I countnbsp;36 degrees on the horizon weftward from thenbsp;iouth point, and make a mark on that place ofnbsp;the globe over which the reckoning ends, andnbsp;bringing the mark under the graduated edgenbsp;of the brafs meridian, I find it to be under 30^:nbsp;degrees in fouth latitude: keepingit there, I countnbsp;in the equator the number of degrees betweennbsp;the meridian of London and the brafen meridiannbsp;(which now becomes the meridian of the requirednbsp;place) and find it to be 42|-. Therefore annbsp;upright plane at London, declining 36 degreesnbsp;weftward from the fouth, would be a horizontalnbsp;plane at that place, whofe latitude is 3O4 degreesnbsp;fouth of the equator, and longitude 42^ degreesnbsp;weft of the meridian of London.

quot;Which difference of longitude being con verted into time, is 2 hours 51 minutes.

The vertical dial declining weftward 36 degrees at London, is therefore to be drawn in all refpe(fts as a horizontal dial for fouth latitudenbsp;3ot degrees �, fave only, that the reckoning ofnbsp;the hours is to anticipate the reckoning on thenbsp;horizontal dial, by 2 hours 51 minutes : for fonbsp;much fooner will the fun come to the meridiannbsp;of 'London, than to the meridian of any placenbsp;whofe longitude is 42-1 degrees weft from London.

2. But to be more exaft than the globe' will ftiew us, we fhall ufe a little trigonometry.

Let N E SW be the horizon of London, whofe zenith is Z, and P the north pole of the xxilfnbsp;fphere ; and let Z ^ be the pofition of a vertical Fig. i.*nbsp;plane at Z, declining weftward from 5 (thenbsp;fouth) by an angle of 36 degrees; on whichnbsp;plane an erefl: dial for London at Z is to benbsp;defcribed. Make the femidiameter Z D perpendicular to Z i), and it will cut the horizon in D,

36 degrees weft of the fouth S, Then, a plane in the tangent H D, touching the fphere in D,nbsp;will be parallel to the plane Z igt;-, and the axis ofnbsp;the fphere will be equally inclined to both thcfcnbsp;planes.

Let fVbe the equinoflial, whofe elevation above the horizon of Z (London) is 384 degrees 5 and P R D he the meridian of thenbsp;place D, cutting the equinoflial in R. Then,nbsp;k is evident, that the arc R D is the latitude ofnbsp;the place D (where the plane Z h would be horizontal) and the arc ^ is the difference ofnbsp;longitude of the planes Z h aqd D H.

In the fpherical triangle WTgt;R^ the arc WO is given, for it is the complement of the plane�snbsp;6nbsp;nbsp;nbsp;nbsp;decli-

354

declination fi'om S the fouth; which complement is 54P (viz. 90��36'�:) the angle at in which the meridian of the place D cuts thenbsp;equator, is a right angle j and the angle R PFDnbsp;meafures the elevation of the eqiiinoftial abovenbsp;the horizon of Z, namely, 384 degrees. Saynbsp;therefore, as radius is to the co-fine of thenbsp;plane�s declination from the fouth, fo is the cofine of the latitude of Z to the fine of 72 D th�nbsp;latitude of D ; which is of a different denomination from the latitude of Z, becaufe Z and Dnbsp;are on diff�rervt fides of the equator.

3o'=^Z nbsp;nbsp;nbsp;9.79415

N. B. When radius is made the firfi: term, it may be omitted, and then, by fubtrafting itnbsp;mentally from the fum of the other two, thenbsp;operation will be fhortened. Thus, in the pre-fent cafe.

To the logarithmic fine of PVR=z* 54� 0' 9.90796 Add the logarithmic fine of R D�f 38� 30' 9.79415

Their fum�radius - . -gives the fame folution as above keep to this method in the following part of thenbsp;work.

To find the difference of longitude of the places D and Z, fay, as radius is to the co-finenbsp;of ^84- degrees, the height of the equinoflial atnbsp;Z, fo is the co-tangent ot 36 degrees, the plane�snbsp;declination, to the co-tangent of the differencenbsp;of longitudes. Thus,

To the logarithmic fine of ¹ 51� 30' 9.89354 Add the logarithmic tang, of-f 54� 0' 10.13874

� Their fum�radius - nbsp;nbsp;nbsp;_nbsp;nbsp;nbsp;nbsp;.nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;10.03228

is the neareft tangent of 47� 8' � JV R-, which is the co-tangent of 42� 52' =: R ^ the difference of longitude fought. Which difference,nbsp;being reduced to tiriie, is 2 hours 514 minutes.

3. And thus having found the exadt latitude and longitude of the place D, to whofe horizonnbsp;the vertical plane at Z is parallel, we lhall proceed to the conftruflion of a horizontal dial fornbsp;the place D, whofe latitude is 30� 14' fouth;nbsp;but anticipating the time at D by 2 hours 51nbsp;minutes (neglefting the 4 minute in pradlice)nbsp;becaufe D is fo far weftward in longitude fromnbsp;the meridian of London; and this will be anbsp;true vertical dial at London, declining weftwardnbsp;36 degrees.

Affume any right line C 5 L for the fubftileFig. z. of the dial, and make the angle K C P equal tonbsp;the latitude of the place (viz, 30'' 14'') to wholenbsp;horizon the plane of the dial is parallel; thennbsp;C RP will be the axis of the ftile, or edge thatnbsp;calls the fhadow on the hours of the day, in thenbsp;dial. This done, draw the contingent line Enbsp;cutting the fubftilar line at right angles in K;

and from K make K R perpendicular to the axis C R P. Then K G (�KR) being made radius,nbsp;that is, equal to the chord of 60' or tangent ofnbsp;45� on a good fedtor, take 42� ^2' (the difference of longitude of the places Z and D) fromnbsp;the tangents, and having fet it from K to M,nbsp;draw C M for the hour-line of XII. Take K Nnbsp;equal to the tangent of an angle lefs by 15nbsp;degrees than K M; that is, the tangent 22� 52' �,nbsp;and through the point iVdraw C N for the hour-line of I. The tangent of 12� 52' (which isnbsp;15� lefs than 27� 52') fet off the fame way, willnbsp;give a point between K and iV, through whichnbsp;the hour-line of II is to be drawn. The tangent of 2� 8' (the difference between 45� andnbsp;42� 52') placed on the other fide of C X,, willnbsp;determine the point through which the hour-linenbsp;of 111 is to be drawn: to which 2� 8', if thenbsp;tangent of 15� be added, it will make 17� 8';nbsp;and this fet off from K towards on the linenbsp;E ^ will give the point for the hour-line ofnbsp;IV : and fo of the reft.�The forenoon hourlines are drawn the fame way, by the continualnbsp;addition of the tangents 15�, 30�, 45�, amp;c. tonbsp;42� 52' (=the tangent of K M) for the hoursnbsp;of Xi, X, IX, amp;c. as far as neceffary; that is,nbsp;until there be five hours on each fide of thenbsp;fubftile. The fixth hour, accounted from thatnbsp;hour or part of the hour on which the fubftilenbsp;falls, will be always in a line perpendicular tonbsp;the fubftile, and drawn through the center C.

4. In all ereft dials, C M, the hour-line of XII, is perpendicular to the horizon of thenbsp;place for which the dial is to ferve: for thatnbsp;line is the interfedfion of a vertical plane withnbsp;the plane of the meridian of the place, bothnbsp;which are perpendicular to the plane of the

hprizon: and any line HO, or h o, perpendicular to C M, will be a horizontal line on the plane of the dial, along which line the hoursnbsp;may be numbered : and C M being f;t perpendicular to the horizon, the dial will have its truenbsp;pofition.

5. nbsp;nbsp;nbsp;If the plane of the dial had declined by annbsp;equal angle toward the eaft, its dcfcripticn wouldnbsp;have differed only in this, that the hour-line ofnbsp;XII would have fallen on the other fide of thenbsp;fubftile C L, and the line H O would have anbsp;fubcontrary pofition to what it has in thisnbsp;figure.

6. nbsp;nbsp;nbsp;And thele two dials, with the upper pointsnbsp;of their fViles turned toward the north pole, willnbsp;ferve for the other two planes parallel to them ;nbsp;the one declining from the north toward thenbsp;eaft, and the other from the north toward thenbsp;weft, by the fame quantity of angle. The likenbsp;holds true of all dials in general, whatever benbsp;their declination and obliquity of their planes tonbsp;the horizon.

CASE 11.

7. If the plane of the dial not only declines. Fig, 5.nbsp;reclines, ox inclines. Suppofe its declination from fronting the fouth S b'; equal to the arcnbsp;S D on the norizon ; and us reclination benbsp;equal to the arc Dd of the vertical circle D Z:nbsp;then it is plain, that if the quadrant of altitudenbsp;Z d D, on the globe, cuts the point D in thenbsp;horizon, and the reclination is counted upon thenbsp;quadrant from D to d% the interfeiftion of thenbsp;hour-circle P R d. with the equinodial IV^E,nbsp;will determine R d, the latitude of the pla^ T,

whole hor�fton is parallel to the given plane Zh �ix. Z \ and R i^will be the difference in longitudenbsp;of the planes at d and Z.

Trigonometrically thus: let a great circle pafs through the three points W, d, E-, and innbsp;the triangle JVD d, right-angled at T, the Tidesnbsp;IV D and D d are given and thence the anglenbsp;D fVd\s found, and fo is the hypothenufe fVd.nbsp;Again, the difl'erence, or the fum, of DWdnbsp;and D IV R, the elevation of the equino�lialnbsp;above the horizon of Z, gives the angle d WR ;nbsp;and the hypothenufe of the triangle IV R d wasnbsp;juft now found ; whence the fides R d and TVRnbsp;are found, the former being the latitude of thenbsp;place and the latter the complement of Rnbsp;the difference of longitude fought.

Thus, if the latitude of the place Z be 52� 10' north the declination S D oi the plane Z hnbsp;(which would be horizontal at d) be 36�, andnbsp;the reclination be 15�, or equal to the zrc D d-,nbsp;the fouth latitude of the place d, that is, thenbsp;arc R lt;f, will be 15� 9'; and R ^ the difference of the longitude, 36� 2'. From thefenbsp;tiara, therefore, let the dial (Fig. 4.) be de-fcribed, as in the former example.

8. Only it is to be obferved, that in the reclining or inclining dials, the horizontal line v/ill not ftand at right angles to the hour-line ofnbsp;XII, as in ered dials; but its pofition may benbsp;found as follows.

Fig. 4. To the common fubftilar line C K L, on which the dial for the place d was defcribed,nbsp;drav.r the dial C r p m 12 for the place T, whofenbsp;declination is the fame as that of d (viz. the arcnbsp;S D �, and HO, perpendicular to C m, the hourline of XII on this dial, will be a horizontal linenbsp;on the dial CPRM XII. For the declination

of both dials being the fame, the horizontal line remains parallel to itfelf, while the ereft pofitionnbsp;of one dial is reclined or inclined with refpeft tonbsp;the pofition of the other.

Or, the pofition of the dial may be found by applying it to its plane, fo as to mark the truenbsp;hour of the day by the fun, as ftiewn by anothernbsp;dial �, or by a clock, regulated by a true meridian line and equation table.

9. There are feveral other things requifite in the practice of dialing-, the chief of which Inbsp;fhall give in the form of arithmetical rules,nbsp;fimple and eafy to thofe who have learnt the elements of trigonometry. For in pradical arts ofnbsp;this kind, arithmetic Ihould be ufed as far asnbsp;it can go -, and fcales never trufted to, except innbsp;the final conftrudion, where they are abfolutelynbsp;necelfary in laying down the calculated hour-diftances on the plane of the dial. And although the inimitable artifts of this metropolisnbsp;have no occafion for fuch inftrudions, yet theynbsp;may be of fome ufe to ftudents, and to privatenbsp;gentlemen who amufe themfelves this way.

To the longarithmic fine of the given latitude, or of the ftile�s elevation above the plane of thenbsp;dial, add the logarithmic tangent of the hournbsp;* diftance from the meridian, or from the

* That is, of If, 30, 45, 60, 75�, for the liottrs of f, n, Hi, JV, V it, the afternoon: .-.nd XI, X, JX, ViTi,nbsp;VII in the forenoon.

f fubftile ; and the fum minus radius will be the logarithmic tangent of the angle fought.

For, in Fig. 2. C is to �T M in the ratio compounded of the ratio of ^ C to K G (~K R)nbsp;and of KG lo KMwhich, making C K thenbsp;radius, 10,000000, or 10,0000, or 10, or. i,nbsp;are the ratio of 10,000000, or of 10,0000, ornbsp;of 10, or of I, to K G X K M.

Thus, in a horizontal dial, for latitude 51 � ^0', to find the angular diftance of XI in thenbsp;forenoon, or I. in the afternoon, from XII.

The fum�radius is -the logarithmic tangent of ii angle which the hour-line of XI or I makesnbsp;with the hour of XII.

And by computing in this manner, with the fine of the latitude, and the tangents of 30,nbsp;45, 60, and 75�, for the hours of II, III, IV,nbsp;and V in the afternoon -, or of X, IX, VIII,nbsp;and VII in the forenoon -, you will find theirnbsp;angular diftancesfrotn XII to be 24� 18', 38� 3',nbsp;53� 35', and 71� 6'-, which are all that there

tances may be fet off from XII by a line of chords; or rather, by taking 1000 from a fcalenbsp;of equal parts, and fetting that extent as a radius from C to XII j and then, taking 209 of

f In all horizontal dials, and ereft north or fouth dials, the fobftile and meridian are the fame : but in all decliningnbsp;dials, the fubftile line makes an angle with the meridian.

t In which cafe, the radius C .ST is fuppofed to be divided into looooeo equal part;,

the fame parts (which, in the tables, are the natural tangent of ii� 50') and fecting themnbsp;from XII to XI and to I, on the line h 0, which Fig.nbsp;is perpendicular to C XII : and fo for the reftnbsp;of the hour-lines, which in the table of naturalnbsp;tangents, againft the above diftances, are 4.51,nbsp;782, 1355, and 2920, of fuch equal parts fromnbsp;XII, as the radius C XII contains 1000. Andnbsp;laftly, fet off 1257 (the natural tangent of 51quot;

30') for the angle of the (file�s height, which is equal to the latitude of the place.

The reafon v/hy I prefer the ufe of the tabular numbers, and of a fcale decimally divided, to that of the line of chords, is becaufe there isnbsp;the leaft chance of miftake and error in this way;nbsp;and likewife, becaufe in Ibme cafes it gives usnbsp;the advantage of a nonius' divifion.

In the univerfal ring-dial, for inftance, the divifions on the axis are the tangents of thenbsp;angles, of the fun�s declination placed on eithernbsp;fide of the center. But inftead of laying themnbsp;down from a line of tangents, I would make anbsp;fcale of equal parts, whereof 1000 flrould an-fwer exaftly to the length of the ferni-axjs, fromnbsp;the center to the infide of the equinoctial ring;nbsp;and then lay down 434 of thefe parts towardnbsp;each end from the center, which would limit allnbsp;the divifions on the axis, becaufe 434 are thenbsp;natural tangent of 23quot; 29b And thus by anbsp;nonius affixed to the Aiding piece, and takir.gnbsp;the fun�s declination from an� Ephen.eris, andnbsp;the tangent of that declination from the table ofnbsp;natural tangents, the Aider might be always ,jcnbsp;true to within two minutes of a degree.

And this fcale of 434 equal parts might be placed right againft the 23.^ degrees of the fun�snbsp;declination, on the axis, inftead of the fun�snbsp;A a 4nbsp;nbsp;nbsp;nbsp;place,

place, which is there of very little ufe. For then, the Aider might be fet in the ufual way,nbsp;to the day of the month, for common ul'e ; butnbsp;to the natural tangent of the declination, whennbsp;great accuracy is required.

The like may be done wherever �a fcale of fines or tangents is required on any inftrument.

'The latitude of the place, the fun's declination, and his hour diftance from the meridian, being given;nbsp;to find [v.) his altitude �, (2.) his azimuth.

Pig* 3- �. Let d be the fun�s place, d R, his declination ; and in the triangle P Z d, P d the fum, or the difference, of d R, and the quadrant P Rnbsp;being given by the fuppofition, as alfo the complement of the latitude P Z, and the anglenbsp;d P Z, which meafures the horary diftance of dnbsp;from the meridian; we fliall (by Cafe 4. ofnbsp;Keill�s Oblique fpheric Trigonometry) find thenbsp;bafe Z d, which is the fun�s diftance from thenbsp;zenith, or the complement of his altitude.

And (2.) As fine Z d: fine P d: �. fine d P Z : d Z P, or of its fupplement D ZS, the azimuthalnbsp;diftance from the louth.

Or, the pradlical rule may be as follows. Write A for the fine of the fun�s altitude, Lnbsp;and I for the fine and co-fine of the latitude, Dnbsp;and d for the fine and co-fine of the fun�s declination, and H for the fine of the .horary diftance from VI.

t. When the declination is toward the ele� vated pole, and the hour of the day is betweennbsp;XII and VI j '\t \s A L D H I d, andnbsp;J-LD.

3. When the declination is toward the de-prelTed pole, we have A ~ Hid � ZD, and

^~~TT

Which theorems will be found ureful, and expeditious enough for folving thofe problemsnbsp;in geography and dialing, which depend on thenbsp;relation of the fun�s altitude to the hour of thenbsp;day.

Suppofe the latitude of the place to be 514-degrees porth ; the time five hours diftant from XII, that is, an hour after VI in the morning,nbsp;or before VI in the evening; and the fun�s declination 20� north. Required the fun's dtitude?

Then, to log. Z r: log. fin. 51� ^o' 1.89354.¹ add log. D = log. fin. 20� o'quot; 1.53405

Here we confider the radius as unity, and not io,oocoo, by which, inllead of the index g we have� i, as above;nbsp;which is of no farther ufe, than making the work a littlenbsp;eafier.

And thefe two numbers of (0.267664 and 0.151408) make 0.419072 � which, innbsp;the table, is the neareft natural fine of 24� 47',nbsp;the fun�s altitude fought.

The fame hour-dillance being affumed on the other fide of VI, then D D�Hid is 0.116256,nbsp;the fine of 6� 40'i -, which is the fun�s altitudenbsp;at V in the morning, or VII in the evening,nbsp;when his north declination is 20^.

But when the declination is 20� fouth (or towards the depreffed pole) the difference Hid� L D becomes negative, and thereby fhew thar,nbsp;an hour before VI in the morning, or paft VI innbsp;the evening, the fun�s center is 6� 40 i belownbsp;the horizon.

In the fame latitude and north declination, from the given altitude to find the hour.

Let the altitude be 48*^; and becaufe, in this cafenbsp;nbsp;nbsp;nbsp;(the natural fine of

And, if the declination 20� had been towards the fouth pole, the fun would have been de-prelTed 18� below the horizon at 164 minutesnbsp;after VI in the evening at which time, thenbsp;twilight would end; which happens about thenbsp;22d of November, and ipth of January, in thenbsp;latitude of 5i�4 north. The fame way may thenbsp;end of twilight, or beginning of dawn, be foundnbsp;for any time of the year.

NOTE I. If in theorem 2 and 3 (page 363) A is put = o, and the value of H is computed,nbsp;we have the hour of fun-rifing and fetting fornbsp;any latitude, and time of the year. And if wenbsp;put H � o, and compute A, we have the fun�snbsp;altitude or depreffion at the hour of VI. Andnbsp;laftly, if //, A, and B are given, the latitudenbsp;may be found by the refolution of a quadraticnbsp;equation; for / zzy/ i�L'',

NOTE

As, if~it was required, wbat is the greateji length of day in latitude 51� 30' ?

To the log. tangent of 51� go' 0.0993948 Add the log. tangent of 23quot; 29' 1.6379563

the log. fine of the hour-diftance 33� f \ in time 2 h. 12^ m. The longeft day thereforenbsp;is 12 h. 4 h. 25 m. r= 16 h. 25 m. Andnbsp;the fhorteft day is 12 h. � 4 h. 25 m. = 7 h.nbsp;35 �1- .

Thus, if the longed: day is 13�: hours =2x6 h. 45 m. and 45 minutes in time being equalnbsp;to 1degrees.

And the fame way, the latitudes, where the feveral geographical climates and parallels begin,nbsp;may be found ; and the latitudes of places, thatnbsp;are afligned in authors from the length of theirnbsp;days, may be examined and correded.

NOTE 3. The fame rule for finding the longeft day in a given latitude, diftinguifhes thenbsp;hour-lines that are necefiary to be drawn on anynbsp;dial from thofe which would be fuperfiuous.

In lat. 52� 10' the longeft day is 16 h. 32 m. and the hour-lines are to be marked from 44 m.

In the fame latitude, let the dial of Art. 7. Fig. 4. be propofed ; and the elevation of itsnbsp;ftile (or the latitude of the place d, whofe horizon is parallel to the plane of the dial) beingnbsp;9'; the longed day at d, that is, the longed:nbsp;time that the fun can illuminate the plane of thenbsp;dial, will (by the rule H zz �� L D) benbsp;twice 6 hours 27 minutes =: 12 h. 54 m. Thenbsp;difference of longitude of the planes d and Znbsp;was found in the fame example to be 36� 2' ;nbsp;in time, 2 hours 24 minutes; and the declination of the plane was from the fouth towards thenbsp;weft. Adding therefore 2 h. 24 min. to 5 h.nbsp;33 m. the earlieft: fun-rifing on a horizontal dialnbsp;at d, the fum 7 h. 57 m. fhews that the morning hours, or the parallel dial at Z, ought tonbsp;begin at 3 men. before VIII. And to the latednbsp;fun-fetting at d, which is 6 h. 27 m. adding thenbsp;fame two h. 24 m. the fum 8 h. 51 m. exceedingnbsp;6 h. 16 m. the lated fun-fetting at Z, by 35 m.nbsp;Ihews that none of the afternoon hour-lines arenbsp;fuperfluous. And the 4 h. 13 m. from III h.nbsp;44 m. the fun rifing at Z to VII h; 57 m. thenbsp;fun-rifmg at d, belong to the other face of thenbsp;dial; that is, to a dial declining 36� from northnbsp;to eaft, and inclining 15�.

If H, I, and D are given, then (by Art, 2. of Rule II.) from H having found the altitudenbsp;and its complement Zd\ and the arc P D (the

diftance from the pole) being given ; fay, As the co-fine of the altitude is to the fine of thenbsp;diftance from the pole, fo is the fine of the hour-diftance from the meridian to the fine of thenbsp;azimuth diftance from the meridian.

Let the latitude be 51� 30' north, the declination 15� 9' fouth, and the time II h. 24 m. in the afternoon, when the fun begins to illuminate a vertical wall, and it is required to findnbsp;the pofition of the wall.

Then, by the foregoing theorems, the complement of the altitude will be 81� nbsp;nbsp;nbsp;and

P d the diftance from the pole being 109� 5', and the horary diftance from the meridian, ornbsp;the angle P Z, 36�.

Take the log. fin. 81� 32'4- 1.99525 Remains -----nbsp;nbsp;nbsp;nbsp;1.75861 = log.

This praxis is of Angular ufe on many oc-cafions; in finding the declination of vertical planes more exactly than in the common way,nbsp;efpecially if the tranfit of the fun�s center is ob-ferved by applying a ruler with fights, eithernbsp;plain or telefcopical, to the wall or plane, whofcnbsp;declination is required.�In drawing a meridianline, and finding the magnetic variation.�Innbsp;finding the bearings of places in terreftrial fur-veys; the tranfits of the fun over any place, ornbsp;his horizontal diftance from it being obferved,nbsp;together with the altitude and hour.�And

thence determining fmall differences of longitude.�In obferving the variation at fea, amp;c.

The learned Mr, Andrew Reid invented an inftrument feveral years ago, for finding thenbsp;latitude at fea from two altitudes of the fun, ob-ferved on the fame day, and the interval of thenbsp;obfervations, meafured by a common watch.nbsp;And this inftrument, whofe only fault was thatnbsp;of its being fomewhat expenfive, was made bynbsp;Mr. Jachfon. Tables have been lately computednbsp;for that purpofe.

But we may often, from the foregoing rules, refolve the fame problem without much trouble;nbsp;efpecially if we fuppofe the mafter of the fhip tonbsp;know within 2 or 3 degrees what his latitude is.nbsp;Thus.

pute the hours of obfervation for both fuppo-fitions. If one interval of thofe computed hours coincides with the interval obferved, thenbsp;queftion is folved. If not, the two diftances ofnbsp;the intervals computed, from the true interval,nbsp;will give a proportional part to be added to, ornbsp;fub�rafted from, one of the latitudes affbmed.nbsp;And if more cxactnefs is required, the operationnbsp;may be repeated with the latitude alreadynbsp;found.

But whichever way the queftion is folved, a proper allowance is to be made for the differencenbsp;of latitude arifing from the fhip�s courfe in thenbsp;time between the two obfervations.

To iht gnomonic projedion, there is fometimes added a ftereographic proje�lion of the hour-circles, and the parallels of the fun�s declination,nbsp;on the fame horizontal plane the upright fidenbsp;of the gnomon being floped into an edge, Handing perpendicularly over the center of the pro-jedlion: fo that the dial, being in its due pofition,nbsp;the (hadow of that perpendicular edge is a vertical circle pafling through the fun, in the ftereographic projedion.

The months being duly marked on the dial, the fun�s declination, and the length of the day atnbsp;any time, are had by infpedion (as alfo his altitude, by means of a fcale of tangents). But itsnbsp;chief property is, that it may be placed true,nbsp;whenever the fun fliines, without the help Of anynbsp;other inftrument.

Let d be the fun�s place in the ftereographic projedlion, x dyz the parallel of the fun�s declination, Z i a vertical circle through the fun�snbsp;center, P d the hour-circle; and it is evident,nbsp;that the diameter of this projedion beingnbsp;placed duly north and fouth, thefe three circlesnbsp;will pafs through the point d. And therefore,nbsp;to give the dial its due pofition, we have Onlynbsp;to turn its gnomon toward the fun, on a horizontal plane, until the hour on the commonnbsp;gnomonic projedioh coincides with that markednbsp;by the hour-circle P d, which paftes through thenbsp;interfedio.n of the ftiadow Z d with the circle ofnbsp;the fun�s prefent declination.

The Babylonian and Italian dials reckon the hours, not from the meridian, as with us, but

from the fun�s rifing and fetting. Thus, in Plate Italy, an hour before fun-fet is reckoned the 23dnbsp;hour i two hours before fun-fet, the 2 2d hour ;nbsp;and fo of the reft. And the lhadOw that marksnbsp;them on the hour-lines, is that of the point of anbsp;ftile. This occafions a perpetual variation between their dials arid clocks, which they muftnbsp;correft from time to time, before it arifes to anynbsp;f�nfible quantity, by fetting their clocks fo muchnbsp;fafter or flower. And in Italy, they begin theirnbsp;day, arid regulate th?ir clocks, not from fun-fet,nbsp;but from about mid-twilight, when the AveMarianbsp;is faid; which correds tlie difference that wouldnbsp;otherwife be betweeh the clock and the dial.

The improvements w'hich have been made in all forts of inftruments and machines for meafur-ing time, have rendered fucli dials of littlenbsp;accouric. Yet, as the theory of them is ingenious, and they are really, in foihe refpeds, thenbsp;beft contrived of any for vulgar ufe, a general ideanbsp;of their deferiptiOri rriay not be uriacceptable.

Let Fig. 5. repfefent an erebf direct fouth wall, on which a Babylonian dial is to be drawn,nbsp;Ihewing the hours from fun rifing; the latitudenbsp;of the place, whofe horizon is parallel to tlienbsp;wall, being equal to the ahgle KC R. Make,nbsp;as for a common dial KG�KR (which is perpendicular to CR) the radius of the cquinodialnbsp;^ and draw R S perpendicular to C K fornbsp;the ftile of the dial; the fhadow of whofe pointnbsp;R is to mark the hours, when SR is fet uprightnbsp;cri the plane of the.dial.

Then it is evident, that in the contingent line AB the fpaces K i, K 2, � 3, amp;c. beingnbsp;taken equal to the tangents'of the hour diftancesnbsp;from the meridian, to the radius KG, one, two,nbsp;three, amp;c. hours after fun rifing, on the equi-rioffial day ; the ftiadow of the point R will be'

length of a day is 14 equinoftial hours, the unequal hour is then |4- or ^ of an hour, thatnbsp;is, 70 miriiues �, and the nodurna! hour is 50nbsp;minutes. 1 he firft watch begins at VII (fun-iet)i the fecund at three times 50 minutes after,nbsp;viz. !X h. 30 m. the third always at midnight;nbsp;tr,e morning watch at 4- hour paft II.

If it were req ,ired to draw a dial for {hewing thefc unequal hours, or lath parts of the day,nbsp;v.'e muft take as many declinations of the fun asnbsp;are thought ncccfiary, from the equator towardsnbsp;each tropic : and having computed the fun�snbsp;altitude and azimuth for Vi-j-r\r5 parts, amp;c.nbsp;of each of the diurnal arcs belonging to the declinations alTumcd : by thefe, the feveral pointsnbsp;in the circles of declinat'on, where the fhadownbsp;of the ftile�s point falls, are determined : andnbsp;curve lines drawn through the points of annbsp;homologous divifion will be the hour-lines re-cjuired.

Of the right placing of dials., and having a true meridian line for the regulating of clocks andnbsp;watches.

The plane on which the dial is to reft, being duly prepared, and every thing necelTaiy fornbsp;fixing it, you may find the hour tolerably exadnbsp;by a laige equinoftial ring dial, and fet yournbsp;watch to it. And then the dial may be fixed bynbsp;the watch at your leifure.

If you would be more exaft, take the fun�s altitude by a good quadrant, noting the precifenbsp;time of obfcrvation by a clock or watch. Then,nbsp;compute the time for the altitude obferved, (bynbsp;the rule, page 364) and fet the watch to agreenbsp;with that time, according to the fun. A Hadley\

quadrant is very convenient for this purpofe ; for, by if you may take the angle between thenbsp;fun and his image, rcfiefted from a balbn ofnbsp;water: the half of which angle, fubtra�ling thenbsp;refraftion, is the altitude required. '1 his isnbsp;beft done in fummer, and the nearer the lun isnbsp;to the prime vertical (the eaft or weft azimuth)nbsp;when the obfervation is made, fo much thenbsp;better.

Or, in fummer, take two equal altitudes of the fun in the fame day; one a.iy time between 7 andnbsp;JO o�clock in the morning, the other between 2nbsp;and 5 in the afternoon ; noting the moments ofnbsp;thefe two obfervations by a clock or watch : andnbsp;if the watch (hews the oljlervations to be atnbsp;equal diftances from noon, it agrees exa�'tlynbsp;with the lun if nor, the watch muft be cor-re�ed by half the difference of the forenoon andnbsp;afternoon intervals; and then the dial may benbsp;fee true by the watch.

'1 hus, for example, fuppofe you have taken the fun�s altitude when it Vv'as 20 minutes paftnbsp;Vill in the morning by the watch ; and found,nbsp;by obferving in the afternoon, that the fun hadnbsp;the fame altitude io minutes before IlII; thennbsp;it is plain, that the watch was 5 minutes toonbsp;faft for the fun : for 5 minutes after XII is thenbsp;middle time between VIII li. 20 m, in thenbsp;morning, and III h. 50 m. in the afternoon; andnbsp;therefore, to make the watch agree with the fun,nbsp;it muft be fet back five minutes.

A good meridian line, for regulating clocks A ?nert-. or watches, may be had by the followingnbsp;method.

Make a round hole, almoft a quarter of an inch diameter, in a thin plate of metal; and fixnbsp;the plate in the top of a iouth window, in fuch anbsp;B b 3nbsp;nbsp;nbsp;nbsp;manner

manner, that it may recline from the zenith at an angle equal to the co-latitude of your place, asnbsp;nearly as you can gnefs �, for then, the plate willnbsp;face the fun direftly at noon on the equinodtialnbsp;days. Let the fun ihine freely through the holenbsp;into the room �, and hang a plumb-line to thenbsp;ceiling of the room ; at leaft five or fix feet fromnbsp;the window, in fuch a place as that the fun�snbsp;rays, tranfmitted through the hole, may fallnbsp;upon the line when it is noon by the clock *,nbsp;and having marked the faid place on the ceiling,nbsp;take away the line.

Having adjufted a Aiding bar to a dove-tail groove, in a piece of wood about 18 inches long,nbsp;and fixed a hook into the middle of the bar, nailnbsp;the wood to the above-mentioned place on thenbsp;deling, parallel to the fide of the room in whichnbsp;the window is: the groove and bar being towards the floor. Then, hang the plumb-linenbsp;upon the hook in the bar, the weight or plummet reaching almoft to the floor -, and the wholenbsp;will be prepared for farther and proper adjuft-ment.

This done, find the. true folar time by either of the two laft methods, and thereby regulate,nbsp;your clock. Then, at the moment of next noonnbsp;by the clock, when the fun fhines, move thenbsp;Aiding bar in the groove until the fhadow of thenbsp;plumb-line bifeds the image of the fun (madenbsp;by his rays tranfmitted through the hole) on thenbsp;floor, wall, or on a white fcreen placed on thenbsp;north fide of the line ; the plummet or weightnbsp;at the end of the line hanging freely in a pail ofnbsp;water placed below it on the fioor.gt;^But becaufenbsp;this may not be quite correfil for the firfl: time,nbsp;on account that the plummet will not fettle immediately, even in water j it may be farther cor-

refted

recSed on the following days, by the above method, with the fun and clock; and fo broughtnbsp;to a very great exalt;5lnefs.

N.B. The rays tranfmitted through the hole, �will caft but a faint image of the fun, even on anbsp;white fcreen, unlefs the room be fo darkenednbsp;that no fun-fliine may be aljowed to enter, butnbsp;what comes through the fmall hole in the plate.nbsp;And always, for fome time before the obferva-tion is made, the plummet ought to be immerfednbsp;in a jar of water, where it may hang freely ; bynbsp;which means the line will fjon become heady,nbsp;which otherwife would be apt to continuenbsp;fwinging.

As this meridian line will not only be fuffi-cient for regulating of clocks and watches to the true time by equation tables, but alfo for mollnbsp;aftronomical purpofes, I fhall fay nothing of thenbsp;magnificent and expenfive meridian lines atnbsp;Bologna and Rome, nor of the better methods bynbsp;which aftronomers obferve precifely the tranficsnbsp;of the heavenly bodies on the meridian.

Shewing how to calculate the mean time of any New or hull Moon, or Eclipfe, from the creation of thenbsp;world to the year of CHRIST 5800.

IN the following tables, the mean lunation is about a 20th part of a fecond of time longernbsp;than its meafure as now printed in the thirdnbsp;edition of my Aftronomy �, which makes a difference of an hour and 30 minutes in 8000nbsp;years.�But this is not material, when only thenbsp;mean times are required.

EXAMPLE I.

Required the time of new moon in September, 17^4? (a year not inferted in the table)

birth � nbsp;nbsp;nbsp;�nbsp;nbsp;nbsp;nbsp;1753nbsp;nbsp;nbsp;nbsp;10 9 24 56

And join September nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;2 22 21 8

Thefe times, being collefted, would Ihew the mean time of the required new moon innbsp;September 1764, to be on the 26th day, at 2nbsp;hours 2 min. 12 fee. paft noon. But, as it is innbsp;a leap-year, and after February, the time is onenbsp;day too late. So, the true mean time is September the 25th, at 2 m. 12 fee. paft II in thenbsp;afternoon.

N. B.

N. B. The tables always begin the day at noon, and reckon thenceforward, to the noonnbsp;of the day following,

To find the mean time of full moon in any given year and month after the Chrifiian Mr a.

Having colledlcd the moon�s mean motion from the fun for the beginning of the givennbsp;year and month, and fubtrafted their fum fromnbsp;12 figns (as in the former example) add 6 fignsnbsp;to the remainder, and then proceed in all re-fpedts as above.

And the remainder will be Next lefs mean mot. for 40nbsp;min. fubt. _nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-

So, the mean time, according to the tables, is the nth of September, at 7 hours 40 minutesnbsp;8 feconds paft noon. One day too late, beingnbsp;after February in a leap year.

And thus may the mean tiine of any new or full moon be found, in any year after the ChriFnbsp;tian iEra.

��0 find the mean time of new or full jnoon in any given year and month before the Chrijlian JEra.

If the given year before the year of CHRIST I be found in the third column of the table,nbsp;under the title Tears before and after CHRIST,nbsp;write it out, together with the given month,nbsp;and join the mean motions. But, if the givennbsp;year be not in the table, take out the nextnbsp;greater one to it that you find ; which beingnbsp;ftill farther hack than the given year, add asnbsp;many cornpleat years to it as will bring thenbsp;time forward to the given year-, then join thenbsp;month, and proceed in all refpeds as above.

EXAM-

The next greater year in the table is 600; which being 15 years before the given year,nbsp;add the mean motions for 15 years to thofe ofnbsp;600, together with thofe for the beginning ofnbsp;May.

So,

So, the mean time by the tables, was the 29th of May, at 3 hours 3 min. 14 fee. paftnbsp;noon. A day later than the truth, on accountnbsp;of its being in a leap-year. For as the year ofnbsp;CHRIST I was the firft after a leap-year,nbsp;the year 585 before the year i was a leap-yearnbsp;of courfe.

If the given year be after the Chriftian .Aira, divide its date by 4, and if nothing remains, itnbsp;is a leap-year in the old ftile. But if the givennbsp;year was before the Chriftian Mrz (or Year ofnbsp;CHRIST 1) fubtra�l one from its date, andnbsp;divide the remainder by 4; then, if nothingnbsp;remains, it was a leap-year j otherwife not.

To find whether the fun is eclipfed at the time of any given change, or the moon at any given full.

From the Table of the fun's mean motion (or diftance) from the moorss afeending node, colleftnbsp;the mean motions anfwering to the given time �,nbsp;and if the refult Ihews the fun to be within 18nbsp;degrees of either of the nodes at the time ofnbsp;new moon, the fun will be eclipfed at that time.nbsp;Or, if the refult Ihews the fun to be within 12nbsp;degrees of either of the nodes at the time of fullnbsp;moon, the moon will be eclipied at that time, innbsp;or near the contrary nodci otherwife not.

exam

The moon changed on the 26th of September 1764, at 2 h. 2 m. (negleSing the feconds) after noonnbsp;(See Example I.) Whether the fun wasnbsp;eclipfed at that time ?

Now, as the defcending node is juft oppofite to the afcending, (viz. 6 figns diftant from it) andnbsp;the tables fhew only how far the fun has gonenbsp;from the afcending node, which, by this exam-ple, appears to be 6 figns 9 degrees 32 minutesnbsp;34 feconds, it is plain that he miift have thennbsp;been eclipfed; as he was then only 9� 32' 34quot;nbsp;Ihort of the defcending node.

E X A M-

remainder, fubtra�t the next lefs mean motions belonging to whatever menth you find them innbsp;the table ; and from heir remainder fubtradl thenbsp;next iels mean motion for days^ and fo on fornbsp;hours minulei : the refuk of all which willnbsp;fhew tne time of the fun�s mean conjundionnbsp;with the afeending node of the moon�s orbit.

Required the time of ti e fun's conjunSlion with the afeending node in the year 17D4

And there remains nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;2 29 55 45

Hence

Hence it appears, that the fun will pafs by the moon�s afeending node on the 27th of March,nbsp;at 14 hours 5 minutes paft noon; viz, on thenbsp;28th day, at 5 minutes paft II in the morning,nbsp;according to the tables : but this being in anbsp;leap-year, and after February, the time is onenbsp;day too late. Confcquently, the true time is atnbsp;5 mm. paft II in the morning on the 27th day jnbsp;at which time, the defcending node will be di-redlly oppofne to the fun.

It 6 figns be added to the remainder arifing from the firft fubtradtion, (viz from 12 figns)nbsp;and then the work carried on as in the laftnbsp;example, the refult will give the mean time ofnbsp;the fun�s conjuntftion with the defcending node.nbsp;Thus, in

To find when the fun will be in conjundiion with the defcending node in the year 1764 ?

fubt. - nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;016 37 4

So that, according to the tables, the fun will be in conjundlion with the defeending node on thenbsp;16th of September, at 21 hours 31 minutes paftnbsp;noon : one day later than the truth, on accountnbsp;of the leap-year.

When the moon changers within 18 days before or after the fun�s conjundtion with cither of the nodes, the fun will be eclipfed at thatnbsp;change : and when the moon is full within 12nbsp;days before or after the time of the fun�s con-jundtion with either of the nodes, ftie will benbsp;eclipfed at that full: otherwife not.

If to the mean time of any eclipfe, either of the fun or moon, we add 557 Julian years 21 daysnbsp;18 hours II minutes and 51 feconds (in whichnbsp;there are exadlly 6890 mean lunations) we fhallnbsp;have the mean time of another eclipfe. For atnbsp;the end of that time, the moon will be eithernbsp;new or full, according as we add it to the timenbsp;of new or full moon; and the fun will be onlynbsp;45quot;' farther from the fame node, at the end ofnbsp;6nbsp;nbsp;nbsp;nbsp;the

	Moon fjom fun.				Moon from fun.				Moon from lun. 1
VJ cegt;	s	0				0			IVl.	/	//	///
					M.					//
					M.				5,	//	//?	'/-/
I	0	12	II	27	S.	//	///	f///	Th.	/ /	////	V
2	p	24	22	53	-
		24	22	53
3	I	6	34	20	I	0	3'	29	31	15	44	47
. 4	I	18	45	47	2	1	0	57	32	t6	15	16
5	2	0	57	13	3	1	31	26	33	16	45	44
, 6	2	13	8	40	4	2	I	54	34	17	1�	13
7	2	25	20	7	5	2	32	23	35	17	46	42
8	3	7	31	34	6	3	2	52		18	17	10
9	3	19	43	0	7 8	3	33	20	37	18	47	39
10	4	I	54	27	7 8	4	3	49	38	�9	18	7
It	4	14	5	54	9	4	34	18	39	19	48	36
12	4	2�	17	20	to	5	4	46	40	20	19	5
*3	5	8	28	47	11	5	35	15	4'	20	49	33
14	5	20	40	�4	12	6	5	43	42	21	20	2
'5	6	2	51	40'	13	6	3�	12	43	21	50	31
16	6	'5	3	7	14	7	6	41	44	22	20	59
J7	6	27	14	34	15	7	37	9	4.5	22	5�	28
18	7	9	26	0	16	8	7	38	46	23	21	56
#19	7	21	37	27	17	8	38	6	47	2 3	52	25
20	8	3 4�		54	18	9	8	35	48	24	22	54
21	8	16	0	21	19	9	39	4	49	24	53	22
22	8	28	I I	47	20	to	9	32	50	25	23	51
23	9	to	23	14	21	to	40	I	51	25	54	IQ
H.	9	22	34	4�	22	1 i	JO	30	52	26	24	48
25	to	4 46		7	23	11	40	58	53	26	55	17
26	) 0	I�	57	34	24	12	11	27	54	27	25	45
27	10	29	9	i	25	12	41	55	55	27	56	14
28	II	I I	20	27	26	13	12	24	5�	28	26	43
29	11	23	31	54	27	13	42	53	57	28	SI	II
30	0	5 43		21	2�	14	13	21	58	29	27	40
31	0	17 54		47	29	14	43	SO	59	29	58	8
32	I	0	6	IS	30	15	14	18	60	30	28	37

I Lunation ~zg'' 12^ 4.4� 5* 6�'' zi'' i4V2^viQ�

be added to the time for which the moon�s mean diftance from the fun is given. But, when the mean time of anynbsp;new or full moon js required in leap-year after February,nbsp;a day mull: be fubtrafled from the mean time thereof, asnbsp;found by the tables. In common years they give the daynbsp;right.

Years

39^ nbsp;nbsp;nbsp;of tie Sun's mean Motion from tie Moon's

Afcending Node.

In leap years,' after Fe�ir�ary, a'dd� one day and one day�s motion to the time at which the fun's mean dif-ance from the afcending node is required.

I N D E X.

INDEX.

jOanger of people�s rifing haftily ii? a coach or boat when it is likelynbsp;nbsp;nbsp;nbsp;to be overfetnbsp;nbsp;nbsp;nbsp;14

Days lengthened by the refradlion of the fun�s rays 204 Declination of thenbsp;nbsp;nbsp;nbsp;fun and flatsnbsp;nbsp;nbsp;nbsp;3CQ

Defcending velocity, gives a power of equal afcent 12 Dialingnbsp;nbsp;nbsp;nbsp;316�377

Face of the heaven and earth, how reprefented in a machinenbsp;Fermentationsnbsp;Eire dampsnbsp;Fluids, their preffurenbsp;Fire enginenbsp;Forces, centralnbsp;��combinednbsp;Forcing pump

Hour-circles Hydraulic enginesnbsp;Hydroftaticsnbsp;Hydroftatic balancenbsp;-paradoxnbsp;�bellowsnbsp;-tables

Inadlivity of matter Inclined planenbsp;Infinite divifibility of matternbsp;Intermitting fprings

346

fmall animals in the milt of a cod-filh Lenfes, their propertiesnbsp;Lever, its ufe

INDEX.

Long (Rev. Dr.) his nbsp;nbsp;nbsp;c^rijusnbsp;nbsp;nbsp;nbsp;experimentnbsp;nbsp;nbsp;nbsp;withnbsp;nbsp;nbsp;nbsp;anbsp;nbsp;nbsp;nbsp;cnn-

Objedls, how their images are formed nbsp;nbsp;nbsp;bynbsp;nbsp;nbsp;nbsp;means of

� nbsp;nbsp;nbsp;�why they appear coloured whennbsp;nbsp;nbsp;nbsp;feennbsp;nbsp;nbsp;nbsp;through

Optic nerve, why that part of the image nbsp;nbsp;nbsp;whichnbsp;nbsp;nbsp;nbsp;falls

Silver, how much heavier than its bulk of water S/are (Dr.) his dangerous experimentnbsp;Solidity of matternbsp;Specific gravities of bodiesnbsp;Spedtacles, why fome eyes require themnbsp;Spirituous liquors, to know whether they are genuinenbsp;or notnbsp;nbsp;nbsp;nbsp;160

Tablesfor calculating new and full moons and eclipfes 384 Telefcopes, refradling and refledlingnbsp;nbsp;nbsp;nbsp;227�232

SUPPLEMENT

LECTURES.

The Defcription of a new and fafe Crane, which has four different Powers, adapted to differentnbsp;Weights.

TH E common crane confills only of a large wheel and axle; and the rope, bynbsp;which goods are drawn up from fliips,nbsp;or let down from the quay to them, winds ornbsp;coils round by the axle, as the axle is turned bynbsp;men walking in the wheel. But, as thefenbsp;engines have nothing to flop the weight fromnbsp;running down, if any of the men happen to tripnbsp;or fall in the wheel, the weight defcends, andnbsp;turns the wheel rapidly backward, and tofies thenbsp;men violently about within it; which has pro-duced melancholy inftances, not only of limbsnbsp;^ ^ ^nbsp;nbsp;nbsp;nbsp;broke.

MECHANICS.

broke, but even of lives loft, by this ill-judged conftruftion of cranes. And befides, they havenbsp;but one power for all forts of weights; fo thatnbsp;they generally fpend as much time in raifing anbsp;fmall weight as in raifing a great one.

Thefe imperfections and dangers induced me to think of a method of remedying them. Andnbsp;for that purpofe, 1 contrived a crane with anbsp;proper ftop to prevent the danger, and withnbsp;different powers fuited to different weights; fonbsp;that there might be as little lofs of time as pof-fible ; and alfo, that when heavy goods are letnbsp;down into ftiips, the defeent may be regular andnbsp;deliberate.

This crane has four different powers; and, I believe, it might be built in a room eight feet innbsp;width : the gib being on the outfide of th�nbsp;room.

Three trundles, with different numbers of ftaves, are applied to the cogs of a horizontalnbsp;wheel with an upright axle ; and the rope, thatnbsp;draws up the weight, coils round the axle. Thenbsp;wheel has 96 cogs, the largeft trundle 24 ftaves,nbsp;the next largeft has 12, and the fmalleft has 6.nbsp;So that the largeft trundle makes 4 revolutionsnbsp;for one revolution of the wheel; the next makesnbsp;8, and the fmalleft makes 16. A winch isnbsp;occafionally put upon the axis of either of thefenbsp;trundles, for turning it �, the trundle being thennbsp;ufed that gives a power beft fuited to the weight:nbsp;and the handle of the winch deferibes a circle innbsp;every revolution equal to twice the circumference of the axle of the wheel. So that thenbsp;7nbsp;nbsp;nbsp;nbsp;length

As the power gained by any machine, or eno-ine whatever, is in diredt proportion as thenbsp;velocity of the power is to the velocity of thenbsp;weight; the powers of this crane are eafily efti-mated, and they are as follows.

If the winch be put upon the axle of the largeft trundle, and turned four times round,nbsp;the wheel and axle will be turned once round :nbsp;and the circle defcribed by the power that turnsnbsp;the winch, being, in each revolution, double thenbsp;circumference of the axle, when the thicknefsnbsp;of the rope is added thereto �, the power goesnbsp;through eight times as much fpace as the weightnbsp;rifes through: and therefore (making fomenbsp;allowance for friftion) a man will raife eightnbsp;times as much weight by the crane as he wouldnbsp;by his natural ftrength without it; the power,nbsp;in this cafe, being as eight to one.

If the winch be put upon the axis of the next trundle,the powerwillbeas fixteentoone,becaufenbsp;it moves i6 times as fail; as the weight moves.

If the winch be put upon the axis of the frnalleft trundle, and turned round ; the powernbsp;will be as 32 to one.

But, if the weight fhould be too great, even for this power to raife, the power may benbsp;doubled by drawing up the weight by one ofnbsp;the parts of a double rope, going under a puUevnbsp;in the moveable block, which is hooked to thenbsp;weight below the arm of the gib ; and then thenbsp;^ ^ 3nbsp;nbsp;nbsp;nbsp;power

MECHANICS.

againft the edge of the wheel [7, and thereby hinder the too quick defcent of the weight; andnbsp;will quite ftop the weight if pulled hard. Andnbsp;if the man who pulls the lever, Ihould happennbsp;inadvertently to let it go; the elaftic bar willnbsp;fuddenly pull it up, and the catch will fall downnbsp;and ftop the machine.

IV W are two upright rollers above the axis or upper gudgeon of the gib E : their ufe is tonbsp;let the rope C bend upon them, as the gib isnbsp;turned to either fide, in order to bring the weightnbsp;over the place where it is intended to be letnbsp;down.

JV. B, The rollers ought to be fo placed, that if the rope C be ftretched clofe by their utmoftnbsp;fides, the half thicknefs of the rope may benbsp;perpendicularly over the center of the uppernbsp;gudgeon of the gib. For then, and in no othernbsp;pofition of the rollers, the length, of the ropenbsp;between the pulley in the gib and the axle ofnbsp;the great wheel will be always the fame, in allnbsp;pofitions of the gib: and the gib will remain innbsp;any pofition to which it is turned.

When either of the trundles is not turned by the winch in working the crane, it may be drawnnbsp;off from the wheel, after the pin near the axis ofnbsp;the trundle is drawn our, and the thick piece ofnbsp;wood is raifed a little behind the outward fup-porter of the axis of the trundle. But this isnbsp;not material: for, as the trundle has no friflionnbsp;on its axis but what is occafioned by its weight,nbsp;it will be turned by the wheel without any fen-fible refiftance in working the crane.

MECHANICS.

A Pyrometer, that makes the Erpanfton of M�taP by Heat vifibk to the five and forty thoufandthnbsp;Part of an Inch.

The upper furface of this machine is repre-fcnted by Fig. i. of Plate II. Its frame A BCD is made of mahogany wood, on which is a circlenbsp;divided into 360 equal parts ; and within thatnbsp;circle is another, divided into 8 equal parts. Ifnbsp;the fhort bar E be pulhed one inch forward (ornbsp;toward tne center of the circle) the index e willnbsp;be turned 125 times round the circle of 360 partsnbsp;or degrees. As 125 times 360 is 45,000, �tis evident, that if the bar � be moved only the 45 ,ooodthnbsp;part of an inch, the index will move one degreenbsp;of the circle. But as in my pyrometer, the circlenbsp;is 9 inches in diameter, the motion of the indexnbsp;is vifible to half a degree, which anfwers to thenbsp;ninety thoufandth part of an inch in the motionnbsp;or pufhing of the Ihort bar E.

One end of a long bar of metal F is laid into a hollow place in a piece of iron G, which isnbsp;fixed to the frame of the machine �, and thenbsp;other end of this bar is laid againft the end ofnbsp;the Ihort bar �, over the fupporting crofs barnbsp;HI: and, as the end � of the long bar is placednbsp;clofe againft the end of the Ihort bar, �tis plain,nbsp;that if F expands, it will pulh E forward, andnbsp;turn the index e.

�I he machine Hands on four fhort pillars, high enough from a table, to let a fpiric-lampnbsp;be put on the table under the bar F-, and whennbsp;that is done, the heat of the flame of the lampnbsp;expands the bar, and turns the index.

Put on the brafs bar F, and fet the index to the 360th degree : then put the lighted lampnbsp;under the bar, and count the number of fecondsnbsp;in which the index goes round the plate, fromnbsp;360 to 360 again; and then blow out the lamp,nbsp;and take away the bar.

This done, put on an iron bar F where the brafs one was before, and then fet the index tonbsp;the 360th degree again. Light the lamp, andnbsp;put it under the iron bar, and let it remain juftnbsp;as many feconds as it did under the brafs one ;nbsp;and then blow it out, and you will fee hownbsp;many degrees the index has moved in the circle :nbsp;and by that means you will know in what proportion the expanfion of iron is to the expanflonnbsp;of brafs; which 1 find to be as 2 iq is to 360, or

The bars ought to be exadly of equal fize-, and to have them fo, they fhould be drawn, like

When the lamp is blown out, you will fee the index turn backward �, which {hews that thenbsp;metal contratfts as it cools.

MECHANICS.

In Fig. 2. A a is the fhort bar, which moves between rollers ; and, on the fide a it has 15nbsp;teeth in an inch, which take into the leaves of anbsp;pinion B in number) on whofc axis is thenbsp;wheel C of joo teeth, which take into the 10nbsp;leaves of the pinion D, on whole axis is thenbsp;wheel � of too teeth, which take into the 10nbsp;leaves of the pinion �, on the top of whole axisnbsp;is the index above mentioned.

Now, as the wheels C and E have 100 teeth each, and the pinions D and F have ten leavesnbsp;each; �tis plain, that if the wheel C turn oncenbsp;round, the pinion F and the index on its axisnbsp;will turn 100 times round. But, as the firfl:nbsp;pinion B has only iti leaves, and the bar A-anbsp;that turns it has 15 teeth in an inch, which isnbsp;12 and a fourth part more ; one inch motion ofnbsp;the bar will cattle the laft pinion F to turn annbsp;hundred times round, and a fourth part of annbsp;hundred over and above, which is 25. So that,nbsp;'\f A a ho pulhed one inch, F will be turned 125nbsp;times round.

A filk thread ^ is tied to the axis of the pinion D, and wound feveral times round it; and thenbsp;other end of the thread is tied to a piece ofnbsp;flender watch-fpring G which is fixed into thenbsp;ftud H. So that, as the bar � expands, andnbsp;pufhes the bar A a forward, the thread windsnbsp;round the axle, and draws out the fpring; andnbsp;as the bar contrafts, the fpring pulls back thenbsp;thread, and turns the work the contrary way,nbsp;which pufhes back the Ihort bar A a agai'nfl; thenbsp;long bar �. This fpring alwap keeps the teethnbsp;of the wheels in contafl: with the leaves of

In Fig. I. the eight divifions of the inner circle are fo many thoufandth parts of an inchnbsp;in the expanfion or contradlion of the bars �,nbsp;which is juft one thoufandth part of an inch fornbsp;each divifion moved over by the index.

This machine is reprefented by Fig. i. of Plate III, in which, A is a pipe or channel thatnbsp;brings water to the upright tube B. The waternbsp;runs down the tube, and thence into the horizontal trunk C, and runs out through holes atnbsp;d and e near the ends of the trunk on the contrary fides thereof.

The upright fpindle D is fixt in the bottom of the trunk, and ferewed to it below by thenbsp;nut g-, and is fixt into the trunk by two crofsnbsp;bars at �; fo that, if the tube B and trunk Cnbsp;be turned round, the fpindle D will be turnednbsp;alfo.

The top of the fpindle goes fquare into the rynd of the upper mill-ftone H, as in commonnbsp;mills; and, as the trunk, tube, and fpindle turnnbsp;round, the mill-ftone is turned round thereby. The lower, or quiefeent mill-ftone is reprefented by /; and K is the floor on which itnbsp;refts, and wherein is the hole L for letting the

meal run through, and fall down into a trough which may be about M. The hoop or cafenbsp;that goes round the mill-ftone refts on the floornbsp;Jf, and fupports the hopper, in the commonnbsp;way. The lower end of the fpindle turns in anbsp;hole in the bridge-tree GF, which fupports thenbsp;mill-ftone, tube, fpindle, and trunk. Thisnbsp;tree is moveable on a pin at h, and its other endnbsp;is fupported by an iron rod N fixt into it, thenbsp;top of the rod going through the fixt bracketnbsp;* O, and having a fcrew-nut o upon it, above thenbsp;bracket. By turning this nut forward or backward, the mill-ftone is raifed or lowered atnbsp;pleafure.

Whilft the tube B is kept full of water from the pipe J, and the water continues to run outnbsp;from the ends of the trunk the upper mill-ftone H, together with the trunk, tube, andnbsp;fpindle turns round. But, if the holes in thenbsp;trunk were ftopt, no motion would enfue evennbsp;though the tube and trunk were full of water.nbsp;For,

If there were no hole in the trunk, the pref-fure of the water would be equal againft all parts of its fides within. But, when the waternbsp;has free egrefs through the holes, its prelTurenbsp;there is entirely removed; and the preflurenbsp;againft the parts of the Tides which are oppofitenbsp;to the holes, turns the machine.

A Machine for demonflrating that, on equal Bottoms, the Prejfure of Fluids is in Proportion to their perpendicular Heights, without any regardnbsp;to their ^antities.

and the machine for lliewing it is repre-fented in Fig. 2. of Plate III. In which A \% �a. box that holds about a pound of water, a h c d enbsp;a glafs-tube fixt in the top of the box, having anbsp;fmall wire within it; one end of the wire beingnbsp;hooked to the end F of the beam of a balance,nbsp;and the other end of the wire fixt to a moveablenbsp;bottom, on which the water lies, within thenbsp;box; the bottom and wire being of equalnbsp;weight with an empty fcale (out of fight in thenbsp;figure) hanging at the other end of tiie balance.nbsp;If this fcale be pulled down, the bottom will benbsp;drawn up within the box, and that motion willnbsp;caufe the water to rife in the glafs-tube.

Put one pound weight into the fcale, which will move the bottom a little, and caufe thenbsp;water to appear juft in the lower end of thenbsp;tube at a; which Ihews that the water prelTesnbsp;with the force of one pound on the bottom; putnbsp;another pound into the fcale, and the water willnbsp;rife from a to b'm the tube, juft twice as highnbsp;above the bottom as it was when at a-, and then,nbsp;as its preffure on the bottom fupports two poundnbsp;weight in the fcale, �tis plain that the preffurenbsp;on the bottom is then equal to two pounds.nbsp;Put a third pound weight in the fcale, and thenbsp;3nbsp;nbsp;nbsp;nbsp;water

water will be raifed from h to c \n the tube, three times as high above the bottom as whennbsp;it began to appear in the tube at a ; whichnbsp;Ihews, that the fame quantity of water thatnbsp;prefled, but with the force of one pound onnbsp;the bottom, when raifed no higher than �,nbsp;preflTes with the force of three pounds on thenbsp;bottom when raifed three times as high to e innbsp;the tube. Put a fourth pound weight into thenbsp;fcale, and it will caufe the water to rife in thenbsp;tube from c to d, four times as high as it wasnbsp;when it was all contained in the box, whichnbsp;fliews that its prelTure then upon the bottom isnbsp;four times as great as when it lay all within thenbsp;box. Put a Afch pound weight into the fcale,nbsp;and the water will rife in the tube from d to if,nbsp;five times as high as it was above the bottomnbsp;before it rofe in the tube ; which fhews that itsnbsp;prefllire on the bottom is then equal to fivenbsp;pounds, feeing that it fupports fo much weightnbsp;in the fcale. And fo on, if the tube was llillnbsp;longer j for it would ftill require an additionalnbsp;pound put into the fcale, to raife the water innbsp;the tube to an additional height equal to thenbsp;fpace de-, even if the bore of the tube was fonbsp;fmall as only to let the wire move freely withinnbsp;it, and leave room for any water to get roundnbsp;the wire.

Hence we infer, that if a long narrow pipe or tube was fixed in the top of a cafk full ofnbsp;liquor, and if as much liquor was poured intonbsp;the tube as would fill it, even though it werenbsp;fo fmall as not to hold an ounce weight of liquor ; the prefibrc arifing from the liquor innbsp;the tube would be as great upon the bottom,

HYDROSTATICS.

and be in as much danger of burfting it out, as if the cafk was continued up, in its full fize, tonbsp;the height of the tube, and filled with liquor.

In order to account for this furprifing affair, we muft confider that fluids prefs equally in allnbsp;manner of diredions; and confequently thatnbsp;they prefs juft as ftrongly upward as they donbsp;downward. For, if another tube, as �, be putnbsp;into a hole made into the tpp of the box, andnbsp;the box be filled with water; and then, if waternbsp;be poured in at the top of the tube a b c d e, itnbsp;will rife in the tube � to the fame height as it docsnbsp;in the other tube; and if you leave off pouring,nbsp;when the water is at c, or any other place in thenbsp;tube a b c d e, you will find it juft as high in thenbsp;tube �; and if you pour in water to fill the firftnbsp;tube, the fecond will be filled alfo.

Now it is evident that the water rifes in the tube �, from the downward prefTure of the wa-teft in. the tube a b c d e, on the furface of thenbsp;water, contiguous to the infide of the top of thenbsp;box; and as it will ftand at equal heights innbsp;both tubes, the upward prefTure in the tube � isnbsp;equal to the downward prefTure in the other tube.nbsp;But, if the tube � were put in any other part ofnbsp;the top of the box, the rifing of the water in itnbsp;would ftill be the fame : or, if the top was fullnbsp;of holes, and a tube put into each of them, thenbsp;water would rife as high in each tube as it wasnbsp;poured into the tube a b c d e \ and then thenbsp;moveable bottom would have the weight of thenbsp;water in all the tubes to bear, befides the weightnbsp;of all the water in the box.

And

. feeing that the water is preffed upward into each tube, �tis evident that, if they be allnbsp;taken away, excepting the tube a b c d e, andnbsp;the holes in which they ftood be flopt up-, eachnbsp;part, thus ftopt, will be preffed as much upward as was equal to the weight of water in eachnbsp;tube. So that, the upward preffure againft thenbsp;infide of the top of the box, on every part equalnbsp;in breadth to the width of the tube ah c d e, willnbsp;be preffed upward with a force equal to thenbsp;whole weight of water in the tube. And confe-quently, the whole upward preffure againft thenbsp;top of the box, arifing from the weight ornbsp;downward preffure of the water in the tube, willnbsp;be equal to the weight of a column of water ofnbsp;the fame height with that in the tube, and of thenbsp;fame thicknefs as the width of the infide of thenbsp;box : and this upward preffure againft the topnbsp;will re-aft downward againft the bottom, andnbsp;be as great thereon, as would be equal to thenbsp;weight of a column of water as thick as thenbsp;moveable bottom is broad, and as high as thenbsp;water ftands in the tube. And thus, the paradox is folved.

The moveable bottom has no friftion againft the infide of the box, nor can any water getnbsp;between it and the box. The method of making it fo, is as follows :

In Fig. A B C D reprefents a feffion of the box, and abc d\s the lid or top thereof, whichnbsp;goes on tight, like the lid of a common papernbsp;fnuff-box. E is the moveable bottom, with anbsp;groove around its edge, and it is put into anbsp;bladder f g, which is tied clofe around it in thenbsp;E e

,8 nbsp;nbsp;nbsp;H Y DROSTATICS.

groove by a ftrong waxed thread the bladder coming up like a purfe within the box, and putnbsp;over the top of it at a and i all round, andnbsp;then the lid prefled on. So that, if water benbsp;poured in through the hole / / of the lid, it willnbsp;lie upon the bottom �, and be contained in thenbsp;fpace � h within the bladder �, and the bottom may be raifed by pulling the wire r, whichnbsp;is fixed to it at E: and by thus pulling thenbsp;wire, the water will be lifted up in the tube k,nbsp;and as the bottom does not touch againft thenbsp;infide of the box, it moves without fridion.

Now, fuppofe the diameter of this round bottom to be three inches (in which cafe, the area thereof will be 9 circular inches) and the diameter of the bore of the tube to be a quarter of annbsp;inch; the whole area of the bottom will be 144nbsp;times as great as the area of the top of a pinnbsp;that would fill the tube like a cork.

And hence it is plain, that if the moveable bottom be raifed only the 144th part of an inch,nbsp;the water will thereby be raifed a whole inch innbsp;the tube; and confequently, that if the bottomnbsp;be raifed one inch, it would raife the water tonbsp;the top of a tube 144 inches, or 12 feet, innbsp;height.

N. B. The box muft be open below the moveable bottom, to let in the air. Other-wife, the preflTure of the atmofphere would benbsp;fo great upon the moveable bottom, if it benbsp;three inches in diameter, as to require 108nbsp;pounds in the fcale, to balance that preffure�nbsp;before the bottom could begin to move.

In F/g-. I. of PLATE IV. ABCD'is an oblong fquare box, in one end of which is anbsp;round groove, as at a, from top to bottom, fornbsp;receiving the upright glafs tube /, which is bentnbsp;to a right angle at the lower end (as at i in Fig. 2.)nbsp;and to that part is tied the neck of a large bladder K, (Fig. 2.) which lies in the bottom of thenbsp;box. Over this bladder is laid the moveablenbsp;board L {Fig. 1, and 3.) in which is fixt an upright wire M and leaden weights, N N, tonbsp;the amount of 16 pounds, with holes in theirnbsp;middle, which are put upon the wire, over thenbsp;board, and prefs upon it with all their force.

The crofs bar p is then put on, to fecure the tube from falling, and keep it in an upright poli-tion : And then the piece EFG is to be put on,nbsp;the part G Aiding tight into the dove-tail�dnbsp;groove H, to keep the weights NN horizontal,nbsp;and the wire M upright �, there being a roundnbsp;hole e in the part E F for receiving the wire.

Tlffere are four upright pins in the four corners of the box within, each almoA an inch long, for the board L to reft upon; to keep it fromnbsp;preAing the fides of the bladder below it clofenbsp;together at Arft.

The whole machine being thus put together, pour water into the tube at top; and thenbsp;Water will run down the tube into the bladdernbsp;below the board i and after the bladder has beennbsp;E e 2nbsp;nbsp;nbsp;nbsp;filled

20 nbsp;nbsp;nbsp;hydrostatics.

filled up to the board, continue pouring water into the tube, and the upward preffure which itnbsp;will excite in the bladder, will raife the boardnbsp;�with all the weight upon it, even though thenbsp;bore of the tube fhould be fo fmall, that lefsnbsp;than an ounce of water would fill it.

This machine a�ls upon the fame principle, as the one laft defcribed, concerning the Hydro-jlatical paradox. For, the upward preffurenbsp;againft every part of the board (which thenbsp;bladder touches) equal in area to the area of thenbsp;bore of the tube, will be preffed upward with anbsp;force equal to the weight of the water in thenbsp;tube; and the fum of all thefe preffures, againftnbsp;fo many areas of the board, will be fufficient tonbsp;raife it with all the weights upon it.

In my opinion, nothing can exceed this Ample machine, in making the upward preffure of fluids evident to fight.

In Fig. I. of Plate V. Let ab cd\it z hill, within which is a large cavern A A near thenbsp;top, filled or fed by rains and melted fnow onnbsp;the top a, making their way through chinksnbsp;and crannies into the faid cavern, from whichnbsp;proceeds a fmall ftream C C within the body ofnbsp;the hill, and iffues out in a fpring at G on thenbsp;fide of the hill, which will run conftantly whilftnbsp;the cavern is fed with water.

From the fame cavern A A, let there be a fmall channel D, to carry water into the cavern

B i and from that cavern let there be a bended channel Ee F, larger than A joining with thenbsp;former channel C C, as at � before it comes to thenbsp;fide of the hill: and let the joining at � benbsp;below the level of the bottom of both thefenbsp;caverns.

As the water rifes in the cavern 5, it will rife as high in the channel E e F: and when it rifesnbsp;to the top of that channel at e, it will run downnbsp;the part e F and make a fwell in the fpringnbsp;C, which will continue till all the water is drawnnbsp;off from the cavern B, by the natural fyphonnbsp;Ee Fi (which carries off the water fafter fromnbsp;than the channel D brings water to it) and thennbsp;the fwell will ftop, and only the fmall channelnbsp;C C will carry water to the fpring G, till thenbsp;cavern B is filled to B again by the rill D-, andnbsp;then the water being at the top e of the channelnbsp;Ee F, that channel will a�l: again as a fyphon,nbsp;and carry off all the water from B to the fpringnbsp;G, and fo make a fwelling flow of water at G asnbsp;before.

To illuftrate this by a machine (Fig. 2.) let J be a large wooden box, filled with water andnbsp;let a fmall pipe C C (the upper end of which isnbsp;fixed into the bottom of the box) carry waternbsp;from the box to G, where it will run off con-ftantly, like a imall fpring. Let another fmallnbsp;pipe D carry water from the fame box to thenbsp;box or well B, from which let a fyphon EeFnbsp;proceed, and join with the pipe CC at �: thenbsp;bore of the fyphon being larger than the bore ofnbsp;the feeding-pipe D. As the water from thisnbsp;pipe rifes in the well 5, it will alfo rife as highnbsp;in the fyphon EeF and when the fyphon isnbsp;E c 3nbsp;nbsp;nbsp;nbsp;full

22 nbsp;nbsp;nbsp;HYDRAULICS.

full to the top e, the water will run over the bend down the part e F, and go off at thenbsp;mouth G; which will make a great ftream atnbsp;G: and that ftream will continuei till the fyphonnbsp;has carried off all the water from the well B �,nbsp;the fyphon carrying off the water fafter from Bnbsp;, than the pipe D brings water to it: and thennbsp;the fwell at G will ceafe, and only the waternbsp;from the fmall pipe C C will run off at G, tillnbsp;the pipe D fills the well B again ; and thennbsp;the fyphon will run, and make a fwell at G asnbsp;before.

And thus, we have an artificial reprefentation of an ebbing and flowing well, and of a reciprocating fpring, in a very natural and fimplonbsp;manner.

An Account of the Principles by which Mr. Blakey propofes to raife Water from Mines, or- fromnbsp;Rivers, to fupply Powns and Gentlemen's^Seats,nbsp;by his new invented Fire-Engine, for which henbsp;has received His MAJESTY�S Patent.

Although I am not at liberty to de-fcribe the whole of this firnple engine, yet I have the patentee�s leave to defcribe fuch anbsp;one as will Ihew the principles by which it alt;5Vs.

In Fig. 4. of Plate IV. let ^ be a large, ftrong, clofe velle! �, immerfed in water up tonbsp;the cock b, and having a hole in the bottom,nbsp;with a valve a upon it, opening upward withinnbsp;the veffei. A pipe B C rifes from the bottom

HYDRAULICS.

of this veflel, and has a cock c in it near the top, which is fmall there, for playing a verynbsp;high jet d. E is the little boiler (not fo big asnbsp;a common tea-kettle) which is conne�ted withnbsp;the veflel A hy the fteam pipe F-, and G is anbsp;funnel, through which a little water mull benbsp;occafionally poured into the boiler, to yield anbsp;proper quantity of fteam. And a fmall quantitynbsp;of water will do for that purpofe, becaufe fteamnbsp;pofleflTeth upwards of 14,000 times as muchnbsp;fpace or bulk as the water does from which itnbsp;proceeds.

The vefiel A being immerfed in water up to the cock E open that cork, and the water willnbsp;rufh in, through the bottom of the vefTel at 0,nbsp;and fill it as high up as the water ftands on itsnbsp;outfide ; and the water, coming into the veflel,nbsp;will drive the air out of it (as high as the waternbsp;rifes within it) through the cock b. When thenbsp;water has done ruftiing into the veflTel, fhut thenbsp;cock b, and the valve a will fall down, and hinder the water from being pufhed out that way,nbsp;by any force that prefteth on its furface. AHnbsp;the part of the veffel above b, will be full ofnbsp;common air, when the water rifes to b.

Shut the cock c, and open the cocks d and e-, then pour as much water into the boiler �nbsp;(through the funnel G) as will about half fillnbsp;the boiler; and then Ihut the cock r/, and leavenbsp;the cock e open.

This done, make a fire under the boiler and the heat thereof will raife a fteam from thenbsp;water in the boiler; and the fteam will makenbsp;its way thence, through the pipe Fy into thenbsp;E e 4nbsp;nbsp;nbsp;nbsp;vellel

vcflel /�; and the fteam will comprefs the air (above b) with a very great force upon the fur-face of the water in

When the top of the veflel J feels very hot by the fteam under it, open the cock c in thenbsp;pipe C; and the air being ftrongly comprelTednbsp;in J, between the fteam and the water therein,nbsp;will drive all the water out of the veflel J, upnbsp;the pipe B C, from which it will fly up in a jet

which is made in this manner after Mr. Blakey�s, three tea-cup fulls of water in the boiler willnbsp;aftbrd fteam enough to play a jet 30 feet high.

When all the water is out of the vcflel and the compreflfed air begins to follow the jet,nbsp;open the cocks b and d to let the fteam out ofnbsp;the boiler E and veffel A, and fhut the cock enbsp;to prevent any more fteam from getting into yf;nbsp;and the air will rufli into the veflel throughnbsp;the cock b, and the water through the valve a-,nbsp;and fo the veflel will be filled up with water tonbsp;the cock b as before. Then fhut the cock bnbsp;and the cocks c and d, and open the cock e;nbsp;and then, the next fteam that rifes in the boilernbsp;will make its way into the veflTel A again 5 andnbsp;the operation will go on, as above.

When all the water in the boiler E is evaporated, and gone off into fteam, pour a little more into the boiler, through the funnel G.

In order to make this engine raife water to any gentleman�s houfe ; if the houfe be on thenbsp;bank of a river, the pipe B C may be continued

�p to the intended height, in the diredtion H L Or, if the houfe be on the fide or top of a hill,nbsp;at a diftance from the river, the pipe, throughnbsp;which the water is forced up, may be laid alongnbsp;on the hill, from the river or fpring to the houfe.

The boiler may be fed by' a fmall pipe if, from the water that rifes in the main pipenbsp;�CHI-, the pipe K being of a very fmall bore,nbsp;fo as to fill the funnel G with water in the timenbsp;that the boiler E will require a frefh fupply.nbsp;And then, by turning the cock d, the water willnbsp;fall from the funnel into the boiler. 1 he funnel fhould hold as much water as will about halfnbsp;fill the boiler,

�When either of thefe methods of raifing water, perpendicularly or obliquely, is ufed, there willnbsp;be no occafion for having the cock c in thenbsp;main pipe BCHI: for fuch a cock is requifitenbsp;only, when the engine is ufed as a fountain.

' A contrivance may be very eafily made, from a lever to the cocks d, and e fo that, by pulling the lever, the cocks b and d may be openednbsp;when the cock e muft be fhut �, and the cock enbsp;be opened when b and d muft be fliut.

The boiler E fliould be inclofed in a brick wall, at a little diftance from it, all around; to give liberty for the flames of the fire under the boiler tonbsp;afcend round about it. By which means, (thenbsp;wall not covering the funnel G) the force of thenbsp;fleam will be prodigioufly increafed by the heatnbsp;round the boiler ; and the funnel and water innbsp;it will be heated from the boiler; fo that, the

boiler will not be chilled by letting cold water into it i and the rifing of the fleam will be fanbsp;much the quicker.

Mr. Blakey is the only perfon who ever thought of making ufe of air as an intermediate bodynbsp;between fleam and water; by which means, thenbsp;fleam is always kept from touching the water,nbsp;and confequently from being condenfed by it.nbsp;And, on this new principle, he has obtained anbsp;patent: fo that no one (vary the engine how henbsp;will) can make ufe of air between fleam andnbsp;water, without infringing on the patent, andnbsp;being fubjedl to the penalties of the law.

This engine may be built for a trifling expence, in comparifon of the common fire engine now in ufe: it will feldom need repairs, andnbsp;will not confume half fo much fuel. And as itnbsp;has no pumps with piftons, it is clear of all theirnbsp;fridlion: and the effeft is equal to the wholenbsp;ftrength or compreffive force of the fleam:nbsp;which the eff��t of the common fire engine nevernbsp;is, on account of the great fri�tion of the piftonsnbsp;in their pumps.

In %. I. of PL ATE VI. ^BCD'isa, wheel, which is turned round, according to thenbsp;order of the letters, by the fall of water E F,nbsp;which need not be more than three feet. Thenbsp;axle G of the wheel is elevated fo, as to makenbsp;an angle of about 44 degrees with the horizon �,nbsp;and on the top of that axle is a wheel H, whichnbsp;turns fuch another wheel / of the fame number

of teeth: the axle K of this laft wheel being parallel to the axle G of the two former wheels.

The axle G is cut into a double-threaded fcrew (as in Fig. 2.) exadlly refembling the fcrewnbsp;on the axis of the fly of a common jack, whichnbsp;muft be (what is called) a right-handed fcrew,nbsp;like the wood-fcrews, if the firft wheel turns innbsp;the direftion ABCD-, but muft be a left-handednbsp;fcrew, if the ftream turns the wheel the contrarynbsp;way. And, which-ever way the fcrew on thenbsp;axle G be cut, the fcrew on the axle K muft benbsp;cut the contrary way j becaufe thefe axles turnnbsp;in contrary dire�lions.

The fcrews being thus cut, they muft be covered clofe over with boards, like thofe of anbsp;cylindrical cafk; and then they will be fpiralnbsp;tubes. Or, they may be made of tubes of ftiffnbsp;leather, and wrapt round the axles in Ihallownbsp;grooves cut therein ; as in Fig. 3.

The lower end of the axle G turns conftantly in the ftream that turns the wheel, and the lowernbsp;ends of the fpiral tubes are open into the water.nbsp;So that, as the wheel and axle are turned round,nbsp;the water rifes in the fpiral tubes, and runs outnbsp;at L, through the h�les M, N, as they comenbsp;about below the axle. Thefe holes (of whichnbsp;there may be any number, as four or fix) are innbsp;a broad clofe ring on the top of the axle, intonbsp;which ring, the water is delivered from thenbsp;upper open ends of the fcrew-tubes, and fallsnbsp;into the open box N.

The lower end of the axle K turns on a* gudgeon, in the water in N\ and the fpiralnbsp;�nbsp;nbsp;nbsp;nbsp;tubes

28 nbsp;nbsp;nbsp;HYDRAULICS.

tubes in that axle take up the water from iV, and deliver it into fuch another box under thenbsp;top of K on which there may be fuch anothernbsp;wheel as J, to turn a third axle by fuch a wheel

raifed to any given height, when there is a ftream fufficient for that purpofe to afl on thenbsp;broad float boards of the firft wheel.

This engine is reprefented in PLATE VII. In which ABCD is a wheel, turned by waternbsp;according to the order ot the letters. On thenbsp;horizontal axis are four fmall wheels, toothednbsp;almofl: half round : and the parts of their edgesnbsp;on which there are no teeth are cut down fo, asnbsp;to be even with the bottoms of the teeth wherenbsp;they ftand.

The teeth of thefe four wheels take alternately into the teeth of four racks, which hang by twonbsp;chains over the pullies ^ and L �, and to thenbsp;lower ends of thefe racks there are four ironnbsp;rods fixed, which go down into the four forcingnbsp;pumps, S, R, M and N. And, as the wheelsnbsp;turn, the racks and putnp-rods are alternatelynbsp;moved up and down.

Thus, fuppofe the wheel G has pulled down the rack I, and drawn up the rack K by thenbsp;chain: as the laft tooth of G juft leaves thenbsp;uppermoft tooth of �, the firft tooth of H isnbsp;ready to take into the lowermoft tooth of thenbsp;rack K and pull it down as far as the teeth go;

and then the rack I is pulled upward through the whole fpace of its teeth, and the wheel G isnbsp;ready to take hold of it, and pull it down again,nbsp;and fo draw up the other.' � 'quot;In the famenbsp;manner, the wheels E and F work the racks Onbsp;and P.

Thefe four wheels are fixed on the axle of the great wheel in fuch a manner, with refpeft tonbsp;the pofitions of their teeth ; that, whilft theynbsp;continue turning round, there is never onenbsp;inftant of time in which one or other of thenbsp;pump-rods is not going down, and forcing thenbsp;water. So that, in this engine, there is nonbsp;occafion for having a general air-veflel to all thenbsp;pumps, to procure a conftant ftream of waternbsp;flowing from the upper end of the main pipe.

The piftons of thefe pumps are folid plungers, the fame as defcribed in the fifth Lelt;5ture of mynbsp;book, to which this is a Supplement. Seenbsp;PLATE XI. Fig. 4. of that book, with thenbsp;defcription of the figure.

From each of thefe pumps, near the lowefl: end, in the water, there goes off a pipe; with anbsp;valve on its fartheft end from the pump; andnbsp;thefe ends of the pipes all enter one clofe box,nbsp;into which they deliver the water: and into thisnbsp;box, the lower end of the main condu�l pipe isnbsp;fixed. So that, as the water is forced or pufhednbsp;into this box, it is alfo pufhed up the main pipenbsp;to the height that it is intended to be raifed.

There is an engine of this fort, defcribed in Ramellds work: but I can truly fay, that Inbsp;2nbsp;nbsp;nbsp;nbsp;never

DIALLING.

The faid model is not above twice as big as the figure of it, here defcribed, I turn it by anbsp;winch fixed on the gudgeon of the axle behindnbsp;the water wheel and, when it was newly made,nbsp;and the piftons and valves in good order, I putnbsp;tin pipes 15 feet high upon it, when they werenbsp;joined together, to fee what it could do. Andnbsp;I found, that in turning it moderately by thenbsp;winch, it would raife a hogfhead of water in annbsp;hour, to the height of 15 feet.

dialling.

IN Fig. I. of PLATE VIII. ABCDrt-prefents a cylindrical glafs tube, clofed at both ends with brafs plates, and having a wire ornbsp;axis EFG fixt in the centers of the brafs platesnbsp;at top and bottom. This tube is fixed to a horizontal board H, and its axis makes an anglenbsp;with the board equal to the angle of the earth�snbsp;axis with the horizon of any given place, fornbsp;which the cylinder is to ferve as a dial. And itnbsp;mull be fet with its axis parallel to the axis ofnbsp;the world in that place the end E pointing tonbsp;the elevated pole. Or, it may be made to movenbsp;upon a joint; and then it may be elevated fornbsp;any particular latitude.

There are 24 ftraight lines, drawn with a diamond, on the outficie of the glafs, equidiftant from each other, and all of them parallel to thenbsp;axis. Thefe are the hour-lines; and the hours

DIALLING.

are fet to them as in the figure: the XII next B ftands for midnight, and the oppofite XII, nextnbsp;the board //, ftands for mid-day or noon.

The axis being elevated to the latitude of the place, and the foot-board fet truly level, with thenbsp;black line along its middle in the plane of thenbsp;meridian, and the end N toward the north ; thenbsp;axis E FG will ferve as a ftile or gnomon, andnbsp;caft a lhadow on the hour of the day, among thenbsp;parallel hour lines when the fun fhines on thenbsp;machine. For, as the fun�s apparent diurnalnbsp;motion is equable in the heavens, the fhadow ofnbsp;the axis will move equably in the tube; and willnbsp;always fall upon that hour-line which is oppofitenbsp;to the fun, at any given time.

The brafs plate A D, at the top, is parallel to the equator, and the axis EFG is perpendicularnbsp;to it. If right lines be drawn from the center ofnbsp;this plate, to the upper ends of the equidiftantnbsp;parallel lines on the outfide of the tube j thefenbsp;right lines will be the hour-lines on the equi-nodtial dial A Dt at 15 degrees diftance fromnbsp;each other : and the hour-letters may be fet tonbsp;them as in the figure. Then, as the lhadow ofnbsp;the axis within the tube comes on the hour-linesnbsp;of the tube, it will cover the like hour-lines onnbsp;the equinoftial plate A D.

If a thin horizontal plate e � be put within the tube, fo as its edge may touch the tube allnbsp;around i and right lines be drawn from the centernbsp;of that plate to thofe points of its edge which arenbsp;cut by the parallel hour-lines on the tube; thefenbsp;right lines will be the hour-lines of a horizontalnbsp;dial, for the latitude to which the tube is ele-6nbsp;nbsp;nbsp;nbsp;vated.

dialling.

vatcd. For, as the fhadow of the axis Comes fucceffively to the hour-lines of the tube, andnbsp;covers them, it will then cover the like hourlines on the horizontal plate e �, to which thenbsp;hours may be fet j as in the figure.

If a thin vertical plate g C, be put within the tube, fo as to front the meridian or 12 o�clocknbsp;line thereof, and the edge of this plate touchnbsp;the tube all around �, and then, if right lines benbsp;drawn from the center of the plate to thofe pointsnbsp;of its edge which are cut by the parallel hourlines on the tubci thefe right lines will be thenbsp;hour-lines of a vertical fouth-dial: and the fhadownbsp;of the axis will cover them at the fame times whennbsp;it covers thofe of the tube.

If a thin plate be put within the tube fo, as to decline, or incline, or recline, by any given number of degrees ; and right lines be drawn fromnbsp;its center to thehour-linesof the tube; thefe rightnbsp;lines will be the hour-lines of a declining, inclining, or reclining dial, anfwering to the likenbsp;number of degrees, for the latitude to which thenbsp;tube is elevated.

And thus, by this fimple machine, all the principles of dialling are made very plain, andnbsp;evident to the fight. And the axis of the tubenbsp;(which is parallel to the axis of the world innbsp;every latitude to which it is elevated) is the ftilenbsp;or gnomon for all the different kinds of fun-dials.

And laftly, if the axis of the tube be drawn out, with the plates AD, (?�, and g C upon it;nbsp;and fet it up in fun-fhine, in the fame pofition asnbsp;they were in the tube j you will have an equi-

noftial dial A D, ^ horizontal dial e �, and a vertical fouth dial ^ C ; on all which, the time of the day will be fhewn by the fhadow of the axisnbsp;or gnomon E F G.

Let us now fuppofe that, inftead of a glafs tube, A B C D IS a cylinder of,wood ; on whichnbsp;the 24 parallel hour-lines are drawn all around,nbsp;at equal diftances from each other; and thar,nbsp;from the points at top, where thefe lines end,nbsp;right lines are drawn toward the center, on thenbsp;flat furface A D : Thefe right lines will be thenbsp;hour-lines on an equinoctial dial, for the latitudenbsp;of the place to which the cylinder is elevatednbsp;above the horizontal foot or pedeftal H andnbsp;they are equidiftant from each other, as in Fig. 2.nbsp;which is a full view of the flat furface or top

D of the cylinder, feen obliquely in Fig. i. And the axis of the cylinder (which is a ftraightnbsp;wire E FG all down its middle) is the ftile ornbsp;gnomon ; which is perpendicular to the planenbsp;of the equinoctial dial, as the earth�s axis is perpendicular to the plane of the equator.

To make a horizontal dial, by the cylinder, for any latitude to which its axis is elevated;nbsp;draw out the axis and cut the cylinder quitenbsp;through, as at ^ ^ fg, parallel to the horizontalnbsp;board H, and take off the top part e A Dfe-, andnbsp;the feClion e hf g e will be of an elliptical form,nbsp;as in Fig. 3. Then, from the points of thisnbsp;feCtion (on the remaining part e B Cf) wherenbsp;the parallel lines on the outfide of the cylindernbsp;meet it, draw right lines to the center of thenbsp;feClion v and they will be the true hour-lines fornbsp;a horizontal dial, as ab c d a\n Fig. 3. which maynbsp;be included in a circle drawn on that feClion.

34 nbsp;nbsp;nbsp;D I AL LING.

Then put the wire into its place again, and it �will be a ftiie for calling a lhadow on the timenbsp;of the day, on that dial. So, E (Fig. 3.) is thenbsp;ftiie of the horizontal dial, parallel to the axis-of the cylinder.

To make a vertical fouth dial by the cylinder, draw out the axis,, and cut the cylinder perpendicularly to the horizontal board /y, as atnbsp;giC kg, beginning at the hour line (B ge A) ofnbsp;XII. and making the feflion at right angles tonbsp;the line S HN on the horizontal board. Then�nbsp;take off the upper part g ADC, and the face ofnbsp;the fedlion thereon will be elliptical, as (hewn innbsp;Fig. 4. From the points in the edge of this fec-tion, where the parallel hour-lines on the roundnbsp;furface of the cylinder meet it, draw right linesnbsp;to the center of the fedion; and they will benbsp;the true hour-lines on a vertical dircd fouth dial,nbsp;for the latitude to which the cylinder was ele-�vated : and will appear as in Fig, 4. on whichnbsp;the vertical dial may be made of a circular fhape,nbsp;or of a fquare fhape as reprefented in the figure-And F will be its ftiie parallel to the axis of thenbsp;cylinder.

And thus, by cutting the cylinder any way� fo as its feftion may either incline, or decline, ornbsp;recline, by any given number of degrees ; andnbsp;from thole points in the. edge of the fedtionnbsp;where the outfide parallel hour-lines meet it,nbsp;draw right lines to the center of the fedtion; andnbsp;they will be the true hour.lines, for the like declining, reclining, or inclining dial: And thenbsp;axis of the cylinder will always be the gnomonnbsp;or ftiie of the dial. For, which-ever way thenbsp;plane of the dial lies, its ftiie (or the edge thereof

DIALLING.

that cafts the (hadow on the hours of the day) muft be parallel to the earth�s axis, and pointnbsp;toward the elevated pole of the heavens.

S'0 delineate a Sun-Dial on Paper ; which, when fafted round a Cylinder of Wood, fhall Jhew thenbsp;Dime of the Day, the Sun's Plate in the Ecliptic^nbsp;and his Altitude, at any 'Time of Ohfervation.nbsp;See PLATE IX.

Draw the right line a A B, parallel to the top of the paper ; and, with any convenient openingnbsp;of the compafles, fet one foot in the end of th�nbsp;line at a^ as a center, and with the other foot de-fcribe the quadrantal arc A E, and divide it intonbsp;90 equal parts or degrees. Draw the right linenbsp;AC, at right angles to a AB, and touching thenbsp;quadrant A E zx the point A. Then, from thenbsp;center a, draw right lines through as many degrees of the quadrant, as are equal to the fun^snbsp;altitude at noon, on the longeft day of the year,nbsp;at the place for which the dial is to fervc;nbsp;which altitude, at London, is 62 degrees : andnbsp;continue thefe right lines till they meet the tangent line A C �, and, from thefe points of meeting, draw ftraight lines acrofs the paper, parallel to the firft right line A B, and they will benbsp;the parallels of the fun�s altitude, in whole degrees, from fun-rife till fun-fet, on all the daysnbsp;of the year.� - Thefe parallels of altitude multnbsp;be drawn out to the right line B D, which mullnbsp;be parallel to A C, and as far from it as is equalnbsp;to the intended circumference of the cylinder oilnbsp;which the paper is to be pafted, when the dial isnbsp;drawn upon it.

Divide the fpace between the right lines AC and B D (at top and bottom) into twelve equalnbsp;F f 2nbsp;nbsp;nbsp;nbsp;parts

DIALLING.

parts, for the twelve figns of the ecliptic j and, from mark to mark of thefe divifions at topnbsp;and bottom, draw right lines parallel to AC andnbsp;B D ; and place the charafters of the i2 figns innbsp;thefe twelve fpaces,atthe bottom, as in the figure:nbsp;beginning with icf or Capricorn, and endingnbsp;with K or Pifces. The fpaces including thenbsp;figns fhould be divided by parallel lines intonbsp;halves; and if the breadth will admit of itnbsp;without confufion, into quarters alfo.

At the top of the dial, make a fcale of the months and days of the year, fo as the days maynbsp;ftand over the fun�s place for each of them innbsp;the figns of the ecliptic. The fun�s place, fornbsp;every day of the year, may be found by anynbsp;common ephemeris: and here it will be beft tonbsp;make ufe of an ephemeries for the fecond yearnbsp;after leap year �, as the neareft mean for the fun�snbsp;place on the days of the leap-year, and on thofenbsp;of the firft, fecond, and third year after.

Compute the fun�s altitude for every hour (in the latitude of your place) when he is in thenbsp;beginning, middle, and end of each fign of thenbsp;ecliptic; his altitude at the end of each fignnbsp;being the fame as at the beginning of the next.nbsp;And, in the upright parallel lines, at the beginning and middle of each fign, make marks fornbsp;thefe computed altitudes among the norizontalnbsp;parallels of altitude, reckoning them downward,nbsp;according to the order of the numeral figures fetnbsp;to them at the right hand, anfwering to the likenbsp;divifions of the quadrant at the left. And,nbsp;through thefe marks, draw the curve hour-lines,nbsp;and let the hours to them, as in the figure,nbsp;reckoning the forenoon hours downward, and

DIALLING.

tude Ihould alfo be computed for the half hours ; and the quarter lines may be drawn, very nearlynbsp;in their proper places, by eftimation and accuracy of the eye. Then, cut off the paper at thenbsp;left hand, on which the quadrant was drawn,nbsp;clofe by the right line A C, and all the paper atnbsp;the right hand clofe by the right line S D �, andnbsp;cut it alfo clofe by the top and bottom horizontal lines; and it will be fit for palling round thenbsp;cylinder.

This cylinder is reprefented in miniature by Fig. I. PLATE X. It fhould be hollow, tonbsp;hold the ftile D E when it is not ufed. Thenbsp;crooked end of the ftile is put into a hole in thenbsp;top AD oi the cylinder; and the top goes onnbsp;tightifli, but muft be made to turn round on thenbsp;cylinder, like the lid of a paper fnuff-box. Thenbsp;ftile muft ftand ftraight out, perpendicular to thenbsp;fide of the cylinder, juft over the right line ABnbsp;in PLATE IX, where the parallels of the fun�snbsp;altitude begin : and the length of the ftile, ornbsp;diftance of its point e from the cylinder, muft benbsp;equal to the radius a A oi the quadrant AE 'innbsp;PLATE IX.

Place the horizontal foot B C oi the cylinder on a level table where the fun lliines, and turn thenbsp;top A D till the ftile ftands juft over the day ofnbsp;the then prefent month. Then turn the cylinder about on the table, till the fliadow of thenbsp;ftile falls upon it, parallel to thefc upright linesnbsp;which divide the figns; that is, till the fhadownbsp;be parallel to a fuppofcd axis in the middle ofnbsp;the cylinder : and then, the point, or loweft endnbsp;F f 3nbsp;nbsp;nbsp;nbsp;of

DIALLING.

of the fhadow, will fall upon the time of the day, as it is before or after noon, among thenbsp;curve hour-lines; and will lltew the lun�s alci^nbsp;tude at that time, amongft the crofs parallels of hianbsp;altitude, which go round the cylinder : and, atnbsp;the fame time, it will Ihew in what fign of thenbsp;ecliptic the fun then is, and you may very nearlynbsp;guefs at the degree of the fign, by eftimation ofnbsp;the eye.

The ninth plate, on which this dial is drawn, may be cut out of the book, and palled round anbsp;cylinder whofe length is 6 inches and 6 tenthsnbsp;of an inch below the moveable top and itsnbsp;diameter 2 inches and 24 hundred parts of an

of it may be had at Mr. Cadell�s, bookfeller in the Strand, London. But it will only do fornbsp;London, and other places of the fame latitude.

When a level table cannot be had, the dial may be hung by the ring Fat the top. And when itnbsp;is not ufed, the wire that ferves for a ftile maynbsp;be drawn our, and put up within the cylinder;nbsp;and the machine carried in the pocket.

Tc make three Sun-dia^s upon three different Planes, fs as they may a.ll Jhevo the Time of the Day bynbsp;one Gnomon,

On the flat board ABC, defcribe a horizontal dial, according to any of the rules kid down innbsp;the Ledlure on Dialling; and to it fix its gnomonnbsp;F G H, the edge of the fhadow from the fidenbsp;FG being that which fhews the time of the day.

To this horizontal or flat board, join the upright board EDC, touching the edge G H ofnbsp;the gnomon. Then, making the top of the

DIALLING.

�gnomon at G the center of the vertical fouth dial, defcribe a fouth dial on the board E D C.

Laftly, on a circular plate IK defcribe an �quinoftial dial, all the hours of which dial arenbsp;�equidiftant from each other ; and making a flitnbsp;i; d \n that dial, from its edge to its center, in thenbsp;XII o�clock line ; put the faid dial perpendicularly on the gnomon AG, as far as the flit willnbsp;admit of; and the triple dial will be (inilhed ; thenbsp;fame gnomon ferving all the three, and /hewingnbsp;the fame time of the day on each of them.

This dial is repre/ented by Fig. i of PLATE XI, and is moveable on a joint C, for elevatingnbsp;it to any given latitude, on the quadrant C o 90,nbsp;as it Hands upon the horizontal board Thenbsp;arms of the crofs /land at -right angles to thenbsp;-middle part and the top of it from a to �, isnbsp;-of equal length with either of the arms neormk.

Having fet the middle line / a to the latitude of your place, on the quadrant, the board Anbsp;level, and the point N northward by the needle; _nbsp;the plane of the crofs will be parallel to thenbsp;plane of the equator ; and the machine will benbsp;reflified.

Then, from III o�clock in the morning, till VI, the upper edge k I o( the arm i 0 will caft anbsp;iliadovv on the time of the day on the fide of thenbsp;arm c m: from VI till IX the lower edge i ofnbsp;the arm i 0 will call: a /hadow on the hours onnbsp;the fide 0 y. From IX in the morning to XII atnbsp;noon, the edge ab oi the top part a n v^ill caft anbsp;lhadow on the hours on the arm nef: from XIInbsp;to III in the afternoon, the edge c d oi the topnbsp;F f 4nbsp;nbsp;nbsp;nbsp;part

DIALLING.

part will caft a fliadow on the hours on ths arm k I m: from III to VI in the evening, thenbsp;edge g h will caft a Ihadow on the hours onnbsp;the part p s-, and from Vi till IX, the Ihadownbsp;of the edge e f will ftiew the time on the topnbsp;part a n.

The breadth of each part, a h, c f, amp;c. muft be fo great as never to let the fltadow fall quitenbsp;without the part or arm on vgt;/hich the hi urs arenbsp;marked, when the fun is at his greateft dedina*nbsp;tion from the equator.

To determine the breadth of the fides of the arms which contain the hours, fo a? to be in juftnbsp;proportion to their length ; make an anglenbsp;ABC{V\g. 2.) of ajt degrees, which is equalnbsp;to the fun�s greateft declination; and fuppofenbsp;the length of each arm, from the fide of the longnbsp;middle part, and alfo the length of the top partnbsp;above the arms, to be equal to B d.

Then, as the edges of the Ihadow from each of the arms, will be parallclto B e, making an anglenbsp;of 254: degrees with the fide B d oi the arm whennbsp;the fun�s declination is 234: degrees; �tis plain,nbsp;that if the length of the arm be B J, the leaftnbsp;breadth that it can have, to keep the edge 5 e ofnbsp;the Ihadow B eg d from going off the fide of thenbsp;arm d e before it comes to the end e d thereof,nbsp;muft be equal to e d or dB. But in order tonbsp;keep the fliadow within the quarter divifions ofnbsp;the hours, when it comes near the end of thenbsp;arm, the breadth thereof fliould be ftill greater,nbsp;fo as to be almoft doubled, on account of thenbsp;diftance between the lips of the arms.

DIALLING,

Divide this arc into fix equal parts, and through the diyifion marks draw right lines a g, a igt;, amp;c.nbsp;continuing three of them to the arm c e, whichnbsp;are all that can fall upon it; and they will meetnbsp;the arm in thefe points through which the linesnbsp;that divide the hours from each other (as innbsp;Fig. I.) are to Ipe drawn right acrofs it.

Divide each arm, for the three hours it contains, in the fame manner ; and fet the hours to their proper places (on the fides of the arms) asnbsp;they are marked in Fig. 3. Each of the hournbsp;fp^ces Ifiould be divided into four equal parts,nbsp;for the half hour� and quarters, in the quadrantnbsp;e f and right lines fhould be drawn throughnbsp;thefe divifion marks in the quadrant, to thenbsp;arms of the crofs in order to determine thenbsp;places thereon where the fub-divifiops of thenbsp;hours muft be marked.

This is a very fimple kind of univerfal dial; it is very eafily made, and will have a pretty uncommon appearance in a garden.-1 havefeen

DIALLING.

Jin univerfal Bid, /hewing the Hours of the Bay by a terre/trial Globe, and by the Shadows of federalnbsp;Gnomons, at the fame fime: together with allnbsp;the Places of the Earth which are then enlightenednbsp;by the Sun ; and thofe to which the Sun is thennbsp;fifing, or on the Meridian, or Setting.

This dial (See PLATE XII.) is made of a thick fquare piece of wood, or hollow metal.nbsp;The fides are cut into femicircular hollows, innbsp;�which the hours are placed; the ftile of eachnbsp;hollow coming out from the bottom thereof,nbsp;as far as the ends of the hollows projeft. Thenbsp;corners are cut out into angles, in the inftdes ofnbsp;�which, the hours are alfo marked; and the edgenbsp;of the end of each fide of the angle ferves as anbsp;ftile for calling a lhadow on the hours markednbsp;on the other fide.

In the middle of the uppermoll fide or plane, there is an equinoftialdial; in the center whereof, an upright wire is fixt, for calling a lhadownbsp;on the hours of that dial, and fupporting afmallnbsp;terreftrial globe on its top.

The whole dial Hands on a pillar, in the middle of a round horizontal board, in whichnbsp;there is a compafs and magnetic needle, fornbsp;placing the meridian ftile toward the fouth. Thenbsp;pillar h^as a joint with a quadrant upon it, dividednbsp;into 90 degrees (fuppofed to be hid from fightnbsp;under the dial in the figure) for fetting it to thenbsp;latitude of any given place; the fame way asnbsp;already defcribed in the dial on the crofs.

The equator of the globe is divided into 24 equal parts, and the hours are laid down upon it

DIALLING.

6t thefe parts. The time of the day may be known by thefe hours, when the fun fliines upoixnbsp;the globe.

To re�lify and ufe this dial, fet it on a level table, or foie of a window, where the fun Ihines,nbsp;placing the meridian ftile due fouth, by meansnbsp;of the needle; which will be, when the needlenbsp;points as far from the north fleurs-de-lis towardnbsp;the weft, as it declines weftward, at your place.nbsp;Then bend the pillar in the joint, till the blacknbsp;line on the pillar comes to the latitude of yournbsp;place in the quadrant.

The machine being thus reflified, the planeof its dial-part will be parallel to the equator, thenbsp;wire or axis that fupports the globe will be parallel to the earth�s axis, and the north pole ofnbsp;the globe will point toward the north pole ofnbsp;the heavens.

The fame hour will then be Ihewn in feveral of the hollows, by the ends of the lhadows ofnbsp;their refpeftive ftiles ; The axis of the globenbsp;will caft a lhadow on the fame hour of the day,nbsp;in the equinoftial dial, in the center of which itnbsp;is placed, from the 20th of March to the 23d ofnbsp;September; and, if the meridian of your placenbsp;on the globe be fee even with the meridian ftile,nbsp;all the parts of the globe that the fun fhinesnbsp;upon, whl anfwer to thofe places of the realnbsp;earth which are then enlightened by the fun.nbsp;The places where the lhade is juft coming uponnbsp;the globe, anfwer 10 all thofe places of the earthnbsp;to which the fun is then fetting; as the placesnbsp;where it is going olf, and the light coming on,nbsp;anfwer to ali the places of the earth where the funnbsp;is then rifing. And laftly, if the hour of VI

DIALLING,

be marked on the equator in the meridian of your place (as it is marked on the meridian ofnbsp;London in the figure) the divifion of the lightnbsp;and fliade on the globe will fliew the time of thenbsp;day.

The northern ftile of the dial (oppofite to the fouthern or meridian one) is hid from fight innbsp;the figure, by the axis of the globe. The . oursnbsp;in the hollow to which that dile behuins, arenbsp;alfo fuppofed to be hid by the ob'-nbsp;nbsp;nbsp;nbsp;.� of

the figure: but they are the fame as ii,. .quot;gt;\)rs in the front-hollow. Thofe alfo in the rightnbsp;and left hand femicircular hollows are moftlynbsp;hid from fight; and fo alfo are all thofe on thenbsp;fides next the eye of the four acute angles.

On a thick fquare piece of wood, or metal, draw the lines a c and b d, as far from each othernbsp;as you intend for the thicknefs of the flile abednbsp;and in the fame manner, draw the like thick-iiefs of the other three ftiles, e f g h, i k I m, andnbsp;n 0 p (It all Handing outright as from the center.

With any convenient opening of the com-paffes, 2l% a A (fo as to leave proper ftrength of ftuff when X J is equal xa a A) fet one footnbsp;in �, as a center, and with the other foot de-feribe the quadrantal arc A c. Then withoutnbsp;altering the compafies, fet one foot in ^ as anbsp;center, and with the other foot deferibe the quadrant d B. All the other quadrants in the figurenbsp;muft be deferibed in the fame manner, and with

the fame opening of the compafles, on their centers lt;?, �; k-, and �, o: and each quadrantnbsp;divided into 6 equal parts, for fo many hours,nbsp;as in the figure ; each of which parts muft benbsp;fub-divided into 4, for the half hours and quarters.

At equal diftances from each corner, draw the right lines//), and K-p, Lq, and Mq, Nr, andnbsp;Or, P s, and -, to form the four angularnbsp;hollows IpK, LqM, Nr O, and P s making the diftances between the tips of thefe hollows, as IK, L M, NO, and P each equalnbsp;to the radius of the quadrants ; and leaving fuffi-cient room within the angular points, ygt;, r,nbsp;and s, for the equinodtial circle in the middle.

To divide the infides of thefe angles properly for the hour-fpaces thereon, take the followingnbsp;method.

Set one foot of the compafles in the point 7, as a center ; and open the other to K, and withnbsp;that opening, defcribe the arc K t: then, without altering the compaflTes, fet one foot in K,nbsp;and with the other foot defcribe the arc It.nbsp;Divide each of thefe arcs, from I and K to theirnbsp;interfedtion at t, into four equal parts; andnbsp;from their centers / and K, through the pointsnbsp;of dlvifibn, draw the right lines I 14., 15,nbsp;16, IT, and Ki, K 12, Kii �, and theynbsp;will meet the fides Kp and Ip of the angle Ip Knbsp;where the hours thereon muft be placed. Andnbsp;thefe hour-fpaces in the arcs muft be fubdividednbsp;into four equal parts, for the half hours and

40 nbsp;nbsp;nbsp;-DIALLING.

hours in the infides where thofe lines meet theirij as in the figure : and the like hour-lines will benbsp;parallel to each other in all the quadrants and innbsp;all the angles.

Mark points for all thefe hours, on the upper fide and cut out all the angular hollows, andnbsp;the quadrantal ones quite through the placesnbsp;where their four gnomons muft ftand ; and laynbsp;down the hours on their infides, as in Platenbsp;XII, and then fet in their four gnomons, whichnbsp;muft be as broad as the dial is thick 5 and thisnbsp;breadth and thicknefs muft be large enough tonbsp;keep the ftiadows of the gnomons from evernbsp;falling quite out at the fides of the hollows, evennbsp;when the fun�s declination is at the greateft.

Laftly, draw the equingiftial dial in the middle, all the hours of which are equidiftant from each other and the dial will be finilhed.

As the fun goes round, the broad end of the lhadow of the ftile abed will Ihew the hoursnbsp;in the quadrant A c, from fun rife till VI in thenbsp;morning j the lhadow from the end M will Ihewnbsp;the hours on the fide L q from V to IX in thenbsp;morning ; the Ihadow of the ftile e f g hxn. thenbsp;quadrant D g (in the long days) will ihew thenbsp;hours from fun-rife till VI in the morning; andnbsp;the ihadow of the end N will ihew the morningnbsp;hours, on the fide 0 from III to VII.

Juft as the ihadow of the northern ftile abed goes off the quadrant A e^ the ihadow of thenbsp;fouthern ftile i k I m begins to fall within thenbsp;quadrant FI, at VI in the morning ; and ibewsnbsp;the time, in that quadrant, from VI till XI1 atnbsp;4nbsp;nbsp;nbsp;nbsp;noon i

DIALLING.

noon �, and from noon till VI In the evening in the quadrant m E. And the fhadow of the endnbsp;O flicws the time from XI in the forenoon tillnbsp;III in the afternoon, on the lide r as thenbsp;lhadow of the end P fhews the time from IX innbsp;the morning till I o�clock in the afternoon, onnbsp;the fide ^s.

At noon, when the lhadow of the eaftern ftile efg h goes off the quadrant h C (in which ftnbsp;Ihewed the time from VI in the morning tillnbsp;noon, as it did in the quadrant g D from fun-rife till VI in the morning) the lhadow of thenbsp;weftern ftile n opq begins to enter the quadrantnbsp;Up i and fhews the hours thereon from XII atnbsp;noon till VI in the evening j and after /d�a/ tillnbsp;fun-fet, in the quadrant j G: and the end ^nbsp;calls a lhadow on the fide P s from V in thenbsp;evening till IX at night, if the fun be not feenbsp;before that time.

The lhadow of the end / Ihews the time on the fide Kp from III till VII in the afternoonnbsp;and the lhadow of the ftile a bed Ihews the timenbsp;from VI in the evening till the fun fets.

The lhadow of the upright central wire, that fupports the globe at top, fhews the time of thenbsp;day, in the middle or cquinodlial dial, all thenbsp;fummer half year, when the fun is on the north:nbsp;fide of the equator.

In this fupplement to my book of Leflures, all the machines that I have added to my apparatus, fince that book was printed, are de-fcribed, excepting two j one of which is a model

DIALLING.

of a mill for fawing timber, and the other is a model of the great engine at London-bridge,nbsp;for raifing water. And my reafons for leavingnbsp;them out are as follow.

Firft, I found it impoffible to make fuch a drawing of the faw-mill as could be underttood inbsp;becaufe, in whatever view it be taken, a greatnbsp;many parts of it hid others from fight. And,nbsp;in order to Ihew it in my Ledtures, 1 am obligednbsp;to turn it into all manner of pofitions.

Secondly, Becaufe any perfon who looks on Fig. I. of Plate XII in the book, and readsnbsp;the account of it in the fifth Lecture therein,nbsp;�will be able to form a very good idea of thenbsp;London-bridge engine, which has only twonbsp;wheels and two trundles more than there are innbsp;Mr. Alderfedquot;^ engine, from which the faid figurenbsp;was taken.

	� nbsp;nbsp;nbsp;K.{'
-r}-.

SS	-V�

				Revolu-	Cogs		Rev. of
	Velo-	Velo-	Revolu-	tions of	Cogs	in	the
. ? O tanbsp;rrnbsp;rt p cr	city of the water	city of thenbsp;wheel	tions of thenbsp;wheel	the mill- ftone	lliC wheel and Haves in		miil-Hanfper min. bynbsp;thefe
CD	/rr fe-	per fe-	per	for one	the		ftaves
?�� o �-n	cond.	cond.	minute.	of the wheel.	trundle.		and cogs.
*r\	0 M 1? � 0	0 M **j w'b	C M 0 01 0	0 M 0 50 w 0	n	tr. r*	0 M 0 J� � 0
n	� nbsp;nbsp;nbsp;0	^ 0 aj 0 quot;I	lt; � nbsp;nbsp;nbsp;rt -1 lt; jjJ	% � rc � lt;	eg	rt	lt; JO'S r* ��
I	8 .02	2 .67	2.83	2X .20	127	6	59.92
2	11 -34	3 78	4 .00	I 5 .00	105	7	60.00
3	13.89	4-63	4.91	12 .22	98	8	60.14
4	16 .04	5-3.5	5-67	10.58	95	9	59-87
5	�7 93	5.98	6.34	9,46	85	9	59.84
6	19.64	6.55	6.94	8.64	78	9	60. ?o
7	2X .21	7.07	7-50	8 .00	72	9	60.00
a	22 .68	7-56	8 .02	7.48	67	9	59-6/
9	24.05	8 .02	8.51	7 .05	70	10	59-57
lO	25-35	8.45	8.97	6 .69	67	10	CO .09
11	26.59	8 .86	9.40	6.38	64	10	60 .i 6
12	27.77	9 .26	9 .82	6.11	61	10	59.90
13	28 .91	9 -64	10.22	5.87	59	10	60.18
14	30 .00	10.00	10.60	5 .66	56	10	59-36
15	31 -05	gt;0-35	10.99	5 -46	55	10	60.48
i6	32 .07	10.69	11-34	5 -29	53	10	60.10
17	33	XI .02	II .70	5-13	51	10	59-67
18	34.02	II -.34	12 ,02	4-99	50	10	�0.10
19	34-95	II .65	12.37	4 -85	49	10	60.61
20	35.86	11-95	12 .68	4-73	47	10	59-59
r	2	3	4	5	6		7

	Quantity	Weight	In avoir-
A zr	in cubic	in troy	dupoife
OQ rr*	inches.	ounces.	ounces.
1	3770	19,89	21.85
2	75-40	39-79	43.69
3	11^.10	59.68	65-54
4	150.80		87-39
5	188.50	99-M	109.24
6	226.19	119-37	13 1.08
7	263.89	139.26	152-93
8	301-59	159.16	174.78
9	33929	179.06	196.63
10	376.99	198.95	218.47
20	753-98	397-90	436.95
3�	1130.97	596.85	655.42
40	1507.97	795.80	873.90
50	18S4.96	994-75	1092.37
6o	2261.95	1193.70	1310.85
70	2638.94	1392.65	1529.32
80	3015-93	1591.60	1747-^0
90	3392.92	1790,56	1966.27
too	3769 91	1989.51	2184,75
200	7539.82	3979.00	4369.50

	24- Inches diameter.
n a	Quantity	Weight	In avoir-
3-	in cubic	in troy	dupoife
UQ pr	inches.	ounces.	ounces.
I	58.90	31.08	34-14
2	117.81	62.17	68.27
3	176.71	93.26	102.41
4	235.62	124.34	*36.55
5	294.52	155-43	170.68
6	353-43	186.52	204.82
7	412-3.3	217.60	238.96
8	471.24	248.69	273.09
9	530.14	279.77	307.23
lO	589.05	310.86	34�-37
20	1178.ro	621.72	682.73
30	1767.15	932.58	1024.10
40	2356.20	1243.44	1365.47
50	2545-25	1554-30	1706.83
6o	3534-29	1865.16	2048.20
70	4123.34	2176.02	2389.57
80	4712.39	2486.88	2730.94
90	530J.44	2797.74	3072.30
100	5890.49	3108.60	2413.67
200	11780.98	6217,20	4827,34

3 Inches diameter.
rs) agt;	Quantity	Weight	In avoir-
rt	in cubic	in troy	dupohe
OQ P*	inches.	ounces.	ounces.
1	84.8	44.76	49.16
2	169.6	89-53	98.31
3	254-5	134.29	*47-47
4	2 39-3	179.06	196.63
5	424.1	223.82	245-78
6	508.9	268.58	294.94
7	593*7	313-35	344-*0
8	698.6	358.11	393-25
9	763-4	402.87	442-41
ro	848.2	447.64	49*-57
20	1696.5	895.28	983.14
30	2544-7	1342.92	1474.70
40	3392-9	1790.56	1966.27
	4241.1	2238.19	2457.84
60	5089.4	2685.83	2949.41
70	5937-6	3*33-47	3440.98
80	6785.8	3581.11	3932.55
90	7634-1	4028.75	4424.1 2
100	8482.3	4476.39	4915.68
200	16964.6	8952.78	9831.36

ro ngt; rt S** p-	Quantity in cubicnbsp;inches.	Weight in troynbsp;ounces.	In avoir- dupoife ounces.
I	285.r	150 5	164.3
2	570.2	300.9	328.5
3	855-3	45�-4	492.8
4	1140.4	601.8	657.1
5	1425-5	752.3	821.3
6	1710.6	9O2.7	985.6
7	�995-7	1053.2	1149.9
S	2280.8	1203.�	1314.2
9	2565.9	J354-I	1478.4
10	2851.0	1504.6	1642.7
20	5702.0	3009.1	3285.4
30	11553-0	4513-7	4928.1
40	11404.0	6018.2	6570.8
50	14255.0	7522.8	8213.5
60	17106.0	9027.4	9856.2
70	19957.0	10531.9	11498.9
80	22808.0	12036.5	13141.6
90	25659.0	13541-1	147843
100	28510.0	15045.6	16426.9
200	57020.0	30091.2	32853-9

0			( nbsp;nbsp;nbsp;�quot; Irt �� I'i � Id h� [6 � ct�'. ci			��14	�14	�14
0			1 00 lt;A. (Sj ?- 0 00	vO			0	00 VO
			j nbsp;nbsp;nbsp;COnbsp;nbsp;nbsp;nbsp;tonbsp;nbsp;nbsp;nbsp;N			N	d
			1 Hl-i- nbsp;nbsp;nbsp;wtr! M'c5w!rl *-101	)�\|e4			�14
0			00 nbsp;nbsp;nbsp;N 0 Cslt;^		CO	�	ov		to.
0			j CO CO CO lt;0 ts ts N	CJ	C4	N		quot;quot;	�4
			-It*
0			CT'VO nbsp;nbsp;nbsp;�- OCC Cv.	CO	d	0
			cococomcic^ M N	N	C5	N
			M,*,'- ^p) -�fj				,
0	0		CO 0 00 rgt;.vo ^ tI-	CJ	0			1 ^	in
	�lt;h		CO CO CO C^ ci nbsp;nbsp;nbsp;CJ C4	C�	C^		-	-	-
			-jrj- nbsp;nbsp;nbsp;H'fS'*-				�1 ft
0	1		^ � 00 vO �~cgt; nbsp;nbsp;nbsp;CO C4	0	0	t'.	to		d
VO	CO		COCON^^NNN^^	N			'quot;�		��
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0		4-	gt;~00 lo'cj-coc� *-gt; 0	Ov		I��		ro
			c0C^NNC^CJNC4	p�	�w
						�^14
tn	rJ		0\ nbsp;nbsp;nbsp;^ co quot;� '�� unbsp;nbsp;nbsp;nbsp;sij			to	CO	N	��
	to		NNNNMNt�'-'
			Nlrh nbsp;nbsp;nbsp;Ol' .�l c5�^ � nbsp;nbsp;nbsp;nbsp;o\|-f	�14	�Ic*			�(4
0	0		JO 10 CO hH 0 c^i Onoo vo		to TT		CO	gt;�	0
rf-	e^.							�M	�*
	-.If�		H*** nbsp;nbsp;nbsp;cs[rj-	Hirt			Cl 14
	00 vO cn 0 evoo 00 0			to ^ CO			�x	0	Ov
	M			t-�			M
	wJ -t		Mfelt; wjH (-[h i-Icfl
0	VO		ri- N 0 OsOO t^vO to Ti- CO N				M	0
tn	*N			tm	?1			M-
			?H\|Tj--,rtH.lei
ij*\			N 0 00 lgt;.VO nbsp;nbsp;nbsp;CO CO		d	��	0
N
	�yl	�	t-l nbsp;nbsp;nbsp;cil'iquot;
0	lt;w		GvOO VO to ^ nbsp;nbsp;nbsp;*0 CO		M	0
N	N			�

A cubic inch of	Troy weight.			Avoirdup,		Compa rative weight.
A cubic inch of	oz.	pw. gr.		OZ.	drams.	Compa rative weight.
Very fine gold_^ -	TO	7	3-83	I	5.80	19.637
Standard gold -	9	^9	6.44	10	14.90	18.888
Guinea gold -	9	7	17.18	10	4.76	17-793
Moidore gold -	9	0	19.84	9	14.71	17.140
Quickfilver - -	7	7	I r.6r	8	1-45	14.019
Lead	5	19	17-55	6	9.08	11.325
f ine iilver - -	5	16	23.23	6	6.66	11.087
Standard filver -	5	I I	3-36	6	1-54	10-535
Copper	4	13	7.04	5	1.89	8.843
Plate-brafs	4	4	9.60	4	IO.C9	8.000
Steel - - -	4	2	20.12	4	8.70	7.852
Iron - - -	4	0	15.20	4	6.77	7.645
Block-tin - -	3	17	5.68	4	3-79	7.321
Speltar	3	14	12.86	4	1,42	7 065
Lead ore - nbsp;nbsp;nbsp;-	3	�I	17.76	3	14.96	6.800
Glafs of antimony	2	15	16.89	3	0.89	5.280
German antimony	2	2	4.80	2	5.04	4.000
Copper ore - -	2	I	11.83	2	4-43	3-7'5
Diamond - nbsp;nbsp;nbsp;-	I	15	20.88	I	15.48	,3.400
Clear glafs - -	I	^3	5.58	I	13.16	3150
Lapis lazuli - -	I	12	527	I	12.27	3-054
Welch afbcibos -	I	10	17-5?	I	10.97	2.913
White marble -	I	8	13.41	I	Q.06	2.707
Black ditto	I	8	12.65	I	9.02	2.704
Rock cryftal -	I	8	I.QO	I	8.6f	2.658
Green glafs - -	I	7	L5-3^	I	8.2 6	2.�20
Corneliaigt;gt;ftone -	I	7	1.21	I	7-73	2.568
�Flint - - -	T A	6	19.63	I	7-53	2.542
Hard paving fione	I	5	22.87	I	6.77	2.460
Live fulphur -	I	I	' 2.40	I	2.52	2.000
Nitre - nbsp;nbsp;nbsp;- -	I	0	1.08	I	1-59	I.goo
Alabafter -	0	^9	18.74	I	1-35	1.875
Dry ivory - nbsp;nbsp;nbsp;-	0	^9	6.09	1	0.89	1.825
Brimftone - -	0	18	23.76	I	0.66	1.800
Alum . - _	0	17	21.92	0	15-72	1.714

A cubic inch of	'i'roy wtight.			Avoirdiip.		Coinpa- ra.nve weight.
A cubic inch of	oz	pw.	gr-	OZ.	d'aras.	Coinpa- ra.nve weight.
Ebony	0	II	18.82	0	10.34	1117
Human blood -	0	II	2.89	0	9.76	1.054
Amber	0	10	20.79	0	Q*5t	I 030
Cow�s milk	0	10	20.79	0	9 54	1.030
Sea water - nbsp;nbsp;nbsp;-	0	10	20.79	0	9-54	1.030
Pump water	0	10	13-30	0	9 26	1.000
Spring water	0	10	12.94	0	9.25	0999
Diiblled water -	0	10	11.42	0	9.20	0993
Red wine - nbsp;nbsp;nbsp;-	0	10	11.42	0	9.20	0.993
Oil of amber -	0	10	7-63	0	9.06	0.978
Proof fpirits -	0	9	1973	0	8.62	0.931
Dry oak	0	9	18.00	0	8.56	0.925
Olive oil - nbsp;nbsp;nbsp;-	0	9	15.17	0	8.45	0.913
Pure fpirits - -	0	9	3-27	0	8.02	0 866
Spirit of turpentine	0	9	2.7�	0	7-99	0.864
Oil of turpentine	0	8	S-53	0	7-33	0.772
Dry Crabtree -	0	8	1.69	0	7.08	0.765
Saliafras wood -	0	5	2.04	0	4.46	0.482
Cork	0	2	12.77	0	2.21	0.240!

a cp	2 T) pa f ?	� ngt; cp	S quot;0 tr. pa rT ^ CA nbsp;nbsp;nbsp;03 � �	� 0 qq	2 ^ tr. Bgt; fr 3
I	59*99	31	51*43	61	2q.09
2	59.96	32	50.88	62	28.17
3	59.92	33	50.32	63	27*24
4	59-85	34	49*74	64	26.30
5	59*77	35	49*15	65	2536
6	59*67	36	48.54	66	24.41
7	59-56	37	47.92	67	23*44
8	59-42	38	47.28	68	22.48
9	59.26	39	46.63	69	21.50
lO	59.09	40	45.97	70	20.52
11	58.89	41	45.28	71	19*53
12	58.69	42	44*59	72	18.54
gt;3	58.46	43	43.88	73	17*54
14	58.22	44	43.16	74	16.53
15	57*95	45	42.43	75	15.52
16	57*67	46	41.68	76	14.51
*7	57*38	47	40.92	77	13*50
18	57.06	48	40.15	78	12.48
19	56*73	49	39*36	79	11.45
20	56.38	50	38.57	80	10.42
21	56.02	51	37.76	8t	9*38
22	55*63	52	36.94	82	8-35
23	55.23	53	36.11	83	7*32
24	54*81	54	35*27	84	6.28
25	54*38	55	34-41	85	5.24
26	53*93	56	33*55	86	4.20
27	53*46	57	32.68	87	3*15
28	52.96	58	31*79	88	2.10
29	52.47	59	30.90	89	1.05
30	51-99	60	30.00	90	0.00

A I�ablc /hewing the /un�					s place and declination.
May.					June.
C	Sun'	s PI.	Sun s	Dec.	C	Sun�s	PI.	Sun's	Dec,
yy	D.	M.	D.	M.	{/gt;	D.	M.	D.	M.
1	10 � 55		15 N 7		I	lO n 44		22 N 5
2	11	53	15	25	2	11	41	22	13
3	12	51	�5	43	3	12	39	22	2i
4	13	49	16	0	4	13	3amp;	22	28
5	14	47	16	18	5	H	34	22	35
6	*5	45	16	35	6	45	3'	22	41
7	16	43	16	5*	7	(6	28	22	47
8	'7	41	17	8	8	17	26	22	53
9	18	39	^7	24	9	18	�23	22	58
lO	19	36	�7	40	10	'9	20	23	3
11	20	34	17	55	11	20	18	23	7
12	21	32	18	lO	12	21	15	23	11
13	22	30	18	25	13	22	12	23	15
44	23	28	18	40	14	23	9	23	18
'5	24	25	18	54	^5	24	7	23	20
16	25	23	19	8	16	25	4	23	22
17	26	21	^9	22	�7	26	1	23	24
18	27	gt;9	19	35	18	26	58	23	26
'9	28	16	19	48	19	27	56	23	27
20	29	14	20	1	20	28	53	23	28
21	0 II I I		_20	13	21	29	50	23	28
22	1	9	20	25	22	0 25 47		23	28
23	2	7	20	37	23	I	45	23	28
24	3	4	20	48	24	2	42	23	27
25	4	2	20	59	25	3	39	23	26
26	4	59	21	10	2b	4	36	23	24
27	5	57	21	20	27	5	33	23	21
28	6	54	21	30	28	6	31	23	�9
29	7	52	21	39	29	7	28	23	16
3�	8	49	21	49	30	8	25	23	12
31	9	47	21	57

Sun�s meridian altitude �	60�	3�'
Sun�s declination, add nbsp;nbsp;nbsp;�	%o	10
Complement of the latitude -	80	40
Subtra�l: from - , , - -	90	0
Remains the latitude - - -	9	20
Sun�s meridian altitude - nbsp;nbsp;nbsp;-	70�	20'
Sun�s declination, add - -	23	20
The fum is -----	93	40
From which f�btra�l - - -	9�	0
Remains the latitude - - -	3	40:

c	dun from node				�^un t om n ce			Siquot;	...	m node.
O;	s	0	/ �			0		M.
					M.
I	0	1	2	19				To	//// V
.	0
	0		4	3�
3	0	3	6	57	I	0	2 36	31	1	20 31
4	0	4	9	16	2	0	5 '2	32	1	23 7
5	0	5	11	3^gt;	3	0	7 4*^	33	I	25 43
6	0	6	13	54	4	0	10 23	34	1	28 9
7	0	7	j6	*3	5	0	12 59	35	I	31 55
8	0	8	18	32		0	15 35	3amp;	1	33 31
9	0	9	20	51	7	P	18 11	37	I	36 6
10	0	10	23	10	8	0	20 47	3S	I	38 42
n	0	11	25	29	9	0	23 23	37	I	41 18
12	0	:2	27	48	10	0	25 58	40	I	43 54
^3	0	30		7	i 1	0	28 33	41	I	46 36
H	0	H 32		2fc	12	0	31 9	42	I	49 5
15	0	15	34	15	13	0	33 45	43	I	51 41
	0	16	37	4	14	0	21	44	1	54 17
17	0	17	39	23	15	0	38 57	45	I	56 53
18	0	18	4^	4'	16	0	41 32	46	I	59 29
19	0	19 44		0	17	0	44 8	47	2	2 5
20	0	20	46	19	1�	0	46 44	48	2	4 41
	0	21	48 38		19	0	49 20	49	2	7 17
22	0	22	50	52	20	0	51 5^	50	2	9 53
23	0	23	53	16	21	0	54 32	51	2	12 29
24	0	24 55 35			22	0	57 ^	52	2	15 5
2J	c	25	57	54	^3	0	59 43	53	2	17 41
2t�	0	27	0	13	24	I	2 19	54	2	20 17
27	0	28	2	32	25	I	4 55	55	2	2^ 53
28	0	29	4	SI	26	1	7 3*	56	2	,25 29
29	I	0	7.	10	27	I	10 7	,57	2	28 4
30	1	I	9 29		28	I	12 43	58	2	30 40
3^	1	?	n	48	29	I	15 9	59	2	33 i9
32	I	3	14	7	30	I	17 55	6.0	2	35 52

mm

Puh�ijhed hy the fame Author.

LECTURES

SELECT SUBJECTS

The USE of the GLOBES, The ART of DIALING,

The Calculation of the Mean Tim^of New and Full Moons and Eclipses.

By JAMES FERGUSON, F.R.S.

;i nbsp;nbsp;nbsp;:

. ;

PREFACE.

PREFACE.

PREFACE.

PREFACE.

PREFACE.

CONTENTS.

LECTURE VII.

LECTURE XII.

LEG-

LECTURES

SELECT SUBJECTS.

I, If

And

e 3 nbsp;nbsp;nbsp;to

Plate w.

the

Of central Forces,

Of the ^idesl

the

high

'Ibi EartUs Motton demonjlraud. nbsp;nbsp;nbsp;45

diftance

CD

�2 nbsp;nbsp;nbsp;Of the mechanical Powers.

i. �

fr-

round

remains

Of Water-Mills.

more:

I nbsp;nbsp;nbsp;muft

The

The MILL-WRIGHT�s TABLE.

Such

Of Wind-Mills.

3 nbsp;nbsp;nbsp;by

92 nbsp;nbsp;nbsp;Of Wheel-Carriages.

LECT.

L E C T. V.

preffed

Firft,

�f

Of Hydraulic Engines.

135

Hydrojiatical Talles.

The

Hydrojiatical tables.

As

Hydrcftatical �Tables.

Hydrojiaiical �Tables.

Hydroftatical �Tables.

The fire-engine comes next in order to be ex- The/n plained; but as it would be difficult, even by engint.

the

Hydroftatical �Tables'^

Hydrojiatical �Tables'.

power

Hydroj�atical Tall�S^

3. When

For

Hydraulic ^ahle.

This table is c.Mcu'aied to the meafure of ale gallons, at 282 Cubic inches per gallon.

Water

moft

158 nbsp;nbsp;nbsp;Of the fpecifx Grfivities of Bodies.

A Table of the fpecific gravities of feveral folid and fluid bodies.

The

\0f the fpecific Gravities of Bodies. The Table concluded.

A Tabl�

A Table for reducing Troy weight into Avoirdupoife weight.

o o o 0 2 2nbsp;OOP

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