The nature of the luminous objefts that are feen in the heavens, and of which thenbsp;moon is the neareft to us; their number, their dif-tances, their -movements, with the appearancesnbsp;which arife therefrom, and the ufeful purpofes tonbsp;which the human fpecies has applied the knowledge of thofe particulars, form the fcience ofnbsp;aftronotny.

T o the vulgar eye the heavenly bodies offer an unprofitable, confufed, but pleafing, Ipedlacle. Thenbsp;leaft obfervation fhews that the feafons, the lengthsnbsp;of days and nights, the viciffitudes of heat and cold,nbsp;amp;c. are connefted with particular fituations of thenbsp;celeftial bodies. Farther obfervations point out thenbsp;entire dependance of the former upon the latter, asnbsp;VOL. jv,nbsp;nbsp;nbsp;nbsp;Bnbsp;nbsp;nbsp;nbsp;alfo

The periods of the moft remarkable phenomena have been afcertained from time immemorial; andnbsp;when we confider the accuracy of certain obferva-tions, the fcarcity of opportunitieSj and the want ofnbsp;the telefcope as well as of other inftruments, we arenbsp;forced to acknowledge and to applaud the ingenuitynbsp;of our forefathers.

Every age has added fomethlng to the flock of aftronomical knowledge; but, fince the fixteentbnbsp;century, the advancement has been much more rapid than the fimple proportion of the times; andnbsp;we may with fatisfadlion boaft of the aftronomicalnbsp;dlfcoveries which have been made within the laftnbsp;30 years.

The prefent knowledge of this moft noble fcience can affign a proper reafon for almoft every particular phenomenon ; it fubjedls them to ftrifl, to un-anfv/erable, calculation ; and deduces effcntial benefits from the refuks.

The vulgar, v^hofe minds feldom connecl more than tv;o ideas, may laugh at the employment ofnbsp;examining with unwearied toil, what is fo far removed from us ; and they may wonder that aftro-nomers fhould b� fo anxious to afeertain not onlynbsp;the day or the hour, but even the very momentnbsp;when a certain celeftial appearance is to take place,,nbsp;or when a ftar, which is hardly vifible, will comenbsp;within a certain diftance of the fun, or of the moon.

But whoever endeavours to trace the influence, whether immediate or remote, of thofe peculiar accuracies upon fcience in general, and upon the va-i'ious human affairs; whoever confiders, that theynbsp;afford the means, and the only accurate means, bynbsp;which the mariner can navigate the oceans, and cannbsp;find his exact fituation at Tea j which afford thenbsp;accurate meafurement of time j by which the realnbsp;diftances of places upon the furface of the earth cannbsp;be determined ; which furnifli ftandards of weightsnbsp;and meafures, amp;c. whoever, I fay, confiders thisnbsp;various and cxtenfive influence, will undoubtedlynbsp;find abundant reafons for admiring and for encou-raging the utmoft diligence and the moft fcrupulousnbsp;accuracy in the fludy of aftronomy.

Were the motions of the celeftial objefts uniform and regular, the calculation of their afpefts wouldnbsp;be accompllfhed with facility. But the apparentnbsp;irregularities of thofe objedts, render the inveftiga-tion of their movements, and the calculations fornbsp;their appearances, extremely intricate; nor couldnbsp;the fcience have attained the prefent much improved ftate, had it not been affifted by all thenbsp;fublimefl branches of mathematics, and by the admirable mechanical improvements of later times ;nbsp;fuch as time-keepers, telefcopes, quadrants, andnbsp;other inflruments.

Before we enter into the particular ftatement of the number, the order, the motions, and the

mutual dependence of the celeftial objedls j as allb' before we endeavour to determine their real fromnbsp;their apparent motions and fituations, it will be ne-celTary to ftate certain principles, which, thoughnbsp;obvioufly true, will however much affifl. the beginner in the comprehenfion of the fcience, as alfonbsp;will render the fubfequent chapters more perfpicu-ous and concife.

IT has been fliewn in the principles of optics, (vol. III.') that our fight judges of the diftancesnbsp;of objefts of unknown fizes and fhapes, only by thenbsp;converging of the optical axis, and by the parts ofnbsp;thofe objeds appearing more or lefs diftind ; butnbsp;when the objed is beyond a certain limit, which 'nbsp;hardly exceeds a few miles, the inclination of thenbsp;optical axis of our eyes becomes unalterable, andnbsp;diftind vifion becomes doubtful. Therefore thofenbsp;objeds which are at immenfe diftances from us, asnbsp;the celeftial bodies, appear as if they were fituatednbsp;on the internal furface of an hollow fphere, and wenbsp;might eafily be led to believe that they are equallynbsp;diftant from us, had we not other moft conclufivenbsp;proofs of their being varioufty removed from us, asnbsp;well as from each other.

It is almoft ufelefs to obferve that the angular diftances of objeds are quite different from their linear or true diftances. The angular diftance relates to^anbsp;particular point as a centre, and is meafured by the .nbsp;arc of a circle which has that point for centre.

Thus, to a fpeftator at A, fig. i. Plate XXVI. the angular difiance of the two obje�ls, B and C, isnbsp;nieafured by the arc FG, of the circle HFG, whofenbsp;centre is A j and it is immaterial whether this circlenbsp;be large or fmall j for the arc which is interceptednbsp;by the lines AB, AC, (whofe inclination BAC isnbsp;the angular diftance between the objefts B and C)nbsp;bears always the fame proportion to the whole circle of which it is a part j viz. FG is fuch a partnbsp;of the circle HFG, as/|- is of the c'xxcXc hfg.

The arc FQ may happen to be a tenth or a thirtieth, of, in fliort, any other part of the whole circle; butnbsp;for the conVenicncy of expi effing this part, the wholenbsp;circle is divided, or is fuppofed to be divided, into 360nbsp;equal parts called degrees, each degree is fubdividednbsp;into 60 equal parts called minutes, each minute isnbsp;divided into 60 equal parts called Jeconds each fe-cond is likewife divided into 60 equal parts callednbsp;thirds, and lb on �, but divilions, fmaller than a fe-cond, are more commonly exprefied in decimals ofnbsp;a fccond; then if the arc F G be the tenth part ofnbsp;the circle, it is faid to be equal to 36 degrees j be-caufe 36 is the tenth part of 360 �, if it be thenbsp;30th part of the circle, it is faid to be equal to lanbsp;degrees, becaufe 11 is the 30th part of 360 and fonbsp;forth.

Inftead of the word degrees, a fmall � is more commonly placed on the right hand fide of the �nbsp;number, and a little above it j inftead of the wordnbsp;minutes a little ftroke is more commonly annexed to

the

tlie number j and two fuch ftrokes denote feconds, amp;c.: thus, the expreffion 24�, 13',nbsp;nbsp;nbsp;nbsp;means 24

It is evident that in fig. i, to a fpedlator at A, the objeds B and C j or D and C, or D and E, or Bnbsp;and �, have exadlly the fiune angular diftance,nbsp;though their real diftances from each other are fonbsp;evidently various. Hence it follows, that the pove-ments of a diftant body cannot be known, except bynbsp;the change of the angular diftance between that andnbsp;fome other body which is either fixed or moving innbsp;a determinate way. When a body moves in a ftraightnbsp;line, either dircdlly towards us or from us, we judgenbsp;of its approaching to, or of Its receding from, us, bynbsp;the apparent enlargement or contradlion of its di-menfions; as is fiiewn by the plaincft propofitionsnbsp;of trigonometry; and from the meafuremcnts ofnbsp;thofe dimenfions, and one or two more data, we cannbsp;frequently determine the real fize of the body.�nbsp;That the fame body in motion will appear to movenbsp;either regularly or irregularly, or even to ftandnbsp;ftill, according to the different fituations of thenbsp;fpeflator, will be iliuftrated by the following example .

Let a body A, fig. 2, Plate XXVI. move regularly along the circumference of the circle ABCD, VIZ. fuppofe it to defcribe equal arcs in equal times jnbsp;then it is clear that to a fpedlator fituated at E,nbsp;which is the centre of the circle^ the body A will

appear to move equably and regularly one way j buC if the fpeftator be fituated at any other point withinnbsp;the circle, as for inftance at H, then the fame bodynbsp;A, will appear to move at different rates, accordingnbsp;as it comes nearer to, or' goes farther from, the ob-ferver; for, fuppofe the arcs AF, GC, to be equal,nbsp;and of courfe to be defcribed in equal times; thennbsp;the angle A H F, being fmallcr than tlie anglenbsp;G H C, the revolving body will appear to movenbsp;flower from A to F, than from C to G. Yet itnbsp;muft be obferved that the body A will always appearnbsp;to move one way, and not to go back or to fland ftillnbsp;during any quantity of time; as is the cafe when thenbsp;fpedlator himfelf is in motion, or when he is fituated out of the circle, but in the fame plane. Let,nbsp;for inflance, a body move equably along the circumference of the circle A B D F P, fig. 3, Platenbsp;XX�VI.} viz. to defcribe the equal arcs A B, B D,nbsp;D E, E F, amp;c. in equal times j and fuppofe thenbsp;fpedlator to be fituated at O in the fame plane innbsp;which the circle is, but out of its circumference jnbsp;then when the body moves from A to B, its apparent motion is nieafured by the angle A O B, or bynbsp;the arc H L, which it will appear to defcribe. Innbsp;an equal portion of time the body defcribes the arcnbsp;B D (equal to A B}, and this apparent motion isnbsp;meafured by the angle BOD, or by the arc L M,nbsp;which is fmallcr than the arc HL; and of courfenbsp;the body will appear to have flacked its motion.�nbsp;In another equal portion of time the body goes

front jj to E; but as this arc DEj nearly coincides yith the line D M O, the body will-appear to benbsp;almoft ftationary during that time. It then proceeds from E to F, in another equal portion ofnbsp;time, but now the body will appear to go back fromnbsp;M to I; viz. to be retrograde, and this retrogradanbsp;motion will continue until the body reaches the arcnbsp;QJ�, where it will again appear to be almoft fta-inbsp;tionary j then it will appear to go again from thenbsp;left towards the right, amp;c.

This optical inequality (as the aftronomers call it), muft evidently be various, according as the Ipefta-tor is fituated near to or farther from the circularnbsp;path ; hence thofe, who are fufficiently ikilled in thenbsp;mathematics, may from the obfervations of thofenbsp;unequal movements, often determine the dlftancCnbsp;of fuch a moving body from the place of obferva-tion; and from the appearance of its motions, asnbsp;feen from a certain place, they may determine whatnbsp;appearance its motions muft have from fome othernbsp;given place.

If, inftead of being in the fam.c plane, the fpefta-tor be fttuated above the plane of the circular path, the motion of the body muft likewife appear unequal ; excepting however when the fpeftator is innbsp;fame point of the ftraight line which paffes thi ough

If, inftead of moving in a circular, the body moved in an elliptical, orbit j fimilar apparent inequalities

qualities muft evidently take place. Hitherto the IpeiElator has been fuppofed to remain immoveable,nbsp;cither within or without the circular path of thenbsp;moving body. But when the place of the obfervernbsp;is itfelf alfo in motion, then the appearances will benbsp;very different, as may be eafily conceived by re-flefling on the apparent motion of bodies to perfonsnbsp;on a failing fliip; or as it may be deduced from whatnbsp;has been faid with refpedl to relative morion in thenbsp;firft volume of thefe Elements.�In this cafe notnbsp;only the regularly moving body may appear tonbsp;move irregularly, but quick motions may appearnbsp;flow, and flow motions may appear quick ; bodiesnbsp;at reft may appear to move, and moving bodiesnbsp;may appear to be at reft ; or their movementsnbsp;may appear to be quite contrary to what they reajlynbsp;are.

Before we conclude this chapter, and before we begin to examine what belongs to the celeftial ob-jeflis, it will be neceffary to remove fome erroneousnbsp;ideas, which are pretty commonly entertained by un-jnftrudled perfons concerning the earth which wenbsp;inhabit.

The fbortnefs of our fight enables us to behold but a very frnall portion of the furface of the earthnbsp;at one time, and that portion appears to be an im-menfe plain with fome accidental elevations, callednbsp;mountains, hills, amp;c. and fome deprefllons moftlynbsp;filled with water, fuch as feas, lakes, amp;c.

bevond a doubt, that what, at firft fight, appears to be a vaft flat, or plain, is, in truth, a convex fur-face; and upon a ftridter inquiry, it appears to be thenbsp;furface of an oblate fpheroid, viz. of a globe a littlenbsp;comprefTed on two oppofite fides.�Some of thenbsp;obfervations which prove the reality of this figure,nbsp;are hereto briefly fubjoined. Others of a nicernbsp;nature will be found in other chapters of this part.

It is conftantly obferved by all mariners, that as they fail from any high objeifts, fuch as mountains,nbsp;rocks, fteeples of churches, amp;c. they .firfl; begin tonbsp;lofe fight of the lower parts of thofe objefts, andnbsp;then gradually lofe fight of their higher parts. Alfonbsp;perfbns on the fhore firfl; difcover the upper parts ofnbsp;the mafts of approaching veffels, and then by degrees fee the lower parts in proportion as the veflelnbsp;comes nearer to the fliore. In the fame manner,nbsp;when failors approach a country, they firfl: difcovernbsp;the highefl parts of that country from the tops ofnbsp;the mafts, and then fee the loweft parts, or fee thenbsp;fame parts from the deck of the fhip.

In all thofe cafes, the obftrult;fl:ion to the fight antes from the intervening curvature of the earth ;nbsp;and in this refpeft no alTiftance can be derived fromnbsp;the ufe of the telefcope ; for the telefcope will onlynbsp;enable the obferver to fee more diftinftly that partnbsp;of the objed which is not behind the convexity ofnbsp;the earth. Thus in fig. 4, Plate XXVI. the loweftnbsp;part of the objeft A cannot be feen by the veffei at

earth.

earth T. The velTel E will be able to fee a fmaller part of the fame objefl A, becaufe a greater quantity of curvature is between that objecT and thenbsp;veffcl E. When the veffel fails farther off, as atF,nbsp;the objedt A difappears entirely.

So far the obfervations prove that the furface of the earth is convex ; but that this curvature returnsnbsp;into itfelf, viz. is continued all round without anynbsp;interruption, is proved by this; namely, that variousnbsp;navigators have failed all round the earth, and at laftnbsp;have returned to the very fame place from whichnbsp;they originally failed. They have not indeed failednbsp;jn an exadl circle, for that is prevented by the fitu-ation of the lands; but by going in and out according as the coafts happened to lie, they have kept onnbsp;the fame courfe upon the whole, and have arrived tonbsp;the fame place from another fide.

Thqfe who level grounds for the purpofe of forming canals, amp;c. foon perceive that the real level is not a ftraight line,' but a curve, whofe centre isnbsp;the fame as the centre of the earth. The furfacenbsp;of water, which is level, follows the fame curvature.

Were the earth a perfedt fphere, the curvature would be the fame in every part of its furface ; butnbsp;the moft accurate obfervations and meafurementsnbsp;which have been made with the niceft inftruments,nbsp;Ihew that this curvature differs a little in differentnbsp;parts, and from thofe differences, according to thenbsp;latcft meafurements, it lias been calculated, ift, that

the

the real figure is not much different from that of a fpheroid generated by the motion of a femi-ellipfis,nbsp;about its minor axis j sdly, that its axis or Ihorteftnbsp;diameter, viz. a line fuppofed to be drawn throughnbsp;its centre, from one of its flatteft parts to the other,nbsp;is nearly equal to 7893,5 Englilh miles, and itsnbsp;longeft diameter, viz. a line drawn through thenbsp;centre from one moft protuberant part of its furfacenbsp;to the other, is equal to 7928 EngUff miles. Thenbsp;whole circumference is equal to 24855,43 Engliflinbsp;miles ¹. Since the figure of the earth differs fo littlenbsp;from a fphere, therefore, for the purpofes of agronomy, the earth is confidered as a perfect fphere.

quot;When we fpeak of the furface of the earth, we take no notice of mountains, hills, feas, amp;c.nbsp;but we confider the whole as an uniform furface; for,nbsp;in fad, the mountains and other elevations arenbsp;to the furface of the earth, no more than grains ofnbsp;fand are to the furface of a globe of 8 or 10 feet innbsp;diameter. When the diftance of the furface of thenbsp;earth from its centre is mentioned in general, it isnbsp;always meant of the furface near the level of thsiea.nbsp;All places above that level, viz. more diftant from

The French, according to their lateft determination of their meafures, fuppofe this whole circumference to be dnbsp;vided into 40 millions of parts, which they call metres. Frontnbsp;the moft accurate admeafurements, it appears, that, at the

The fiirface of the terraqueous globe is irregularly fpotted with lands and water. The greater part (viz. almoft three quarters) of its furface isnbsp;occupied by the latter. The fhape and extent ofnbsp;thofe fpots are ufually -delineated upon a globe,nbsp;which of courfe reprefents the earth, and is callednbsp;the terrejlrial globe¹.

When the furface of the cerreflrial globe with the fiiape of the lands, the coafts, amp;c. is delineated,nbsp;either entirely or in part, upon a flat furface j fuchnbsp;a delineation is called a map or chart, A completenbsp;fet of fuch maps, has been called a terrejlrial atlas.

The navigators of all feas and of all times; the travellers, and the inhabitants of all countries, feenbsp;the fame expanfe of heaven over their heads, thenbsp;fame fun, moon, amp;c. which proves that the terraqueous globe is not attached to any other body,nbsp;but chat it exifts by itfalf perfectly Infulated in thenbsp;unfathomable expanfe of the Univerfe.

Dr. Long endeavoured to determine what proportion the land bears to the fea by the following ingenious method.nbsp;He took the flips of paper which are made for covering thenbsp;furfece of a terreftrial globe, and, by means of a pair ofnbsp;fciflars, he feparated that part which reprefents thelandfromnbsp;that which reprefents the fea. He then weighed thofe twonbsp;parcels of paper feparately, and found that the papers whichnbsp;reprefented the land weighed 124 grains ; the others weigh

It is a confequence of this uncontrovertible theory, that all the inhabitants of the earrh, beingnbsp;tlirefted with their feet towards the centre of h,nbsp;rrSuft be varioufly inclined to one another, like thenbsp;fpokes of a wheel; and the inhabitants of thofcnbsp;countries, which are diametrically oppofite, mufl;nbsp;have their feet diredly oppofzte. Such peoplenbsp;are called antipodes refpedtively, viz. thofe of onenbsp;country are the antipodes of thofe of the othernbsp;country.

Hence alfo it appears, that, with refpedt to the Univerfe, there is no real up or down; for what isnbsp;upper or over the head of one perfon, is pofitednbsp;otherwife with refpedt to another perfon. But innbsp;relation to the globe we inhabit, the words up ornbsp;down, above or below, mean the ficuations nearernbsp;to, or farther from the centre of the earth, than we,nbsp;or than ether given objedls, are.

It is the general artraciion of the matter of the whole terraqueous globe (as lias been alreadynbsp;explained *) that keeps us, and every particlenbsp;of matter, tending towards the centre of it.�nbsp;.We (hall prefently fee that this fame power adtsnbsp;univerfally throughout, at leaft, the folar fyftem;nbsp;and that every phenomenon of aftronomy, as far asnbsp;can be traced, is regulated by the laws .of motion,nbsp;and by thofe of univerfal attradlion.

With refpe�l to the heavenly Ipace which fur* rounds the earth, the ftudent of natural phiIofbph7nbsp;muft relihquilh feveral incoherent ideas, which henbsp;may have imbibed from common prejudices, andnbsp;from allegorical, poetical, or fuperftitious, ex*nbsp;preffions. The cahopy of heaven, the ftarry firmament, theceleftial fpheres, the'cryftalline fphere, thenbsp;empyreal regions, the vaulted hca\'en, the primumnbsp;nwlile, and fuch like expneffions, have no real and de-ternninate meaning. Theyare fiditious, hypotheticalnbsp;allegorical, and, upon the whole, ufelefs words, whichnbsp;can only miflead and confufe the underftandin�.

Wliat we perceive beyond our atmofphere is the fun, the moon, and a number of lucid and apparentlynbsp;fm'all bodies, called ftars, planets, and comets ; andnbsp;, thofe are demonftratively at different diftances fromnbsp;us as well as from each other j but of the immenfenbsp;fpace in which they exift and move, we have not thenbsp;fmallcft knowledge either from reafoning or fromnbsp;experience. We fee no boundary, no fhel), nonbsp;arch, no vault, rlo limit.�The blue fky, as is commonly called, is the colour of, or the refledionnbsp;from, our atmofphere, which extends not many .nbsp;miles above the furface of the earth *. For, befidesnbsp;other reafons, when the moon is not full, viz. whennbsp;only a portion of it is illumined, the other portion

� See vol. II. chap. Vlll. of thefe'Elements. Alfo Prieft-ley�s Hiftory of Villon, Light, and Colours. Period VI. Sed. ill. Chap. IV.

of it appears blue, or of the colour of the Iky, which Would not be the cafe if the blue colour proceedednbsp;from fome thing beyond the moon. '

Since to our eyes the celeftial bodies appear as if they were all equally diftant from us �, therefore, innbsp;order to affift the underhanding, or to inftrudt thenbsp;ftudents bf aftronomy, the ftars and other celeftialnbsp;bodies are Commonly reprefented upon a convex,nbsp;and fometimes upon a concave, fpherical f�rface of.nbsp;a few inches, or a few feet, in diameter. Such arti-^ ficial reprefentation of the celeftial bodies is ufuallynbsp;called a celeftial globe. When all the ftars or part ofnbsp;them only is delineated upon a flat furface, fuch de^nbsp;lineation is called a celeftial flaniffhere, or map, ornbsp;plate, and a complete fet of fuch plates has beennbsp;called a celeftial atlas.

vot. IV.

OF THE APPARENT SYSTEM OF THE WORLD, AND THE DEFINITION OF THE TERMS PRINCIPALLYnbsp;USED IN ASTRONOMY.

The incomparably fuperior fplendor of the fun in the day time, renders all the other ce-leftial bodies invifible to our naked eyes, exceptingnbsp;the moon, which fometimes may be barely diftin-guifhed; and two or three much fmaller bodies,nbsp;which in fome favourable circumftances may be juftnbsp;difcerned, whilft the fun is vifible yet *.

* In the day time, the refraflion and refledlion of the fun�s light from the atmofphere renders the ftars invifible to us evennbsp;when we turn our backs to the fun; but if we look at the heavens through a very long tube in the day time, the abovemen-tioned refiedled light will not penetrate a great way withingt;thenbsp;cavity of the tube; and therefore the ftars may be perceivednbsp;through it. A tube fufficiently long to anfwer this purpofenbsp;is difficultly conftruded and managed; but deep pits, andnbsp;deep wells, are in fa6l long tubes j hence, from the bottomsnbsp;of thofe places the ftars may be feen in the day time.�Anbsp;good telefcope will alfo flxew the ftars in the day time.

I nbsp;nbsp;nbsp;At

At night, viz, during the abfence of the fun, the moon frequently affords more light than all thenbsp;other celeftial objefts. The other numerous brightnbsp;bodies, which we perceive befides the moon, are innbsp;general called fars. They appear to differ much innbsp;magnitude, but they feem to be vaftly fmaller thannbsp;the moon. Eight of them are called planets ; thenbsp;reft are czWtA fixed fiars, for reafons which will benbsp;mentioned prefently. The comets areduminous bodies, which are feen not very frequently, nor at certain or determinable times.

Thefe, in ftiort, are all the objefts which we perceive in the heavens j the afpecfts and the motions of thofe objedls form the whole fubjeft of aftro-nomy. And here we may obferve, once for all,nbsp;that the circles, the curves, the lines, axes, poles,nbsp;points, and the figures of the conftellacions, ofnbsp;which frequent mention is made in aftronomy, arenbsp;not vifible things ; but they only exift in our imagination, and they have been adopted, and are ufed,nbsp;for the neceffary purpofe of communicating ournbsp;ideas to other perfons, or for expreffing meafures,nbsp;fituations, motions, amp;c.

When an obferver is fituated on a large extended plane, or in an open fea, he will find his fight cir-cumferibed by a great circle, which divides the vifible part of the heavens from that which is hid innbsp;confequence of the opacity of the earth j or wherenbsp;the furface of the globe we inhabit feems to meetnbsp;the heavens. That circle is called the Jenfibh ho~

rizon. The rational horizon is a circle in the heavens, fuppofed to be formed by the interfeclion of a plane,nbsp;which paffes through the centre of the earth, and isnbsp;parallel to the fenfible horizon. The planes ofnbsp;thole two horizons are diftant from each other bynbsp;the femidiameter of the earth; but with refpe�t tonbsp;the heavens, they may be fafely fuppofed to coincide } for the diftance of the fixed ftars from us isnbsp;fo immenfe, that the diameter of the earth is a merenbsp;nothing with refpeft to it. Hence the horizon divides the heavens into two equal parts; viz. the vi-fible, which is above it, from the invifible which isnbsp;below it.

With refpeft to the earth ; viz. if by the horizon we mean the boundary of that part of the earth�snbsp;furface which is feen by the fpeftator, then it is evident that the horizon is more extended in proportion . as the fituation of the obferver is more elevated ; for inftance, if the obferver be fituated dolenbsp;to the furface of the earth, G D E F, fig. 5, Platenbsp;XXVI. as at lt;?, he will fee a very fmall portionnbsp;of its furface ; becaufe the vifual line is a tangent,nbsp;(or nearly a tangent) to the furface of the earth atnbsp;that pointif he be fituated at h, then the vifualnbsp;line b E will touch the earth at E, and of courfenbsp;the horizon will be the circle, which is denoted bynbsp;the line DE.�If the fpeftator be fituated at c, hisnbsp;horizon will be G F ; and if the fpeftator flood atnbsp;an immenfe difiance, then his horizon would benbsp;equal to the circumference of the earth j viz. to

' OI:

It is evident, that every fpeflrator has a different horizon j therefore, ftriaiy fpeaking, thchalf of thenbsp;heavens which is feen by any one fpeftator, is notnbsp;precifely the fame half that is feen by another fpec-tator at the fame time.

To us Europeans the fun, the moon, the planets, and moft of the ftars, appear to go continually round the earth, and to perform each revolution innbsp;about 24 hours. I fay about 24 hours j for fomenbsp;of the celeftial objedls perform it flower thannbsp;others. They rife on one fide of the horizon, whichnbsp;is called the eajt^n fide, pafs obliquely over it, andnbsp;defcend on the oppofite fide, which is called the wej-tern ftde of the horizon ; then they rife again, amp;c.

If a perfon will obferve the heavens in the night time, he will find that the ftars feem to perform, ornbsp;to move along, different circles j fome larger,nbsp;others fmaller ; gradually diminifhing towards anbsp;certain part of the heavens, until fome of them per-

* The greateft diftance h E, from which an eye fituated any where above the furface of the earth, as at b, wil pernbsp;ceive an objedt E on the furface of the earth, is one � ^nbsp;plane triangle b E C, right-angled at E. Its other two 1 Csnbsp;are the radius EC of the earth, and C b, which is the fum ofnbsp;the radius and height a 1..�When ab\^ known, the diftancenbsp;J E is found by the following rule �� Add the height ab tonbsp;the diameter of the earth; multiply the fum by the height a 5;nbsp;then the fquare root of the produdl is the diftance b E. 1nbsp;rule depends on Prop. 47th, B, I.; and on Prop. 6th, B* ,

c j nbsp;nbsp;nbsp;form

fo^iTi circles fo fmall as not to be difcerned without proper inftruments. In fliort, the whole apparentnbsp;fphere fcems to move round an axis, and of courfenbsp;there are two points in the heavens, which, beingnbsp;the extremities of that axis, do not feem to .move atnbsp;all. Thofe points are called the poles of the world-,nbsp;one being called the arSlic, or the north, pole �, andnbsp;the other the antar5lic, oxjouth, pole. The axis it-felfi or the line which joins thofe poks, is called thenbsp;axis of the world.

In this metropolis we can perceive one pole only, namely, the north pole, which is elevated above thenbsp;horizon at an angle of 51quot; 31quot;. In truth, we cannotnbsp;perceive the pole itfelf; (which is an imaginarynbsp;point) but we may determine the fituation, or thenbsp;angular altitude, of that immoveable point, by examining the ftars,. which, being near it, revolvenbsp;without ever going below the horizon j for by takingnbsp;a mean of the leaft, and greateft, obferved altitudesnbsp;of any one of thofe ftars, we have the altitude of thenbsp;pole itfelfj it being evident that in its circular revolution each ftar muft rife as much above the pole asnbsp;it defcends below it.

A pretty large ftar, called the north polar ftar, is fituated near the north pole, and to the naked eye itnbsp;appears to be quite ftationary ; but when examinednbsp;by means of a fixed telefcope, or of other aftrono-mical inftruments, it is found to defcribe a fmallnbsp;circle, which proves that it is not quite at the pole.

Befides the poles, there are feveral other remarkable points, determined and conftantly ufed by the

cf the JVorldy^c, nbsp;nbsp;nbsp;^3

aftronomers, �which are therefore necefiary to be de fcribed. One of thofe points is called the zenithnbsp;and is the higheft point of the heavens, or thatnbsp;which is exactly over our heads. The oppolite ornbsp;lowed: point of the heavens, which is direftly undernbsp;our feet, is called the nadir. If a plummet be freelynbsp;fufpended, and if it be fuppofed to be infinitely exnbsp;tended both upwards and downwards, its thread willnbsp;pafs through the zenith and nadir. Thofe pointsnbsp;are alfo called the plee of the horizon *. All circles,nbsp;drawn through the zenith and nadir, which of courfenbsp;muft be perpendicular to the horizon, are callednbsp;vertical circles, or azimuths- Two of the innumernbsp;able circles, which may be defcribed through thofe ^nbsp;points, are peculiarly remarkable ; viz. that whichnbsp;paffes through them, and at the fame time throughnbsp;the poles of the world, is called the meridian. Thisnbsp;circle divides the fphere into two equal parts, one ofnbsp;which is the eajiern, and the other the �weftern, he-tnifphere. quot;When the celeftial bodies in their dailynbsp;courfe arrive at that part of the meridian whkh isnbsp;above the horizon, then they are faid to culminate,nbsp;viz, to be at their greateft elevation; for beyondnbsp;the meridian they defcend towards the horizon, andnbsp;when they are at that part of the meridian, which isnbsp;below the horizon, then they are faid to be. at theirnbsp;greateft depreffionj for beyond that limit they again

* In fpherles every circle of the fphere has two poles, which are the points on the furface of the fphere, where anbsp;ftraight line, paffing through the centre of the circle andnbsp;perpendicular to the plane of it, meets the furface.

c 4

rife towards the horizon. Therefore the meridian divides the time of the celeftial bodies courfe abovenbsp;the horizon, into two equal parts, and it alfo dividesnbsp;into two equal parts the period of their courfe belownbsp;the horizon ; hence, when the fun is at the meridiannbsp;in the day time, it is noon or midday (whence the meridian has derived its name) j and when the fun is atnbsp;the meridian below the horizon i viz. at night, itnbsp;is then faid to be midnight.

The other remarkable circle amongft the azimuths, is that which is perpendicular to the meridian, and is called the prime vertical. This circle divides the eaftern and weftern Tides of the horizon,nbsp;each into two equal parts. Thofe points of inter-fedlion are called the true eajl and voeft points j fonbsp;that the meridian and the prime vertical divide thenbsp;horizon into four equal parts, and the points of di-vifion, viz. the nortby the eaft, the Joutb, and thenbsp;wejl, have been called the principal, or cardinal,nbsp;points of the horizon; for each quarter of the horizon is fubdivided into eight partsj fo that the wholenbsp;horizon is�divided into 32 parts, which are callednbsp;the rhumbs, or the points of tbe compafs, from theirnbsp;being generally, marked upon the cards of the mariner�s compalTes,.

The fituation of the above-mentioned points is fo commonly underftood, that it will be almoft fuper-fluous to obferve, that if we turn our backs towardsnbsp;the north pole, we fhall then have the fouth exaddynbsp;before us, the eaft on the left, the weft on the right

han4

hand fide, the zenith over our heads, the nadir under our feet, the meridian pafling over our heads,nbsp;and under our feet, viz. through the north, the zenith, the fouth, and the nadirj and the prime verticalnbsp;pairing over our heads, and from our right to our leftnbsp;hand, through the eaft, zenith, weft, and nadir.

It is evident upon the leaft rcfledtion, that as the horizon is different for every fpeftator, or for everynbsp;point of the furface of the earth, fo the cardinalnbsp;points, and the rhumbs in general, which are the di-vifions of the horizon, muft be different for everynbsp;fpedlator; and fo muft alfo be the zenith and thenbsp;nadir, which are the poles of the horizon ; but for anbsp;fixed obfervatory, or for a given fpot, thofe circlesnbsp;and points are fixed and immoveable. TJre meridian is the fame, and the prime vertical is differentnbsp;for all thofe obfervers or fpots which are in the famenbsp;line, but only north or fouth of each other �, whereasnbsp;the prime vertical is the fame,' and the meridian isnbsp;different for all thofe obfervers or fpots, which arenbsp;only eaft and weft of each other.

That arc of the horizon of any particular place, ^hich is intercepted between the meridian and azimuth circle that paftes through a particular celeftialnbsp;objefl: at any given time, is called the azimuth ofnbsp;that celejiial ohjeEl. The arc of the horizon which

. nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;*nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-- w.-wnbsp;nbsp;nbsp;nbsp;j aiici CUV.. a/jiiliULi

iphere, is called the equator or equinoSiial, which divides the Iphere into two equal parts, and is perpendicular to the axis of the world, as alfo to thenbsp;plane of the meridian. In this metropolis, whennbsp;we place ourfelves with our backs to the north, asnbsp;has been mentioned above, the equator Hands obliquely before us, viz. it paffes through the eaft andnbsp;weft points of the horizon, and croffes the meridiannbsp;at a point which makes an angle of 38�, 29' withnbsp;the horizon. To thofe who are fituated fouth of us,nbsp;the interfefbion of the equator with the meridian isnbsp;higher up, and to thofe who are north of us, that in-terfeftion is lower down. The poles of the worldnbsp;are the poles of the equator.

Now, if we fuppofe the planes of various meridians, as well as of the equator, and of the rational horizon, to cut the furface of the earth, then thenbsp;fame circles which are fuppofed to exifl: in the heavens, may likewife be conceived to exifl: on the fur-face of the earth. Alfo that point of the furface ofnbsp;the earth, which is exadly under the north pole ofnbsp;the world, is called the mrth pole of the earth; andnbsp;the fame thing muft be underftood of the fouthnbsp;pole.

The ufe which is made of thofe points and circles on the furface of our globe, will be fhewn hereafter;nbsp;but we Ihall obferve for the prefent, that thenbsp;fituation of the equator with its axis and its poles,nbsp;which are the fame as the axis and the poles of thenbsp;world, appears differently fituated to the different

inhabitants of the earth. Thofe different fituations may be reduced to three fpecies, and thefe have obtained peculiar appellations; viz. to thofe perrons'nbsp;who live exadtly under the equator, the poles of thenbsp;world muft appear in the horizon, and the equatornbsp;tnuft be perpendicular to the horizon, viz. muft cutnbsp;it at right angles; hence that fituation is called thenbsp;right pojition of the Jfhere. To thofe who live un-rnbsp;der either of the poles of the earth, one of the polesnbsp;of the world muft be over their heads, and the equator muft coincide with, or be parallel to, the horizon ; hence that fituation is called a faralleljphere.nbsp;And laftly, to all the other inhabitants of the earthnbsp;the fphere is faid to be in an oblique pofition, becaufenbsp;the equator is neither perpendicular nor parallel,nbsp;but oblique, to the horizon. Thus in fig. 6. Platenbsp;XXVI. NEHS reprefents the celeftial fphere, or anbsp;meridian; acb reprefents the earth, N and S arenbsp;the poles of the world, N S is its axis, and E E isnbsp;the equator. Now to us at a, who are neither undernbsp;the equator at c, nor under the poles at b, the fpherenbsp;is faid to be oblique, becaufe the equator E � isnbsp;neither perpendicular, nor parallel, but oblique, tonbsp;our horizon HH. To thofe who live at r, v:z.nbsp;under the equator, the fphere is faid to be right, becaufe the equator E E is perpendicular to their horizon, w'hich is N S. And to thofe who live at b,nbsp;'^iz. under the poles, th? fphere is faid to be parallel, becaufe the equator E E coincides with, or Isnbsp;the fame as, their horizon.

The

The apparent movements of the ftars, which are performed in circles parallel to the equator, mull,nbsp;of courfe, appear to be performed in circles perpendicular to the horizon to thofe who live under thenbsp;equator at c, and to them (who likewife fee thenbsp;poles of the world in their horizon) all the ftarsnbsp;inuft appear to rife and to fet in every revolution,nbsp;and in every revolution they fee all the ftars fuc-ceftlvcly. But to thofe who live under the poles atnbsp;h, the ftars move in circles parallel to the horizon,nbsp;fo that they never rife or fet, and confequently thofenbsp;people can only fee half the ftars, viz. one hemi-fphere, whilft the other is never feen by them, itnbsp;remaining conftantly below their horizon. To thofenbsp;who live neither under the equator, nor under thenbsp;poles, the ftars appear to move in circles oblique tonbsp;the horizon, and they fee a greater or a ftnallernbsp;number of the ftars pafs in fucceffion, according asnbsp;they are fituated nearer to the equator or nearer tonbsp;the poles. Thus to us fuuated at a, all the ftarsnbsp;which are fituated within the portion PEH, OEH,nbsp;are feen fucceflively; but thofe which are about thenbsp;fouth pole S) viz. in the portion H S O, are nevernbsp;feen by us, becaufe, as the fjahere revolves round thenbsp;axis NS, the portion HSO, never rifes above ournbsp;horizon HH. And the ftars, which are in thenbsp;portion El N P, about the north pole N, are alwaysnbsp;within our fight, becaufc that portion HNP, ofnbsp;the fphere, never goes below our horizon H H.

limits the part HNP, that never goes below the horizon of any given place, is called the circle ofnbsp;perpetual apparition. The circle H O, parallel tonbsp;the equator, which lirnlts the part HSO, that nevernbsp;rifes above the horizon of any given place, is callednbsp;the circle of perpetual occultaticn.

Not all the celeftial objefts appear to a fpeaator in a fixed place, to rife conftantly from, or to fetnbsp;at, the fame refpeftive points of the horizon;

The fixed ftars properly fo called, (which comprehend all the celeftial objefts, excepting the fun, the moon, eight planets, and fome comets, whichnbsp;appear now and then) do move with that uniformity, viz. they move along the fame tracks ornbsp;circles, and preferve the fame diftances from eachnbsp;other; hence they have been ^^tnon^\n3.ttl^fixedJiars\nbsp;and therefore the aftronomers ufe them as fixednbsp;^ points with which, and by which, the motions ofnbsp;the other celeftial objeefts are compared and ex-prefied. The whole fphere, or all the fixed ftars,nbsp;perform their revolution; viz. go from the meridian of a given place, and return to the fame place,nbsp;conftantly in the fpace of 23 hours, 56 minutes, andnbsp;4 feconds.

The fun rifes and fets every day at different points of the horizon, and it alfo crolfes the meridian ofnbsp;any place every day at a different point; but itnbsp;never goes farther from the equator than about

23� 28', either towards the north or towards the fouth of it. The time of its rifing, fetting, and ofnbsp;croffing the meridian, is not always the fame; it being fometimes later, and at other times fooner, thannbsp;on the preceding day. The difference is pro-greffively increafing and decreafing. Upon thenbsp;whole k amounts only to a few minutes; and, at anbsp;mean, its revolution (which is called the fun�snbsp;daily revolution from its producing the viciffitudesnbsp;of day and night) employs 24 hours, viz. 3'',nbsp;56'' longer than the revolution of the fixed ftars jnbsp;or rather, we divide the mean time of the fun�snbsp;daily revolution, into 24 parts, which we callnbsp;hours. The fixtieth part of an hour is called anbsp;minute of time, and the fixtieth part of a minute isnbsp;called a Jecond of time.

If the very great fplendor of the fun did not prevent our feeing the ftars in the day time, We lliould find that the fun (which, as has been faid above,nbsp;moves flower than the flats) is left conllantly behind ; viz. every day more tow'ards the eaft, andnbsp;likewife a little more towards the north, or towardsnbsp;the fouth. In fliort, if every day at noon, when thenbsp;fun croffes the meridian of a given place, we markednbsp;the exadl place of its centre in the heavens amongnbsp;the ftars, and if when the fun has returned to thenbsp;fame point of the heavens, all which period takesnbsp;up 365 days, 5 hours, 48', 49�, and is called thenbsp;mean Jolar year, we drew a line along all thofe

This circle interfefts the equator at two qppofitc points, and its plane forms an angle of about 23� 28 gt;nbsp;with the plane of the equator. This circle, which isnbsp;the annual path of the fun, is called the ecliptic jnbsp;the angle, which it forms with the equator, is callednbsp;the obliquity of the ecliptic j and the points where itnbsp;interfeds the equator are called the equinoxes, or thenbsp;equinoSHal points,

A broad portion of the heavens, which ftretches about 8� on each fide of the ecliptic, and of courfenbsp;follows its diredion all round the heavens, is callednbsp;the zodiac.

Since the ecliptic is a fixed circle, and every day the fun is found in a different point of it; thereforenbsp;every day the fun feems to perform its revolution innbsp;a circle parallel to the equator, but which recedesnbsp;farther and farther from it, until it reaches its greateftnbsp;diftance j which, as has been faid above, is aboutnbsp;23� 28^ from it towards the north; after which thenbsp;daily courfe of the fun is performed in a circle,nbsp;�which approaches the equator gradually until itnbsp;Coincides with the equator, then it begins again tonbsp;tecede from it towards the fouth, until it reaches itsnbsp;greateft fouthern diftance, which is likewife equalnbsp;about 23� 28'; then it approaches the equatornbsp;a.new, an� fo forth.

Now when the fun is at its greateft diftances from the equator, the circles parallel to the equator which

it nearly defcribes at thofe two points, are called th� tropics, and that which is towards the north is callednbsp;the tropic of Cancer, whilftthat which is towards thenbsp;fouth is called the tropic of Capricorn. The diftancenbsp;of the f�n, as well as of any other celeftial objeiSt,nbsp;from the equator, is called the declination of thatnbsp;objefb, and it is north ox fouth declination, accordingnbsp;as the objedt is on the north, or the fouth of thenbsp;equator.

It has been faid above, that if the fplendor of the fun did not prevent our feeing the ftarsnbsp;which are near it, we Ihould find it every daynbsp;near a different fiar. But though we cannot feenbsp;the ftars that happen to be near the fun} yet, bynbsp;means of proper inftruments, we can obtain the re-fult exadtiy in the fame manner as if we faw them ;nbsp;for knowing the time of the revolution of the ftars,nbsp;and likewife knowing their refpedlive fituations, thenbsp;aftronomers, by examining the time of the fun�snbsp;palfage over the meridian, which differs a little innbsp;different days, as alfo by examining its daily altitude, when it croffes the meridian at noon, can determine with great precifion which ftar mull: crofsnbsp;the meridian at the fame time, and through thenbsp;fame point, or within a certain diftance of it.

The moon appears to rife from, and to fet every day at, different points of the horizon, and likewifenbsp;to crofs the meridian at different points j but withnbsp;much more irregularity than the fun. It alfo movesnbsp;much flower than the fun j fo that if one night it

of the World, yc. nbsp;nbsp;nbsp;33

be found near a certain ftar, on the following night it will be feen much to the eaft of that ftar; viz.nbsp;about 13�, or rather more ; on the following nightnbsp;it will be found about as much more backward, andnbsp;fo on. It likewife advances at the fame time towards the north or towards the fouth. Indeed, fonbsp;rapid is its motion, that if any attentive perfon willnbsp;watch its courfe amongft the ftars during a few hoursnbsp;only, he will plainly perceiv'C her change of place.nbsp;All this retrogradacion, which is called the 'propernbsp;movement of the moon, viz. from the time that it isnbsp;feen near a certain ftar, and until it comes near it

The different appearances (or as they are more commonly called the phajes) of the moon, are thenbsp;phenomena which are more particularly ftriking andnbsp;more generally remarked in the heavens, even bynbsp;the rudeft nations of the earth. During the 27 ornbsp;28 days of her proper movement, we perceive thenbsp;moon affording more or lefs light, or, ftrewing anbsp;fmaller or larger part of its illuminated dife. Fornbsp;about three days out of the 27, the moon is almoftnbsp;invifible; then we begin to fee it in the evening towards the weft, fomew'hat like a luminous arch withnbsp;pointed extremities, properly called cufps or horns.nbsp;In that ftate it is denominated a crefeent: for its luminous part increafes gradually until it appears afternbsp;feven days, like a femicircle. It is then at the apparent diftance of go� from the fun, and we fay that it is

feven

leven or eight days after, it gets quite oppofite to the fun, and Ihines with its entire circular dife, in whichnbsp;ftate we call it the Jull moon. After that period thenbsp;luminous part of the moon begins to decreafe, andnbsp;when it comes again within 90� of the fun, but onnbsp;the other fide, we fay it is at its hji quarter. Itnbsp;I :ftly gets too near the fun, where we lofe fight ofnbsp;it for a lliort time, and the moment it paffes beyond the meridian of the fun�s centre, we call it thenbsp;vew moon; for, a day or two after this, we begin tonbsp;fee it again towards the weft �, and fo forth. Thenbsp;convex part of the moon�s illuminated portion, ornbsp;the.more convex of its two fides, is always turnednbsp;towards the fun

Amongft the ftars there are, as we have already noticed, eight luminous bodies, which the nakednbsp;eye can hardly diftinguilh from the fixed ftarsjnbsp;but which, when viewed through a telefcope, havenbsp;very different afpe�ts j and when examined , withnbsp;refpeft to their motions, are found to be quite different from the fixed ftars j for though they appearnbsp;to move like the other ccieftial bodies, from eaft tonbsp;weft, yet each of them performs that apparent revo-

* The period of each of the four remarkable phafes of the moon which is performed in the fpace of feven or eight days,nbsp;and likewife the whole lunation or the period of its entire revolution which is performed in about 28 days, feems to havenbsp;fuggefted the general cuftom of counting by months andnbsp;weeks. See de la Lande�s Aftronomy,

lution

lution in a different time : hence they all change their mutual diftances, as well as their fituations with refpedtnbsp;to the fixed ftars; for inftahce, one evening one ofnbsp;them will be feen near a certain ftar, the next evening it will be found near fome other ftar, which isnbsp;to the eaft of the former j on the following eveningnbsp;it will be found ftill more eafterly, and fo on for anbsp;number of nights ; then perhaps it will appear tonbsp;tgt;e ftationary j viz. it will remain near the fame ftarnbsp;during fome nights j after which it will move to-''^ards the weft of that ftar, amp;c.

From fuch irregular or wandering movements, thofe eight celeftial objedts have been denominatednbsp;Planets, The aftronomers have given them pecu-iiar names ; and for the conveniency of expreffingnbsp;them upon globes, tables, amp;c. they are often denoted by peculiar charadters. Here follow theirnbsp;names and charadlers.

Mercury 5 j Venus ? j Mars $ ; Ceres Ferdinm-dea i Pallas; Jupiter % ; Saturn Tj ; and the Geor-gium Sidus, or Georgian Planety which, by fome, has alfo been called either Uranius, or Berjchel � ¹.

Mercury, Venus, Mars, Jupiter, and S i been known from time immemorial; the Georgian p ^enbsp;was difcovered by Dr. Herfchel about 20 years ago.

Ceres was difcovered by Mr. Piozzi, an Italian aftronomer, on the ift of January i8oi, or the foft day of thenbsp;century. The laft, or Pallas, was difcovered by Dr,

Since the ftars properly fo called, are confidered as fixed points in the celeftial fphere, which fervetonbsp;denote the movements peculiar to the fun, the moon,nbsp;the planets, and the comets; and whofe fituationsnbsp;are likewife ufeful for other purpofes j thereforenbsp;afironomers have laboured with great afliduity tonbsp;determine, with the utmoft accuracy, their fituationsnbsp;in the heavens, or their diftances from each other;nbsp;and fuch diftances are laid down in books, or catalogues, or tables. This however has been morenbsp;particularly the cuftom of latter times ; for the ob-fervers of very remote antiquity parcelled the wholenbsp;into irregular aflemblages, to which they gave thenbsp;names of men, of birds, of fifties, amp;c. according tonbsp;fome faint or diftant refemblance, which that particular arrangement feemed to indicate. Then, innbsp;order to fpecify any particular ftar of a certain arrangement or imaginary figure, they fpoke, for in-ftance, of the ftar on the fhoulder of Orion, or onnbsp;the tail of the fifh, amp;c. And fuch is the afliftancenbsp;which thofe imaginary figures afford to the memory,nbsp;that this cuftom is ftill continued, viz. of expreffingnbsp;the ftars by their fituations in thofe imaginary figuresnbsp;of men, fifties, birds, amp;c. which are called afterijmsnbsp;or conftellations. The modern more accurate aftrono-mers ufe thofe conftellations for the purpofe of in-of Bremen,quot; on th� 28th of March 1802.'�I do not knownbsp;that any particular chara�lers have as yet been appropriatednbsp;to the two laft difcovered planets.

dlcating the general aflembkge of ftars in a certain portion of the heavens; but they diftinguifh eachnbsp;particular ftar by a Greek letter^ or by the figuresnbsp;of numbers, as i, i, 3, amp;c. and mark its truenbsp;place by mentioning its diftances from particular

Some of the principal fixed, ftars have peculiar names, fuch as Aldebaran, Sirius, Regulus, amp;c.

We fhall treat of the conftellations, as alfo of the particular ftars which are contained in them, in another chapter of this part; but for the prefent it willnbsp;be necelTary juft to mention that the zodiac is occupied by twelve conftellations, whofe names andnbsp;characters are as follow :

Aries 'v, �Taurus �, Gemini n. Cancer Leo Slgt; Virgo �E, Libra =0=, Scorpio tn., Sagittarius P, Ca~nbsp;pricorms kf, Aquarius cx, and Pifces X. Thofenbsp;conftellations are fuppofed to divide the zodiac, ornbsp;the ecliptic, into 12 equal parts �, therefore 30 degrees are afllgned to each of them? 12 times 30nbsp;making 360'*, or the whole circle. They are fitu-ated in the order in which they are mentioned above

Having thus given a general or fuperficial view of the number and movements of the principalnbsp;celeftial bodies, as well as of the moft remarkablenbsp;circles and points that are ufed in the fcience ofnbsp;aftronorny ; it will be necefiary to indicate fome ofnbsp;the moft ftriking effefts that are produced by

D 3 nbsp;nbsp;nbsp;the

the abovementioned circles and points, in determining diftances and pofitions 5 but to this I ftiall briefly prefix a few of the more remarkable properties of the circles of a fphere, by way of refrefhingnbsp;the memory of the ftudents, who are fuppofed tonbsp;have previoufly ftudied fpherical geometry, trigonometry, amp;c.

If a plane cut a fpherical furface, the fedlion will be a circle. If the plane pafs through the centre ofnbsp;the fphere, the fedtion is called a great circle of thenbsp;fphere j it being the largefl: circle that can be drawnnbsp;upon the fphere ; but if the cutting plane do not pafsnbsp;through the centre of the fphere, then the fedlionnbsp;will be a kjjer circle. Therefore all great circles ofnbsp;the fphere have the fame common centre, and cutnbsp;one another as well as the fphere, into two equalnbsp;parts. But lefl�r circles have not the fame centrenbsp;with the fphere, and they may be cut unequally by anbsp;great circle, or by another leffer circle.

A fpheric angle is the inclination of two great circles, and is meafured by an arc of a great circlenbsp;intercepted between the legs of that angle, at 90�nbsp;diftance from the angular point. When two circles interfedt one another, the oppofite angles arcnbsp;equal,

A fpheric triangle is a figure formed on the furface of the fphere by the mutual interfedtions of threenbsp;great circks.

The poles of a circle are thofe two points on the furface of the fphere, where a ftraight line paffingnbsp;through the centre of the circle, and perpendicular

from it; but thofe of a lefler circle are not cquidiftant. When two great circles are perpendicular to each other, they mult pafs through each other snbsp;poles; and then either of them is called fecondarynbsp;to the other. Thus the meridians are faid to benbsp;fecondaries to the equator, and the azimuths are

A great circle perpendicular to a lefTer circle, rttuft pafs through the poles of the latter j but the

The projeStion of the fphere is the reprefentation of its circles, points, amp;c. upon a flat furface; andnbsp;thofe reprefentations of circles may be either ftraightnbsp;lines, or circles, or eiliples, or other curves, according as the circles lie in the diredtion of the eye of thenbsp;obferver, or perpendicular, or oblique to it; andnbsp;likewife according to the nature of the projeftion, of

The equator on the earth, which is juft under the celeftial equator, is a great circle which divides thenbsp;earth into two equal parts, namely, the northern andnbsp;the fouthern hemifpheres. This imaginary circle

paffes through the continent of Africa, croffes the Indian ocean, as alfo the iflands of Sumatra and Borneo j it paffes along the whole extent of the Pacificnbsp;ocean, and the continent of South Annerica. Thisnbsp;circle is commonly called fimply the line, and whennbsp;navigators go from one fide of it to the other, theynbsp;commonly fay that they have crojjed the line.

The Ihorteft diftance of a place on the furface of the earth from the equator, is called the latitude ofnbsp;that place, and is faid to be north or Jouth latitude,nbsp;according as the place is fituated on the northern ornbsp;I'outhern hemifphere. This latitude is meafured bynbsp;an arc of the meridian of that place thus the latitude of London is faid to be 51� 31' north; thenbsp;latitude of Lifbon is 38� 42' north; 'the latitude ofnbsp;the Cape of Goodhope is 34� 29 fouth, amp;c. Placesnbsp;that are exadlly under the equator, have no latitude ; and the latitude of thofe, which are exaftlynbsp;under the poles, is 90� north or fouth*.

A leffer circle paffing through any place, parallel to the equator, is called a parallel of latitude; and,nbsp;of courfe, all places through which that circle paffes,nbsp;have the fame latitude.

The longitude of one place from another on the furface of the earth, or what is, more properly, callednbsp;their difference of longitude, is the diftance of their

The latitude of a place is equal to the elevation of the pole of the fame denomination, above the horizon of thatnbsp;place.

meridians

meridians from one another,' which is meafured by the arc of the equator, that is intercepted by thofenbsp;meridians j and is expreffed in degrees, minutes,nbsp;amp;c. In general, the longitude is reckoned from anbsp;certain meridian, and is called eafi or wefi longitude,nbsp;according as the places lie eaft or weft of that meridian.

Now the equator being a fixed and immutable circle, the latitude niuft unavoidably be reckonednbsp;from that line ; but fince there is no fixed and general meridian �, therefore the longitude may benbsp;reckoned from the meridian of any place at plea-fure. For a long time it has been the generalnbsp;cuftom to reckon the longitude from the meridian of Teneriffe, one of the Canary Iflands; thatnbsp;ifland being for many years the moft weftern landnbsp;known. But at prefent the moft prevailing cuftom is for every principal nation to reckon thenbsp;longitude from the meridian of its capital. Thusnbsp;the Eng�ifh begin to reckon from, or confider as,nbsp;the firft meridian, that which paffes through London, or rather through the Royal Obfervatory atnbsp;Greenwich. The French begin to count the longitude from the Obfervatory of Paris. Therefore,nbsp;according to the French reckoning, the longitude ofnbsp;Greenwich is 2� 25' weft; and, according to the

Then, in order to ftate the fituation of places upon the furface of the earth, it is neceffary to

Ipecify both their latitudes and their longitudes, and fuch ftarements are always found annexed to thenbsp;names of towns, capes, amp;c. in geographical dictionaries, and other works on the fubjedt of geography.

In order to eftimate real diftances in miles from the ftatement of the latitudes and longitudes of anynbsp;two places, the reader muft obferve, ift. Thatnbsp;when the two places are under the fame meridian,nbsp;or have the fame longitude, and differ only in latitude, then their difference of latitude converted intonbsp;miles, at the rate of 69,043 Englifh miles per degree, will give their real diftance in miles ¹. 2d]y,nbsp;That when the places have the fame latitude, andnbsp;differ in longitude only, then their real diftance cannot be had by converting their difference of longitude into miles, according to the above-mentionednbsp;rate, unlefs the two places are both under the equator ; for fince the meridians approach each other, according as they recede from the equator, and at laft donbsp;all meet at the poles; therefore the diftance betweennbsp;two places, which have the fame difference of longi-

A degree of latitude, or of longitude at the equator in nautical affairs, is generally reckoned equal to 60 miles,nbsp;commonly called geographical miles; but fince it appearsnbsp;from the lateft meafurements that the whole circumferencenbsp;of the earth is equal to 24855,43 Englifh miles ; thereforenbsp;dividing this number by 360�, we have the length of onenbsp;degree equal to 69,043 Englilh miles.

tude, diminilhes in proportion as their latitude in-creafes, viz. according as they recede from the equator; the diminution being in the ratio of radiusnbsp;to the cofine of the latitude j viz. the length of anbsp;degree of longitude at the equator is to the lengthnbsp;of a degree of longitude at a given latitude, as radius is to the cofine of that latitude. Therefore,nbsp;�when two places have the fame latitude, convertnbsp;their difference of longitude into miles, at the rarenbsp;69,043 miles per degree; then fay, as radius isnbsp;to the cofine of the latitude of the two places, fo isnbsp;the number of miles juft found, to a fourth proportional, which is the real diftance in miles betweennbsp;the tv/o places. 3dly, When the places differ innbsp;longitude as well as in latitude, then their real diftance in miles muft be found by the refolucion of anbsp;^�ght-angled fpherical triangle, according to the rulesnbsp;of trigonometry; or it may be found mechanically,nbsp;with tolerable accuracy, upon a terreftrial globe,nbsp;the ufe of which will be fhewn hereafter.

In the heavens the diftance of the fun, moon, and other objefts from the equator, is called their decli-nation, which is north or fouth, according as the ob-jedt is north or fbuth of the equator; and it is evident that the declination cannot be more than 90�.nbsp;I^fie fixed ftars, being difperfed all over the hea-are to be found in every degree of declination , but the declination of the fun never exceedsnbsp;. 23� 28'.

equator, or the fecondaries to the celeftial equator, are alfo called circles of declination, or meridians, becaufenbsp;upon them the declination is meafured. Twenty-fournbsp;of thofe fecondaries, that are at 13� diftance one fromnbsp;the other, and which, of courfe, divide the equatornbsp;into 24 equal parts (for 360�, divided by 15%nbsp;quotes 24), are called hour circles �, becaufe the fun,nbsp;in its apparent diurnal motion, paffes over 15� innbsp;every hour.

The right ajcenfion of a celeftial body, is an arc of the equator interfered between one of the equi-nodlial points, called the firft point of Aries, and anbsp;declination circle paffing through that body. Tliisnbsp;arc is meafured according to the order of the fun�snbsp;apparent motion *. The oblique ajcenfion of a ce-Jeftial body is an arc of the equator, interceptednbsp;between the firft point of Aries, and that point ofnbsp;the equator, which rifes W�ith that body in annbsp;oblique fphere. The ajcenjional difference is thenbsp;difference between the right and oblique afeen-fion.

Thus it appears that the diftance from the equator, and the diftance from a given meridian, which, for places upon the furface of the earth, are callednbsp;xhp latitude longitude �, for celeftial objeds arenbsp;called the declination and right ajcenfion.

^ y

* It is called right afcenfion, becaufe in a right fphere the declination-circle, which paffes �rrough'the given body, rifssnbsp;witli that body above the horizon.

The latitude and longitude of a celeftlal objeft, are Its .diftance from the ecliptic, meafured upon a fe-condary of the ecliptic (hence fecondaries to thenbsp;ecliptic are alfo called circles of celeftial latitude);nbsp;and its diftance from a fecondary of the ecliptic thatnbsp;paffes through the firft point of Aries (viz, wherenbsp;the ecliptic interfefts the equator), or an arc of thenbsp;ecliptic interfered by two of its fecondaries, viz. onenbsp;which paffes through the firft point of Aries, and thenbsp;other which paffes through the given body. If thenbsp;Celeftial body be ftippofed to be feen From the centrenbsp;of the earth, its longitude is called geocentric longitude. If it be fuppofed to be feen from the centrenbsp;the funy k is then called heliocentric longitude.nbsp;�^tid the fame thing muft be underftood of the latitude of the celeftial bodies; viz. ifc may be geocentric^nbsp;tgt;r heliocentric.

Let us now return to the courfe of the fun, qind let us endeavour to explain the lengths of daysnbsp;^ud nights, the feafons, and other things whichnbsp;depend upon it.� As the fun moves in the periodnbsp;of one year all along the ecliptic, from weft tonbsp;caft, and as the ecliptic croffes the equator in twonbsp;points, and is inclined to it at an angle of about 23�

, therefore the fun, twice in the year, muft be ^he equator, at which time its declination is 0�;nbsp;twice in the year muft be fartheft from the equa-'nbsp;nbsp;nbsp;nbsp;� ^^cn its decimation is about 23� 28^; once on

the equinoctial points, (becaufe when the fun is at thofe points, the days are equal to the nights) other¹nbsp;wife called the fint point of Aries, and firft point ofnbsp;quot;Lilra. A great circle, or a fecondary to the equator, pafling through thofe points, is called the equinoctial colure. The latter two points are called thenbsp;JolJlitial points, becaufe thofe points (which are thenbsp;firft point of Cancer, and the firft point of Capricorn) are the laft ftations of the fun, after which itnbsp;begins again to draw near to the equator. It is atnbsp;thofe two points chat the tropics touch the ecliptic.nbsp;A fecondary to the equator, pafilng through thenbsp;folftitial points, is called the JolJlitial colure.

In fig. 7, Plate XXVI. nahsb reprefents the earth 5 NCSE reprefents the apparent celeftialnbsp;fphere, or our meridian, as fituated with refpeft tonbsp;our latitude, viz, 51� 31' north, EE istheequa-tor, C D the ecliptic, which incerfefts the equator atnbsp;an angle COE of zf 28C CT is the tropic ofnbsp;Cancer, which is parallel to the equator, and touchesnbsp;the ecliptic at its moft northerly point C, which isnbsp;the firft point of Cancer. RD is the tropic ofnbsp;Capricorn, likewife parallel to the equator, andnbsp;touching the ecliptic at its moft foutherly point D,nbsp;which is the firft point of Capricorn. H H is ournbsp;horizon, London being at z, and our zenith at Z.nbsp;N S is the axis of the world, of which N is thenbsp;north, and S the fouth, pole¹.

O is

For the fake of perfpicuity the fphere in this figure is proje6led orthographically, and the meridian NCHSDT is

O is one interfeftion of the ecliptic with the equator, or the firft point of Aries. The other in-terfecfion, or the firil point of Libra, being on thenbsp;oppofite fide. C is one folftitial point; namely,nbsp;the firft point of Cancer; and D is the other fol-ftitial point! namely, the firft point of Capricorn.

^ovv, on the 20th of March the fun will be found at O, viz. where the ecliptic interfefts thenbsp;equator; therefore it will appear to move roundnbsp;the earth, together with the whole fphere, in aboutnbsp;24 hours, and its path will coincide with the equa-tor. On the following day the fun will be found,nbsp;tiot at O, but in another point of the ecliptic a littlenbsp;caftward of O, as, for inftance, at P, and, with thenbsp;''^hole fphere, will appear to turn round the earth innbsp;^ circle parallel to the equator, for inftance, alongnbsp;the dotted circle i, 2, the arc E i being its declination for that day. On the enfuing day the funnbsp;'^hl be found farther from O, as for inftance at Qjnbsp;^nd, moving with the whole fphere, will appear tonbsp;turn in a circle parallel to, but a little farther from,nbsp;the equator, and fo on; until in about three monthsnbsp;tune, viz. on the 2jft of June, it will reach thenbsp;folftuial point C of Uie ecliptic ; and on that day itnbsp;'''dl appear to turn with the tropic C T; its north

prirnifive circle ; therefore all the circles, whofe planes ^gt;�2 perpendicular to the primitive, fuch as the equator, thenbsp;t�opics, the ecliptic, Sic, are reprefented by right lines.

declinatioa CE being anarch of about 23� 28'. After thiS;, the fun will continue to move on thenbsp;ecliptic, and after about three months longer, viz.nbsp;on the 23d of September it will reach the' other in-terleftion of the ecliptic with the equator. Proceeding {till farther, in about three months more,

folflitial point D of the ecliptic, at which time it will appear to move along the tropic D R. Nearnbsp;three months after, it will reach again, the equi-nodlial point O ; having performed the whole courfenbsp;of the ecliptic from the weft towards the eaft, innbsp;the compafs of 12 months j after which it beginsnbsp;to perform a fecond and fimilar revolution, amp;c.�nbsp;This motion of the fun, being once underftood,nbsp;the following confequences will be readily comprehended.

1. When the fun is at the point O of the ecliptic, and appears to move along the equator E E j then, fmee EE is a great circle, and the horizonnbsp;HH is likewife a great circle; therefore they muftnbsp;cut each other into two equal parts; hence, at thatnbsp;time, half,the apparent daily courfe of the fun isnbsp;performed above the horizon, and the other half isnbsp;performed below it; or, in other words, the day isnbsp;equal to the night. When the fun is in any othernbsp;point of the ecliptic, between O and C, its dailynbsp;courfe will be performed in lejfer circles parallel tonbsp;the equator; which leffer circles are cut into twonbsp;unequal parts by the horizon, becaufe they are not

perpendicular to the horizon ; thus the circ�e C T is cut by the horizon H H, into two unequal patts,nbsp;whereof C 3 is the largeft, and 3 T the fhorceft;nbsp;for fince CT is cut at 5, into two equal parts bynbsp;the great circle NOS ; therefore C3, being longernbsp;than the half C 5, muft be much longer than thenbsp;fegmentT3. Of any one of thofe circles, alongnbsp;which the fun appears to perform each daily levolu*nbsp;tion, that portion, which is above the horizon, isnbsp;called the diurnal arch, and that which is below thenbsp;horizon, is called the jio^iurnal arch ; the halves ofnbsp;which, viz. from the horizon to the meridian as 3C,nbsp;and 3T j or as ij, and ay, are refpeaively callednbsp;the Jemidiurndl, and the feminoSiurnal, arches. Therefore, from the 20th of March, at which time thenbsp;funis at the point O, until the 21ft of June, atnbsp;which time the fun is at the point C of the ecliptic jnbsp;the diurnal arches, or the days, grow continuallynbsp;longer than the noflurnal arches, or the nights.nbsp;After that, the days begin to IhorC^n, and thenbsp;nights to lengthen, in proportion as the fun drawsnbsp;nearer to the autumnal equinox, and on the 23dnbsp;of September, when the fun is exaftly at that point,nbsp;the day becomes equal to the night. Pi oceedingnbsp;0:111 farther towards the fouthern part of the eclip-the fun again performs its daily courfe in leffernbsp;citcles, which are unequally divided by the horizon;nbsp;this difference, however, that now the noBurnalnbsp;longer than the diurnal arches; viz. the nightsnbsp;grow continually longer than the days, until the funnbsp;IV.nbsp;nbsp;nbsp;nbsp;Enbsp;nbsp;nbsp;nbsp;reaches,

the ecliptic, at which time the femi-dinrnal arch R 4, or the day is the /horteft, and the feminoftur-nal arch D 4, or the night is the Jongeft. Thennbsp;the days begin to lengthen again, amp;c.

In Ihorc, during the 12 months, four remarkable changes, or period.', or feafons, may be diftinguifli-ed, viz. I ft. From the vernal equinox, on the 20thnbsp;of March, when the fun is at O in the ecliptic, untilnbsp;the fummer folftice, on the aift of June, when thenbsp;fun is at C, zdly, From the laft-mentioned time,nbsp;until the fun reaches the autumnal equinox on thenbsp;2 td of September. 3dly, From the 23d of September, until the 2?d of December, when the funnbsp;reaches the winter fclftice. 4thly, and laftly. Fromnbsp;the laft-mentioned time until the fun reaches againnbsp;the point O, on the 20th of March ; thofe periodsnbsp;form the four feafons of the year, which are attendednbsp;with different degrees of temperature, different fertility of the ground, amp;c. Thofe differences arifenbsp;from the following three caufes, that is, ift, becaufenbsp;when the fun is longer above the horizon (as innbsp;fummer) than below' it, the ground, by beingnbsp;longer expofed to its rays, acquires more heat thannbsp;when the fun remains a fliort portion of the 24 hoursnbsp;above the horizon ; idly, becaufe, when the fun getsnbsp;nearer to our zenith, its rays, coming lefs obliquely,nbsp;fall upon a given fpot in greater quantity than whennbsp;they are more oblique ; and 3dly, becaufe when thenbsp;fun is nearer to the zenith, i s rays go a Ihorter way

cf the V/crld, ֒f. nbsp;nbsp;nbsp;5^

tlifoiigb the at!Tiofp!iere, and, of courfe, are lefs ob-ftruded by it, than whea they are more oblique '� �

II. nbsp;nbsp;nbsp;The elTefts, which we have juft defcnbed,nbsp;are fuch as take place in our latitude} but in ochernbsp;latitudes they differ confiderably, as wjll be eafilynbsp;comprehended by attending to fig- 7 5

lerving that when the fun is advancing towards tne f^orthern hemifphere, it muft recede from thenbsp;fouthtrn hemifphere; and therefore whilft the daysnbsp;are growing longer to us, and the nights fnorter;nbsp;the reverfe muft take place with refpect to the inhabitants of the fouthern hermlphere ; viz. the daysnbsp;muft be diminifhin^T and the nights muft be growingnbsp;longer, therefore, when it is fummer to us, it muftnbsp;be winter to them, and 'vice 'verja. But when thenbsp;ft'n is at the equinoftial points, the days are equalnbsp;to the nights all over the earth, becaufe the fun thennbsp;rnoves along the equator, which, being a great circle,

III. . Excepting when the fun is at the equino�lialnbsp;points, the lengUi of the fame day, viz. of the fun�snbsp;continuance above the horizon, is different accord¹

But the ditference is fo fmall, that the effed which arife therefrom, is vaftly overpowered by the above mnbsp;tinned three caufes.nbsp;nbsp;nbsp;nbsp;ing

�ns; to the difference of latitude; for in that proper� tion the parallels of declination are more or lefs inclined to the horizon; and, of courfe, arc more ornbsp;lefs unequally divided by the horizon of each particular place. Thus, for inftance, on the 4th of Ma}�*nbsp;vve have about co hours of day lighl, and about fournbsp;hours of darknefs; but on the fame 4th of Maynbsp;thofe, whofe latitude is farther north, have anbsp;longer continuance of day light, and a fliofter ofnbsp;darknefs 5 whereas thofe who live nearer to thenbsp;equator than we do, have a (hotter continuance ofnbsp;daylight, and a longer of darknefs. In ilrort, tonbsp;thofe who live under the equator, the days are always equal to the nights, becaufe every parallel of.nbsp;declination, or every apparent revolution of the funnbsp;is divided into two equal parts by their horizon. Butnbsp;the horizons of other places cut the parallels of declination more and more unequally, in proportion asnbsp;thofe places are more and more diftant trom thenbsp;equator; whence the difference between the daysnbsp;and the nights increafes accordingly. But to thofenbsp;w'hofe latitude exceeds 66� 32'', either fouth ornbsp;north, the fun remains above the horizon duringnbsp;feveral days fucceffively in fummer, and remainsnbsp;quite invifible during feveral days fucceffively innbsp;winter.

In order to underfland the reafon of this phenomenon, it muft be previoufly confidered, that when an opaque globe, like the earth, is expofed to a verynbsp;diftant luminous objedt, like the fun, it can have not

more than half its furface illuminated at tne fan.e time, and the boundary of that illuminated paitnbsp;rounl the fphere, forms a great circle, the axis ofnbsp;which, if produced, will pafs through the luminousnbsp;objefl:. Now when the fun is at the foliftitial pointnbsp;C, it is then vertical to chat part of the earth (viz.nbsp;tothefpotij, the latitude of which is about 23nbsp;28' north j for fuch is the angle COE. Now fincenbsp;the circle hb^ which forms the boundary of light,nbsp;being a great circle, is 90� diftant from its pole i -,nbsp;and nnce the arch e n is iikewile j therefore thenbsp;dUlance hn of the boundary of light from the pole

muft be equal to i e, viz. 113� 28 ; time the portion anh, of the earth mud; be conftantlynbsp;illuminated that is, the fun muft appear to go roundnbsp;and round for feveral days, without ever fetting. Itnbsp;is alfo evident that an equal portion bsf of the earth,nbsp;round the fouth pole f, mud remain as long in aqnbsp;uninterrupted darknefs. The circles h a, and bf,nbsp;which limit ^hofe fpots, and which are about 23�

28 diftant from the poles (viz. as much as the tropics are from the equator), are called the polarnbsp;circles, ha being the north, and the Jouth, polarnbsp;circles, otherwife called the arbl-it;, and the antarbfk,nbsp;circles. When the fun, after the foliftice, drawsnbsp;nearer to thc' equator, tpe boundary of light muft ofnbsp;courle approach the poles; hence a fmaller portionnbsp;of the earth, round the north pole, will have con-�nbsp;ftant day light, and an equal; portion round the

the Tun, having croffed the equator, advances to* wards the fouth�rn hemifphere, then the boundarynbsp;of light recedes from the north pole n that i-, anbsp;larger and larger portion of the earth round thatnbsp;pole, will be left in continual darknefs, vvhilft annbsp;equal fpot round the foiuh pole s will enjoy conftantnbsp;day light, and fo on. Therefore the inhabitants ofnbsp;the north pole (fuppofing that fame may livenbsp;there) muft fee the fun above their horizon (w'hichnbsp;coincides with the equator) moving parallel'to itnbsp;during fix months of the year; viz. from the vernalnbsp;equinox to the autumnal equinox 5 and mull a!to-eether lole fight of it during the other fix months ;nbsp;whereas the inhabitants of the fouch pole mull havenbsp;a conftant night during the former fix months, andnbsp;a conltant day light during the latter fix months,nbsp;iV. As the fun moves from one tropic to thenbsp;other, and back again to the former tropic in thenbsp;GOLirfe of every year, and as the tropics are aboutnbsp;0,3� 20' diftant from the equator ; therefore the funnbsp;is vertical to, or paffes over the zenith of, diff�rentnbsp;places on the fur ace of the earth, provided the latitudes of thofe places do not go beyond 23� 2S'nbsp;north or fouth of the equator. That portion or zonenbsp;of the earth which is within thofe two latitudes, ornbsp;which is betvveen the tropics, is called the torridnbsp;�zone, from the great heat to which it is expofed.nbsp;The portions hna, and fsb, which are limited bynbsp;the polar circles, are called the- north and the Joutbnbsp;frifd zones j the remaining parts of the earthy, which

are

of the World-, nbsp;nbsp;nbsp;55

are between the tropics and the polar circles^ arc Called the tejifperate zcties. Thus the fuiface ofnbsp;the earth is fuppofed to be divided into five

After the above mentioned confequences of the fun s daily and annual courfe, it will be necefiary tonbsp;rnention fome irregularities refpedting it, the caufenbsp;of which will be explained hereafter; as alfo the

If we count the time from the vernal equinox to the autumnal equinox, and likewife the time fromnbsp;tlie autumnal equinox to ihe next vernal equinox, wenbsp;fhall find that the former period exceeds the latternbsp;by about eight days, which (hows that the fun r c-

� The following ufekfs diftinaion refpeaing thefhadows which are caft by the different inhabitants of the earth,^ .snbsp;generally mentioned by the writers on aftronorny.nbsp;habitants of the torrid zone are called dmphijci'h b^cau ,nbsp;different times of the year, their meridian fhadowsnbsp;retted towards both poles, but when the fun is over tlieirnbsp;heads, then their (ha^ow falls under then feet, or rather t eynbsp;form no fhadow fimuar to the human body, and at that tinnbsp;they are called Afcli, or fhadowlefs, T hofc '''bo live in t ^nbsp;temperate zones, are called HeUroJeii, becaufe theirnbsp;dian fhadows are projected towards one poL only at afiynbsp;time of the year. Latlly, the inhabitants of the frigidnbsp;zones are called Perifeii, becaufe when the fun is conrnbsp;fiantly above their horizons, their fhadows are fucceffivelynbsp;^retied towards all the points of the compafs,in 24 hours,

mains E 4

mams about eight days longer on the northern half of the ecliptic than on the other half of it. .

Aftronomers confider the year under two dif-tindions; viz. the Jolar and the ajiral. The tropical or Jolar year-, upon which the feafons depend, is the exafl time in which the fun moves all roundnbsp;from one equinox to the fame again, and whichnbsp;period has been found to be equal to 365 days,nbsp;5 hours, 48' 49quot;. The ajiral year is the time thatnbsp;the fun employs in going from one fixed part of thenbsp;heavens, viz. from a given fixed far, all round,nbsp;and again to the fame precife point of the heavens ;nbsp;and this period or afiral year is a little longer thannbsp;that of the folar year, viz. it is equal to 36^ days, 6nbsp;hours, 12quot;, which is longer than the folar year bynbsp;20', 23 , of timej or to an arc of 50quot;,25 (for, in 20',nbsp;23// of time, the fun percurs an^arch of 50quot;,25* ) jnbsp;fo that the fun, as feen from the earth, arrives at thenbsp;equinqdial point, viz. at the equator, a little beforenbsp;it arrives at that fame precife point of the heavens,nbsp;with which it coincided, when it eroded the equatornbsp;on the preceding year. This difference between thenbsp;period of the fun�s going from one equinox to thenbsp;fame, and the period of its going from a given ftar,

* This is eafily determined by means of the common rule of proportion; For fuice the fun�s apparent daily motionnbsp;performs an entire circle in 24. hours j therefore we fay asnbsp;24 hours are to 360 dcgixer, fo are 20' 23quot; to a fourthnbsp;proportional.

or part of the heavens, to the fame again, is called the precejjion of the equinoxes. This preceffion in onenbsp;year is very criflinjt, but the accumulation of it afternbsp;a number of years, produces a confiderable difference, which can by no means be palTed unnoticed;nbsp;thus, in a hundred years (which is called �i^Jeculurnbsp;preceffion) it amounts to 1�, 23', 45 ; ^.nd the difference, which it has produced fince the ftars werenbsp;firft ob'erved, and their pofitions were delineated, is

Novices in aflronomy do not, in general, readily comprehend the real meaning of the preceffion of thenbsp;equinoxes j therefore it will be necetfary to explain

How can the fun return to the fame equinox at the end of every year, w'ithout returning to the famenbsp;Ipot in the heavens, or to the fame fixed flat ? is thenbsp;ufual difficulty. In order to clear this difficulty thenbsp;reader muft recolleft that the equator is a circlenbsp;�which, being equidiftant from the poles, divides thenbsp;celeftial fphere into two equal portions. Now, ifnbsp;tne poles were fiationary, viz. coincided conftantlynbsp;with the fame fpofs in the heavens, then the equatornbsp;would likewife pafs conftantly over the fame fixednbsp;ftarsj and w'ould cut the ecliptic conftantly at thenbsp;fame points; for the ecliptic is an invariable circle,nbsp;�^tz- it paffes always over the fame ftars. But itnbsp;has been obferved, that the poles are fubjeft to a

at one time any one of the two points in the heavens, which do not revolve with the daily revolution of th� reft of the fphere, and which we, for thatnbsp;reafon, call the poles, be near a certain ftar, fomenbsp;years after it will be found near fome other ftar; ornbsp;in other words, the polar ftar is not always thenbsp;fame. It appears from the refult of calculationsnbsp;cftablifhed upon the obfervacions made during fe-veral centuries, that the path of either of the polesnbsp;�is a circle, the pole of which coincides with thenbsp;pole of the ecliptic, and that the pole will movenbsp;along that circle fo very (lowly, as to accompliflinbsp;the whole revolution in 25791 years nearly. Thenbsp;diameter of this circle is equal to twice the inclination of the ecliptic to the equator, viz. to aboutnbsp;27�.

Now, as the ecliptic is a fixed circle in the heavens; but the equator, which muft be equidiftant from the poles, moves vdth the poles; therefore thenbsp;equator muft be conftantly changing its interfeiftionnbsp;with the ecliptic. And from the beft obfervationsnbsp;it appears that the equator cuts the ecliptic everynbsp;year 50quot;,25 more to the weftwards, than it did thenbsp;year before: hence the fun�s arrival at the equino�lialnbsp;point precedes its arrival at the fame fixed (pot of thenbsp;heavens every year by 20' 23'' of time, or by annbsp;arc of 50quot;,25. Thus, by little and little, thefenbsp;cquinoftial points will cut the ecliptic mor� andnbsp;more to the weftward, until, after the long period

of ihc W59 of 2,5791 years, they will cut it again at the famenbsp;point precifely.

The 12 conftellations, which, as has been mentioned in the preceding pages, occupy the whole zodiac, have given their names to 12 equal portionsnbsp;of the ecliptic, each portion confifting of 30 , andnbsp;each portion was marked by the fign, mark, ornbsp;charafter, peculiar to the conftellation to waich itnbsp;belonged, or with which it coincided when the con-ftelladons were firft noticed, at w�hich time the vernal equinox took place in the conftellation of Aries,nbsp;the fummer folftice in that of Cancer, amp;c. but onnbsp;account of the preceffion of the equinoxes, the con-fttllations no longer coincide with thofe points ; fornbsp;inftance, the vernal equinox is in the conftellation ofnbsp;iPifees, and the conftellanon of Aries is now confi-derably removed from it, and is gone nearer to thenbsp;fummer folftice-, arrd fo are all the other conftellations removed; yet their characlers have been leftnbsp;to denote the fame parts of the ecliptic �, thus thenbsp;vernal equinox is called the firft point of Aries, and

From what has been fald above, it appears that not only the equinoftial points, but alfo the foliftitial

It is now neceffary to explain the civil or com-tnon way of reckoning the year,�It has been faid above, that the length of the aftral year is 365nbsp;days, 6 hours, 9', i V', and that the length of the

48', 49�* Then, fince the feafons and the lengths �f days and nightsdepend upon thelatter, it is thereforenbsp;natural to life the lail, viz. the folar year, for the pur-pofes of civil fociety. N ow as the period of that yearnbsp;docs not cor,fill of a number of entire days; therefore, beginning to reckon from any day, one yearnbsp;after that, or the new year, ought to begin whennbsp;365 days, 5 hours, 48�, 49quot;, are elapfed; and thenbsp;next year ought to begin when twice that period, ornbsp;�when 730 days, 11 hours, 37', 38quot;, are elapfed ;nbsp;which would make an enormous coniufion : on thenbsp;other hand, if the 5 hours, 48'', 49quot;, be neglecfed,nbsp;the accumiulation of fo many neglected 5 hours, amp;c.nbsp;after a number of years, would produce a confider.-able difference between the folar and the civil year^nbsp;and the fealbns would not fall conflantly en the famenbsp;months.

It is eafy to obferve that the 5 hours, 48', 49quot;, �will amount to nearly 24 hours, viz. to a whole daynbsp;at the end of every four years. Therefore Juliusnbsp;Ctefar, willing to remedy this irregularity, orderednbsp;that every fourth year fhould have an intercolarynbsp;day^ viz. fhould confiic of 366 clays ; whereas everynbsp;one of the other three years confifts 01365 days; and,nbsp;this mode of reckoning, which has prevailed evernbsp;fince, has thence been called the Julian method ^nbsp;and that every fourth or Julian year, has been uni-verfally called Bijexiikyear in England, leap year.nbsp;The additional day which that year has above everynbsp;one of the three prcceji.ng, or of the three fucceed-

years, was by tiW ancknt Romans added to the asd of Febvuarv fo that in a leap year they reckoned the a3d of Febrnary twice over, viz. accordmnbsp;to their way of reckoning, in that year they had twonbsp;fixth days preceding the calends of Marc .

(viz. from bisjextus) that year was called a ipx n year. At prefenc we add the inteicolary a) anbsp;end of Febrnary; fo that the month of Februarynbsp;has 2,8 days during three fuccelTive years, ut ynbsp;fourth, or leap, year, it has 29 days. ^

Thus the compenfation would be fufficient, 1 t folar year confided of 365 days and 6 hours,nbsp;caufe the fix hours of ail the four years, amounti ^nbsp;to 24 hours, would be exaftly equal to the addinonbsp;day, which is allowed to every fourth year, butnbsp;fince the odd time amounts to 5 hours, y'�', 49quot;nbsp;Which is 11', iiquot;, Ihort of 6 hours; and the accumulation of thofe 11'gt; 11 gt; amounts tonbsp;nbsp;nbsp;nbsp;.

plete day in about 130 years ; therefore, the a^ m of one day every four years is evidently too tnuv. ,nbsp;by 4 times 11', ii''; viz. by 44� 44 � or by aboutnbsp;one day in 130 years. In faft, at the council onbsp;Nice (A. D. 325.) the vernal equinox fed on thenbsp;2ift March; but the equinox continually falhngnbsp;back, it appeared at the time of Pope Gregory tienbsp;*3di, that the fun came to the vernal equinox onnbsp;the I ith of March, therefore the difference betweennbsp;the folar and the civil years, a.m.ounted to 10 whole

Pope ordered that the calendar flaould be corrected^ by taking lo whole days out of it; and according-lyj in the year of our Lord 1582, the day followingnbsp;the 4th of Odtober, inflead of being called the 5th,nbsp;was called the 15th; by means of which alterationnbsp;the real equinox was relfored to the 21 ft of March:nbsp;and in order to prevent, as much as poffible, the likenbsp;irregularity in future, the fame pope ordained, thatnbsp;every looth year, which according to the Juliannbsp;mode was to be a biflextile year, Ihould be a com-rnon year, viz. of 365 days ; but becaufe that wasnbsp;too much, every 400th year was to remain biftex-tile. In other words, to leave out a biflextile-daynbsp;in February at the end of every century of years notnbsp;divifible by four, reckoning them common years ofnbsp;365 days each; fuch as the 17th century, or thenbsp;year 1700, the 18th centuryj or the year iSco, amp;c.nbsp;and to retain the bilTextile day in February at thenbsp;end of thofe centuries, which are divifible by 4*nbsp;ilich as the i6th, acth, 24th centuries, amp;c. or thenbsp;years 1600, 2000, 2400, amp;c. Thus the prefentnbsp;year 1,802 is faid to be the fixth year after the leapnbsp;year, for the year 1800, viz. the ^ 8th century, beingnbsp;not divifible by 4, was reckoned a common year.

This new form of reckoning, viz. with the juft and necelTary corredtion which was ordained bynbsp;Pope Gregory, is called the Gregorian^ or thenbsp;fyle, and has been adopted by almoft all the enlightened nations of the world. There are fomcj

What has been faid above, concerning the deviation of the true vernal equinodlill point from its ufual day in March, nauft be likewife underftood ofnbsp;the otner equinociial point, as alfo of the fohftitiainbsp;points; for according as one of them deviates fromnbsp;its ufual day, io muft the others evidently deviatenbsp;from their uiual days.

[ 64 �]

CHAP. Iir.

TH E apparent movements of the celeftial bodies have been defcribed in the precedingnbsp;chapter, fufficiently to give a general and compre-henfive idea of the whole. With this viev/, as alfonbsp;for the purpofe of avoiding confufion of ideas, thenbsp;moft minute particulars, together v/ith the pradti-cal methods of taking and calculating the fame, havenbsp;been relerved for future chapters. In that view fe-veral apparent irregularities have been pointed out,nbsp;which, together with various other confiderations,nbsp;prove that the celeftial bodies muft move in pathsnbsp;different from what they appear to perform.

We hate fhewn in the fir ft chapter of the pre-fent part, that regular movements may appear to be very irregular; as alfo that bodies aftually innbsp;motion may appear to be at reft; or, vice quot;verfaynbsp;that Jaodies at reft may appear to be in motion,nbsp;according to the fituation of the fpeftator.

The evidence of our fenfcs, frequently fallacious, and hardly ever correct, muft be fubmitted to thenbsp;Mnbsp;nbsp;nbsp;nbsp;- fuperiority

Superiority of reafon and demonftration. Whert the fame appearances may be produced by various difnbsp;ferent caufes; that caufe muft be admitted, be-*

Sieved, or preferred, which is warranted by reafon; not that which implies an abfurdity, or which bearsnbsp;no analogy to the known works of nature. Whennbsp;perfons in different boats, move in different di-tedtions along the fea coaft, they TCAy at firft fightnbsp;imagine that they are ftanding ftilh and the land isnbsp;moving; but it is eafy to conclude, that this is anbsp;fallacious appearance; for, on account of the boatsnbsp;moving'in different direftions, the land ought like-'wife to move in different dircfl:icns at the fame

Thus alfo to a fpeftator on the plane, the clouds feem to be as high as the moon ; but that they arenbsp;'^atlly diftant from it, is clearly proved by thofe whonbsp;afcend to the tops of high mountains for they feenbsp;the clouds below their feet, at the fame time thatnbsp;the moon feems to be as much above their heads as

The fun, the moon, and efpecially the planets, appear to move with great irregularities round thenbsp;earth ; therefore it is moft probable that they movenbsp;round fome ocher centre, agreeably to fome generalnbsp;laws of nature; and analog rus to the other, evennbsp;what we call the meaneft works of nature, whichnbsp;our utmoft endeavours always find to be ftrrdtiynbsp;conformable to, or depending on, iome fimple andnbsp;general law.

Various hypothefes have been formed, or idea! fyftems of the w^orld have been framed, for the pur*nbsp;pofe of accounting for the apparent irregularities ;nbsp;the principal of which fyftems we fliall mention innbsp;this chapter ; but in order to (how how far any onenbsp;of them may anfwer the defircd objeft, it will benbsp;neceflary prevloufly to mention fome of the moftnbsp;ftriking appearances, or difficulties, which they arenbsp;intended to explain, and to obviate.

The moon and the eight planets are evidently opaque bodies, and they only Ihine by reflecting thenbsp;light which they receive from the fun ; which is deduced from this, viz. that their illuminated part isnbsp;always that which is directly towards the fun, thenbsp;reft being always dark. From the appearance alfonbsp;of the boundary of light and darknefs upon theirnbsp;furfaces, we conclude that they are fpherical ornbsp;nearly fpherical bodies; which is confirmed by moftnbsp;of them having been found to turn periodically roundnbsp;their axes.

The moon, we are led to fuppofe, keeps nearly within the fame diftance of the earth; for her apparent diameter does not vary much; and from oftennbsp;repeated meafurements, it appears to be never leftnbsp;than if, 30quot; j nor ever greater than 33'.

The moon comes to the meridian later every day, cuts it at different heights, and remains a different length of time above the horizon. Its phafes,nbsp;or appearances of its fhining part, have already beennbsp;deferibed.

The

OfthetrUiSjJ}�mo/lh�Pferygt;^^-

'^hen viewed through a telefcope, is found to un dergo changes analogous to thofe of the mooh. Hernbsp;apparent diameter varies confiderably, fometimesnbsp;being five or fix times greater than at other timesinbsp;She is fometimes found to come to the meridiannbsp;^ith the fun; it then precedes the fun, fo as to appear to move from eaft to weftgt; and this precedencynbsp;increafes until it becomes equal to 3 hours 10', ofnbsp;to an arc of 47�, 30'. At this period V enus fee msnbsp;to be ftationary for a foort time, after which thenbsp;time of her coming to the meridian before the funnbsp;decreafes gradually, and at laft they both come tonbsp;the meridian at the fame time. After this coinci-;-dence, foe culminates later than the fun, and continues to move apparently from weft to eaft, until foenbsp;comes to the meridian about 3 hours 10' laten^nbsp;which is her greateft elongation trom the fun j fornbsp;at this period foe again feems to remain ftationarynbsp;for a foort time, then foe appears again to movenbsp;from eaft to weft, and fo on. The declination ofnbsp;Venus varies confiderably; fometimes recedingnbsp;frorn the equator as much as 27* north or louthnbsp;of it. When Venus appears eafterly of the fun, fot^nbsp;fots after the fun, of courfe is feen in the evening,nbsp;snd is then called thenbsp;nbsp;nbsp;nbsp;When foe ap

pears weftward of the fun, foe then rlfes before the fun, and being feen in the morning* is called thenbsp;morning ftar.

Mercury is foldoro foen, on account of its fnort - -nbsp;nbsp;nbsp;nbsp;diftance

diftance from die fun, which never exceeds i hour 50' in time, or an arch of about 27� 30'. It performs its movements much quicker than Venus;nbsp;but, as far as has been obferved. it has been foundnbsp;to move like Venus, viz. to be fometimes diredt, atnbsp;other times retrograde, and at its greateft elongations from the fun, ftationary.

The planet Mars fometim.es appears to come to the meridian together with the fun, at other times itnbsp;precedes or follows the fun. It is fome time diredtlynbsp;oppofite to the fun, fo as to be feen on the meiidiannbsp;at midnight. When Mars is thus oppofite to thenbsp;fun, its diameter is about five times greater thannbsp;when it appears near to, and comes to the meridian at the fame time with, the filn. The apparent motion of Mars is alfo fometimes diredt, ornbsp;from eaft to weftj fometimes retrograde. Betweennbsp;thofe changes it appears ftationary for a fhort time.nbsp;Its phafes may be clearly difcerned through a te-lefcope j for its fhining part is fometimes full andnbsp;round, and at other times gibbous, but never hornednbsp;like the new moon.

The like remarks are true with refpeef to thp other planets. They being alfo diredt, retrograde, or ftationary at different times, and, as farnbsp;as Can be obferved, fliewing different phafes, likenbsp;Mars.

The principal hypothefes or fyftems of the world, which have been formed in ordei* to account fornbsp;thofe phenomena, may be reduced to three, which

known by the names of the Ptolemaic, the ^ychonic, and the Copeniican, or Newtonian, ff-tems.

Ptolemy, an Egyptian philofopher, who wrote aboiit the year 140, endeavoured to eftablifh thenbsp;vulgar idea, which is derived from firft appear-^tices, uncontrolled by reafon. He fuppofed thatnbsp;the earth was fixed and immoveable in the centre ofnbsp;the univerfe, and that all the celeftial bodies performed their revolutions about it in the followingnbsp;order, viz. the Moon was next to it, then camenbsp;Mercury, Venus, the Sun, Mars, Jupiter, andnbsp;Saturn ; the other three planets not being-known atnbsp;that time. Beyond Saturn, he fuppofed the ex-tftence of various immenfe orbs, which he callednbsp;the ftarry firmament, and the cryftalline orbs undernbsp;names of primum mobile, and ccelum empyreum jnbsp;which were fuppofed to turn round the earthnbsp;once m 24 hours, befides their having proper andnbsp;peculiar movements.

If this fyftem had been true, the planets Mercuiy and Venus ought fometimes to have been feen innbsp;ppofition to the fun, which phenomenon was nevernbsp;^ oeed not adduce more objedlions;nbsp;naturally be nianifefted in fpeaking ofnbsp;true fyftem, wdfich'was revived by the genius ofnbsp;Pruflia^'^^ ^�P^''tgt;icus, who was born at Thorn innbsp;eftnbsp;nbsp;nbsp;nbsp;which was afterwards

, I faid the fyftem revived by Copernicus; for the fame had long before been introduced into Greecenbsp;by the great Pythagoras, and his difciplcs, who hadnbsp;probably learned it from the wile men of thenbsp;Eaft-

According to this fyftem, which we lhall prc-fcntly defcribe in a more particular manner, the fun remains immoveable in the centre, and all thenbsp;planets, reckoning the earth one of them, movenbsp;round it at different diftances, and in different times.nbsp;Mercury being neareft to the fun ; then the othersnbsp;come in the following order with refpedl to theirnbsp;diftances; viz. Venus, the Earth, Mars, Jupiter,nbsp;and, laftly, Saturn.

This fyftem was adopted and retained, uhtil Ariftotle, and the philofophers that came after him,nbsp;embraced the vulgar, or Ptolemaic, fyftem ; andnbsp;their authority impofed it upon mankind, till Copernicus revived the Pythagorean idea j and the in-duftry, the difcoveries, and the reafoning of almoftnbsp;all the fucceeding philofophers, eftablilhed it uponnbsp;the ftrongeft foundation of rational evidence.

I have fdid almoft all the philofophers, amp;c, j be-caufe another fyftem, which partakes of both the above-mentioned fyftems, was offered to the publicnbsp;by Tycho Brahe, a very diftinguiflred Danilh aftro-nomer, who has otherwife rendered effential fervicesnbsp;to aftronomy, and who wrote about the middle ofnbsp;the 16th century. This diftinguiflred charadternbsp;fcems to have adrnired the fimplicity and the beauty

the Copernican fyftem ; but a ftrict interpreta tion of, and his refpeft for, certain paffages of thenbsp;Bible, prevented his affent to the idea of the earth snbsp;motion, in confequence of whici; he formed thenbsp;following fyftem. He fuppofed the earth to ftandnbsp;immoveable in the centre of the univerfe, and thenbsp;fun to revolve about it every 24 hours : the planetsnbsp;he thought went round the fun in their periodicalnbsp;times,. Mercury being neareft to the fun, thennbsp;Venus, Mars, Jupiter, and Saturn, and of courfenbsp;to revolve allb round the earth. But fome ofnbsp;Tycho�s difciples fuppofed tire earth to have anbsp;diurnal motion round its axis, and the fun, withnbsp;^11 the planets, to move round the earth in one

The embarrafirnent and perplexity, under which this fyftem laboured, were too evident. The nroftnbsp;inconftftent fuppofjtion was, that the planets performed their revolutions round two centres, viz. thenbsp;diurnal round the earth, and the periodical roundnbsp;the fun. But its inconfiftencies will be naturallynbsp;tnanlfefted by the following defeription of the truenbsp;or Copernican fyftem, which foon after Tycho�snbsp;tinre was confirmed and explained in almoft, all itsnbsp;parts, by the unanfwerable arguments and wonderful difeoveries of Repler, Galileo, Newton, andnbsp;others.

According to this fyftem, the fun, an immenfc globe, conftantly emitting abundance of heat andnbsp;light, is fituated in a parr of the univerfe, where

r 4 nbsp;nbsp;nbsp;I*

it revolves about a centre, which centre is within its furface, and which has not been found to alter itsnbsp;diftance from the fixed ftars.

The planets (of which our earth is one) do all revolve about the fun at different diftances, therefore in different orbits (viz. paths), and in differentnbsp;times. The comets, when they do appear, arenbsp;alfo found to go round the fun. The order, innbsp;which the planets are fituated with refpeft to theirnbsp;diftances from the fun, is as follows ; Mercury isnbsp;neareft to the fun, Venus is the'next, then comesnbsp;the Earth, Mars, Ceres, Pallas, Jupiter, Saturn,,nbsp;and, laftly, the Georgian planet.

The Moon goes round the earth, and of courfe with it, round the fun. Jupiter, when viewednbsp;through a pretty good telefcope, is feen to have fournbsp;moons, which revolve in different paths about it,nbsp;and go with it round the fun. Saturn alfo, whennbsp;viewed through a powerful telefcope, is found tonbsp;be attended by feven moons, which revolve in different orbits round it, and go with it round the fun.nbsp;Befides the feven moons,'Saturn is alfo found tonbsp;have a remarkable ring, which will be defcribednbsp;hereafter. The Geoi-gian planet, when viewednbsp;through the moft powerful telefcopes, appears tonbsp;have' fix moons, which move in different orbitsnbsp;about that planet, and go, with it round the fun.nbsp;The other five planets have not been found to havenbsp;any, moons.

The above-mentioned m.oons are otherwife called � �nbsp;nbsp;nbsp;nbsp;JatelliteS]

Of the true Syftem of the Warid, nbsp;nbsp;nbsp;73

falellites, or feccndary planets; their refpeftive primary f-onets being thofe about 'wnich they revolve. Anbsp;the planets move from the eaft tow aids the weft,nbsp;and in the fame diredion do the moons revolvenbsp;round their primaries j excepting thole of thenbsp;Georgian planet, which feem to move in a contrary direction. ,

Befides the above-mentioned movements round the fun, the earth and moft of 1 he planets have a rotatory motion round their own axes, which motion is mnbsp;the diredion from eaft to weft ; and, reafoning fromnbsp;analogy, it feems probable that all the planets, asnbsp;well as the fatellites, move round their refpedive

axes in the fame diredlion, viz. from eaft to Weft,

Before we proceed any farther, it will be ne-ceffary to affift the learner in the comprehenfion of this fyftem by a diagram. See fig. 8, Plate XXVI.nbsp;which exhibits a view of this fyftem, as it wouldnbsp;appear to a fpedator fituated at a confiderable dif-tance above the fun, in a line perpendicular to thenbsp;earth�s orbit. But it muft be cbferved, that in thisnbsp;figure the diftances of the planets from the fun, annnbsp;of the fatellites from their primaries, are not repre-fented in their due proportions, which the fize ofnbsp;the plate cannot admit of j nor are their orbits re-prefented In their true Ihapes, which are eUiplkal,nbsp;But fo little different from circles, that, in a diagram of this fort, they could hardly be diftinguilbednbsp;Irbm circular paths,

With refpedt to this figure, we need only obfervc that the motion of all the planets round the fun,nbsp;which ftands in the centre, is in the diredtion of thenbsp;letters ABCDE, and the motion of the fatellitesnbsp;round their primaries, is in the diredlion of the letters ahcde. The marks or charadlers of fuchnbsp;planets, as have any charadler given them by thenbsp;aftronomcrs, are marked upon their refpedlive orbits in a line from ihe centre of the figure upwards. The aftronomers denote the fun by the cha-radler O.

Thus (we have faid above) w'ould the planets appear to move, if the fpedlator were fituated abovenbsp;the fun in a line perpendicular to the orbit of thenbsp;earth. But fuppofe that the fpedlator fhould benbsp;fituated fideway, viz. in the fame plane with thenbsp;orbit of the earth, but farther from the fun thannbsp;any of the planets; then, it is evident, that if thenbsp;orbits of the planets were all in the fame plane, thenbsp;fpedlator wmuldfee the planets move all in the famenbsp;ftraight line. This, however, is not the cafe j fornbsp;the orbits of the planets are a little inclined to eachnbsp;other; in confequence of which the fpedlator wouldnbsp;fee them move backwards and forwards, in lines inclined to each other, fomewhat like thofe of fig. 9,nbsp;Plate XXVI.

Of the real diftances of the fixed liars from the fun, as alfo from each other, we are utterly ignorant. Certain it feems, that the diftance of thenbsp;ueareft fixed liar froin us exceeefs by a great many

millions

Oiillions of times the diameter of the largeft plane-tory orbitj as that of the Georgian planet. It is not in our power to fay whether the ftars are of equalnbsp;bulks, and appear of different fizes, only on accountnbsp;of their different diftances; or they differ both innbsp;fize and diftance. Every circumftance we are acquainted with feems to fhew that they fhine by thenbsp;emiffion of their own light, and that therefore theynbsp;are of the nature of our fun. Probably each flar isnbsp;the centre of a particular fyftem, and has a numbernbsp;of planets revolving about itfelf, and deriving bothnbsp;light and heat from it; but thofe planets, if exifting,nbsp;are quite invifibie to us.

If it be fuppofed that each ftar is equal to our fun, the extremely fmall diameters under which theynbsp;appear, and which cannot be meafured with certainty by means of any micrometer, is fufficient tonbsp;indicate the aftonifhing diftances to which even the

After having indulged our fancy in a Ihort contemplation of fo many funs, and fo many fyftems*

Jet us return to our folar fyftem, and enquire what retains the planets in their orbits round the fun.

This queftion, which had long perplexed the moft Jfarned and inquifitive ph�lofophers, was at lengthnbsp;farisfafforily anfwered by Sir Ifaac Newton s theory.nbsp;A fimple but general theory, which he deduced fromnbsp;the known laws of nature, which he demonftratednbsp;ftriflly to account for all the phenomena, and

I fliall endeavour briefly to explain the principles of this theory j but, for the comprehenfion of whatnbsp;follows, the attentive reader flrould recoliedl whatnbsp;has been explained in the firfl; volume of thefe Elements, refpecling the doftrine of motion, efpeciallynbsp;concerning the curvilinear motion of a body, whichnbsp;is aded upon by two powers at the fame time,nbsp;one of which powers is uniform, and the othernbsp;variable.

Newton obferving, according to the known theory, that the attractive force of the earth ads atnbsp;all thofe heights which are acceffible to us, and thatnbsp;it decreafes in proportion as the fquares of the dif-tances increafe, naturally conjedured that it mightnbsp;act at all other diftances under the fame law of decrement j therefore the force of that attradion at anynbsp;given diftance being known, one may ealily calculate the quantity of that force at any other givennbsp;diftance.

Newton likewife, obferving that the attradion is mutual amongft the terreftrial bodies, juftly fuppofednbsp;that all the bodies of the fyftem might mutually at-trad each other, their attradive forces being as thenbsp;quantities of matter diredly, and the fquares of thenbsp;diftances inverfely.

in the world at its creation, it is evident that, fooner or later, according to their diftances, the planets,nbsp;both primary and fecondary, would have all beennbsp;drawn with an accelerated motion direftly towardsnbsp;the fun, which is by far the largeft body of thenbsp;fyftem; and the whole would have coakfced m onenbsp;body. Therefore Newton fuppoled that at thenbsp;creation each planet was impelled by a fingle ftroke,nbsp;fuch as would by itfelf compel it to move at fomenbsp;uniform rate in a ftraight line for ever, in a direftionnbsp;perpendicular to that of the fun�s atrraftion ; provided it moved in an unrefifting medium, or with anbsp;proportionate retardation in a refifting mediumnbsp;Now thofe premifes being admitted, it neceffaiilynbsp;Allows, that the adion of both powers, (viz. of thenbsp;sttradive force which ads unremittedly, and of thenbsp;above-mentioned impulfe) would compel each planet to move in a curve line concave towards thenbsp;common centre of attradion, wiiich centre muftnbsp;be within the fun, in confequence of the great fizenbsp;of that luminary

With thofe principles Newton began to calculate and ftridly to demonftrate, the confequences which,nbsp;tnufl neceffarily arife therefrom, and proved thatnbsp;the periods, the diftances, the velocities, and thenbsp;very Qiapes of the planets, fuch as had been ob-ferved by aftronomers, were conformable to thofe

The rnediutn through which the planets move, if not lt;\uite unreiifting, nmft very nearly approach that ftate.nbsp;t See the ^th chapter of the firft part of thefe Elements.

7? Of the true Syftem of the Worldi ^c. principles. The apparent inequalities of the motionsnbsp;of the primary planets, of the fatellites, and efpeciallynbsp;of our moon, are all depending on the fame j and itnbsp;is wonderful to remark, that every aftronomicalnbsp;difcovery or terreftrial meafurement, made fincenbsp;Newton�s time, has been found conformable to hisnbsp;theory.

Thus we have drawn a concife, comprehenfive, but fuperfidal fketch of the folar fyftem. It is nownbsp;neceflary to enter into a more particular examinationnbsp;of its parts.�The fixes, lhapes, and movements ofnbsp;each primary as well as fecondary planet; theirnbsp;diftances from the fun and from each other; theirnbsp;phafes, their mutual dependence; and the beft practical methods of afcertaining thofe particulars, will benbsp;defcribed in the following chapters.

[ 79 3

CHAP. IV. nbsp;nbsp;nbsp;\

quot;^^ENUS and Mercury certainly furround the ^ fun, and their orbits are included within the ^nbsp;earth�s orbit j whence they are called the inferiornbsp;-planets.

That they really furround the fun is evident fiom their having been feen fometimes before, then on onenbsp;fide, then beyond, the fun, (which is proved by thenbsp;diminution of their apparent fize, and by their difap-pearing behind the fun) after which they are feen onnbsp;the other ade, amp;c. When they are before the fun,nbsp;they generally are above or below its dife; but fome-times they appear like dark fpots over thedife itfelfnbsp;of the fun.

That their orbits are within the orbit of the earth is alfo evident; for otherwife they would fometinaesnbsp;be feen in oppoftion to the fun; viz. would appearnbsp;to rife from the horizon when the fun appears tonbsp;� fet, which is never the cafe.

On the contrary, the orbits of all the other planets include that of the earth; whence they arc

called

called the fuperior planets �, and, in fadt, at proper periods, they are feen in oppcfition to the fun, viz.nbsp;they are feen to rile when the fun appears tonbsp;fet j or they are feen upon the meridian at midnight.

That the orbits of the planets are fo fituated is alfo proved from the appearance of their luminousnbsp;faces; for of that half of each planet, which is illuminated by the fun, we can only fee fuch a portionnbsp;as the above-mentioned fituationsof their orbits cannbsp;poffibly admit of. Thus, when Venus V, fig. lo,

^ Plate XXVI. is nearly m cenjunSion with the fun S, viz. is feen from the earth T, in the fame part of the'nbsp;heavens, her bright face appears full and round;nbsp;becaufe ail her illuminated face is turned towards us.nbsp;On the contrary, when Venus is nearly between thenbsp;earth and the fun, as at -u, then its bright face is turnednbsp;entirely from us, in confequence of which Ihe dif-appears, or is feen like a dark fpot upon the difc ofnbsp;the fun. When Venus is not quite between us andnbsp;the fun, tlren Ihe appears horned like the newnbsp;moon, or more or lefs illuminated, according to itsnbsp;fituafion.

The fuperior planets are never feen horned, be-caufe they can never get between the earth and the fun, rior nearly fo. Thus Mars M, whofe orbitnbsp;includes that of the earth T, and includes likewifenbsp;the fun, always preferves a full and finning face, a$nbsp;at M or OT; but when it ftands at O or P, it-appearsnbsp;a little gibboasj or fomewhat deficient from full.�nbsp;! .. .nbsp;nbsp;nbsp;nbsp;The

The fame thing may be faid of the other fuperior planets.

All the plajicts, the earth included, move in el liptical orbits, though not much different from circles ; and the fun is fituated at, or near to, one ofnbsp;the foci of each of them. That focus is called thenbsp;focus. If we fuppofe the plane of the earth'snbsp;tgt;tbit, which cuts the fun through the centre, to benbsp;extended as far as the fixed ftars, it will mark amongnbsp;them a great circle, which is the ecliptic^ and withnbsp;��^hich the fituations of the orbits of all the othernbsp;planets are compared. A trajeBory is the curve

path in general of any celcflial body.

The planes of the orbits of all the other planets

do alfo pafs through the centre of the fun j but if extended as far as the fixed ftars, they form circlesnbsp;different from one another, as alfo from the ecliptic ; one part of each orbit being on the north, andnbsp;the other on the fouth, fide of the ecliptic. There-fore the orbit of each planet cuts the ecliptic in twonbsp;oppofite points, which are called the nodes of thalnbsp;particular planet; and the nodes of one planet cutnbsp;the ecliptic in places different from the nodes ofnbsp;another planet. A line which paffes from one ofnbsp;the two nodes of a planet to the other, or the lin'Cnbsp;in which the plane of the orbit of that planet cutsnbsp;^he plane of the ecliptic, is called the line of nodes.

, That node, where the planet paffes from the fouth to the north fide of the ecliptic is called the afeend-.

and the aftronomers denote it by the cha-voc. IV. nbsp;nbsp;nbsp;onbsp;nbsp;nbsp;nbsp;ra�fer

rafter �. The other node is called the dejcending node, as is denoted by the charafter es .

The anglcj which the plane of a planet�s orbit makes with the plane of the ecliptic, is called thenbsp;inclination of that planet�s orbit.

A perpendicular being let fall from a planet to the ecliptic, the angle, which is formed at the fun,nbsp;by two lines, one drawn from the point where thenbsp;perpendieular falls, and the other from the earth tonbsp;the fun, is denominated the angle of commutation.nbsp;The line between the above-mentioned point wherenbsp;the perpendicular falls, and the fun or the earth, isnbsp;called the curtate dijlance from the fun or from thenbsp;earth.

A line drawn from the lower focus of a planet�s orbit, (viz. where the fun is) to either end of thenbsp;conjugate axis of its orbits (which line is equal tonbsp;half the tranfverfe axis) is called the mean dijlance ofnbsp;that planet. But according to Ibme authors, thenbsp;mean dijlance is a mean proportional between the twonbsp;axes of that planet�s orbit.

The diftance of either focus from the centre of the elliptical orbit, is called its excentricity.

The apjes, or affides, are two points in a planet�s . orbit, which are fartheft and neareft to the fun j thenbsp;former of which is called the higher apfis, or aphelion j the latter is called the lower apfts, or the perihelion. The diameter, which joins thofe two points,nbsp;is called the line of the apfides, and is fuppofed tonbsp;pafs through the centre of the fun. , They are not, ,nbsp;however, always in the fame ftraight line which paffes

through the fun j for they are fometimes out of a *^*ght line, making an angle greater or lefs thannbsp;and the difference from 180� is called thenbsp;potion of the line of the afjides. When tlie angle isnbsp;^ s than 180�, the motion is faid to be in anteceden-; viz. contrary to the order of the figns of thenbsp;ecliptic. When the angle is greater than 180�, thenbsp;�potion is faid jq confequentia, or in the order ofnbsp;figns.

^hen the fun and the moon are neareft to the gt; they are faid to be in perigee.�When at their

The argument of latitude is the angle formed in the �^et s Orbit, at the fun, by two lines, one of whichnbsp;*^omes from that planet, and the other from its af-^�^nding node.

nie by the radius veSior, or line drawn from the to the planet, and the line drawn from the fun tonbsp;^ aphelion of the planet. The mean anomaly is thenbsp;^^gular diftance of a planet from its aphelion (takennbsp;fame time with the true anomaly), fuppofingnbsp;tnove uniformly with its mean angular velo-

planet a perpendicular to the line of the apfides, be drawn till it meet the circumference of the circle jnbsp;then the angle formed by two lines, one drawn froi'Hnbsp;the centre of the planet�s orbit to the aphelion, anlt;inbsp;the other to the point where the perpendicula*quot;nbsp;through the planet�s place, interfeds the circumference of the circle, is called the excentric anoma^inbsp;or the anomaly of ihe eentre.�

The direSi motion of a planet, as feen from the earth, is when it appears to move from weft tonbsp;eaft, viz. according to the order of the figns, or innbsp;conje^uentia. Its retrograde motion, or motion in aH'nbsp;tecedentia, is when it appears to move from eaft tonbsp;weft, viz. contrary to the order of the figns. Butnbsp;when the planet feems to remain a certain time ionbsp;the fame place, it is then faid to be ftationary.

When feen from the earth, it is evident that the inferior planets inuft have tv/o conjundions withnbsp;the fun, and that they muft be dired in their fupe-rior conjundions, retrograde in their inferior con-jundions, and ftationary fome time before and aftet-But the fuperior planets are dired at the time oinbsp;their conjundion with the fun, retrograde at thenbsp;time of their oppofition, and ftationary fome timenbsp;before and after their oppofition.

quot; The apparent velocities of the planers, whether dired or retrograde, are accelerated from one of tlie^nbsp;ftationary points, to the midway between that andnbsp;the following ftationary point j from thence the/nbsp;are retarded until the next ftation. Their greateft

Yelcitivs to tht Plon�fs. nbsp;nbsp;nbsp;^5

velocity is in their conjunftlons, and their greatefl: retrograde velocity is in the oppofition ofnbsp;fuperior pi aners, and in the lower conjunaion ofnbsp;the inferior planets.�

The inferior planets appear fmalleft in their di-rea: motion, and larged in their retrograde motion. The fuperior planets appear largeft in their oppofition to the fun, and fmalleft in their con-junaion. The inferior cannot appear to go farthernbsp;from the fun than the angle which the radius of theirnbsp;Ofhit fubtends at the earth.

Even when fcen from the fun, the planets do not appear to move equably in their orbits. In othernbsp;'*'^ords the real movements of the planets, (the earthnbsp;^oing one of them) are not equable in their orbits }nbsp;in fotne parts of their orbits they move fafter,nbsp;or percur a greater fpace, than in others, thoughnbsp;always move the fame way. But thofe whichnbsp;at firft fight may appear to be irregularities, will,nbsp;Upon ftrict examination, be found regulated by certain genera], conftant, and admirable laws ; the prin-'-'Pal of which are as follows:

E If a ftraight light be drawn from a planet to Ein, and this line be fuppofed to be carried alongnbsp;the periodical morion of the planet, then thenbsp;areas, which are defcribed by this right line and thenbsp;path of the planet, are proportional to the rimes ofnbsp;planet�s motion j for inftance, the area thus de-**^ribeti in two hours is the double of that which isnbsp;defcribed in one hour, and a third part of that which

is defcribed in fix hours; though the arc which defcribed by the planet itfelf in two hours, is notnbsp;the double of the arc which is defcribed by thenbsp;fame in one hour; nor the third part of that whichnbsp;is defcribed by the fame in fix hours.

11. The planets are at different diftances frofri the fun, and perform their periodical revolutions iitnbsp;different times; but it has been found that the cubesnbsp;of their diftances, or of the principal axes of theitnbsp;elliptical orbits, arc conftantly as the fquares of theitnbsp;periodical times; viz. of the times of performingnbsp;their periodical revolutions.

Thofe two remarkable propofitions are called! Kepler�s laws j becaufe Kepler was the firft, whogt;nbsp;by a careful examination of the diftances and pe'nbsp;riodical times of the planets, found them out j butnbsp;it was Sir I. Newton, who demonftrated them oUnbsp;the principles of attraftion, amp;c. according to hisnbsp;theory ¹.

This wonderful harmony, which has been to regulate the motions of the planets round th^nbsp;fun, as alfo to regulate the motions of the fatellit^¹nbsp;round their refpeftive primaries; and the want

The above-mentioned propofitions, together with what' ever relates to the velocities, amp;c. of bodies revolving

forts of regularity, when the fun and planets fuppofed to turn round the earth as a cen-are quite fufficicnt to confirm the Coperni-can fyfteim, were we even in want of any othernbsp;proofs.

� ftall endeavour to render the principle of this grand theory j namely, the miverjal attraSiion,nbsp;tnore intelligible to beginners, by means of the following familiar explanations and examples.

The centre of attradlion of the folar fyftem, which been faid jq be within the body of the fun, muftnbsp;�ot be confidered as a point endued with the attrac*nbsp;'�*ve power; but it muft be tonfidered as the pointnbsp;^�^oilibrium between all the bodies of the folarnbsp;fyftem,nbsp;nbsp;nbsp;nbsp;point of equilibrium between the fun

any one planet, is nearer to the centre of the ^*^0 than to the centre of the planet, by as much as'nbsp;^^0 buih or attraftive power of the planet is lefsnbsp;the bulk or the attractive power of the fun.nbsp;j Call this the firft centre of equilibrium, then,nbsp;confider a fecond planet, the centre of equili-between the firft centre and this planet, willnbsp;oearer to the firft centre than to the planet, by asnbsp;l^^ch as the attractive force of the fecond planet isnbsp;^ ^ than the combined attractive force of the funnbsp;fitft planet. Thus we may take into the ac-^^Unt a third planet, then a fourth, amp;c. Laftiy,nbsp;^oinmon centre of attraftion of them all will benbsp;to be within the body of the fun, becaufe thenbsp;o 4nbsp;nbsp;nbsp;nbsp;bulk

The attraftive forces are not only to be obferved between the planets and the fun, but they are mutual and proportional between them all j fo that thenbsp;planets attract each other; and, in fa�t, when theynbsp;come near, they fenfibly difturb each other�s motion.nbsp;The primary planets attra�l their iatcllites, and thenbsp;latter attradl the former. The moon raifes tides innbsp;the ocean, in confequcnce of its attraftion, amp;c.

The mutual attraftion of bodies is familiarly illu-ftrated by the example of a .boat and ftiip upon water, and tied by a rope, whence a ftrong evidence of the true fyftem is derived. � Let a mannbsp;� either in a fhip or boat pull the rope (it is thenbsp;fame in effeft at which end he pulls, for the ropenbsp;� will be equally ftretched throughout) the ihipnbsp;and boat will be drawn towards one another j butnbsp;� with this difference, that the boat will move asnbsp;� much fafter than the ihip, as the fhip is heaviernbsp;� than the boat. If the fhip is looo or loooonbsp;� times heavier than the boat, the boat will benbsp;� drawn lOOO or loooo times fafter than die fhip;nbsp;and meet proportionably nearer the place fromnbsp;which the fhip fet out. Now, whiift one maonbsp;� pulls the rope, endeavouring to bring the fhipnbsp;�� and boat together, kt another man in the boatnbsp;endeavour to row it off fideways, or at right'nbsp;� angles, to the rope j and the former, inftead ofnbsp;being able to draw the boat to the fhip, willnbsp;3nbsp;nbsp;nbsp;nbsp;� find

it enough for him to keep the boat from going farther off; whilft the latter, endeavouringnbsp;to row off the boat in a ftraight line, will, bynbsp;toeans of the others pulling it towards the fhip,nbsp;row the boat round the (hip at the rope�s lengthnbsp;from her. Here the power employed to drawnbsp;the fhip and boat to one another, reprefents thenbsp;attraction of the fun and planets, by whichnbsp;the planets would fall freely tov;ards the fun withnbsp;^ Ruick motion, and would alfo in falling attradtnbsp;the fhn towards them. And the power employed to row off the boat, reprefents the projectile force impreffed cm the planets at right-3ng!es, or nearly fo, to the fun�s attradion; bynbsp;'*'hich means the planets move round the fun,nbsp;3rid are ^kept from falling to it. On the othernbsp;hand, if it be attempted to make a heavy fhip gonbsp;round a light boat, they will meet fooner than thenbsp;fr'ip Can get round, or the fhip will drag the boatnbsp;� after it.

Let the above principles be applied to the fun and earth, and they will evince, beyond a poffi-^ bility of doubt, that the fun, not the earth, is thenbsp;centre of the fyftem; and that the earth movesnbsp;*ound the fun as the other planets do.

For, if the fun moves about the earth, the s attradive power muff draw the fun to-it from the line of projedion, fb as to

end its motion into a curve. But the fun being leafl; 227000 times as heavy as the earth, by

� being fo much weightier as its quantity of matter � is greater, it muft move 227000 times as flowlynbsp;� toward the earth, as the earth does toward thenbsp;� fun; and confequently the earth would fall to thenbsp;� fun in a fhort time, if it had not a very ftrongnbsp;projectile motion to carry it off. The earthnbsp;therefore, as well as every other planet in thenbsp;quot; fyftcm, muft have a re�tilineal impulfe to preventnbsp;� its falling into the fun.

� There is no fuch thing in nature as a heavy body moving round a light one as its centre ofnbsp;� motion. A pebble fattened to a mill-ftone by anbsp;quot; firing, may by an eafy impulfe be made to circu-� late round the mill-ftone; but no impulfe cannbsp;quot; make a mill-ftone circulate round a loofe pebble,nbsp;for the mill-ftone would go off, and carry thenbsp;� pebble along with it.

� The fun is fo immenfely bigger and heavier � than the earth, that if he was moved out of hisnbsp;� place, not only the earth, but all the other planets,nbsp;� if they were united into one mafs, would be car-� ried along with the fun, as the pebble would benbsp;� with the mill-ftone.�*

I lhall conclude this chapter with a very plain and familiar illuftration of the planet�s elliptical orbits,nbsp;taken from the fame laft quoted author, for the fakenbsp;of thofe readers who are not qualified to read the de-

monftrations of the theory of curvilinear motion, as given in the firft volume of thefe Elements.

� If a planet at B, fig. i. Plate XXVII. gravi-quot; tates, or is attrafted toward the fun S, fo as to � fall from B to in the time that the projectilenbsp;quot; force would have carried it from B to X, it willnbsp;� deferibe the curve B Y, by the combined adtionnbsp;� of thefe two forces, in the fame time that thenbsp;� projeftile force fingly would have carried it fromnbsp;� B to X, or the gravitating power fingly havenbsp;quot; caufed it to defeend from B to j; and thefe twonbsp;quot; forces being duly proportioned, and perpendicularnbsp;'' to each other, the planet, obeying them both,

� But if, whilft the projeftile force would carry � the planet from B to h, the fun�s attraftion (whichnbsp;� conftitutes the planet�s gravitation) lEould bringnbsp;quot; it down from B to i, the gravitating power wouldnbsp;quot; then be too ftrong for the projeftile force j andnbsp;� Would caufe the planet to deferibe the curvenbsp;� B C. When the planet comes to C, the gravidnbsp;� tating power (which always increafes as thenbsp;� fquare of the diftance from the fun S diminilhes)nbsp;� will be yet ftronger for the projeftile force j and

To make the projeftile force balance the gravitating power fo exaftly, as that the body may move in a circle, thenbsp;projeftile velocity of the body muft be fuch as it would have

acquired by gravity alone in falling half the radius of the circle.nbsp;nbsp;nbsp;nbsp;,

� by confpiring in fome degree therevrith, will ac-celerate the planet�s motion all the way from C � to Kj caufing it to defcribe the arcs E C, C D,nbsp;� D E, E F, amp;c. all in equal times.

� Having its motion thus accelerated, it thereby � gains fo much centrifugal force, or tendency tonbsp;� fly off at K in the line K k, as overcomes thenbsp;fun�s attraftion; and the centrifugal force beingnbsp;� too great to allow the planet to be brought nearernbsp;the fun, or even to move round him in the circlenbsp;K �, amp;c. it goes off, and afcends in the curvenbsp;� KLMN, amp;c. its motion decreafing as graduallynbsp;from K to B, as it increafed from B to K, be-caufe the fun�s attraftion now afts againft thenbsp;� planet�s projedtile motion, juft as much as itnbsp;adfed with it before. When the planet has gotnbsp;round to B, its projeflile force is as much dimi-� nilhed from its mean ftate about G or N, as itnbsp;was augmented at K; and fo the fun�s attraftionnbsp;� being more than fufficient to keep the planetnbsp;from going off at B, it deferibes the fame orbitnbsp;� over again, by virtue of the fame forces ornbsp;powers.

double projedtile force will always balance *' a quadruple power of gravity. Let the planetnbsp;� at B have twice as great an impulfe from thencenbsp;� towards X, as it had before j that is, in the famenbsp;length of time that it was projedted from B tonbsp;� as in the laft example, let it now be projedtednbsp;� from B to f j and it will require four times as

much gravity to retain it in its orbit; that is, it muft fall as far as from B to 4, in the time thatnbsp;the projectile force would carry it from B to r;nbsp;otherwife it would not defcribe the curve BD, asnbsp;is evident by the figure. But, in as much timenbsp;as the planet moves from B to C in the highernbsp;part of its orbit, it moves from I to K, or fromnbsp;K to L, in the lower part thereof; becaufe, fromnbsp;the joint aCtion of thefe two forces, it muft always defcribe equal areas in equal times throughout its annual courfe. Thefe areas are repre-fented by the triangles BSC, CSD, DSE, ESF,nbsp;amp;c. whofe contents are equal to one another,nbsp;quite round the figure.

� Should it appear ftrange, that when one of the two forces has got the better of the other, it fhouldnbsp;not continue to carry the planet on in its direction ; the difficulty will be removed by confider-ing the effeCls of thofe powers as defcribed in thenbsp;preceding paragraphs. Suppofe a planet at B tonbsp;be carried by the projeftiie force as far as fromnbsp;to b, in the time that gravity would havenbsp;brought it down from B to i ; by thefe twonbsp;forces it will defcribe the curve BC. When thenbsp;planet comes down to K, it will be but half asnbsp;far from the fun S, as it v/as at B ; and therefore,nbsp;by gravitating four times as ftrongly towards him,nbsp;it Would fall from K to V in the fame length ofnbsp;time that it would have fallen from B to i, in thenbsp;higher part of its orbit, that is, through four times

� as much fpace; but its projedtile force is then fo much increafed at K, as would carry it from Knbsp;� to k in the fame time j being double of what itnbsp;� was at B, and is therefore too ftrong for the gra-� vitating power, either to draw the planet to thenbsp;� fun, or caufe it to go round him in the circlenbsp;� Y^lmn, amp;c. which would require its falling fromnbsp;� K to w, through a greater fpace than gravity cannbsp;draw it, whilft the projedtile force is fuch as wouldnbsp;carry it from K to ^; and therefore the planetnbsp;quot; afeends in its orbit KLMN, decreafing in its ve-� locity for the caufes already affigned.�

C 95 ]

OF THE MOTION OF THE EARTH ROUND THE SUN, AS also of the motion round her ownnbsp;AXIS,

T T has been fhewn in the preceding, pages, that, on various accounts, the earth, analogous to thenbsp;of the planets, moves round the fun, and notnbsp;^0 fun round the earth. It is now necefl'ary to ex-^Oiine the various particulars which belong to thatnbsp;Motion, and to fliew that the phenomena are thenbsp;as if the fun moved round the earth after thenbsp;Apparent manner which has been defcribed in thenbsp;^cond chapter of this part.

The real motion of the earth is in an elliphs, ^car one focus of which the fun is fituated *.

According to De la Lande�s determination, if we reckon ��anfcerfe axis of this elliptical orbit equal to 200000,nbsp;th^'' mean diftance of the earth from the fun, viz. fromnbsp;^ focus, in which the fun is fituated, is looooo ; and thenbsp;^oentricity of its orbit is 1681,395.

According ta the baft eftimates in round numbers, the ^an diftance of the earth from the fun is 95 millions of

gS nbsp;nbsp;nbsp;Of the Motion of the Earth

If we fuppofe that the plane of the earth�s orbit be extended as far as the fixed ftars, it will therenbsp;mark a circle, which is the ecliptic, and fo im-menfely great is the diftance of the fixed ftars fromnbsp;the folar fyftem, that whether the earth be in onenbsp;part or another of its orbit, the ftars will conftantlynbsp;appear to have the fame order, relative fituation,nbsp;and magnitude.

Sinee the plane of the earth�s orbit pafles through miles ; the tranfverfe axis of its elliptical orbit is twice thatnbsp;diftance, viz. is equal to 190 millions of miles, and the ex-centricity is I597325 miles.

Dr. Keill, calculating the true anomaly, on the fuppofi-tion that the tranfverfe axis of the earth�s orbit is to the ex-centricity as 100000 to 1691, found it equal to 29� 2' 54''-

The greateft equation of the centre (viz. the difference between the true and mean anomaly) according to Dr.nbsp;Maflcelyne�s determination for the year 1780, is 1� 55'nbsp;30'',9. It is generally allowed that this equation and thenbsp;excentricity are fubjedt to a regular diminution.

The earth�s aphelion at prefent is when the fun is in 8* 40 12^' of 03-, and the increafing annual motion of thisnbsp;aphelion according to the beft obfervations, is about i'nbsp;2quot;. And the preceifton of the equinoxes being about 50quot;,25nbsp;annually, we fhall have 11',75 for the a�ual motion of thenbsp;aphelion. The time required by the fun to pafs overnbsp;of longitude, being added to the fdereal year-, will givsnbsp;365'^, 6\ I4', 2quot;, for the anomoUJlic year., or the time occupied by the earth in revolving from aphelion to aphelion*nbsp;Mr. O�Gregory�s Aftronomy, �. 316.

fun, it follows that, whilft we inhabitants of the ^arth, fee the fun in the direiflion of a certain pointnbsp;�f the ecliptic, an obferver in die fun would fee thenbsp;^arth in the direftion of the oppofite part of thenbsp;ecliptic j thus, in fig- ii. Plate XXVI. S repre-^^nts the fun, A B C D is the orbit in which thenbsp;^arth moves from the weft to the eaft, fo as to perform the entire revolution in the compafs of onenbsp;year. The external circle is the ecliptic, with thenbsp;^2 figtts marked upon it. Now a fpeftator at Snbsp;^ill perceive the earth at A, as if it coincided withnbsp;'^�te fig5 When the earth is at B, the fame fpec-tator will perceive it to coincide with as ; and fonbsp;*^'1* But an inhabitant of the earth, when the earthnbsp;at A, will fee the fun as if it v/ere at and whennbsp;earth is at B-, he w-ill perceive the fun as coin-^iding with vf, amp;c. It is evident from the figure,nbsp;^hat whether the fun be fuppol�ed to move round thenbsp;or the latter round the former, the apparentnbsp;^^nual motion of the fun along the ecliptic muft benbsp;fame.

fiefides the above-mentioned annual motion, the �arth has a motion round its own axis, which pro-^uces the viciffitudes of day and night, whence it isnbsp;^^lled the diurnal rotation ; and which is analogousnbsp;quot;the movements of the other planets; for, of thenbsp;�^her planets, thofe which, from their having fpotsnbsp;^Pon their furfaces, may be feen to move, have beennbsp;^nd to have a fimilar motion round their own

VOL. IV.

This diurnal motion of the earth round its ov/n axis, (viz. round an imaginary line) is performed fromnbsp;the weft towards the eaft in 24 hours; and everynbsp;point of its furface muft defcribe a whole circle innbsp;the fame time, excepting the two points whigh arenbsp;at the extremities of the axis, viz. the poles. Thenbsp;different parts of the earth�s furface muft likewilenbsp;defcribe larger or fmaller circles, according as theynbsp;are nearer to, or farther from, the poles j thofenbsp;parts, which are equidiftant from the poles, defcrib-ing the largeft circle, which circle is the equator.

Now, as a fpedlator on the furface of the earth muft turn with it in the dire�lion from the weft towards the eaft, it is evident that all the bodies of thenbsp;univerfe which do not adhere to the earth, muft appear to turn in a contrary direflion, viz. from thenbsp;eaft tow'ards the weft; and thofe celeftial bodies,nbsp;which are diredly over the equator of the earth, muftnbsp;appear to defcribe the largeft circles, whilft; thofenbsp;which are diredly over the poles of the earth, muftnbsp;appear to remain immoveable; hence we attributenbsp;to the ftars, or to the heavenly fphere, the fame axis,nbsp;poles, equator, amp;c, as if that fphere turned, and thenbsp;earth ftood ftlll.

In confequence of this rotatory motions of the earta, and becaufe the parts of it, which, beingnbsp;nearer to-tlie equator, defcribe larger circles, and ofnbsp;qnbsp;nbsp;nbsp;nbsp;courfe

If the axis of the earth had been fituated in a po-fition perpendicular to the plane of the earth�s orbir* �which is the fame as the plane of tire ecliptic, thenbsp;circle of the interledion of light and darknefs wouldnbsp;have evidently palTed through the poles of the earth,nbsp;and of courfe the days would have been conftantlynbsp;equal to the nights. But the cafe is, that the axisnbsp;of the earth is inclin�d to the plane of the ecliptic,nbsp;and makes an angle with it of about 66� 32'.nbsp;Therefore the plane of the ecliptic does not coincide with that of the equator, but muft make annbsp;angle with it of 23�, 28quot; (viz. an angle equal tonbsp;the complement, or to what 66� 32' wants, ofnbsp;SO�.)

This inclination of the axis, or of the ecliptic, varies a little as it ought to do, agreeably to- thenbsp;Newtonian theory*. In the year 1736, Dr. Maf-kelyne determined the obliquity of the ecliptic, as itnbsp;is called, to be 23�, 28quot;, xd' �, and it appears thatnbsp;it diminifoes at the rate of 50quot; in a century, ornbsp;half a fecond in a year. But to prevent obfcurity,

* About 2100 years ago, Pytheas found the obliquity of the ecliptic to be 23�, 49', 30quot;. about A. D. 880. Alba-tegnius found it equal to 23�, 35', 40quot;. A. D. Ii40�nbsp;Almaeon found it equal to 23�, 33', 30�. A. D. 158.nbsp;Tycho Brahe found it equal to 23�, 29', 30quot;. A. D. 1689,nbsp;Flamfteed found it equal to 23�, 28', 56quot;. and A.D. 1736*nbsp;Condamine found it equal to 23�, 28', 24�.

us negle�t this trifling variation, and in the following illuftration, let us con�der this inclination lt;5f the axis, as if it were conftantiy the fame.

Then the axis of the earth, befldes its retaining tfte fame inclination towards the plane of the ecliptic, does alfo remain always diredled to the famenbsp;ftar; or in other words, if a line be drawn parallelnbsp;to that axis whilft the earth is in any part of itsnbsp;'^��bit, then, when the earth is in any other part ofnbsp;^ts orbit, the axis will always be parallel to that line;nbsp;excepting a regular and fmall variation.

Now the various feafons of the year and various i^ogths of days and nights, are owing to the above-'nbsp;tOcntioned inclination of the axis to the orbit, andnbsp;to that axis moving round the ecliptic in a directionnbsp;Parallel to a line nearly immutable. The preceflionnbsp;the equinoxes is owing to the laft-mentionednbsp;^oiall variation. The effedts, in fhort, are the famenbsp;have been explained in the chapter, where thenbsp;Phenomena were defcribed on the fuppofition thatnbsp;earth fto�d immoveable, and the celellial objectsnbsp;^'^ved round it; yet it will be necelTary to illuftratenbsp;tbole effefts on the true theory, by means of a di^�nbsp;or two.

2. Plate XXVII. reprefents the earth in . * ^rcnt parts of its elliptical orbit j the fun S be-in one of Its foci. The fpeftator is fuppofed tonbsp;^ 'vithoot the orbit of the earth at a conflderablenbsp;^nce, and to look i^pon it obliquely,nbsp;the firfl: place it is obfervable, that whether

at A, or at C, or B, o,r D, the axis of the earth is always direfled the fame way, viz. the directions ofnbsp;the axis in all thofe fituations of the earth, are allnbsp;parallel to each other. The fmall deviation whichnbsp;produces the preceffion of the equinoxes, will benbsp;taken notice of in the fequel.

In the fecond place it fliQuld feem, that, on account of the above-mentioned conftant direftion of the axis, if, when the earth is af B, its axis is di-redied towards a certain ftar E �, then, when thenbsp;earth is at A, it ought to point towards fome othernbsp;ftar F, the diftance of which from E muft be equalnbsp;to the tranfverfe axis AB of the earth�s orbit. Thenbsp;apparent diftance of thofe ftars is meafured by thenbsp;angle EAF, which, on account of the parallelifm ofnbsp;the lines EB, AF', is equal to the angle BE A,nbsp;which is the angle under which the orbit of thenbsp;earth would be feen from E5 hence the angle AEB,nbsp;or EAF, is called the parallax of the great orhii.

It is eafy to conceive that the farther the points E and F� are from the earth�s orbit, the ftnaller muftnbsp;the angle EAF, or BE A, be. Now from the mollnbsp;accurate obfervations, it appears that this angle isnbsp;lefs than one minute; and it is not known hownbsp;much fmalier it really is 5 hence we may perceivenbsp;that the diftance of the ftars is aftonifhingly great¹.

If tba angle AEB, or its equal the angle EAF, could be known with certainty, the diftance of the ftars tvould

The caufe of the inequalities of the days and eights at different times of the year, as alfo the different feafonSj will be eafily conceived by infpedlingnbsp;figure ; for they both arife from the inclinationnbsp;the axis of the earth to the orbit.

Firft, In the fpring, when tl;e earth is in that P3rt of its orbit, in which a fpeftator in the funnbsp;''�ould fee the .earth coincide with the fign Libra,nbsp;the ecliptic, the inhabitants of the earth fee thenbsp;in the direction of t, Aries. At that time thenbsp;^'rcle terminator of light and darknefs, paffes throughnbsp;poles n, s-, therefore the earth in its diurnal rc-^^don about its axis n, s, has every part of its furfacenbsp;Inng in the light as in the Ihade; viz. the daysnbsp;equal to the nights; the fun at that time beingnbsp;^UccelTively vertical to the equatorial parts of thenbsp;^arth.

Secondly, As the earth proceeds in its orbit from the Weft towards the eaft, along the figns nt, �, andnbsp;the fun is feen to advance along the figns ti,

23 j aod gradually becomes vertical to thofe parts of the earth which are on tiie north of thenbsp;^�^ttator. So that when the earth is in V, the fun

^ by an eafy trigonometrical calculation; for in the AEB, one fide AB is known, being the tranfverfenbsp;w the earth�s orbit, the angle EBA is equal to the in-^ riation of the axis of the earth to the orbit; therefore,nbsp;''�'''i*iglikewife the ang-le AEB, the other parts would benbsp;calculated.

is in 2S, and is perpendicular to thore parts of the earth, which are under the tropic ; viz. about 23�,nbsp;28', from the equator therefore the inhabitants ofnbsp;the northern hemifphere will enjoy fommer, on account of the folar rays falling more perpendicularly,nbsp;amp;c.; and they will have their days longer than thenbsp;nights in proportion as they are more diftant fromnbsp;the equator; but thofe whofe latitude exceeds 66quot;�,nbsp;32� north, will have conllant day light; for, bynbsp;infpedling the figure, it will be perceived that thenbsp;earth, at that time, in its daily revolution, hasnbsp;all the partynx, within the polar circle, in thatnbsp;half of its furface which is illuminated by thenbsp;fun.

At the fame time the inhabitants of the fouthern hemifphere have winter; their days being fhorternbsp;than their nights, in proportion as they are farthernbsp;from the equator ; and thofe, whofe latitude exceedsnbsp;66% 32', fouth, have conftant night.

The earth then continues its courfe along the figns xx', X, and at the fame time that the funnbsp;is feen to move along the figns il, �'K, and ^; atnbsp;which time the circle terminator of light and dark-nefs paffes again along the poles n, r, of the earth;nbsp;therefore the days are equal to the nights all over thenbsp;earth.

After this the earth advances along the figns K, n, and at w'hich time the inhabitants of thenbsp;northern hemifphere have winter, their days beingnbsp;fhorter than their nights, amp;c.

The

four points of the eclipticj in which the ^^irth is reprefenced in the figure, are called itsnbsp;^^rdinal foints gt;S� and being the folftitial points,nbsp;^hilft and are the equinoftial points j butnbsp;rnuft be obferved, that thofe four fituations ofnbsp;earth, at the two equinoxes and two folftices,nbsp;not equidiftant; becaufe the fun is not in thenbsp;^'^ritre, but in one focus of the earth�s elliptic orbit.nbsp;'I'his will be made more evident by means of fig.nbsp;3' Plate XXVII. where the earth�s orbit is deli-^�^^ted, as it would appear to a fpeflator fituatednbsp;^^ove the plane of it. S is the fun in one of thenbsp;^oci of the eliipfis A C B D. A, B, C, D, are thenbsp;^'fiiations of the earth at the two folftices, and at thenbsp;^Wo equinoxes, (as in fig. 2.) P is' the centre ofnbsp;eliipfis therefore the diftance B P is equal tonbsp;Pj E P is equal to P F, and the elliptical arcsnbsp;EB, BE, FA, are all equal to one another,nbsp;the fun is in the focus S, which is on one fidenbsp;the centre P; therefore in fummer, when thenbsp;^^tth is at B, the fun is farther from it than in thenbsp;quot;'�nter when the earth is at A ; B S being evidentlynbsp;Enger than A S �, and, in faft, the diameter of the

�teateft apparent diameter, in winter, fubcending an ^^gle of 3a' 38'',6, and its leaft diameter, in fum-fubtending an angle of 31' 33�,8.

Parther, the fun becomes perpendicular to the ^^fiuatorial parts of the earth j (that is, the equatornbsp;^^�terfe�ls the ecliptic) when the earth is at C, and

likewife when it comes to D (for th�y muft evidently be in the fame line with the fun); but B E being equal to F.A, and BC being longer than BE;nbsp;BC muft be much longer than CA; and for thenbsp;fame reafon, B D is alfo longer than D A ; confe-quently the earth has a longer arc, CEBFD, tonbsp;percur from the vernal equinox to the autumnal |nbsp;equinox along the figns ===, in, tx, and K, thannbsp;the arc DAC along the figns �Y', �, n, 25, si, andnbsp;*gt;2; the fun, during the fame periods, appearingnbsp;to move along the oppofite figns. Hence the earthnbsp;employs about eight days longer in going fi-om thenbsp;firft point of Libra to the firft of Aries, than innbsp;going from the latter to the former. Or, whichnbsp;amounts to the fame thing, the fun appears to be innbsp;the northern hemifphere about eight days longernbsp;than in the fouthern.

Thofe eight days longer, which the earth employs in going from =2= to t, are not entirely owing to the greatey lengdi of the arc C B P j but isnbsp;partly owing to the earth�s moving along that arcnbsp;at a flower rate than along the arc DAC ; the reafon of which is, that the centre of attradion S isnbsp;farther from the former arc than from the latter, alfonbsp;that the areas S,)'B, ASx, and not the arcs B_y, Ax,nbsp;are proportionate to the tims of the earth�s movingnbsp;along thofe arcs Bj, Ax, (fee page 85, of thisnbsp;volume).

Thus let the earth be at B, from which place, in a certain time, it goes to y, and the line which

Joins the earth and the fun, defcribes the area S Bjy. ^'hen the earth is at A, let it move along an arcnbsp;until the area S K x, which is defcribed by thenbsp;^bove-mentioned line, may be equal to the areanbsp;^ S j ; then the earth will be found to have movednbsp;^bng the arc A x in the fame compafs of time thatnbsp;naoved along the arc By. But thofe arcs Ax,nbsp;are unequal, Ax being longer than Bj; fornbsp;�^bey are nearly in the inverfe proportion of theirnbsp;^'ftances from the fun S. Hence the apparent mo-*�'00 of the fun along the ecliptic, or the real motionnbsp;the earth in her orbit, as feen from the fun, is notnbsp;^tillable, it being flower in the fummer than in thenbsp;Winter *.

The preceflion of the equinoxes, which has been '^^fcribed above, as an irregularity, according to thenbsp;apparent motion of the celeftial bodies, is eafily ex-Pls-ined on the true theory of the folar fyftem.

The earth has been already defcribed to be an ^'^bate fpheroid, viz. to have a greater quantity ofnbsp;*^^tter accumulated about its equatorial parts, innbsp;�-^ufequence of which thofe equatorial parts, beingnbsp;with greater force both by the fun and thenbsp;are drawn fooner under them than if theynbsp;not fo prominent, by about 20', 18quot;, of

^ * The difference of thofe motions is fuch, as that the fun Jttctimes appears to be even 2� fhorter, or more advanced,

time, or 50',25 of a degree in a twelvemonth The efF��l of this is, that the axis of the earth doesnbsp;not remain cxadly parallel to icfelf, though it retains the fame inclination to the plane of the ecliptic j fo that if at prefent it points towards a certainnbsp;ftar, in about 72 years time it will be found directednbsp;to another point of the heavens, which is to thenbsp;weft of that ftar, and at that rate it will proceed tonbsp;move conftantly weftward, and of courfe it willnbsp;dcfcribe a circle round the pole of the ecliptic, thenbsp;radius of which is equal to the inclination of thenbsp;axis of the earth to the axis of the ecliptic, viz. tonbsp;about 23% 28'. That circle will be accomplifhednbsp;in about 26 thoufand years, at the end of whichnbsp;time the axis of the earth will again be parallelnbsp;to the ficuation, ns, of fig. 2. Plate XXVII.nbsp;In the half of that time, viz. in about 13 thoufandnbsp;years, the, half only of that circle will be accom-plifhed, fo that at the end of 13 thoufand years,nbsp;the axis of the earth will ftand in the fituation of thenbsp;dotted line op.

As the poles, or the axis of the earth, performs the above-mentioned movement, it is evident that thenbsp;folftitial and equinoctial points muft likewife movenbsp;at the fame rate.

This motion is faid to be wejiward, or in antecC' dentia, viz. contrary to the order of the figns}

'''vliereas the other motion, whereby the eatth and the planets are carried round the fun, is eaftward,nbsp;Or in confequentia, meaning in ,the direftion of thenbsp;hgns, viz. from Aries to Taurus, then to Gemini,nbsp;Ca-ncer, amp;c.

In confequence of this motion of the axis of the ^arth, or of the preceffion of the equinoxes, thenbsp;oonftellations which formerly coincided with thenbsp;'Cardinal points of the ecliptic, are now removednbsp;Irom them. Thus the conftellation of Aries, whichnbsp;the time of Hipparchus was near the vernalnbsp;^lt;^uinox, viz. near the interfeiSlion of the equatornbsp;'^'ith the ecliptic, is now removed from it, or ra-^^er that interfeftion is removed from the conftel-lotion of Aries, by about 30�, or nearly a wholenbsp;and in the fame manner are all the othernbsp;^Qnfteliations removed about one Qgn from theirnbsp;fituations j yet the twelve portions of thenbsp;^'^hptic, which are called Dodecatimoria, ftill retainnbsp;^he fame names and charafters which they had atnbsp;*^he time of Hipparchus. Thus the interfeftions ofnbsp;equator and the ecliptic are called the be-�inning of v, and the beginning of =2=: but thenbsp;^onftellations of Aries and Libra are now removednbsp;thofe interfedtions. For the fake of diftinc-the twelve portions of the ecliptic are callednbsp;�^^qjirous figns, viz. figns without ftars; and thenbsp;^Onftcllations themfelves arc called fiarry figns.

What has been explained in this chapter re-fpefting the motion of the earth in her orbit round the fun, is applicable, with very little variation,nbsp;to the motions of the other planets in their relpec-tive orbits, as will be Ihewn hereafter.

Atquot;TER the fun, the moon is by far the moil: fplendid of the celeftial objedls ; and as fuchnbsp;has at all times been diftinguifhed, both by thenbsp;and by the moft civilized nations of the earth,nbsp;revolves round the earth, and of courfe it goesnbsp;^'�^h it round the fun. Its orbit is nearly an ellipfe,nbsp;of whofe foci is within the body of the earth,nbsp;that orbit is fubjedt to confiderable variations;nbsp;^'th refpect to figure, excentricity, amp;c. which arenbsp;ll^^omparably greater than the variations of the or-of the earth, or of the other primary planets,nbsp;arifes from the adlion of the fun upon thenbsp;which fometimes confpires with, and at othernbsp;is contrary to, the earth�s adlion upon thenbsp;Yet thofe apparent irregularities are all con-^^�'ntiable to, and depending upon, the grand lawnbsp;�niverfal attraftion or gravitation. Previous tonbsp;^numeration and illuftrations of the lunar movernbsp;therefrom, it w'ill be proper tonbsp;the body itfelf of the moon as far as it is

known, and its phafes, or various appearances under which it is feen from the earth.

The moon is an opaque body, like apy of the planers; therefore that half of it, which is turnednbsp;towards the fun, is illuminated by it, vvhilft its othernbsp;half receives no light from the fun ; and of its illuminated half, we fee fuch a portion as its fituatiounbsp;in her orbit can admit of.

Vvquot;ere the furface of the moon fmooth and po-liflied like the furface of a looking glafs, the image of the fun, which, in certain fituations, would be fe-fleffed to us, would only appear like a very brightnbsp;point. But the furface of the moon is far from being fmooth, and its inequalities refieft the fun�s lightnbsp;in all dire�lions 5 hence we fee all thofe parts of thatnbsp;furface which are illuminated by the fun, and whichnbsp;are at the fame time within the direflion of outnbsp;, fight.

Even to the naked eye fome of thofe irregularities of the moon�s furface appear like lefs bright or darkifh fpots, which appearance has fuggefted thlt;3nbsp;Vulgar idea of the moon�s having a face with eyesgt;nbsp;amp;c. But when viewed through a telefcope, thsnbsp;furface of the moon appears covered with vaft irregularities, with ridgesy mountains, and pits of inf'nbsp;nite variety j but we can fpeak only of the half 0^nbsp;its furface, viz. of that which is turned towards th^nbsp;earth; for it is remarkable that the moort alwa}'�nbsp;turns nearly the fame fide towards the earth, and 0^nbsp;courfe its other half is quite invifible to us,

I fai*^

1 faid it turns nearly the fame fide ; for.fometimes turns a little more of one fide, and at othernbsp;�^'iTies a little more of the other fide, towards us.

^ his is called the moon�s libration, and is owing to her equable rotation about her own axis once in anbsp;''^lonth, in conjunftion with her unequal motion innbsp;htr orbit round the earth. � For if the moonnbsp;� moved in a circle, whole centre coincided withnbsp;the centre of the earth, and turned round her axisnbsp;m the precife time of her period round the earth,nbsp;the plane of the fiime lunar meridian V�ould al-quot;'ays pafs throush the earthj and the fame face of

towards us. But fince the real motion of the moon is in an orbit nearly elliptical, having the

moon about her axis is equable ; that motion, feen from the earth, mull be unequal; fornbsp;^ ^very rneridian of the moon by its rotation, de-F'ribing angles proportional to the times, thenbsp;plane of no one meridian will confiantlv pafsnbsp;nroiigh the earth. Dr. Gregory, in his Elementsnbsp;lt;c Aftronomy, divides the libration of the moonnbsp;into the following three kinds¹.

� Her libration in longitude, or a feeming |h'^tion to and fro, according to the order of the

moon is in her apogee, and when in her perigee; for in both thefe cafes, the plane of her meridian,nbsp;which is turned towards us, is direded alike towards the earth.�

sdly, Her libraticn in latitude, which arifes from hence, that her axis not being perpendicularnbsp;to the plane of her orbit, but inclined to it, fome-times one of her poles, and fometimes the other willnbsp;nod, as it were, or dip a little towards the earth inbsp;and confequently ftie will fometimes Ihew more ofnbsp;her fpots, and fometimes lefs of them, towards eachnbsp;pole. This libration, depending on the pofition ofnbsp;the moon, in refped to the nodes of her orbit, andnbsp;her axis being nearly perpendicular to the plane ofnbsp;the ecliptic, is properly faid to be in latitude. It isnbsp;completed in the time in which the moon returnsnbsp;again to the fame pofition in refped of hHnbsp;nqdes.�

jdly, � There is alfo a third kind of libration* by which it happens, that although another part ofnbsp;the moon be not really turned to the earth, as in th*^nbsp;former libration, yet another is Illuminated by thenbsp;fun. For, fince the moon�s axis is nearly perpeo'nbsp;dicular to the plane of the ecliptic, when fhe is modnbsp;foutherly, in refped to the north pole of the ecliptic, fome parts near to it will be illuminated by th^nbsp;fun, while, on the contrary, the fouth pole will benbsp;darknefs. In this cafe, therefore, if the fun benbsp;the fame line with the moon�s fouthern limit, theOgt;

'vards her afcending node, fhe will appear to dip her northern polar parts a little into the darknbsp;hemifphere, and to raife her fouthern polar partsnbsp;as much into the light one. And the contrary tonbsp;dais will happen two weeks after, while the moon isnbsp;^efcending from her northern limit; for then hernbsp;Northern polar parts will appear to emerge out ofnbsp;�iarknefs, and the fouthern polar parts to dip into it.nbsp;�^nd this feeming libration, or rather thefe efFeftsnbsp;�f the former libration in latitude, depending on th�nbsp;%ht of the fun, will be completed in the moon�snbsp;^nodical revolution.�

^ince the moon moves round the earth in an orbit '^-arly elliptical, the earth being in one of the foci,nbsp;therefore this opaque globular body muft appearnbsp;^^'�ger or fmaller in proportion as it comes nearernbsp;^0) or goes farther from, the earth j and, in faft, itsnbsp;apparent diameter has been found fometimCs tonbsp;^fafurc as much as 34', and at other times notnbsp;than 2.9', 30quot;. When the moon is at itsnbsp;l^can diftance from the earth, its apparent diameternbsp;31', 8quot;, nearly. Its mean diftance from the earthnbsp;240000 miles, or probably fomewhat llrorternbsp;^han a^oooo miles; hence its diameter is reckonednbsp;to about 2180 nodes ; which is to that of thenbsp;^arth as I to 3,65. Therefore the furface of thenbsp;�fioon is to that of the earth as i to 13,3225 (viz.nbsp;^ the fqu^res of their diameters) ; and the bulk ofnbsp;the moon is to that of the earth as i to 48,627 (viz.nbsp;the cubes of their diameters). But on the fuppo-

I 2 nbsp;nbsp;nbsp;fition

fition that the moon is more denfe than the earth in the proportion of 5 to 4, the quantity of matter innbsp;the moon muft be to the quantity of matter in thenbsp;earth, as 1 to 38,9.

The fpots which are feen on the furface of the moon, are not mere variations pf color, or of lightnbsp;and fhade, but they arife from real inequalities ofnbsp;furface, fuch as mountains, vales, pits, ridges, hollows, amp;c. which is evidently proved by their fha-dows, which they call in due direction, according tonbsp;the fituation of tlie fun, and by the elevated partsnbsp;becoming illuminated by the fun before the lowernbsp;parts.

In every fituation of the moon the elevated parts of its furface caft a Ihadow on the adjoining lowernbsp;, parts in the diredlion from the fun. But the cavitiesnbsp;are dark on the fide of the fun.

When the line, which feparates the light from the fhade on the difc of the moon, is turned towards us,nbsp;we fee it through a telefcope, not as a regular line,nbsp;but notched and full of irregularities, efpecially fomenbsp;fmall bright dots or ridges a little diftant from thenbsp;illuminated part of the difc, which are the tops ofnbsp;mountains and other elevated parts, that are illuminated by the fun, before their lower parts * can receive its rays.

That � * By means of micrometrical meafurements, and propetnbsp;calculations, the heights of the lunar mountains have been

That edge of the moon�s difc, which, by its being *^urned towards the fun, is on the illuminated fide ofnbsp;�b appears always fmooth and well defined, evennbsp;*^^rough very good telefcopes; whereas, confideringnbsp;roughnefs of the moon�s furface, we might perhaps expect to fee it jagged or uneven. But it muftnbsp;be confidered, that all the parts adjoining to thatnbsp;^dge of the moon, are full of irregularities, and thatnbsp;the elevations of fome parts may (land before thenbsp;hollows of other parts, fo as to form upon the wholenbsp;appearance of a fmooth furface. It is probable, however, that the atmofphere of the moonnbsp;contribute to the produflion of an apparentnbsp;htiooth edge.

Some of the fpots, however, of the moon feem to be merely the fliadows of elevated places;nbsp;they have been found to vary a little in in-'�^rifity.

p Accurate inftruments, do not agree with each other. J^rn the lateft and moft: accurate obfervations, it appearsnbsp;the moon has mountains of about 25000 Englifh feet,nbsp;Upwards, in height; viz. much higher than our moun-^ tts. Seg Herfchel�s Paper on the Mountains of the Moon,nbsp;hilofophical Tranfa�ions, volume for 1780 j and Schroe-��t s Work on the Heights of Lunar Mountains.

A bright Ipeck or two, or even three, have fome-times been obferved on the dark part of the moon�s dife, and fo far fiom the illuminated part as not tonbsp;depend upon the fun�s rays, Thofe lucid fpots havenbsp;been conjedured to be the eruptions of volcanoes,nbsp;which after a certain time become extind and dif-appear. Dr. Herfchel in 1787 law three of thofenbsp;Volcanoes at once in the dark part of the moonnbsp;two of which were barely vifible or almoft extind;nbsp;the third was more vivid and exhibited an elongationnbsp;like an eruption or lava of luminous matter, refem-bling a fmall piece of burning charcoal, covered bynbsp;a very thin coat of white afhes *.

If there be fire or combullion in the moon, it feems necelfary that the moon lliould have an at-mofphere j yet, until very lately, it has been generally believed that tire moon had no atmofphere-However, the nicer obfervations of latter timesnbsp;made witli the moft improved inllruments, feem tonbsp;prove that the moon has really an atmofphere, w'hichnbsp;is manifefted by the following fads.

It has been remarked by certain aftronomers, that the moon does not always appear equally bright,nbsp;which may probably be owing to its atmofphere be-,nbsp;ing more or lefs loaded with vapours. It is perhapsnbsp;for the fame reafon that, in total lunar eclipfes, thenbsp;colour of the moon is not always the fame, and that

iti total folar eclipfes, a luminous circle round the has fometimes been obferved. Caffini alTertsnbsp;to have obferved, that Saturn, Jupiter, and the fixednbsp;had their circular figures changed into ellip-ticalj when they approached either the dark or thenbsp;t^luminated edge of the moon j which mav naturallynbsp;attributed to the refraftion of a lunar atmofphere.nbsp;^chroeter obferves, that the two cujp or apexes ofnbsp;luminous horns, in a new moon, appear taperingnbsp;to a very fharp and faint prolongation, which is anbsp;ftrong indication of a lunar atmofphere. He alfonbsp;obferved, that when once Jupiter came very near thenbsp;tvyo of its fatellites appeared indiftin�l for anbsp;^ort time before they went quite behind the body ofnbsp;^^0 moon*.

^f We allow to the moon an atmofphere which, refpeft to denfity, amp;c. bears the fame propor-^*00 to its fize, as our atmofphere does to the fize ofnbsp;earth, we muft conclude that the obfcure partsnbsp;�vvdien viewed from the earth, cannot fubtendnbsp;^0 angle as great as one fecond in addition to the ap-P^^rent fize of the moon j and fuch an atmofpherenbsp;to be perfedlly compatible with the above-^^otioned fafts.

Excepting the above-mentioned fmall variation in ^ intenfity of fome of the fpots of the moon, andnbsp;Volcanic appearances, the reft of the moon�snbsp;�ace is not fubjedl to any perceivable changes;

I 4 nbsp;nbsp;nbsp;hepce

hence aftronomers have had ample opportunity of delineating and of defcribing the irregularities of itsnbsp;furface. In faft, feveral aftronomers have publifhednbsp;the Jeknographia,- OT maps of the face of the moon;nbsp;and fome have given niaps of its appearance in allnbsp;the different dates of the moon, from the day thatnbsp;the new moon becomes vifible until it vanilhes. Innbsp;order to diftinguidi the mountains, or other remarkable fpots of the moon from each other, fomenbsp;aftronomers, as Hevelius, have given them thenbsp;names of known places on the furface of tHe earth;nbsp;whilft others have given them the names of diftin-guilhed perfons, fuch as the names of Plato, Archimedes, amp;c. The beft felenographers are Florentius,nbsp;Langrenus, Hevelius, Grimaldus, Caftlni, Ricciolus,nbsp;and De la Hire. A very good drawing of thenbsp;m.oon�s vifible furface was lately made with greatnbsp;care and attention by a diftinguifhed artift, Johnnbsp;Ruffell, Efq. R. A. an engraving of which willnbsp;probably be fpeedily publifhed.

That the phafes of the moon depend on its fuua-tion relatively to the earth and the fun, has been already briefly mentioned in the preceding pages;nbsp;but it will be necelfary in this place to explain andnbsp;to ilkiftrate them by means of a diagram.

In fig. 4, Plate XXVII, RZ reprefents part of the earth�s orbit, T is the earth. The circlenbsp;ABCDEFH reprefents the moon�s orbit, with thenbsp;moon in different parts of it, S is the fun. Herenbsp;in the ffrft place it muft be obferyed, that in

every

every fituation, that half of the moon, as well as of the earth which is facing the fun, is illuminated bynbsp;whilft the other half is in darknefs. PvIN repre-^^nts the circle which feparates the illuminated fromnbsp;the dark part of the moon. PO (which, confider-the fize of the moon with refpeft to its orbit,nbsp;be taken for a right line) 'reprefents the circlenbsp;''^hich divides that half of the moon, v/hich is viable to us, from that which is not vifible to us ;nbsp;^nd which therefore may be called the circle of

Now it is evident, that when the moon is at A, in oppofition to the fun, its illuminated half isnbsp;^'^rtied entirely towards the earth, or the circle ofnbsp;'^'hon coincides with the terminator of light andnbsp;^^rknefs. In that fituation we fay the moon is ftilltnbsp;in that cafe it fltines all night long ; for the funnbsp;the moon being in oppofition, the one muftnbsp;appear to rife when the latter appears to fet j hencenbsp;nioon is on the meridian at midnight.

^Vhen the moon comes to B, then its illumi'. ^^ted half is not turned entirely to waards the earth ;nbsp;��^'^refore we fee the moon as is reprefented atnbsp;viz. the illuminated part will not be quite cir-

122 nbsp;nbsp;nbsp;Of the Phajes and Motions

When the moon is at C, fo that the elongatm, viz. the angle made at the earth by two lines CTnbsp;and STj drawn from the moon and from the fun tonbsp;the earth, may be a right angle, then the half of it5nbsp;illuminated part is vifible from the earth, viz. thenbsp;moon appears as at c *. In this cafe the moonnbsp;appears to be biJeSted, and is. faid to be at its lafinbsp;quarter, ox in her quadrate aJ-peEt, or quadrature,nbsp;becaufe it then appears to be a quarter of a circlenbsp;removed from the fun, STC being a right angle.

pear to a fpeilator fituated in the heavens above the plane of the moon�s orbit, whereas b is as it appe;\rs to a fpedfa-tor on the earth at T. The fame thing muft be underftoodnbsp;of A and a, C and c, amp;c. and he may eafily render this andnbsp;other phafes familiat to himfelf, by placing a candle at fomenbsp;diftance from himfelf, and holding a ball of any kinddn thenbsp;fingers of one hand, which he may place round his head innbsp;various afpedts. In this cafe the candle reprefents the fun,nbsp;the ball reprefents the moon, and the experimenter reprefentsnbsp;the earth.

* The angle of elongation STL, in every fituation of the moon, is always nearly equal to the angle MLO, the arc ofnbsp;which MO is that part of the moon�s illuminated dife,nbsp;which is vifible to us. Thus, when the moon is at F, produce SL towards X ; then the angles TLP and MLS arenbsp;equal, being both right angles; the vertical angles OLS,nbsp;and PLX are alfo equal; therefore MLO is equal to TLX-But TLX is the external angle of the triangle STL, therefore equal to the angles LST, LTS; and becaufe the funnbsp;is at an immenfe diftance, and the angle LST is exceedingly fmail, therefore S T L is nearly equal to T L X, or tonbsp;MLO.

9 nbsp;nbsp;nbsp;When

When the moon is at D, then, as a fmall part of i�:� illuminated part is turned towards th� earth, wenbsp;it horned as at d. All this time the moon hasnbsp;^een waning or decreafing in the extent of its illu-��^inated part, and it continues to do fo until itnbsp;��Caches the point E, which is called its conjunSiionnbsp;�^ith the fun, they both appearing to be in the famenbsp;point of the ecliptic. In that fituation the darknbsp;part of the moon is entirely turned towards thenbsp;of courfe the moon difappears, and in thatnbsp;^^ate we call it the new moon, becaufe prefei|,tlynbsp;^fter that it begins to make its appearance anew,

. continues to increafe until its full, viz. when Comes again at its cppofition A. When thenbsp;^oon is at F, a fmall part of its illuminated facenbsp;�s turned towards the earth, and we fee it as at fnbsp;as we fav/ it when it Rood at D ; with this difference, however, that when at D, the convex fidenbsp;the luminous part was turned towards the eaft,nbsp;f*tu when at F, that convex fide is turned towardsnbsp;the wefl ; for in both cafes it is turned towards thenbsp;ffOj anddn the firft cafe the moon rifes not long before the fun i whereas in the latter cafe it fets notnbsp;after the fun.

When the moon is at G, viz. again in a quadrate ^fpe�l:, GTS being a right angle, it looks as itnbsp;when it Rood at C, excepting that now the con-�''cx part is turned towards the weft, whereas be-.

it was turned towards the eaft; obferve g. In ^his fituation, viz, when the moon is at G, we commonly

monly fay that it is at its firft quarter. The moon then continues to increafe, fo that at H it looksnbsp;gibbous, as reprefented at h; then full, amp;c.

It muft beVemarked, that when we firft begin to fee the new moon, befides the bright part as at f wenbsp;fee the reft of the moon's difc faintly illuminated i thenbsp;reafon of which is, that in that fituation the greateftnbsp;portion of the earth�s illuminated half is turned towards the moon ; fo that the earth performs thenbsp;fame office to the moon as the moon does to us;nbsp;and much more fo ; for the earth appears about 15nbsp;times bigger to a fpeftator in the moon, ,than thenbsp;moon appears to us j therefore the earth refledts anbsp;great deal more of the fun�s light upon the moon,nbsp;than the moon reflefts upon the earth. By infpeft-ing fig. 4, it will be clearly perceived, that thenbsp;earth prefents the fame phafes to the moon, as thenbsp;latter does to us; it being full,to the moon when thenbsp;moon is new to us ; new to the moon when thenbsp;moon is full to us, he.

The pofition of the moon�s cufps, or a right line touching the points of her horns, is alv/ays perpendicular to the ecliptic, but is differently inclined tonbsp;the horizon at different times of the fame day¹nbsp;Sometimes that line is perpendicular to the horizon�nbsp;and then the moon is faid to be in her nonageftm^^

The moon, the earth, and the other planets, being ^paqiie bodies, muft neceffarily call a fliadow on thenbsp;fide oppofite to the fun; and as every one of thenbsp;planets is fmaller than the fun, that fhadow muft;nbsp;^''idently be conical. Now the earth�s conicalnbsp;Ifiadow is longer than the diftance T A of thenbsp;*^000; and the fliadow of the moon, though fhorternbsp;that of the earth, is likewife longer than 'thenbsp;fiaid diftance; therefore, when the moon is at E, viz.nbsp;fi^tween the fun and the earth, its fliadow muft fallnbsp;^Poii part of the earth�s furface (it cannot cover anbsp;quot;'hole lieniifphere, becaufe the moon is muchnbsp;fi�T^aller than the earth) j during whicli time thenbsp;'�^habitants of that part of the earth lofe fight of thenbsp;and this is called an eolipje .of the fun.' A fpec-in the moon would at the fame time fee anbsp;*'^und fpot pafs over the illuminated difc of thenbsp;^arth.

^Ten the moon is at A, then the earth is be-it and the fun, in confequence of which the Ifiadow of the earth covers the whole difc of thenbsp;a.-id this is called an eclif/e of the moon. At

^ then cut by the ecliptic. This never happens when the is on the meridian, except when (he is at the very be-^�^ning of Cancer, or Capricorn. The meaning of this notenbsp;dl be illuftrated by the defeription of the movements of th?nbsp;which will be found in the fubfequent part of the pre-chapter.

the fame time, a fpe(flator in the moon would lofe fight of the fun*. By infpe(51ing fig. 4, it willnbsp;be clearly perceived that an eclipfe of the fun cannbsp;only happen at the time of the new moon, and annbsp;eclipfe of the moon can only happen at the timenbsp;of full moon. Here it may be naturally afkednbsp;why does not an eclipfe of the fun take placenbsp;at every new moon, viz. at every conjunftionnbsp;of the fun and moon ; as alfo why does not annbsp;eclipfe of the moon take place at every full moon,nbsp;viz. at every oppofition ? The anfwer to thisnbsp;queftion is, that the moon, either at the con-jundion or oppofition, feldom paffes acrofs thenbsp;line which joins the centres of the fun and of thenbsp;earth, but generally goes either below or above thatnbsp;line j often however the moon paffes, not with itsnbsp;centre, but with fome other part of its body, acrofsnbsp;that line, and then the eclipfes are not total but far'nbsp;tial, viz. a part only of the fun�s dife, or of thenbsp;moon�s dife, is eclipfed; but the particulars whichnbsp;relate to the time, duration, and quantity of eclipfe�,nbsp;will be examined after the explanation of the moon�snbsp;movements.

� The (hadow of the moon upon the earth, in a fol*'' �eclipfe, is always circular, and the edge of the (hadow of th�nbsp;earth on the moon is always a circular arch, which is anothernbsp;ftrong proof of botli. the moon�s and the earth�s beiiijr crloba-

The

The moon moves along its whole orbit round the �3rth from the weft towards the eaft, at a mean, innbsp;2'7 days, 7 hours, 43', 5'', which compafs of tinae isnbsp;balled a periodical month, or revolution; but thenbsp;^oon, in going from one conjundtion to the next,nbsp;fttiploys a longer time, viz. 29 days, 12 hours,nbsp;44' 3quot;, which time is called a Jynodical month, or anbsp;^^lt;nation. For whilft the moon in its proper orbitnbsp;finiihes its courfe, the earth, together with thenbsp;�^oon and its orbit, are going on their way roundnbsp;fun, and are advanced almoft a whole fign of thenbsp;Ecliptic towards the eaft; fo that the point of thenbsp;*^'Oon�s orbit, which in the former pofition wasnbsp;placed in a right line joining the centres of the earthnbsp;^tgt;d the fun, is now more wefterly than the fun;nbsp;'I'crefore, when the moon has again arrived to thatnbsp;P'^int, it will not yet be feen in conjundtion withnbsp;fun.

Its conjundlion whth the fun; for the accom-Plifiiment of which conjundtion, the moon muft,go

over the arch IM, and fomething more; for whilft the moon is moving along that arc, the earth contiquot;-nues to move on in her orbit. Upon the whole thenbsp;moon performs a fynodical revolution, or whole lunation, (viz. from new moon to new moon) in 29nbsp;days, 12 hours, and 44' 3') being 2 day?, 5 hours,nbsp;and 58 feconds, longer than her mean periodicalnbsp;month

The arc T t, which the earth performs whilft the moon goes from one conjundion with the fun to thenbsp;next conjunftion, is fimildr to the arc /M ; for TSnbsp;being parallel to tl, the angles / ST, and St I, arenbsp;equal; then fince thofe angles are at the centres ofnbsp;the arcs iT and /M, it follows that thofe arcs mufonbsp;be fimilar. Every day the moon .appears to recedenbsp;from the fun by about 12 degrees and fome minutes:nbsp;this is called the diurnal motion of the moon from thenbsp;fun.

The orbit of the moon is not in the fame plane with the orbit of the earth, viz. in the plane of^nbsp;the ecliptic, but is inclined to it at an angle of

� The above-mentioned mean periodical month is the revolution from a fixed point, with reliredi to the equinoxes, and to the fame point again ; but on account of the preceflionnbsp;of the equinoxes, the mean periodical month with refpedl tonbsp;the fixed ftars, viz. the time employed by the moon in goingnbsp;from a given fixed fiar, all round the earth, and again tonbsp;fame liar, is a little longer J viz. it is 27 days, 7 hours,nbsp;40', and 12quot;.

�bout

'3ut 5�; and thofe two planes cut each other in a line, which pafTes through the centre of thenbsp;^^rth ; therefore the centre of the moon cannot benbsp;^^en to coincide with the ecliptic, excepting in thenbsp;^^''0 points at the extremities of the faid right line,nbsp;''�here the two circles interfeft each other. Thofenbsp;' points of interfedlion are called the nodes^nbsp;has been faid of the planets) one of which .Isnbsp;^^lled the ajcending node, or the dragon s bead, and isnbsp;^^rked a ; beyond this node the moon moves alongnbsp;half of its orbit which is on the north fide ofnbsp;ecliptic. The other point of interfeftion is callednbsp;defending node, or the dragon's tail, and is mark-�. Beyond this node, and until it reaches thenbsp;^endino- node, the moon moves along the fouthern

fough the centre of the earth, and joins the two is called the line of nodes. Now it is to benbsp;l^^iTiarked that thofe nodes are not conftantly in thenbsp;^0 place ; or, which is the fame thing, the moon�snbsp;does not confiantly interfedl the ecliptic in thenbsp;points �, fo that the line of nodes continuallynbsp;^oves from the eaft towards the weft, contrary tonbsp;diredtion of the figns of the ecliptic j therefore,nbsp;moon be obferved to crofs the ecliptic at anynbsp;^^fticular place, at the next lunation it will benbsp;. ^'^d to crofs ,the ecliptic at another place, whichnbsp;^ little weftward of the former. By this conti-fhifting from the eaft towards the weft, the linenbsp;^odcs performs the whole revolution in the com-

pafs of about i8 years, 228''. 5''.; after which time the nodes return to the fame points of the ecliptic.

It is et�ident that the centre of the moon is farther from the ecliptic, according as it is farther from thenbsp;nodes. The points of her orbit, which are fartheftnbsp;from the ecliptic, and which are called the limits,nbsp;mult evidently be equidiftant from the nodes. Thenbsp;above-mentioned diftance of the moon from thenbsp;ecliptic, when flie is in different parts of her orbit,nbsp;and which does not exceed 5� 18'6quot;, is called thenbsp;moon�s latitude j for the latitude of a celeftial ob-jeft is its angular diftance from the ecliptic, .and i-snbsp;meafured by an arc of a circle drawn through thenbsp;moon, and perpendicular to the ecliptic.

This deicription of the mooffs motion in her orbit, the inclination of that orbit to the ecliptic,nbsp;and the retrogradation of the nodes, naturally fheWnbsp;why are the eclipfes both of the fun and of the moon,nbsp;fometimes partial, and at other times total, whynbsp;they do not take place at every new and full moon;nbsp;and laftly, why the eclipfes return very nearly in thenbsp;fame order after about every 19 years.

Thus, for the fake of perfpicuity, we hav� de-feribed what relates to the inclination of the moon�s orbit to the ecliptic in a general manner j butnbsp;there are feveral irregularities to be noticed with tC'nbsp;fpect to the inclination and the flaape of that orbit�nbsp;as alfo to the motion of the moon in it.

Upon the whole, the fhape of that orbit is cllip' deal, or nearly fo, as in fig. 6, Plate XXVTI. with

earth at T in one of its foci. AP is the greater and is likewife the line of the apfides, or thenbsp;of the moon�s neareft and greateft diftance fromnbsp;earth. A is the highejl apfis, and is called thenbsp;^Pogeon, or apogee, where the moon is fartheft fromnbsp;earth. P is the lowejl apfis, and is called thenbsp;P^^igeon, or perigee, where the moon is neareft to thenbsp;^^tth. T C is the excentricuy.

^e fhall exprefs the principal irregularities in the following feven paragraphs.

ift. The line of the apfides has been obferved to l^^Ve an angular motion round the earth from thenbsp;towards the eaft, or in the dire�lion of the llgnsnbsp;the ecliptic, but not always conftantly fo j viz.nbsp;apogee of the moon�s orbit, when Ihe is in thenbsp;fy^ygies, goes forward, with refpedl to the fixednbsp;at the rate of 23' each day, and backwardsnbsp;the quadratures by 16' 20quot; per day; thereforenbsp;mean annual motion is 40�; hence it performsnbsp;J-he whole circle, and returns to the fame fituation,nbsp;the fpace of almoft nine years*.

2diy. When the earth (and of courfe the mooa is in the aphelion, the moon�s motion is fome-j^hat quicker than when the earth, amp;c. is in perihe-hence the periodical months of the moon arenbsp;t^tnewhat Ihorter in the former cafe than in the latter.nbsp;3dly. When the moon is in the fyzygies, then,

* De la Lande ftates the tropical revolution of � J lee at 8r. oxxL 8L 34'. ST�- the Mereal revdution atnbsp;3t2.k ii\ IJ'. 39'-, and the diurnal motion at 6.4� gt; _ _

K a

cateris paribus, flie moves round the earth quicker than when flie is in the quadratures. For its gravitynbsp;towards the earth is, by the aftion of the fun, in-creafed in the latter cafe, and diminifhed in tirenbsp;former j fo that from the conjundion to her firftnbsp;quadrature, the gravity of the moon towards thenbsp;earth is continually increafed, and Ihe flackens anbsp;little its motion; from that quadrature to the oppo-fition, her gravity towards the earth is gradually diminifhed, and fhe keeps increafing her motion }nbsp;from the oppofition to the other quadrature, hernbsp;gravity increafes again, and her motion is againnbsp;gradually diminilhed; and laftly, from that quadrature to the conjunction, that gravity is graduallynbsp;diminifhed, and that motion is again gradually in-creafed*. The moon is more didant from thenbsp;earth at the quadratures than at the oppofition to,nbsp;or at the conjunction with, the fun.

4thly. Eefides the above-mentioned caufe, the-unequable motion of the moon in her orbit arifes alfo from the elliptical figure of that orbit, whichnbsp;has the earth in one of its foci �, for as the moonnbsp;miift defcribe equal areas in equal times, round thenbsp;earth, (in the fame manner as the planets have beennbsp;faid to defcribe round the fun), it evidently follows/nbsp;that ceteris paribus, the moon muft move quickernbsp;m her perigeon than in her apogcon.

� * The famous Tycho Brahe, who firft difcovered this in' equality in the moou�s motion, called it the, moon's variation-

^thiy�

Stiily. The orbit icfdf of the moon undergoes '^^rious changes during every revolution; fo that itsnbsp;^xcentricity is continually increafing and decreafihg.nbsp;It is greateft when the line of the apfides coincidesnbsp;^''ith the fyzygia, and leaft when the line of the ap-fides coincides with the quadratures. The differ*-^^ce is fb great as to exceed the half of the leaft ex-^^ntricity.

6thly. The nodes of the moon�s orbit move very ��^'quot;fgularly; fo that the line of nodes fucceiTively acquires all forts of fituation with refpetft: to the fun ;

in the courfe of every year it paffes twice *^urough the fyzygies, and twice through the qua-dratures. During one whole revolution of thenbsp;the nodes go back from eaft to weft withnbsp;*^unfi(ie[-able quicknefs when they are in the qua-dfatures; but having paffed thofe points, they gradually Hacken their motion, and are quite at reftnbsp;'^^en they come to be in the fame direftion with thqnbsp;^^^ygies.

7th]y. inclination-of the plane of the moon�s to- the ecliptic (which has been faid to makenbsp;general an angle of 5�) varies by feveral minutes,nbsp;ud is greateft when the moon is in the quadratures^nbsp;,^d leaft when fhe is in her oppofition or conjunc-^un.nbsp;nbsp;nbsp;nbsp;above-mentioned inclination alfo in-

and is at its maximum, when the nodes .nbsp;nbsp;nbsp;nbsp;lyzygies; but the inclination dimt-

us as the line of nodes has paffed the fyzy-� and is at its minimum when that line coin-

K 3 nbsp;nbsp;nbsp;^ cidcs

cides with the quadratures. Upon the whole, it feems that the inclination of that orbit to the eclip'nbsp;tic is at the leaft about 5'�, and at the moft aboutnbsp;5� 18' 6quot;.

All the irregularities of the moon�s motions arc rather lefs in her oppofition than in her con-junftion.

Thofe which we have called irregularities of the moon�s motion, arc fo far from being real errors ornbsp;defefts, that they are the juft and natural confe-quence of that grand law of nature, the univcrfalnbsp;and mutual gravitation of matter; and the worksnbsp;of nature would be truly defedlive if the above-mentioned apparent irregularities were not foundnbsp;to exift, as has been abundantly demonftrated b/nbsp;the great Newton. What renders the calculationnbsp;of the moon�s influence, motions, and ficuations, atnbsp;different times, extremely intricate and perplexing?nbsp;is the difflcuky of determining the quantities of thofenbsp;forces which adl upon the moon, and upon whichnbsp;the theoretical calculations are eftablifhed. Thenbsp;quantities of thofe forces muft be deduced fromnbsp;their effedts, viz. from obfervations; and thofe ob-fervations require exadt inftruments, and diligentnbsp;obfervers. In fadl, it is owing to the induftry 0^nbsp;late and prefent aftronomers, as alfb to the mechani'nbsp;cal and mathematical improvements of the fhort pe'nbsp;riod which has elapfed fince Newton�s time, tha*-the tables of the lunar motions have been brough*-to

fo a wonderful degree of accuracy, and that they are daily receiving farther correftions.

The only equal motion of the moon, is its revo-^Ution round irs axis, which, either in part or in all, performed exaftly in the fame time, in which Ihenbsp;P^tforms her revolution in her orbit round thenbsp;^^I'th ; hence flie always prefents the lame half ofnbsp;furface to us, whilft its other half is never feennbsp;^ us; yet on account of the moon�s orbit beingnbsp;^^dptical and not circular, as alfo on account of thenbsp;^^clination of that orbit to the ecliptic, we can atnbsp;hrnes fee part of that half of the moon, which, innbsp;general, is not vlfible to us ; and this is the librationnbsp;the moon, as has been mentioned in the precedes pages.

�t follows from the above-mentioned rotation of moon round her axis, that in the compafs of onenbsp;year we inhabitants of the earth have nearly 365 Inbsp;d^ys, whereas the inhabitants of the moon, if therenbsp;any, have only about 12 tV days j every one ofnbsp;days being equal to about 29 | of our days.nbsp;From obfervations carefully made on the fpots ofnbsp;moon, and from proper calculation, it has beennbsp;determined that the axis of the moon is inclined to thenbsp;^'^^'Ptic at an angle of 88� 17' very nearly *,

Caffini found that the nndes of the moon�s equator 2ree with the mean place of the nodes of its orbit; there-r

The

The above-mentioned apparent irregularities of the moon�s motion produce feveral remarkablenbsp;phenomena, with refpe�; to the moon�s rifing to itsnbsp;fetting, and to its continuance above the horizon ofnbsp;thofe places which are not under the equator. T wonbsp;of thofe phenomena have obtained peculiar appellations, viz. the harvef moony and the hunter's moon.

It has been mentioned in the preceding pages, that the moon appears to recede from the fun at the dailynbsp;rate ofabout 12� and feme minutes j but it dees notnbsp;follow that the moon muft rife every day later by 3nbsp;proportionate length of time, viz. by about 50 minutes of time} for, on account of the different anglesnbsp;made by the horizon and different parts of thenbsp;moon�s ,orbit, this retardation differs confiderably innbsp;places of high latitude, and it is only equable ornbsp;nearly fo, with refpedl to places fituated under thenbsp;equator. The caufe of thofe phenomena is clearlynbsp;and familiarly explained by Mr. Fergufon, in thenbsp;16th chapter of his aftronomy, from which I fliallnbsp;make the following abridgement.

The plane of the equinofliial is perpendicular to the earth�s axis; and therefore, as the earth turnsnbsp;round its axis, all parts of the equinodial make equainbsp;angles with the horizon, both at rifing and at fetting�nbsp;fo that equal portions of it always rife or fet in equalnbsp;times, Confequently, if the moon�s motion wet^nbsp;equable and in the equinodial, at the rate of ia� i ^nbsp;from the fun every day, as it is in her orbit, fire w'oult^nbsp;rife and fet 50 minutes later every day than on th^

preceding day; for la� ii' of the equinoctial rife or ^ec in 50' of time in all latitudes.

But the moon�s motion is fo nearly in the ecliptic, *^hat we may confider her at preftnt as moving in it.nbsp;^ow the different parts of the ecliptic, on accountnbsp;its obliquity to the earth�s axis, make very differ- ^nbsp;angles with the horizon; and in equal times,nbsp;'''henever this angle is leaft, a greater portion of thenbsp;Ecliptic rifes than when the angle is I '.rger, as maynbsp;eafily perceived by looking at a common celeftialnbsp;Eiobe. Thus in fig. 7 and 8, Plate XXV'II. L re-Prefents the latitude of London, AB is the horizon,

^ P the axis of the world, E e the equator, K k ecliptic. Now, on account of the oblique po-^�tion of the fphere in the latitude of London, thenbsp;^^iiptic has a high elevation above the horizon,nbsp;quot;taking the angle AUK of about 73� f, as repre,nbsp;^^nted in fig. 7, when the fign of Cancer is uponnbsp;meridian, at which time Libra rifes in the eaft.nbsp;when the other part of the ecliptic is above thenbsp;^'^rizon, viz. when the fign of Capricorn is upon _nbsp;*ke meridian, and Aries rifes in the eaff, then thenbsp;Ecliptic will make v/ith the horizon the much fmallernbsp;A, as reprefented in fig. 8, which angle isnbsp;about 26� that is 47 degrees fmaller than thenbsp;former angle. And by infpefting thofe figures, it maynbsp;eafily conceived that, as the celeftial fphere appearsnbsp;^0 turn round the axis FP in a given portion of time,nbsp;for inftance, three or four hours, a greater portionnbsp;�f the ecliptic will rife during that time, when the

ecliptic is in the fituation of fig. 8, than when it is in the fituation of fig, 7.

In northern latitude.s, the finalleft angle made by the ecliptic and horizon is when Aries rifes, at whichnbsp;time Libra fets; the greatefl; when Libra riles, atnbsp;which time Aries fets. From the rifing of Ariesnbsp;to the rifing of Libra (which is 12 fidereal hours)nbsp;the angle increafcs; and from the rifing of Libra tonbsp;the rifing of Aries , decreafes in the. fame proportion ; hence it appears that the ecliptic rifes fafteftnbsp;about Aries, and floweft about Libra.

On the parallel of London, as much of the ecliptic rifes about Pifces and Aries in two hours, as thenbsp;moon goes through in fix days; therefore, whilftnbsp;the moon is in thefe figns, fhe dilFers but two hoursnbsp;in rifing for fix days together j that is about 20'laternbsp;every day or right than on the preceding, at a meannbsp;rate. But in 14 days afterwards, the moon comesnbsp;to Virgo and Libra, which are the oppofite figns tonbsp;Pifces and Aries; and then Ihe differs almoft fournbsp;times as much in rifing j namely, one hour andnbsp;about 15' later every day or night than the preceding, whilft fil� is in thefe figns. As the figns, Taurus,nbsp;Gemini, Cancer, Leo, Virgo, and Libra, rife fuc-celTively, the angle of the ecliptic with the horizonnbsp;increafes gradually j and decreafes in the fame proportion as thty fet J and for that reafon, the moonnbsp;differs gradually more in the time of her rifing everynbsp;day whilft fire is in thefe figns, and lefs in her fetting^nbsp;aifter which, through the other fix figns, viz. Scor-

Sagittary, Capricorn, Aquarius, Pifces, and �^ries, the rifing difference becomes lefs every day,nbsp;^ntil it be at the ieaft of all, namely, in Pifces andnbsp;�^ries.

The moon goes round the ecliptic in about 27 and 8 hours ; bur not from change to changenbsp;lefs than about 29 days and 12 hours; fo that fhenbsp;in Pifces and Aries at lead once in every luna-and in fome lunations twice.

If the earth had no annual motion, the fun would ^^ver appear to (hifc his place in the ecliptic ; andnbsp;then every new moon would fall in the fame fignnbsp;3nd degree of the ecliptic, and every full moon innbsp;t'te oppofite j for the moon v^^ould go preciielynbsp;thund the ecliptic from change to change. So thatnbsp;the moon was once full in Pifces or Aries, flicnbsp;'�''Quid always be full when flie came round to thenbsp;fame fign and degree again. And hs the full moonnbsp;*'tfes at fun-fet (becaufc when any point of thenbsp;^clipjJc fets, the oppofite point rifes) Ibe would con-ftantly rife within two hours of fan fet, on the pa-f^hel of London, during the week in which (henbsp;full. But in the time that the moon goesnbsp;�quot;t^tind the ecliptic from any conjunction or oppofi-the- earth goes almoft a figij forward ; andnbsp;'�^erefore the fun will feem to go as far forward innbsp;time, namely, 27� i i fo that the moon muffnbsp;27� ! more than round, and as much farther as

^ lun advances in that interva.!, which is 2�-rV� ^ ore fhe can be in conjunction wkh, or oppofite

to, the fun again. Hence it is evident, that there can be but one conjundtion or oppofition of the funnbsp;and nnoon in a year in any particular part of thenbsp;ecliptic. This may be familiarly exemplified by thenbsp;hour and minute hands of a watch, which are nevernbsp;in conjundlion or oppofition in that part of the dial--plate where they were fo laft before.

As the moon can never be full but when fhe is oppofite to the fun, and the fun is never in Virgonbsp;and. Libra, but in our autumnal months, it is plainnbsp;that the moon is never full in the 'oppofite figns,nbsp;Pifces and Aries, but in thefe two months. Andnbsp;therefore we can have only two full moons in thenbsp;year, which rife fo near the time of fun-fet for anbsp;week together, as has been mentioned above. Thenbsp;former of thefe is called the harvejl moon, and thenbsp;latter the hunter's moon.

When the moon is in Pifces and Aries, it min^ rife with nearly the fame difference of time in every*nbsp;revolution through her orbit, which is exadly thenbsp;phenomenon of the harveft moon; but it paffes un-obferved, becaufe in winter thofe figns rife at noon/nbsp;and, being then only a quarter of a circle diftantnbsp;from the fun, the moon in them is in her firft quarter, and rifes at �bout noon, at which time her rifingnbsp;is not noticed. In fpring thofe figns rife with thenbsp;fun, for the fiin is in them, confequently the moonnbsp;being in them too, is in conjundlion with the funinbsp;and therefore its rifing is invifible. In fumnaernbsp;thofe figtis rife at about midnight, and the fun is

three figns, or about 90� before them ; therefore the '^oon in them muft be in her third quarter,nbsp;�'�vhen it giv^s little light, and rifes late, on whichnbsp;�^coi.ints the phenomenon of her rifing for forncnbsp;�^'ghts with, little difference Of time, paffes unno-^'^ed. In autumn, however, the cafe is different inbsp;the figns of Pifces and Aries then rife at aboutnbsp;^^n-fet, and therefore the moon being in them, isnbsp;oppofition to the fun, confequently full, and rifesnbsp;great fplendour when the fun fets, and feems tonbsp;Prolong the day for the advantage of the hufband-at about the harveft time.

In northern latitudes, the autumnal full moons in Pifces' and Aries ; and the vernal full moonsnbsp;Virgo and Libra. In fouthern latitudes, juft thenbsp;*^^''erfe, becaufe the fealbns are contrary. Butnbsp;^�rgo and Libra rife at as fmall angles with thenbsp;l^ririzon in fouthern latitudes, as Pifces and Aries donbsp;the northern; and therefore the harveft moonsnbsp;juft as regular on one fide of the equator as on,nbsp;other.

thefe figns, which rife with the leaft angle, with the greateft, the vernal full moons differ asnbsp;*^rich in their times of rifing every night, as the au-full moons differ in their times of fetcing ;nbsp;fee Yvith as little difference as the autumnal ftillnbsp;^oons rife; the one being in all cafes the reverfenbsp;tire other.

hitherto, with refpeift to thefe phenomena, we fuppofed that the moon�s orbit coincided with

the plane of the ecliptic; but fince her orbit make* with it an angle varying from f to 5� 18'', and crotTesnbsp;it only in the nodes, therefore her rifing when if'nbsp;Pifccs and Aries, will Ibmetimes not differ abovenbsp;one hour and 40' through the whole of the fevennbsp;days; and at other times, when in the fame twonbsp;figns, the time of her rifing, in the courfe of a weeknbsp;will differ full 3 \ hours, according to the differentnbsp;pofitions of the nodes with refpeft to thofe figns inbsp;which pofitions are conftantly changing, the nodesnbsp;going backward through the whole ecliptic if*nbsp;about 18 years and 228 days. This revolution ofnbsp;tfie nodes will caufe the harvefl moons to go throughnbsp;a whole courle of the mofl and leaft beneficialnbsp;ftates, v/ith refped to the harvefl in about 19 years-The following Tijble fhews in what years the harveflnbsp;moons are mofl or leafl beneficial, from the yearnbsp;1800 to 1861 : the columns of years under thenbsp;lefer L, are thofe in which the harvefl: moons arenbsp;leaft beneficial; thofe marked M, fliew when the/nbsp;are the mofl: beneficial; the former falling neareftnbsp;the defeending node, the latter neareft the afeend'nbsp;inn node

Harvefl

� At the polar circles, when the fun touches the ^'ipmer tropic, he continues 24 hours above thenbsp;^'^fizon j and 24 hours below it, when he touchesnbsp;winter tropic. For the fame reafon the fullnbsp;'^��Oon neither rifes in fummer, nor lets in winter,nbsp;'^onfidering her as moving in the ecliptic. For thenbsp;quot;'quot;Iter full moon being as high in the ecliptic as thenbsp;'^rner fun, mull therefore continue as long abovenbsp;horizon and^ tlie fummer full moon being asnbsp;, m the ecliptic as the winter fun, can no morenbsp;than he does. But thefe are only the two fullnbsp;^tgt;ons which happen about the tropics 5 for all thenbsp;^^fiers rife and fet. In fummer the full moons arenbsp;gt; and their ftay is fhort above the horizon, whennbsp;nights are ihorr, and we have leaf!: occafion fornbsp;'^n-light: in winter they go high, and Hay long

above the horizon., when the nfehts are lona:, anc� we want the greatefl; quantity of moon light¹.�

I Ihall conclude this chapter with a Ihort ac- ' count of the fingular appearance of what is called-the horizontal moony and horizontalfun.

In the firft place it mull be remarked, that both the fun and the moon, when they are near the horizon, appear not quite round, but a little oval, thenbsp;longefb axis being parallel to the horizon. Thisnbsp;arifes from the difterept refradfive power of the at-mofphere at different elevations, in confequence ofnbsp;which the lowermoft liiiib of the fun, (and the famenbsp;muff be underftood of the moon) appears more ek'nbsp;vated than the tipper limb j hence the vertical diameter is lltortened a little, whilft the horizontalnbsp;diameter remains unaltered.

But the moft fingular phenomenon is, that both , the fun and the moon, when near the horizon, ap'nbsp;pear to the naked eye much larger than when the/nbsp;are higher up or upon the meridian, which enlarget^ �nbsp;appearance muff undoubtedly be an optical decep'nbsp;tion; for if the diameter both' of the fun and th^nbsp;moon be meafured by means of proper inftruments�nbsp;fuch as a quadrant, a micrometer, amp;c. they willnbsp;found to be fmaller in the former than in the latternbsp;fituation, which is as it ought to be; becaule whe¹^nbsp;they are upon the horizon, thofe celeftial objelt;d¹nbsp;are evidently farther from us by the femi-diaruc�^^''

off when near the horizon ; therefore, in that We alfo conceive it to be a much larger objed;nbsp;�� two unequal objects that fubtend the famenbsp;at the eye, the largeft muff neceffarily be thenbsp;diftant. But upon this principle it fliouldnbsp;that, whenever the moon, or the fun, at a highnbsp;. '^^tion, happens to be rendered indiftind by thenbsp;j quot;^�'pofition of vapours, amp;c. it ought to appear asnbsp;*'�e as it does near the horizon, which does not feemnbsp;the fad.

^ -Another hypothefis is, that the lower part of the Patent celeftial hemifphere feems to us larger

than the higher part of it; for inftance, if we guefs at the altitude of a celeftial object we always conceivenbsp;it to make a greater angle with the horizon, or to benbsp;more elevated than it really is j therefore any portion of that lower part of the hemifphere, or of anynbsp;body in it, appears larger than when the fame isnbsp;higher up. But then one may naturally alk, whatnbsp;makes us conceive the lower parts of the apparentnbsp;celeftial hemifphere to be larger than thofe which arenbsp;higher up * ?

? On this fubjeft the reader may confult Dr. Wallis�� Works, Des Cartesls Works, Dr. Defagulier�s Philofophy?nbsp;Rowning�s Philofophy, Dr. Smith�s Optics, Dr. Prieftley��nbsp;Hiftory of Light, amp;c. Fergufon�s Aftronomy, and almoflnbsp;all the modern Writers on Aftronomy,

flowing of the fea, viz. of its alternately rifing falling on the Ihores of moft countries ; and thenbsp;'^^�^nedtion which feemcd to exift between thofe phe-''^^ena and the movements of the moon, has beennbsp;^^�^arked and is mentioned by the writers of greatnbsp;^''bquify gyj jj ^^5 Kepler who firft Ihewed thatnbsp;�^ttratiion of the moon was the real caufe of it.nbsp;^''^ton, in a mafterly manner, enlarged and de-'^'quot;''ftrated the various parts of the fame theory,nbsp;has alfo received farther correftions and im-'^^nfients from the obfervations and calculationsnbsp;^hfequent philofophers.

'^ery day, a Ihort time after the moon�s paffage meridian, the waters of the ocean are feen

gradually fubfide, until about fix hours after they are at the loweft, which is called the tide of ebb.nbsp;They then gradually rife again, and ,make anothernbsp;tide of flood, or are at their higheft a fliort timenbsp;after the moon has paflTed the inferior part of thenbsp;meridian. After that, the waters ebb again, and fonbsp;forth. The earth by its daily rotation round itsnbsp;axis goes from the moon to the moon again (or thenbsp;moon appears to move round the earth from a givennbsp;meridian to the fame again) in about 24 hours andnbsp;50'; hence in that period there are two tides of floodnbsp;and two of ebb.

The tides are more confiderable about a day and a half after the new, or the full, moon. They are,nbsp;ceteris paribusy alfo greater when the moon is in hernbsp;perigee than in her apagee; and likewife highernbsp;about the equinoxes; fo that the higheft tides arenbsp;obferved when the above-mentioned three circurfl'nbsp;ftances .take place at the fame time, viz. when thenbsp;moon is either new or full, at the fame time thatnbsp;it is in her perigee, and about the time of thenbsp;equinoxes,

Thofe, and other lefs confiderable, phenomena relative to the tides, are eafily fhown to depend onnbsp;the attradlions and pefitions both of the fun and thenbsp;moon, but principally of the moon ; for though thenbsp;fun is immenfely larger than the moon, yet as he 'Snbsp;vaftly more diftant, and the attradtion decreafes in'nbsp;verfely as the fquares ofthe diftances, it follows thatnbsp;the effeft of the moon�s attraftion on the waters

fea, is much more conficierable than that of the fun�s attraftion. At a mean, that of the formernbsp;teckoned to be to that of the latter, as 5

It is evident, that if three or m.ore bodies, be at different diftances from the moon, the neareft ofnbsp;^Igt;etn will be attradled more forcibly than that whichnbsp;3- little farther off; this more forcibly than thenbsp;^^^t, and fo on. After the fame manner it muft benbsp;'�Unfidered that the attradlion of the moon towards

different parts of the earth is not exadly the ; becaufe thofe various parts are not equallynbsp;'^�ftant from it. Thus, in fig. q, Plate XXVII.nbsp;Here

t'ot greater than the force wherewith the folid f^tts of the earth adhere to each other, therefore itnbsp;not produce any derangement of figure among

150 nbsp;nbsp;nbsp;Of the Tides, (Jc.

it more than the waters at D and E, which, as alio the centre B, are equidiftant from the moon; there'nbsp;fore the diltance BA muft become greater than thenbsp;diftance BD, or its equal BE. Alfo the partsnbsp;D, B, and E, being attrafted with greater forcenbsp;than the more diftant waters at C j it follows, that thenbsp;diftance BC muft likewifc become greater thannbsp;or BE} hence it appears that the waters which foC'nbsp;round the earth, muft form, (as far as the fituation^nbsp;of continents, iftands, amp;c. will permit) an oblong'nbsp;or oval, or fpheroidical figure, whofe greater axisnbsp;ac m the diredtion of the moon M, and wholenbsp;fhorter axis is ^1?.

The orbit of the moon being elliptical, having the earth in one of its foci, it follows, that thenbsp;moon�s diftance from tire earth varies conuderably�nbsp;and of courfe its attradtion muft vary accordingly �nbsp;hence the tides are more confiderable when th^nbsp;moon is in her perigee, and lefs fo in her apogee.

The actradlion of the fun produces a fiinil^^ elongation of the fluid which furrounds this gloflc'nbsp;but, as has been mentioned above, not near fo co'^'nbsp;fiderable as that which is produced by the moo'�'nbsp;The effedl is likewife greater when the fun is nea^^^nbsp;to the earth, as in the winter time, than when he **nbsp;farther from it, as in the fummer.time.

It will be readily underftood, that, according the different ficuations of the fun, and the moon,nbsp;tides which are raifed by their refpedtivc attradtio^^'nbsp;will either confpire with, or counieradl:, each oth^''^

a greater or leffer degree. Thus in fig. i, Plate ^XVlII. T is the earth, M the moon, and S thenbsp;^�n. Then A C B D is the fpheroidical figure ofnbsp;fluid part of our globe, which is formed by thenbsp;^ftion of the moon, whereof A B, is the greater axis,nbsp;C D the lefler j viz. the waters at A and B,nbsp;under and oppofite to the moon, are higher thannbsp;^Iteir ufual level j but at C and D they are lowernbsp;^^an their ufual level. EFHG reprefents the ob-Wg figure, which is produced by the aftion of thenbsp;gt; viz. the waters are higher than their ufualnbsp;under the fun at E, and oppofite to it at F ;nbsp;they are lower than their ufual level at .Hnbsp;G. Now by infpefting the figure it will benbsp;comprehended, that if the longer axes of bothnbsp;^hofe fpheroids coincide, as is the cafe at the time ofnbsp;^ ^ll and of a new moon ; viz. when the moon is innbsp;^^^junftion with, or oppofidon to, the fun; then thenbsp;effea; is greater than in any other fituation of thofenbsp;^^ftiinaries. The very high tides, which are raifednbsp;thofe cafes, are called Jpring tides. On the othernbsp;when the lefler axis of one of thofe fpheroidsnbsp;^^incides with the greater axis of the other fpheroid,nbsp;IS the cafe at the quadratures, viz. when the moonnbsp;90� diftant from the fun ; then the two powersnbsp;'^ounterad: each other more or lefs, according asnbsp;^^��her of them is more of lefs powerful. The tidesnbsp;�^hofe cafes, being not fo high as in ordinary, arenbsp;^^lled Keap tides. Thus, where the lefibr axis CDnbsp;the moon�s Ipheroid A C B D coincides with thenbsp;14nbsp;nbsp;nbsp;nbsp;greater

greater axis E F of the fun�s, fpheroid EH FG/ there the two oppofite powers nearly balance eachnbsp;other, and of courfe the rife or fall of the water isnbsp;nearly infenfible. But where the greater axis ABnbsp;of the moon�s fpheroid A C B D coincides with thenbsp;leffer axis HG of the fun�s fpheroid EHFG, therenbsp;the elevation of the waters at A and B (viz. aboutnbsp;the extremities of that greater axis) will be verynbsp;little lefs than if it were not fo counterafted.

The fituationsi of the fun and principally of the moon, with relpedt to their declination or dlftancenbsp;from the equator, produces another remarkable'nbsp;phenomenon relative to the tides ; which is, thatnbsp;the two fucceflive tides of the fame day are more ornbsp;lefs unequal, according as the moon declines morenbsp;or lefs from the equator; fo that they are equalnbsp;only when the moon has no declination, viz. whennbsp;it is in the equator. Thus in fig. 2, Plate XXVIIEnbsp;where the moon M is over the equator Q_R, anynbsp;given part of the earth will have the two fucceffivenbsp;tides equal; for when, by the diurnal rotation of thenbsp;earth round its axis NS, the part R comes to Q^thenbsp;elevation of the water will be as great as in itsnbsp;former fituation at R j and the fame is the cafenbsp;with any other given part at r, for either whennbsp;this part Hands at r,' or when about 12 hours afternbsp;it comes to q, the floods, or the elevations, r d,qiynbsp;of the waters are exadtly equal. But when thenbsp;moon is diftant from the equator, as is reprefentednbsp;in fig. 3, Plate XXVIII. then the fame part of th^^

earth will have the two fucceffive tides of the fame day unequal; for when the given part r is atr, thenbsp;elevation dr o� the water is not equal to the eJe-'^ation q d, which is the high water or tide of thenbsp;fame part, when, about 12 hours after, this part is,nbsp;the diurnal rotation of the earth, come to q.

� In Ihort, when the moon declines from the equator towards either pole, the tides are alternatelynbsp;^�gher and lower at places having north or fouthnbsp;latitude. For one of the higheft elevations, whichnbsp;�a that under tlie moon, follows her towards thenbsp;pule to which flie is neareft, and the other declinesnbsp;�towards the oppofite pole; each elevation deferib-'quot;^g parallels as far diftant from the equator, on op-Pufite fider, as the moon declines from it to eithernbsp;; and, confequently, the parallels deferibed bynbsp;^laefe elevations of tlie water are twice as many de-from one another, as the moon Is from the�nbsp;^^Uator ; increafing their diftancs as the moon in-^�'eafes her declination, till it be at the greateft,nbsp;quot;'hen the faid parallels are, at a mean date, 47quot; fromnbsp;another; and on that day, the tides are moftnbsp;^Uequai in their heights. As Ihe returns towardsnbsp;d'u equator, the parallels deferibed by the oppofitenbsp;^^uvations, approach towards each other, until thenbsp;'^''uon comes to the equator, and then they coincide.

the moon declines toward the oppofite pole, at ^'I�-'al cliftances, each elevation deferibes the famenbsp;Parallel in the other part of the lunar day, which itsnbsp;Ppofite elevation deferibed before. Whdll the

moon

moon has north declination, the greatefl; tides in the northern hemifphere, are when die is above the horizon j and the reverfe whilft her declination isnbsp;fouth

The fame thing muft be underftood with refpe^t to the effeft which is produced by the fun�s attraction j allowing for the difference of powers.

When both the fun and the moon are in the equator, and the moon is in¹ her perigee, that isjnbsp;neareft to the earth, efpecially when new or full;nbsp;then the tides are the highefl! \ becaufe the attraftionnbsp;of the moon is greatefl, becaufe it coincides withnbsp;that of the fun, and becaufe they aft upon the equa-toreal parts of our giobe, which have the greateflnbsp;centrifugal force. And the effeft would be in-creafed ftill more, if at the fame time the fuonbsp;could be neareft to the earth. But, as the funnbsp;is nearer to the earth in winter than in fummer�nbsp;therefore it is nearer to it in February and Oftobennbsp;than about the time of the equinoxes In March andnbsp;September ; hence the greatefl tides take placenbsp;fometimes after the autumnal equinox, and return ^nbsp;little before the vernal equinox.

With refpeft to the time of the return of the tides it is neceffary to obferve, that the tides do no¹-return always at equal intervals of time. In ordetnbsp;to comprehend the reafon of this inequality,nbsp;mufl confider the changeable fituation of the earth's

axis with refpedl to the moon 5 for that axis, iti every lunation, inclines once towards the moon.nbsp;Once from the moongt; and twice fidewife to her;nbsp;oioving gradually from one of thofe fituations tonbsp;the other, exactly as it does wdth refpefl to the funnbsp;in the courfe of one year; the moon going roundnbsp;the ecliptic in one lunar month, as the fun goesnbsp;found the ecliptic in one year.

Farther, as the greateft axis of the fluid fpheroid, formed by the attraftion of the moon, is alv/ays di-tefted towards the moon, if we imagine that anbsp;plane be drawn along that greater axis, and perpendicular to the moon�s orbit, it is evident that thisnbsp;plane marks the two oppofite or fuccelTive tides ofnbsp;dood, fo that when any given place on the furfacenbsp;of the earth croffes this plane, which it does twice anbsp;day, it muft then have high water. Now it is eafynbsp;^0 conceive, that when the axis of the earth is in-,nbsp;alined towards or from the moon,, it muft then laynbsp;the above-mentioned plane, which plane in eithernbsp;thofe cafes muft evidently cut each parallel ofnbsp;latitude into two equal parts; confequently, fincenbsp;earth turns equably round its axis, a given pointnbsp;the furface of it muft be as long in going fromnbsp;interfeftion with that plane to the other inter-f^ftion on one fide of it, as from the latter to thenbsp;former on the other fide of it. Or, in other words,nbsp;tides return to the fame place at equal inter-'^als of time. But when the axis^of the earth in-olifies fidewife to the moon, then the parallels

of latitude are cut unequally by thf above-mentioned � plane; confequently, in that cafe, the tides return to the fame place at unequal intervalsnbsp;of time 5 for that place, liaving a certain latitude,nbsp;will be a longer time in going from one interfedtionnbsp;with the plane to the other interfeclion, than fromnbsp;the latter to the former.

From the foregoing theory, it follows that � when the earth�s axis inclines to the moon,nbsp;the northern tides, if not retarded in their palTagenbsp;through fhoals and channels, nor alfcdled by thenbsp;winds, ought to be greateft when the moon isnbsp;above the horizon, leaft when fhe is below it andnbsp;quite the reverie when the earth�s axis declinesnbsp;from her; but in thofe cafes they return at equalnbsp;intervals of time. When the earth's axis inclinesnbsp;fidewife to the moon, both tides are equally high;nbsp;but they happen at unequal Intervals of time. Innbsp;fummer, the earth�s axis inclines cowards the moonnbsp;when new; and therefore the day-tides in thenbsp;north ought to be higheft, and night-tides loweftnbsp;about the change: at the full, the reverfe. Atnbsp;the quarter, they' ought m be equally high, butnbsp;unequal in their returns; becaufe the earth�s axisnbsp;then inclines fidewife to the moon. In winter thenbsp;phenomena are the fame at full moon, as in fummer at new. In autumn the earth�s axis inclinesnbsp;fidewife to the moon, when new and full; therefore the tides ought to be equally high and uneqnal

'n their returns at thefe times. At the firft quarter tides of flood fliould be leafl; when the moon isnbsp;^hove the horizon, greatctl when flie is below it;

the^ reverfe at her third quarter. In fpring the phc romena of the firft quarter anfwer to thofenbsp;the third q'�.arter in airumn ; and vice verja.nbsp;The neaicr any time is to either of thofe feafons,nbsp;^he more the tides partake of the phenomena ofnbsp;^hefe feafons; and in the middle between any twonbsp;them, the tides are at a mean ftate between thofenbsp;botn

Thofe general rules are perfeddy verified by ex-P^t�.ence as long as no extraneous difturbing caufts 'Qterfere.

It has been but llightly mentioned in the preced-pages of this chapter, that the greateft elevation '^I^the waters takes place fometime after the moon�snbsp;P^flage over the meridian; and the fame thing isnbsp;'�^'tJe with refpedl to the fpring tides, viz. that theynbsp;place fometime after the conjunction, or thenbsp;^Ppofition of the fun and moon. This is the cafenbsp;in open feas, where, at firft fight, it might benbsp;^Pfcdted that the greateft elevation of the waternbsp;''^'^tilcl be diredtly under the moon, w'here th� at-�^^�Ition is ftroneeft. But an obfervation fimilar to

'vhich has been made (page 8p, vol. III.) ^tive to the greateft heat of the day, which takesnbsp;a, confiderable time after the fun�s palTage over

the meridian, will eafily explain the above-mentioned phenomenon of the tides ; namely, that when a certain power communicates an.enei gy, and though thenbsp;adion of that power be actually decreafing; yetnbsp;the efFeft, or the accumulation of the energy, , willnbsp;ftill continue to incrcafe as long as the wafte of thatnbsp;energy in a given time is lefs than the additionnbsp;which is made to it in the fame time. Thus, fup-pofe that a perfon�s expenditure amounts to lOnbsp;pounds per day ; then, if to-day he receives 20nbsp;pounds, to-morrow he will have left lO pounds;nbsp;for he muft fpend the other 10 to-day. Then ifnbsp;to-morrow, inftead of receiving 20 pounds, he receives 15, and, as ufual, he fpends 10 pounds outnbsp;of it, he will have left, in all, 15 pounds; and ifnbsp;the day after to-morrow he receives only 12 pounds,nbsp;and as ufual fpends only 10, he will have left uponnbsp;the whole 17 pounds; which evidently Ihews thatnbsp;though his daily receipt is conftantly decreafing, yetnbsp;his flock is increafing, and will continue to increafenbsp;as long as the daily receipt exceeds the daily expenditure.

Now, with refpeft to the tides, it muft be confi-dered, that the waters of the oceans, once put in motion by the attraction of the fun and moon,nbsp;would of themfelves continue to m.ove for a confi-derable time, though the aCtion of the fun andnbsp;moon fhould be fufpended. Like a bafon of water�nbsp;or like a pendulum, which, if once put in motion,nbsp;will, without the renovation of the impulfe, continue

to vibrate for a confiderable time after. In the like Oianner, if the moon�s attradion fhould ceafe, thenbsp;*^oment Ihe has paffed the meridian, the watersnbsp;of the oceans would Hill continue to rife for fomenbsp;t'nae after, in confequence of the impuife receivednbsp;before the ceffationof the moon�s adion; and therefore they muft continue to rife much more whennbsp;that adion, inftead of being annihilated, is onlynbsp;^�Oiinilhed.

The time which elapfes between the moon�s paiTage over the meridian, and the high water ornbsp;flood, even in open feas, is not always the fame;nbsp;hot it is fometimes longer and at other times fhorternbsp;than ordinary, which arifes from the concurringnbsp;^dion of the fun ; for when the moon is in her firftnbsp;third quarters, the tides raifed by the moon arenbsp;Accelerated by the fun, becaufe in thofe cafes thenbsp;t'^es raifed by the fun alone would come on earliernbsp;|han thofe of the mioon. And when the moon isnbsp;her fecond and fourth quarters, the tides raifednbsp;hy her are retarded by the fun 5 becaufe, in thofenbsp;the tides raifed by the fun alone would comenbsp;later. In general, the greateft height of the waternbsp;open feas, takes place about an hour after thenbsp;*^oon�s meridional paffage.

^ ^efides the acceleration or retardation which arife orti the influence of the fun, the tides are confi-��ably affefted, in point of height and of periodicalnbsp;l�cal circumftances. In the open feasnbsp;of the water is fmall in comparifon to what

it is in contra�led channels, wide-mouthed riversgt; amp;c. where the water is accumulated by the contraction and oppofuion of the banks.

� The tides are To retarded in their paffage through different Ihoals and channels, and other-'nbsp;wnfe fo varioufly affefted by ftriking againft capesnbsp;and headlands, that to different places they happennbsp;at all diftatices of the moon from the meridian ;nbsp;confequently at all hours of the lunar day. Thenbsp;tide propagated by the moon in the German ocean,nbsp;when ffe is three hours paft the �meridian, takes 12nbsp;hours to come from thence to London bridge ;nbsp;where it arrives by the time that a new tide is raifednbsp;in the ocean : and therefore, when the moon hasnbsp;north declination, and we fhould expeft the tide atnbsp;London to be greateft when the moon is above thenbsp;horizon, we find it is leaft j and the contrary whennbsp;fhe has f�uth declination. At feveral places it isnbsp;high-water three hours before the moon comes tonbsp;the meridian ; but that tide which the moon pulhesnbsp;as it v/ere before her, is only the tide oppofite tonbsp;that which was raifed by her when fhe was ninonbsp;hours paft the oppofite meridian.

' � There are no tides in lakes, becaufe they are generally fo fmall, that when the moon is verticalnbsp;file attrafts every part of them alike, and' therefore,nbsp;by rendering ail the water equally light, no part ofnbsp;it can be raifed higher than-another. The Mediter'nbsp;ranean and Baltic feas have very fmall elevations,nbsp;becaufe the inlets by which they communicate with

ocean are fo narrow, that they cannot, in fo Ihort ^ time, receive or difcharge enough to raife or finknbsp;their furfaces fenfibly

The time of high water in different parts of the quot;'Orld, or rather the time which elapfes betweennbsp;'�he high water tide and the moon�s arrival at thenbsp;'^^ridian, can only be learned from experience ; andnbsp;therefore the obfervations made in different placesnbsp;Relative to this, are colledled into tables, which are

he met with in feveral almanacks, and in treatifes fn navigation, fuch as Robertfon�s, Bouguer�s, amp;c.

The action of the moon upon the atmofphere has *^^^n noticed in the fecond. volume of thefe Ele-'hents

[ nbsp;nbsp;nbsp;i62nbsp;nbsp;nbsp;nbsp;]

TH E movements, the appearances, and the mutual influence, of the fun, the earthy andnbsp;the moon, are undoubtedly more ftriking and morenbsp;interefting to us than thofe of the other celeftialnbsp;objedls: hence particular notice has been taken oinbsp;the fame in the preceding chapters of this volume�nbsp;But in defcribing the appearances and'the move'nbsp;ments of the other celeftial objedts we fhall endea-vour to be more concife, efpecially becaufe the fimi'nbsp;larity of their motions to thofe of the earth, wilhnbsp;in a great meafure, fuperfede the neceffitynbsp;giving very minute explanations of feveral parti'nbsp;culars.

In order to facilitate the comprehenfion of follows, the reader is requefted to recolledl wh^tnbsp;has been in a particular manner explained befot^�nbsp;relatively to the planets; namely, that the planets�nbsp;both primary and- fecondary, move in elliptical of'nbsp;bits; and that the primaries, together with the ftjf�nbsp;move round a common centre of gravity, which

�Centre of gravity is not coincident with the centre but is not out of the body of, the fun. Aifo thenbsp;^^condaries, or moons, or fateliices 'which belong tonbsp;^planet, revolve round a centre of gravity commonnbsp;them and to their primary ; fo that in truth thenbsp;point, which deferibes the planetary orbit round thenbsp;is not the centre of fuch a planet as has fatellites,nbsp;is the common centre of gravity of that planetnbsp;its fatellites; thus it is not the centre of thenbsp;^^�'th, but the common centre of gravity of the earthnbsp;moon, tfiat deferibes the annual orbit round thenbsp;This centre of gravity is as much nearer tonbsp;centre of the earth than to that of the moon, bynbsp;much as the quantity of matter in the moon isnbsp;than the quantity of matter in the earth, viz.nbsp;1 to 38,93 therefore, fince the diftance of thenbsp;�fioon from the earth is 240000 miles *j by dividingnbsp;diftance in the above-mentioned proportion, wenbsp;find that the common centre of gravity of thenbsp;and moon is only 6015 miles diftant from thenbsp;^^ntre of the earth, which diftance being but trifling,nbsp;have, for the fake of avoiding prolixity, not no-it in the explanation of the annual movementsnbsp;the earth.

^he reader is likewife requefted to recolleft ^^pler�s general laws relative to the planets ;nbsp;that the areas deferibed by a right line

conneding the centre of attri�dion and the revolving planet, are always proportional to the times in whichnbsp;they are defcribed, and that the cubes of their dif-tances from the fun are as the fquares of the timesnbsp;of their periodical revolutions.

For the fake of brevity, as alfo for the conve-niency of comparifon, the diameters, diftances, revolutions, and other remarkable particulars relatively to the fun and planets, have been difpofed in a table which {lands at the end of this chapter, aniinbsp;concerning which we {hall fubjoin the following eX'nbsp;planatioRs; we {hall then add liich other particular�nbsp;as could not conveniently be ftated in the form of�nbsp;table.

The ill column of the table, which immediately follows tile names of the principal bodies of thenbsp;folar lyflem, contains the apparent mean diametersnbsp;of thofe bodies j that is, when they are at theirnbsp;mean diftances from the earth. Thofe diametersnbsp;have been afeertained by means of micrometricalnbsp;meafurements ; but fome uncertainty exifts withnbsp;refped to the two new planets, Ceres and Pallas j ft*'quot;nbsp;the meafurements of their diameters, as given bynbsp;different aftronomers, do not agree with each other*nbsp;The moft accurate obfervations hitherto made upo*^nbsp;Mars, Jupiter, Saturn, and the Georgium Side��nbsp;prove that there is a fenfible difference between the*''nbsp;equatorial and polar diameters; the former beinSnbsp;longer than the latter, which is undoubtedly owingnbsp;to the greater centrifugal force of their equatori�

P^rts ; as is the cafe with the earth. Though it be ^ot proved by actual obfervations, yet analogy in^nbsp;^uces us to believe, that a fimilar difference exillsnbsp;^^tween the equatoreal and polar diameters of allnbsp;other planets.

The 2nd column of the table contains the di-^tneters which the planets w'ould appear to have to ^ ^Pe�lator in the fun. Thofe are obtained by computation.

The 3d column contains the real mean diame-in Englifh miles. Thofe diameters are ob-tained by computation from their refpe^bive appa-diameters and diftances.

The mean dhtances of the planets from the fun, found numbers of �nglifh miles, are containednbsp;the 4th column of the table. Should any per-wifii to have thofe diftances more accurately, henbsp;�^3y eafily deduce them from the propornO�,dlnbsp;^t^mbers of the 5th xolumn, and by the commonnbsp;of proportion; fuppofing that the mean dif-^^hce of the earth, viz. 95 millions, is futficiently

The mean denfity of all the parts which form each PWet, compared to that of water, is contained innbsp;, ^ 6th column; and the 7th column contains

^ proportion between the quantity of matter in ^ ftin, as alfo in each planet, and that of the earth,nbsp;is reckoned one, or unity j thus Jupiter isnbsp;^�^koned to contain fomewhatmore than 312 timesnbsp;�^'fch matter as the earth, amp;c.

M 3 nbsp;nbsp;nbsp;The

The inclinations, or the angles which the orbit� of the planets form with the plane of the ecliptic, arenbsp;contained in the 8th column.

The- 9th column lliews the inclinations of the axes of fome celeftial bodies to their refpeftive orbits. This column is deficient oh account of thenbsp;very great ditiicuky of making the neceflary obfer-vations �, for this inclination of the axis of a planetnbsp;is only to be deduced from the oblique or curvili'nbsp;near motion of the fpots of the planet.

The diurnal rotations of the icth column are alfo derived frcn-i the motion of the fpots.

The iith column contains the tropical revolOquot; tions, viz. the time employed by each planet innbsp;paffing over the xi figns of the zodiac. Andnbsp;time which each of them employs in going from anVnbsp;fixed liar to the fame again, is contained in the 12thnbsp;column. The particulars of this, as well as ofthlt;^nbsp;two preceding columns, are exprefled in days, hoursjnbsp;minutes, and fecondr.

the ecliptic, towards which the planet is direfter^ when it ftands at that point of its orbit, whichnbsp;the moft diftant from the fun. � Thole parts of th*^nbsp;ecliptic are exprelfed in figns, degrees, minoteS;nbsp;and feconds.

The 14th column contains the fecular motio'^^ of the aplielia of the preceding column ; viz.

'phis

is obtained by dividing the difference between the place of the aphelion, as determined many yearsnbsp;and as afcertained lately, by the number ofnbsp;Centuries, or fradional parts of a century, elapfednbsp;between the above-mentioned two determinations.

Column the 15th, contains the eccentricities of ^he orbits, each mean diftance being rec;-.onednbsp;looooo. From this and the 4th column, thenbsp;^ccentr.city of each orbit mav be had in miles.nbsp;*nus the earth�s mean diftance from the fun .3nbsp;55000000 of miles, and the eccentricity of itsnbsp;'^��bit is 1681,395 � therefore fay, as ic 0000 :nbsp;^^^'*�395 � : 95000000 to a fourth prop utionaF,nbsp;'quot;�2* to 1597325,25, which is the eccentricity of thenbsp;^^�quot;th�s orbit in miles.

j6t:h column contains the greateft equations centres, viz. the difference between the truenbsp;the mean anomaly for each planetary orbit.

. The 17th column Ibews the place of the afcend-node of each planetary orbit, which gives the � ��'^tion of the line or nodes. This may be ex-�^^'^ffed either by the charaders of the figns of thenbsp;or by the number of figns, always reckon-� 0 from the firft point of Aries together with thenbsp;degrees, amp;c. Thus 1% 15^ 20', 43'^ is thenbsp;�, 150^ 2oq 43quot;, and 3% 7�, 55', 32quot;, isnbsp;j..^ ^anae as yquot;,nbsp;nbsp;nbsp;nbsp;^2quot;.�The fame obferva-

M 4 nbsp;nbsp;nbsp;The

The fecular motion of the nodes, or movement in lOo years for each planet, is contained in the 18 thnbsp;cojumn. Thofe are obtained in the fame manner asnbsp;has been faid of the 14th column.

It was impofiible to avoid fome inaccuracies among the particulars of the annexed table, principally becaufe the obfervations, hitherto made, donbsp;not always afford very accurate refultsj we fhalhnbsp;however, endeavour to point them out in the following paragraphs 3 wherein the reader will findnbsp;feveraf particulars relative to the fun and planetSjnbsp;which could not be exp'reffed in the form ofnbsp;table.

The fplendor of the fun even long before the dif-covery of telefcopes has been obferved to vary at different and uncertain times j when viewed throughnbsp;a telefcope, the furface of the fun is almoft alwaysnbsp;found to contain certain dark fpots of various fizesnbsp;and duration. It is from the motion of thole Ipotsnbsp;that the fun has been found to move round its ownnbsp;axis, and that its axis has been found to be incline*^nbsp;to the ecliptic.

The conftant emanation of heat and light from that immenfe body, has long fuggefted the idea ofnbsp;the fun�s being a globe of fire, of the fpots beingnbsp;the fcoria of the burning matter, and of fom^nbsp;acceflion of matter being neceffarily requirednbsp;lupply the conftant wafte which arofe from the emanation of heat and light. But the more or lof�

powerful telefoopes ufed by different obfervers, and *^1^0 tendency of preconceived fyftems, have givennbsp;^irth to a variety of opinions relative to the naturenbsp;the fun. Thus the fpots have been fuppofed tonbsp;bodies of very irregular figures revolving aboutnbsp;^he fun, and very near its furface. Thofe fpots havenbsp;slfo been confidered as the tops of rocks or moim-on the fuppofition that the fun is an opaquenbsp;body covered with a liquid igneous matter. Theynbsp;have likewife been looked upon as excavations in thenbsp;^tttninous matters of the fun. In the year 1788, anbsp;^ery learned and worthy gentleman publifned a dif-^^ttation concerning the light of the fun, in whichnbsp;he advanced that the real body of the fun is lejs thannbsp;apparent diameter; and that sjoe never difeern thenbsp;l)Q^y qJ life fun itfelf, except wheji we behold itsnbsp;j and that the fun is inhabited as well as ournbsp;^�^fth; and is not neceffarily fubjeS to burning heatnbsp;that there is in reality no violent elementary heatnbsp;^^^Jiing in the rays of thefun theinfelves effentially *.

Several years after the publication of the laft l^cntioned opinion. Dr. Herfchel began to publilhnbsp;the Philofophical Tranfaftions, his theory con-'�^tning the nature of the fun, and to which he was lednbsp;hy his numerous obfervations made with,his moftnbsp;ifnprovecl inftruments, and the moft perfevenng in-^uftry. qq-iis theory, in brief, is as follows:

The fun, he thinks, is a moil; magnificent habitable globe furrounded by a double fet of clouds. Thofe, which are nearer its opaque body, are lefsnbsp;bright and more clofely connefted together thannbsp;thofe of the upper ftratum, which form the luminous apparent globe we behold. That luminousnbsp;external matter, as Dr. Herfchel obferves, is neithernbsp;a liquid nor an elaftic fluid of an atmofpheric nature ; for in either of thofe two cafes, it could notnbsp;admit of any chafms, or openings. Therefore, itnbsp;muft be concluded, that this flbining matter exifts innbsp;the manner of empyreal, luminous, or phofphoricnbsp;clouds, refiding in the higher regions of the folarnbsp;acmofphere. The doctor then is of opinion that thenbsp;fpots, commonly fo called, are only accidentalnbsp;openings between the luminous clouds, throughnbsp;which we behold the opaque body of the fun, ornbsp;the inferior, lefs luminous clouds j hence the fpptsnbsp;appear of different fliades. In confequence of thisnbsp;theory. Dr. Herfchel rejefts the old names of fpots,nbsp;nuclei, penuraba;, faculje and luculi, which othernbsp;aftronomers had given to the various appearancesnbsp;on the vifible furface of the fun j and adopts thenbsp;following terms, which we lhall exprefs in his ownnbsp;words; and from an explanation of which the readernbsp;may acquire a more competent idea of his hypO'nbsp;thefis *.

� Openings

� Openings are thofe places where, by the accb 'Cental removal of the luminous clouds'of the fun,nbsp;own folid body may be feen ; and this not beingnbsp;^Ucid, the openings through which we fee it may, bynbsp;^ common telefcope, be miftaken for mere blacknbsp;^Ptgt;ts, or their nuclei.�

� Shallows are extenfive and level depreffions of luminous folar clouds, generally furroundingnbsp;openings to a confiderabie diftance. As theynbsp;lefs luminous than the reft of the fun, they fcemnbsp;have fome diftant, though very imperfecft refem-hlance to penumbras �, which might occafion theirnbsp;having been called fo formerly.�

quot; Ridges are bright elevations of luminous mat-extended in rows of an irregular arrange-l�ient.�

quot; Nodules are alfo bright elevations of luminous *^^tter, but confined to a fmall fpace. Thefe no-and ridges, on account of their being brighternbsp;J^han the general furface of the fun, and alfo differ-*'^8 a little from it in colour, have been called facula?,nbsp;luculi.�

� Corrugations, I call that very particular and re-l^^rkable unevennefs, ruggednefs, or afperity, v^hich peculiar to the luminous folar clouds, and extendsnbsp;^11 over the furface of the globe of the fun. As thenbsp;^^^Ptefied pa,-ts of the corrugations are lefs luminousnbsp;the elevated ones, the dife of the fun has annbsp;appearance v/hich may be called mottled.�

� Indentations are the deprefled or low parts of the corrugations j they alfo extend over the wholenbsp;furface of the luminous folar clouds.�

� Pores are very fmall holes or openings, about the middle of the indentations.�

The planet next to the fun is Mercury. The proximity of this planet to the fun, render^ it fel-dom vifible, confequently the aftronomers have notnbsp;had many opportunities of making numerous andnbsp;accurate obfervations upon it. No fpots have asnbsp;yet been difcovered upon its difc, confequently neither its rotation about its axis, nor the polition ofnbsp;that axis, can be determined 5 yet Mr. Schroeter isnbsp;induced, by fome of his obfervations, to believe thatnbsp;the period of Mercury�s rotation about its axis isnbsp;24 hours and 5 minutes That, according to itsnbsp;fituation with refpedt to the earth and the fun, thisnbsp;planet muft fhew phafes, in great meafure fimilarnbsp;to thofe of the moon, has already been mentioned,nbsp;and I think it needs no farther illuftration. Th^nbsp;tranfit of Mercury over the difc of the fun does bynbsp;no means take place at every revolution of thenbsp;planer; for fince its orbit is inclined to the ecliptic,nbsp;making with it an angle of about feven degrees, andnbsp;croffing it at the two nodes, it is evident that thenbsp;planet cannot be feen to pafs over the difc of the

fun,

uniefs lts nodes happens to be in, or fuffici-cntly near, the line which joins the fun and the

earth.

Venus, vulgarly called the morning or evening according as it precedes or follows the apparentnbsp;^ourfe of the fun, is a very brilliant planet, fituatednbsp;between us and Mercury. It has long been doubtednbsp;''whether any fpots were really vifible upon its difc jnbsp;indeed even at prefent it is far from being ulti-diately determined. Some aftronomers have per-^eived fpots and even mountains upon its difc. Dr.nbsp;^^stfchel, however, could never fee any fuch appearances ; hence he is of opinion, that neither thenbsp;^'^tation of this planet, nor the pofition of its axis,nbsp;as yet be determined, that it has a conhderablenbsp;^'^'�iofphere, and that from its apparent diameter,nbsp;^enus feems to be larger, and not as commonlynbsp;Relieved fmaller than the earth. The fame obfer-^^dons, which hSve been made with refped to thenbsp;P^afes of Mercury, and to its tranfit over the fiin,nbsp;be underftood of Venus alfo. Thofe tranfitsnbsp;of great ufe to aftronomy; but the tranfit ofnbsp;^^nus being much more ufeful on account princi-P^dy of its moving flovrer; no pains have beennbsp;^P^fed in calculating the times of its taking place,

. in obfervine it at the adtaal time. � The chief (Jays Dr. Halley) of thefe conjunction?, is accu-^�ately to determine the fun�s diftance from the earth.nbsp;Its parallax, which aftronomers have in vain attempted

tempted to find by various other methods; for the minutent- fs of the angles required, eafily eludes thenbsp;nictll inftruments. But in obferving the ingrefs ofnbsp;Venus into the fun, and her egreis from the fame,nbsp;the fpace of time between the moments of the internal contaffs, obferved to a fecond of time, viz. ofnbsp;a fecond of an arch, maybe obtained by the affiftancenbsp;of a moderate telefcope, and a pendulum clock, thatnbsp;is confident with itfelf exaftly, for the Ipace of 6 otnbsp;8 hours. Now, from two fuch obfervations rightlynbsp;made in proper places, the diftance of the (utinbsp;within a 5coth part may be certainly concluded.�

Mars is the planet which comes next to the earth in order from the fun. The appearance of thisnbsp;planet is by no means fo bright,^as that of VenuS;nbsp;or even that of Jupiter which is.pauch farther froU'nbsp;the fun. Its colour is fomewhat inclining to red¹nbsp;The beft or moft recent obfervations on this plarie¹^'nbsp;feeiTi to be thofe which have been made bynbsp;Herfchel, who obferved feveral remarkably brigh'^nbsp;fpots near each pole of Mars, which fpots feem^'^nbsp;to have a fmail m.otlon ¹, The refults of his oh'nbsp;fervations are that the inclination of the axis

^ars to the ecliptic is 59�, 22'; the node of its axis in 'yi if, 47'; the obliquity of Mars�s ecliptic isnbsp;28% 42'; the point Aries on its ecliptic anfwers tonbsp;t 19*, 28'. Its equatorial is to its polar diame-nearly as 16 to 15.

�^ext to Mars come the two new planets, viz. Ceres Ferdinandea, and Pallas, which, on ac-'�^Unt of their remarkably fmall fize. Dr. Herfchelnbsp;Pi'opofes to difcriminatc by the appellation of ajte-Nothing particular has as yet been difcoverednbsp;'''ith refpefl. to the appearances of thofe planets.

fometimes appear round and well defined, at ^'^her times they appear to be furrounded by a comanbsp;hazinefs, the denfity and extent of which feem tonbsp;with the ftate of the atmofphere.nbsp;nbsp;nbsp;nbsp;It is faid that

Schroeter fufpefts that the Ceres has two fatel-Ptes. This, however, is much in want of confirmation.

quot;iPhe beautiful planet Jupiter is the next in order, ^ith refpeft to fplendour, diis planet yields, uponnbsp;*�^0 whole, orjy to Venus. When viewed throughnbsp;^ tolerably good telefcope, fome zones or belts arenbsp;^0 upon its difc, which run parallel to its equatornbsp;t nearly fo. Thofe belts are of a darker fliadenbsp;Variable in number, in breadth, and in intenfity;nbsp;they have been generally fuppoled to be, af-^J^blages of clouds, probably driven by certainnbsp;i�'ds of Jupiter�s atmofphere, which may blow innbsp;P^Ticular directions in different parts of that atmofphere.

inofphere, fomewhat like our equinoflial winds,� or the monf�ons. Some large fpots have oftennbsp;been feen in thofe belts, which have vaniflied withnbsp;the contiguous belt. Sometimes the belts are notnbsp;continuate, but interrupted or brokfen j in whichnbsp;cafe the broken end fnews, that the belts as well asnbsp;the above-mentioned fpot revolve in the fame time?nbsp;but it is remarkable that thofe which are nearer thenbsp;poles of the planet revolve fomewhat flower thannbsp;thofe Vv'hich are near its equator; but this time ofnbsp;rotation varies a little, and the time of rotation ofnbsp;the fame fpot diminiflies*.

According to Schroeter, Jupiter�s rotation about its axis is performed in 55�, 37% This rotation is mucji quicker than that of the earth about itsnbsp;axis; hence the difference between the equatorialnbsp;and the polar diameters of Jupiter, is much greaternbsp;in proportion than that which has been found between the two diameters of the earth; the equatorial parts of Jupiter having a very great centrifugalnbsp;force. By the beft meafurements, the polar diarn�'nbsp;ter of Jupiter is to its equatorial diameter as 12 to

* Dr. Herfchel, in the year 1788, obferved that the of revolution of a certain fpot altered in the followifSnbsp;manner. From February 25, to March 2, it revolvednbsp;9*'� 55��, ^0*- From the 2nd to the 14th of March,

9S 51^ 35�*

of the Sun and Planett. nbsp;nbsp;nbsp;177

The axis of Jupiter is nearly perpendicular to Its orbit j fo that upon it the change of feafons mufl:nbsp;next to nothing.

Jupiter is furroun Jed by four moons, or fatellites, different fizes, which move about it in differentnbsp;drnes and different limits of elongation. In confe-tjuence of their different movements, thofe fatellites,nbsp;^igt;ich can never be feen without a telefcope, arenbsp;^O�nd always differently fituated. Fig. 4. Platenbsp;^XVIII. exhibits the fituation of Jupiter and itsnbsp;four fatellites on a particular night j and fig. J,nbsp;^^hibits the fame as they would appear to a fpeftarnbsp;fituated in the heavens, perpendicularly overnbsp;orbits. The numbers i, 2, 3, and 4, denotenbsp;fatellites, and the circles which pafs throughnbsp;in fig. reprefent their orbits; that fatellitenbsp;performs its revolution neareft to the planetnbsp;^''�0 called the firft. the next being called thenbsp;and to on.

f^ is from a variety of appearances, fomewhat 0 thofe of fig. 4, that the knowledge of the realnbsp;dances, periods, and other particulars relative tonbsp;obfnbsp;nbsp;nbsp;nbsp;derived ; and the principal

or them is feen, points out the extent of its '*^5 for this greateft elongation is as much on onenbsp;IV.nbsp;nbsp;nbsp;nbsp;fids

fide of the planet as on the other fide. The time which elapfes between thofe two elongations, isnbsp;about half the fatellite�s periodical revolution, ornbsp;half the time of its greateft elongation on one fide,nbsp;and the next elongation on the fame fide.

2. nbsp;nbsp;nbsp;Every one of the four fatellites, in going fromnbsp;the weftern to the eaftern fide of the planet, certainlynbsp;goes beyond or behind the planet; for in that cafenbsp;they are fometimes hid by the planet, and at othernbsp;times are feen either above or below it, but nevernbsp;over its difc gt; whereas in their cpurfe from the eafternnbsp;to the weftern fide of the planet, thofe fatellitesnbsp;which patfed behind, now pafs over the difc of thenbsp;planet, thofe which palTed above, now pafs below,nbsp;and vice verja which evidently proves that theynbsp;move round Jupiter in the dire�lion from the weftnbsp;towards the eaft, the fame way that all the planetsnbsp;move round the fun.

3. nbsp;nbsp;nbsp;The paths of the fatellites being reducednbsp;their refpeftive planet�s centre, fometimes appeafnbsp;redtilinear, paffing through that centre, and inclinctlnbsp;in a certain dirc�tion to its orbit. Afterwards the/nbsp;change more and more into ellipfcs, during oti�nbsp;quarter of the planet�s annual revolution ; and ahnbsp;the fuperior conjundlions are then made above th^nbsp;planet�s centre, and the inferior conjunftions hdo''^nbsp;it : during a fecond quarter of the planet�s revol'J'nbsp;tion, thel� ellipfes become narrower, the fatelh^^^�

of the Sm and Planets, nbsp;nbsp;nbsp;179

the end-of a fecond quarter of the revolution, all the ellipfes are again become right lines with equal inclination, but in a contrary direftion. In the thirdnbsp;quarter of the revolution, they are formed a-new' -into ellipfes, the fuperior conjunftions are madenbsp;helow the centre, and the inferior ones above. Laftly,nbsp;in the fourth quarter of the revolution, when thenbsp;planet is returning to the fame point of its orbit,nbsp;^hefe ellipfes again decreafe in breadth, and all re-*^nrns to its firft date.�

4. � The times of the fuperior and inferior con-Jnndtions of the fatellites, being compared, their intervals are nearly equal to their femi-revolu-tioii,�

In Ihort, all thofe obfervations prove that the ia-^^hites move all one way, and almoft equably round iheir primary, in curves that return into themfelves jnbsp;planet being in one of the diameters of eachnbsp;i^nrve ; that the planes of the orbits of the fatellitesnbsp;inclined to the plane of the orbit of the primary,nbsp;^nd each erodes it at two points, called the nodes^nbsp;quot;'hich one is the ajeending, and the other the de-node j that when the earth happens to be innbsp;direlt;51;ion of that line of nodes, then the fatellitesnbsp;Appear to move in ftraight lines j otherwife theynbsp;Appear to move in ellipfes, the planes of which arenbsp;^'ii'iied with one fide or with the other towards thenbsp;according as the earth happens to be fituatednbsp;N anbsp;nbsp;nbsp;nbsp;on

�So nbsp;nbsp;nbsp;Of the Naturct ��c.

Every one of the fatellites of Jupiter, like our moon, are liable to be eclipfed by paffing throughnbsp;the fliadow of their primary. Knowing the fituationnbsp;of Jupiter with refpedl to the fun, which gives thenbsp;diredlion of its Ihadow, and the movements of thenbsp;fatellite, one may eafily calculate the time of annbsp;eclipfe of that fatellite. In faft, tables of all thenbsp;eclipfes of thofe fatellites are annually publilhed innbsp;the Nautical Almanac, and other annual publicationsnbsp;of the like kind.

The calculations and obfervations of thofe eclipfes are not merely matters of ufelefs curiofity j but theynbsp;anfwer a moft ufeful purpofe, which is that of finding the longitude of one place from another on thenbsp;furface of the earth, as will be particularly explainednbsp;hereafter. Another grand difcovery was originallynbsp;deduced by Mr. Roemer from thofe eclipfes, and

It is evident that the motion of the fatellites rounlt;l Jupiter is produced by the fame caufes as that of the planet¹nbsp;round the fun; viz. they are attradled by the planet, at th^nbsp;fame time that they are adluated by an impulfive force whichnbsp;prevents their falling upon the planet; hence theynbsp;follow Kepler�s laws; viz. each of them muft deferih^nbsp;round the planet areas -proportionate to the times; and thCnbsp;cubes of their mean diftances from the planet mull be as th�nbsp;lijuares of their periodical times.

has afterwards been confirmed by means of other obfervations, efpecially thofe made by Dr. Bradleynbsp;^pon the fixed ftars ; namely, that light moves notnbsp;ififtantaneoufly, but progreffively, employing a certainnbsp;time in going through a certain fpace; viz. it movesnbsp;the rate of almofl: 200000 miles in one fecondnbsp;of time j which was firfl; determined by obferving,nbsp;that when the earth is between the fun and Jupiter,nbsp;10 which cafe the earth is neareft to Jupiter, thenbsp;oclipfes of the fatellites appear to take place Joonernbsp;hy about 8 I minutes, than they fliould appear according to the calculation as ftated in the tables;nbsp;'''hereas, when the earth is fartheft from Jupiter, ornbsp;^hen Jupiter is beyond the fun, then the eclipfes ofnbsp;'�he fatellites appear to take place about 81 laternbsp;'han they ought to appear according to calculation;nbsp;therefore light takes up a longer time in percurringnbsp;^ greater diftance; and, as the difference betweennbsp;the two diftances of Jupiter from the earth in thenbsp;^bove-mentioned two fituations, is equal to the diameter of the earth�s orbit, which is equal to aboutnbsp;*90000000 miles, we naturally conclude that lightnbsp;employs twice 8 or about 16 | minutes in per-ciirring 190000000 miles.

The elements, or the periods, diftances, and ether particulars, relative to Jupiter�s four fatellites,nbsp;^re ftated in the following table; from which thenbsp;configuration, and the eclipfes of thofe fatellites maynbsp;bo Calculated. It muft be oblerved, however, that

fuch

fuch a table requires to be corredted from time to time, and according as more accurate obfervationsnbsp;are made; for the motions of thofe fatellites arenbsp;fubjedt to irregulariries fimilar to, and even greaternbsp;than, thofe of our moon; they being fubjedl to thenbsp;fame difturbing caufes, and likewife to their mutualnbsp;adlions upon each other.

The

The Sat�llites of Jupiter.

111.	Ild.	llld. ,	IVth.
l'' 18'' 27�	13'* 13'' 13quot;�42*	7lt;i 3h 42quot; 33�	l� 16 32quot;' 8'
Igh 28m J��	jjh ,7m	f s'* 59quot;quot; 36*	i6�* iSh s'quot; 7�
5,67	9,00	14,38	25,30
252797 T 51quot;	40126^ 2' ly	641132 4' 42	1128000 8' 16quot;
,h ym	25quot;' 40�	I** 47^ o'	2^ 23quot; -0
0,9941	0,9967	0,9857	0,9913
iquot; 3quot; 45	jh ,5m nbsp;nbsp;nbsp;-�	I h 3quot;� nbsp;nbsp;nbsp;40�	000
3� 18' nbsp;nbsp;nbsp;3 bquot;	3� 46' o'	3� 25' 57quot; 3� gt;3' 58quot;	2� nbsp;nbsp;nbsp;36nbsp;nbsp;nbsp;nbsp;o''
3� 18' nbsp;nbsp;nbsp;38quot;	3� 16' 0quot;	3� 25' 57quot; 3� gt;3' 58quot;	2� nbsp;nbsp;nbsp;36nbsp;nbsp;nbsp;nbsp;0quot; 2� nbsp;nbsp;nbsp;36'nbsp;nbsp;nbsp;nbsp;0quot;
3� 18' 38quot;	2� 46' nbsp;nbsp;nbsp;o''	3� a' 0quot;
3� nbsp;nbsp;nbsp;4'nbsp;nbsp;nbsp;nbsp;2yquot;	3� 29' 42quot;	3� 11' 14''	2� nbsp;nbsp;nbsp;24'nbsp;nbsp;nbsp;nbsp;51'
3� 4' ^7quot;	2� 34' 0quot;	2� 49' nbsp;nbsp;nbsp;0 quot;	2quot; nbsp;nbsp;nbsp;24'nbsp;nbsp;nbsp;nbsp;5 I
Qii joh 35quot;gt;	!�' 14'' 49quot; 36'	2^ 5^ 32^ 2^�	[U nbsp;nbsp;nbsp;2Qm -qS
10� 14� nbsp;nbsp;nbsp;30'	10� 13quot; 45quot;	lo* 14� 24	10' 16quot; 39
0' nbsp;nbsp;nbsp;o''	2 3	0' O''	4' * 9quot;
6 23 29 20	3 II 22 29	I 20 19 nbsp;nbsp;nbsp;4	0 21 34 16
7 25 31 13	3 23 10 39	I 22 nbsp;nbsp;nbsp;9 19	6 29 50 29

1^4 nbsp;nbsp;nbsp;Of the Natufei iSt.

Saturn comes next to Jupiter in order from the fun. This planet can hardly be diftinguilhed from ^nbsp;fixed ftar by the naked eye i but when teen through anbsp;good telefcope, Saturn exhibits a moft Angular appearance. In fliort, it is furrounded by a thin, flat,nbsp;broad, and luminous ring, as is reprefented in fig*nbsp;6, Plate XXVIII. which does not couch the bodynbsp;of the planet 5 leaving a confiderable fpace allnbsp;round. Befides the ring, this planet is furroundednbsp;by feven moons of different fizes, which revolvenbsp;about it in different periods; but thofe fatelliceSnbsp;cannot be feen without a mofl; powerful tclef-cope.

Upon the body of Saturn, belts, fimilar to thofe of Jupiter, but much lefs diftindl, are alfo vifible,nbsp;and thofe belts feem to be parallel to the plane ofnbsp;the ring, and to the planet�s equator, which is in thenbsp;direction of the ring; the diameter of the planet innbsp;that diredion, being to the diameter perpendicularnbsp;to it, or to its polar diameter, as 11 to 10 nearlf*nbsp;From the motion of feme broken parts of the beltsnbsp;or fpots, it has been lately determined that S'aturnnbsp;turns round its axis, like the other planets, in thenbsp;dire�ion of the figns, in lo**, i6�, 2% nearly.

Saturn�s ring is divided into two parts by a ftrong� permanent, and well defined dark line aaai andnbsp;its outer edge, though very rhin, feems however,nbsp;in the opinion of Dr. Herfchel, to be not flat, hufnbsp;convex.

The ring in general looks brighter than the body

the planet itfelf; and from its caftins: a ftrong fhad. w 11 on the planet, it has been naturally con-Jlt;�'9:ured to be of a fohd nature. The following di-'�'enfions of this double ring of Saturn were deter-*Jhned by Dr. Heifchel.

^utfide diameter of ditto- nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;^nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;184353

^utfide diameter of ditto nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;204883

^teadth of the inner ring nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;aoooo

^'�'^alth of the outer ring nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;7200

Both the planet and its ring turn round the fame ^^fhrnon a-is; but .the ring leems to turn a littlenbsp;flower; viz. the nng turns in its own plane, in lo'�,nbsp;15^4. The fhape of the ring is neai ly circu-but, in conlequence of its oblique fituation.

Since the oblique pofition of Saturn�s ring remains always parallel to itfelf; or, which is the fame thing, fince the axis of that ring, like the axis of thenbsp;earth, is always direfted towards the fame point innbsp;the heavens; therefore twice in a faturnian year thenbsp;ring muft be turned with its edge towards the earthjnbsp;in which cafe it difappears for a Ihort time ; unlefsnbsp;it be viewed through a moft powerful telefcope (indeed I may fay, unlefs it be viewed through Dnnbsp;Herfchel�s 40-feet telefcope); for through it thenbsp;edge of the ring appears like a very flender ray ofnbsp;light palling acrofs the difc of Saturn*. It is evident that as Saturn moves and recedes from one ofnbsp;thofe limits in which the ring is turned edgewife towards the fun, fo one fide or furface of the ring becomes illumined by the fun at the fame time thatnbsp;the other furface is in the dark j and when Saturnnbsp;has paired the other limit, then the latter furface ofnbsp;the ring becomes illumined, and the former is deprived of light.

The fatellites of Saturn have not as yet proved fn ufeful to aftronomy or geography as thofe of Jupt'nbsp;ter; principally becaufe they cannot be feen unkf�nbsp;very powerful telefcopes be ufed. Five of thof^

* � According to Dr. Malkelyne, the plane of the rir^ � pafled through the earth on January 29, 1790 �, the eartl*nbsp;� palling from the northern, or dark, to the fouthern or en-� lightened fide of the ring; the ring, therefore, then he'nbsp;� came vifible, and will continue fo till 1803.�

The following table ftates the particulars wbic^ have been afcertained with refpe�t to the fatellitcsnbsp;Saturn. Speaking of the fatellites of Saturn,nbsp;might have added, that they are retained in their ot'nbsp;bits by the attrafdon of their primary j that th^/nbsp;afi; upon each other, that their periods and otb^''nbsp;particulars are found by the means of peculiar ob'nbsp;fervations, amp;c. but having laid enough withnbsp;fpeft to thofe particulars in our account of Jup�'nbsp;pitcr�s fatellites, it will be fufficient in this placenbsp;fay, that all the remark^ which have been made wit^nbsp;refpedl to the fatellites of Jupiter, are alio appb'nbsp;cable, with few obvious alterations, to the fatelli^^^nbsp;of Saturn.

The Georgiiim Sidus, with its fix fatellites, been entirely difcovered by Dr. Ilerfchel. The planelt;^nbsp;itfelf may be feen with almoft any telefcope, but it*nbsp;fatellites cannot be perceived without the moft poW'nbsp;erful inftrumentSj and the concurrence of all othetnbsp;favourable circumftances. One of thofe fatellites Df'nbsp;Herfchel found to revolve round its primary in 8^'nbsp;ly''. I'�.19�; the period of another he found tobei3^�

11*quot;. 5�. i%5. The apparent diftance of the format* from the planet is 33quot;.; that of the fecond 44^^-s'*nbsp;Their orbits are nearly . perpendicular to the plan^

The other four fatellites were difcovered a confi' derable time after, and of courfe Dr. Herfchel ha*nbsp;had lefs time to make obfervations upon them. The/nbsp;are altogether very minute objedts; fo that the fobnbsp;lowing particulars muft be confidered as beingnbsp;accurate but probable. � Admitting the diftancsnbsp;� of the interior fatellite to be 2 5'',5, its periodbnbsp;quot; cal revolution v/ill be 21��. 25A

� If th� intermediate fatellite be placed at aH *' equal diftance between the two old fatellites,

� neareft exteripr fatellite is about double the dib � t^nce of the fartheft old one j its periodical

	I.	II.	III.	IV.	V.	VI.	VII. '	VIII.	IX.	X.
	Apparent mean diameters. asnbsp;feen fromnbsp;the earth.	Mean diameters -as feennbsp;from thenbsp;fun.	Mean dla,-m'eters in ' Engh'ihnbsp;miles.	Mean diftances from the fun,nbsp;in round numbers of miles.	More accurate proportionalnbsp;numbers of thenbsp;preceding meannbsp;diftances.	Denfities to that ofnbsp;water,nbsp;which is I.	Proportions of the quantifies ofnbsp;matt r.	Inclinations of orbits to thenbsp;ecliptic in 17S0.	Inclinations of axes to orbits.	Rotations diurnal, or round their o\\nnbsp;axes.
8un - nbsp;nbsp;nbsp;.nbsp;nbsp;nbsp;nbsp;.	32'. tquot;,3	- -	883246	. . .	...		333928	-	82quot;. 44'. 0quot;.	25'*. h'�. 8�.
^^cury . nbsp;nbsp;nbsp;.nbsp;nbsp;nbsp;nbsp;.	10quot;.	i6quot;.	3224	37OCOOOO	38710	9k	0,1654	70. 0^. 0
.^us ...	38quot;.		7687	68000000	72333	S4t	0,8899	3�. 23'^35::l	66�. 32'.	o'*. 23''. Zl^J
i�^Farth - -		I fa	79'�.73	95000000	J00000	4l	1	o�. 0'. 0quot;.	66�. 32'.	Iquot;*.
Moon - -	3.'. 8quot;.	4quot;, 6	2180	95000000	I00000	S i	0,025	5�- 9- 3'- at a mean.	8 go.' 17'.	29lt;'.i7''. 44'quot;. 3'-
Mars -___	27quot;.	- I 0' '.	4189	1440C0C00	132369	3l	0,0875	1�. 51'. qquot;.	59�. 22'.	o'.24'�.39�.22.
Ferdinandca	1quot;.		160	260000000	273550			io�. 37'. 56' ,6 in 1801.
^*llas ....	oquot;s		So	266000000	279100			34^ 50'. 40quot;. in i8ci.
^�Piter - nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;.	39quot;-	31quot;-	89170	490000000	520279	��V	312,1	1�. 18'. 56quot;. in 1780.	90�. nearly.	049''. S5�37�-
. . -	18quot;.	16quot;.	79042	900000000	954072	' OtI	97.76	2�. 29'. 50quot;. in 1780.	60�. probably	o'*. 10'�. 16�. 2�.
^^gi�m Sidus -	3quot;- 54quot;		3gt;I12	1800000000	1908352	0-^-5-i 0 0	16,84	0�. 46'. 20''. in 1780.
	XI.		XTI.		xiir.	XIV.	XV.	XVI,	XVTI.	xvni.

Longitudes of 85 5 or places ofnbsp;afcending nodesnbsp;in 1750.

0 O M E other celeftial bodies feem likewlfc to revolve about the fun; but they differnbsp;^��orn the nine planets that have been already de-^'^'^ibed, principally in the following particulars :nbsp;�I'he curves which they defcribe round the funnbsp;^ focus, if they do return into themfelves, as isnbsp;probable, are eliipfes fo very eccentric, thatnbsp;of thofe bodies is only vifible to us whilft itnbsp;^^fcurs that part of its orbit which is in the vicinitynbsp;fun ; but during the much greater part of itsnbsp;it is quite invilible to us. 2. Their periodi-times are fo very long, and difficult to be afeer-^^ined, that it hardly falls to the lot of one man tonbsp;the fame body return twice to the ntighbour-'^od of the fun; and even then it would be diffi-

to identify it. 3. Their Ihapes are neither well � bned nor conftant; but moft of thofe bodies arenbsp;. �^��ounded by an indefinite faint light, a tail, a hairynbsp;''�'adiation, or coma \ from which they have been de-^oininated comets. They are likewife vulgarly called

We are utterly ignorant of the number and of the life of cornets in the fabric of the world.

The number of comet that have been feen and are recorded, is very great¹. But a vail numbernbsp;muft have efcaped notice j for there are feveralnbsp;comets fo very fmall as to be vifible -.mly throughnbsp;telefcopes, and fuch have frequently bet n feen ofnbsp;late years, when particular attenticn has been paidnbsp;to the fubjeft

With refpe�l to the natbre and the ufe of comets� various opinions have been entertained by differeiirnbsp;great and learned philofophers ; bucasnt�ching ver/nbsp;probable has been advanced, I ihali refer thofe whonbsp;wifh to examine fuch opinions to the works of othernbsp;authors f.

The apparent morion of comets, like that of aU other celeftial bodies, is from the eafl, towards th�nbsp;weft, which arifes from the diurnal rotation of tb^nbsp;earth in the contrary direclion. But comets have anbsp;proper and peculiar motion, each difterentnbsp;the others, and this motion is determined by tracingnbsp;the lituation of a comet with reipedl to thenbsp;ftars.

Riccioli reckons 154, until the year 1651. But bienietz reckons 415 until the year 1665.

de plac. Phil, Aulus Gellius. Seneca, lib. VII. Riccio^�� Jim. II. 35. De la Lande�s Aftronomy, book XIX.nbsp;ton�s Prindpia, book III. Vit\pe�s Aftronoroy. Grego�quot;)'nbsp;Aftronomy, chap, XXI.nbsp;nbsp;nbsp;nbsp;^

Of Comets, nbsp;nbsp;nbsp;193

Some comets perform their proper movements from the weft towards the eaft, which is the direc- ^nbsp;^*on followed by all the planets. But others movenbsp;*0 the contrary dire�bion, viz. from the eaft to-quot;'^rds the weft. Some of them move in the planenbsp;the ecliptic, or within the zodiac; whilft othersnbsp;�0 in different direftions, even perpendicular to thenbsp;of the ecliptic.

Upon the whole, it appears that every comet �^oves in a particular curve which has the fun in itsnbsp;j that it moves fo as to defcribe round the �nbsp;areas proportionate to the times; and that thenbsp;appears to be an exceedingly excentric ellipfis jnbsp;quot;'^ich clearly indicates that the comets are retainednbsp;''�'thin certain limits by the fame general law of na-the univerfal gravitation of matter; that theynbsp;be actuated by an impulfive force, which pre-their falling towards the common centre of at-||^^*^ion, and that therefore they move in orbits likenbsp;planetary orbits, only much more excentric.nbsp;k muft be confidered, that fince we fee a cometnbsp;during a very fmall part of its periodical courfe,nbsp;which fmall part we muft calculate and deter-the whole orbit and the periodical time, everynbsp;^11 error committed in the obfervations of thatnbsp;part, produces a confiderable difference in the

of the whole j nor can the quantity of that ^'�Or be cafily verified and corredted by future ob-^^'quot;''ations; firft, becaiife the period or the returnnbsp;^ comet is very long; and fccondly, becaufe thenbsp;IV.nbsp;nbsp;nbsp;nbsp;Qnbsp;nbsp;nbsp;nbsp;comet

comet itfelf cannot be identified. Indeed, the on!/ reafon aflronomers have for faying that a certainnbsp;comet has returned two or three or more times, isgt;nbsp;that when the period of a comet-has been determined from the Obfervation of that fmall portionnbsp;its orbit, which comes within the reach of obfervation ; if after the lapfe of that period a comet appears about the fame part of the heavens, they conclude that it probably is the fame comet. Notnbsp;above fN or feven comets, amongft all thofe whichnbsp;have been feen, have as yet been calculated withnbsp;accuracy fufficient to render their period tolerablynbsp;well known, which fliews that the fubjedl is ftill i''nbsp;its infancy, and a vaft number of farther obferva-tions is ftill wanted for the purpofe of generalizingnbsp;and correding the theory. But the opportuniti^^nbsp;for making fuch obfervations feldom occur 3 thetC'nbsp;fore the prcgrefs of knowdedge, relative to connctsnbsp;has been but flow. The wifeft ancient philofophot^nbsp;confidered the comets as periodical celeftial bodi^^'nbsp;Sir Ifaac Newton concluded, that they mightnbsp;fcribe very excentric ellipfes, and might re-app^�''nbsp;at every revolution. Dr. Halley verified thisnbsp;idea, by aftual calculations upon the obfervations �nbsp;feveral comets. It is fuppofed that it was the f^^^nbsp;comet which appeared in the years 1456, jnbsp;1607, 1682, and 17593 fo that this comet�s per*�nbsp;is about 75 years. Another comet, which wasnbsp;in the year 1532, is fuppofed to be the femenbsp;�was feen in the year j66i, and was expeded abo�*

year 1789 or 1790; but did not appear. According to Halley, the great comet of the year 1680 to re-appear in the year 2254 j and is fuppofed tonbsp;the fame that appeared at the time of Caefar, andnbsp;^^3t appeared alfo in 219 and 2349 before our Sa-''iour�s birth*

Even fuppofing that the period of a comet could Caltulated with fufficient accuracy j yet, confider-the various caufes which muft difturb the regularnbsp;*^otion of that comet, we may eafily imagine thatnbsp;return of that comet may thereby be Ihortenednbsp;lengthened, or diverted, to fuch a degree as tonbsp;^quot;^e it the appearance of a different comet. In con-%Uence of the excentricity of their orbits, thenbsp;^Ottiets muft in their courfes crofs each other, andnbsp;I�kevvife crofs the planetary orbits ; hence they maynbsp;^^��ie fo very near one another, or fo very near anynbsp;the planets, as to difturb their motion, and evennbsp;^ 3s to ftrike againft and deftroy any of them. In-from fuch an addon, it is not improbable thatnbsp;^ path of a comet may be changed into a parabola.

Several of thofe who wifh to account for the delug6 the agency of natural caufes, attribute that great con-^on to the near approach of that comet to the earth; fornbsp;^he attraclion of the moon alone is capable to rarfe' confi-tides, the near approach of a body fo much largernbsp;33 the moon, muft a�l with vaftly greater force. Seenbsp;^ ifton�s New Theory of the Earth 5 and De la Lande�snbsp;��flexionsfur U Comet�^ Paris 1773,

or fome other curve, and thus the comet may return again. As for the methods of computation 0^nbsp;the orbits of comets, I muft refer the ingenious reader to other works * ; but I fliall only mention innbsp;this place, that the paths �f comets have often beennbsp;faid to be parabolical, and have been calculated uponnbsp;that principle, not becaufe they are really fo j for ifnbsp;they were parabolical, they could not return intonbsp;themfelves f hence the comets would continue fofnbsp;ever to recede from the fun j but becaule the properties of a parabolical curve are calculated withnbsp;much greater cafe and expedition than thofe of annbsp;elliptical curve 5 and at the fame time the nature ofnbsp;a parabola is fo very near the nature of a vaftiy eccentric ellipfis, that the refult of the calculation uponnbsp;cither of them is nearly the fame.

The times during which comets remain in fgh�^ are various, but they hardly ever exceed fix month*�nbsp;and fome comets have not been feen for mot^nbsp;than a few nights. Of thofe which have remainc�^

Lande�s Aftrononiy, B. XIX. Vince�s Aflronomy. Via*' raut�s Theor. dii Movem. da Comet'es. D�Alembert�snbsp;Mathem. tom. II. Gregory�s Aftroti. chap, XXI. wh**^'*nbsp;is a concife and fatisfaiSfory DilTertation on Comets :nbsp;Bode�S Papers on the Orbits of Planets and Comets, innbsp;Memoirs of the Berlin Academy, from 1786 tonbsp;and Sir Henry Englefield�s Work on the Orbitsnbsp;Cotr.ets.

fight for fix months together, one is faid to have Appeared in the year 64, at the time of Nero; ano-appeared about the year 6oj, at the time ofnbsp;Mahomet; a third comet of that continuance wasnbsp;in 1240, at the time of the irruption of Tamer-^ane; a fourth appeared in 1729, which remainednbsp;fight from July th� Jiftj 1729J. to the 21ft ofnbsp;January, 1730. Comets that have appeared fornbsp;Sorter periods are recorded by feveral writers andnbsp;Particularly by Riccioli.

The proper movements of comets are alfo djf-^'^tent from each other, and very variable with re-to the fame comet. From the nature of planetary orbits in general, it is eafy to conceive thatnbsp;the comets defcend towards the fun, fo they muftnbsp;^tiicken their pace, until they reach the perihelion,nbsp;which limit, they flacken their pace, and con-^'I^Ue to do fo in proportion as they recede from thenbsp;'''Cinity of the fun. When they are going off, andnbsp;*^^arly vanilhing, they fometimes move fo verynbsp;^^wly as to be hardly difcernable amongft the ftars.

, ^t forne comets have been obferved to move with 1�^tredible quicknefs. The comet which appearednbsp;^472, paffed through 120� in one day. Thenbsp;of 1760, altered its longitude by 411� innbsp;day. The, comet of 1664, moved 164� innbsp;*7 days, amp;c.

^ere the comets near the earth, the above-*^^ntioned quick movements would not excite any ''bonder j but when we confider their prodigiousnbsp;03nbsp;nbsp;nbsp;nbsp;diftances.

�9S nbsp;nbsp;nbsp;'Of Comets.

diftances, which in general far exceed the diftances of the moft remote planets, we cannot but be afto-nilhed at the wonderful velocity with which theynbsp;muft move. Another fource of inequality in thenbsp;apparent motion of comets, arifes from the motionnbsp;of the earth, the effedl of which muft vary according to the dire�tion both of the earth and of thenbsp;comet.

That the comets are at moft aftonifhing diftances from us, is derived from their having little or nonbsp;farallax; viz. when they are viewed from differentnbsp;parts of the furface of the earth, and are referred tonbsp;the fixed ftars, they appear to ftand at the vet/nbsp;fame point of the heavens, or nearly foj whichnbsp;would not be obferved if they were even withiOnbsp;double the diftance of the Georgian planet. I Ihal^nbsp;render this more intelligible by means of a diagraO*nbsp;or two.

Let AEG, fig. 7, Plate XXVIII. be the earth� and D a comet. Then, if the comet D be fc^'^nbsp;from the centre T of the earth, or in that dirc^'nbsp;tion, viz. from O ; the place of that cometnbsp;ferred to the fixed ftars, will appear at G j hotnbsp;when feen from the furface of the earth or placenbsp;the fame comet will appear at E. The formernbsp;called the comet�s true place, and the latter itsnbsp;rent place. Now the diftance GE between the trf^nbsp;and the apparent places, is called the parallax of th^*quot;nbsp;comet. By infpedling the figure, it will benbsp;comprehended, that the farther the comet D is

the

earth, the fmalJer will the diftance G E be, and verfa ; therefore, when that diftance or parallaxnbsp;little or nothing, the diftance of the comet isnbsp;ptodigioufly great; nor can we aiftgn the quantitynbsp;it. The nature of parallaxes will be better ex-Piained hereafter.

The precife place of a comet at any particular ^irne of its appearance, may be determined by mea-^��'ting its diftance from any two contiguous fixednbsp;^^rs j and that place may be marked upon a pla-^ifphere or globe; thus its difterent fituations innbsp;different times during its appearance, niay be mark-down, and a line drawn through thofe points willnbsp;^^^Prefent the track of the comet. The above-^^ntioned diftances muft be taken by means of anbsp;Quadrant, or a micrometer ; but even without anynbsp;inftruments, and merely by the ufe of a thread,nbsp;may find out whether a comet have any pa-J'^tlax, as alfo afcertain its place. A comet, whennbsp;going out of fight, moves fo flowly as notnbsp;^0 change its place fenfibly in a few hours time. Innbsp;^^is cafe therefore let the fuuation of the comet benbsp;obferved twice during the fame night, viz. oncenbsp;''vhen it ftands very h gh above the horizon, andnbsp;Another time when it ftands near'the horizon, whichnbsp;^'�nounts to the fame thing as to obferve it from twonbsp;different places at.the fame time. Then if the cornetnbsp;both obfervations appears to retain the Tamenbsp;^'tuation with refped to the ftars, we may concludenbsp;*^bat it has no fenfible parallax. The fimpie way of

finding the fituation of the comet for this purpofcj is to hold a thread with your two hands, and extending it between you and the comet, to move it bynbsp;trial until it covers two contiguous ftars, at the famenbsp;time that it palTes through the comet j which ihewsnbsp;that the comet is in the diredtion of the two ftars,nbsp;amp;c. If the place of the comet be required momnbsp;accurately for the purpofe of delineating its track,nbsp;you muft obferve once every night, or oftener, bynbsp;means of a thread, the fituation of the comet, withnbsp;refpedt to four ftars, fuch as are contigu�us to itjnbsp;and are marked upon a celeftial globe or plant'nbsp;fphere; for by this means you may every tim^nbsp;make a dot at the precife place upon the globe, andnbsp;afterwards, by joining thofe points with a line, yo^tnbsp;will have the track of the comet. Thus let th^nbsp;comet be at A, fig. 8, Plate XXVIII. between thenbsp;four ftars, B, C, D, E j fo that the line joining th^nbsp;ftars B, D, may pafs through the comet ;nbsp;fo may alfo be the cafe with the line which joins thenbsp;ftars C and E. Then if you extend a thread,nbsp;place the edge of a piece of paper through the fta��^nbsp;C and E, upon a globe or planifphere, where fochnbsp;ftars are marked, and extend another thread throughnbsp;the ftars B and E j the interfeftion of the twonbsp;threads will point out the place A of the com^�'nbsp;upon the globe, or planifphere, where anbsp;may be made, amp;c.

diftances

�^iftances of comets. Moft of them move entirely beyond the planetary orbits, but fome comets havenbsp;'^sfeended below Mars, and it is faid even below�nbsp;^he orbits of the inferior planets.

The figures and fizes of comets vary confidera-and even the fame comet alters its figure in courfe of a few days. Some comets feem to benbsp;Nothing more than a congeries of vapours ill defined,nbsp;^^tanfparent throughout, and refle6ling very littlenbsp;^'Sht. Others are of a fimilar nature, excepting thatnbsp;^ denfer fubftance more opaque, commonly callednbsp;^ Nucleus, is feen within the rare or vapour-like fubftance. Almoft all comets are furrounded by denfenbsp;^ttnofpheres, which partly'refleft the fun�s light,

. ^^d at the fame time prevent that light�s falling in a ^onfiderable quantity upon the nucleus, or what maynbsp;confidered to be folid part of the comet j fonbsp;*^at the folid part, or nucleu's, though brighternbsp;'^han the furrounding part, is, however, not fonbsp;^^'ght as Jupiter, or as part of the moon. But thenbsp;ft^'ghtnefs of a comet changes according as it re-'^sdes from, or approaches, the fun ; and at thenbsp;^^nrie time it puts forth certain elongations of lumi-matter, which have been called hoards, ornbsp;hair, or tails, according to their differentnbsp;Pofitions and appearances j for thofe elongationsnbsp;Sometimes are very Ihort and hardly vifible, whereasnbsp;other times they are extended to a prodigiousnbsp;ft^gtee; and it is remarkable that this luminous

elonga-

elongation or tail, is always direded from the fun, as is Ihewn in fig. 9, Plate XXVIII. where thenbsp;cornet A is reprefented as it appeared fucceffivelynbsp;in two different parts of its progrefs round the funnbsp;S. When the comet is eaftward of the fun, andnbsp;moves from the fun, it is faid to be bearded,nbsp;becaufe the-luminous elongation goes before it-When the comet is weft ward of the fun, and fetsnbsp;after him, it is then faid to have a tail, becaufenbsp;the luminous elongation follows it; and when thenbsp;earth happens to be direcftly between the fun andnbsp;the comer, then the train of light is hid behindnbsp;the body of the comet, and a little of-it onlynbsp;feen on the fides of the comet, which is therebynbsp;faid to have a coma or hairy appearance.

� The tail of a comet, at its firft appearance, is very ftiort, and increafes as the comet ap'*nbsp;proaches towards the fun; immediately afternbsp;perihelion the tail is longeft, and moft luminous,nbsp;and is then generally obferved to be fomewhat bent,nbsp;and to be convex towards thofe parts to which th^nbsp;comet is moving ; the convex fide being rathetnbsp;brighter and better defined than the concave fid^*nbsp;When the tail arrives at its greateft length,nbsp;then quickly decreafes, and foon vanifhes en-tircly ; and about the fame time the cometnbsp;ceafes to-be feen. The matter of which the tailnbsp;is formed is exceedingly rare, and fo verynbsp;lucid, that the light of the fmalleft ftars fuffers nonbsp;3nbsp;nbsp;nbsp;nbsp;diminutio*^

diminution in paffing through if, as is remarked by Newton in his Principia, lib. III. prop.

The fplendour of comets increafes in proportion they approach the fun, though at the fame timenbsp;*heir diameters, in confcquence of their recedingnbsp;the earth, may appear to diminifh.

The fizes of the bodies of comets, as well as of ^^eir tails, is fo various, as that fome of themnbsp;'Cannot be feen without a telefcope, whilft othersnbsp;We even equalled the dife of the funj and filchnbsp;^as that which Seneca relates to have appearednbsp;the time of the emperor Nero. The cometnbsp;^kich Hevelius obferved in the year 1652, feemednbsp;equal the apparent fize of the moon, but itnbsp;W a pale, dim, and difmal afpedt. Severalnbsp;'Comets have been feen, whofe apparent fize exceeded more than four times the dife of Jupiternbsp;Cr of Venus.

The tails of comets are, in general, more expanded and Icfs denfe, in proportion, as they recede from the bodies of the comets. The comet of the year 1744, had the luminous elongation,nbsp;fdnaewhat like a fan, divided into various branches.nbsp;The extenfion of the tails of comets is fomc-CiiTies aftonifhingly great. They have often beennbsp;obferved to extend more than 90% or even half anbsp;Circle ; whence it has been calculated that theirnbsp;^cal lengths muft exceed 60 or 80 millions of

miles. It is remarkable that the tail of the fame comer, obferved at the fame time, appears of difquot;nbsp;ferent lengths from different parts of the earth'snbsp;farface, and it appears longeft from thofe placesnbsp;which have a lower latitude, which probably arifesnbsp;from the fuperior clearnefs and ferenity of the fkynbsp;in thofe places.

Whether the tails of comets be a train of pure light or of vapours, or of fomething eleftricaknbsp;fimilar to the aurora borealis, is impoifible to benbsp;decided ; but it appears that both the increafe ofnbsp;fplendour of a comet, and the appearance of a tail�nbsp;are derived from the fun.

quot; The great comet which appeared in the year 1680, after its departure from the feri-� helien, projeded fuch a tail as extended itfelfnbsp;quot; more than 40'quot; in the heavens j nor can thisnbsp;be a wonder; for it was fo near the fun, thatnbsp;� its diftance from his furface at the �perihelionnbsp;� was but a fixth part of the diameter of thenbsp;� fun�s body; and therefore the fun feen fromnbsp;� the body of the comet, would appear tonbsp;� the greateft part of the heavens, and its app3'nbsp;� rent diameter would not be lefs than 120� 5nbsp;� and therefore the heat it received from thencenbsp;�� muft be prodigioufly intenfe beyond imagina'nbsp;tion; for it exceeded above 30Q0 times thenbsp;� heat of red-hot iron. And therefore we muftnbsp;allow, that the bodies of comets, which can

quot; bear fo great a heat, mud be very denfe, hard, quot; and durable bodies; for if they were nothingnbsp;quot; but vapours and exhalations, raifed from thenbsp;earth and planets, as fome have dreamt, thisnbsp;quot; comet, at fo near an approach to the fun, mudnbsp;� have been quite deftroyed and diffipated.��nbsp;Neill�s Introduftion to Aftronomy, Led. XVII.

Besides the planets both primary and le-condary, and the comets which are feen at uncertain times, all the other lucid and brilliant ob-jeflis, which, during the abfence of the fun, wC perceive in the heavens, are the fixed fiars, fo callednbsp;from their preferving, as far as we know, theifnbsp;fituations with refpeft to each other, without anynbsp;deviation.

The fixed ftars appear to our eyes of different lizes j but it is not in our power to fay, whethefnbsp;that difference arifes from their real differencenbsp;fize, or from their being at different diflances, o'�nbsp;from both thofe caules conjointly. The gradationnbsp;of apparent fize from the largeft to the fmaliei^nbsp;liars, is great and indefinite; yet for the ufe of do-fcription and difcrimination, aftronomei s ditlingoid^nbsp;them into fix, or more, orders, which naturallynbsp;of a vague and indefinite nature ; calling the larg^^nbsp;of them ftars of thefirft magnitude j the next, �nbsp;theJecondmagnitude, and fo forth. The ftars ofnbsp;fixch magnitude are thofe which can barely be dii*'

^'nguiflied by the naked eye. Thofe which can only leen by the help of the telefcope, are called te-^fiopic ftars.

Several of the brighteft and mofl: remarkable ftars are diftinguilhed by peculiar names � but thenbsp;difficulty of difcriminating the particular fituationsnbsp;them all, even of thofe that have peculiar names,nbsp;ftgt;ggefted an expedient which has been adoptednbsp;ftom the remoteft antiquity, and has been followednbsp;^'^d improved in fubfequent periods. By this me-ffiod the ftars are fuppofed to be, as they appear, innbsp;concave furface of a fphere, upon which thenbsp;ftBtires of men, beafts, and other objeds, are fup-Pofed to be delineated ; then the fituation of eachnbsp;ft^t is defcribed by faying, that it is near the tail ofnbsp;^ t^ert^n filh, in the bull�s eye, juft over the Ihouldernbsp;Hercules, amp;c.

The ideal delineations of thofe figures of animals, other objeds, which are called ccnfiellationSy ornbsp;are difperfed all o^^er the heavens, and anbsp;Particular fituation is alfigned to each, as may be-upon a common celeftial globe, or upon anbsp;P^^nifphere; yet fome fpaces remained here andnbsp;which were out of the bounds of the continuous conftellations. The ftars which were con-^^lUed in thofe places, were called unformed ftars;

is impoffible to lay what fuggefted the idea of pting each particular conftellation j but as far as

can be conjeflured from the dark documents hiftory, of tradition, and of fable, they feem tonbsp;have been derived from different caufes, fuch a¹nbsp;from the rainy feafon, �which ufually came ob whei^nbsp;a certain affemblage of ftars appeared above thenbsp;horizon; from,the refemblance, however imper-feft, of certain groups of ftars to particular objects;nbsp;from the defire of recording fome remarkablenbsp;event, or of paying homage to fome diftinguilhednbsp;perfon, amp;c.

Thus, by mentioning the particular conftellation to which each belongs, the ftars may be prettynbsp;nearly, though by no means accurately, deferibed 5nbsp;and this probably was the only mode of deferibingnbsp;the fituations of the ftars during feveral centuries;nbsp;but at the revival of learning and fcience, whennbsp;particular attention began to be paid to aftronomf�nbsp;the above-mentioned indeterminate mode was gra'nbsp;dually improved by the particular defeription of thsnbsp;ftars� apparent magnitude, by annexing a Greeknbsp;letter, ora Roman letter, or a number, to each ftat�nbsp;and by forming catalogues of their right afeenfion�nbsp;and declinations , by which means each particula¹quot;nbsp;ftar may be readily and accurately known ¹.

The moft accurate method of deferibing the brightufif¹ or magnitudes of the ftars, is undoubtedly that whichnbsp;Herfche! his adopted in his excellent catalogues ofnbsp;coraparative brightnefs of the fixed ftars, the firft of whi�h

Of the fixed Stars. nbsp;nbsp;nbsp;scy

The following lift contains the names of the eon-ftellations, the number of ftars, as far as thofe of the fixth magnitude, that are contained in each con-ftellation, as alfo the names and magnitudes ofnbsp;'^Hofe more remarkable ftars of the annexed conciliations, to which particular names ha,ve beennbsp;�iven.

�^^talogues- is publlfhed in the Philofophical Tranfaflions for *796. The others in the following volumes.

This method is to refer a given ftar to two other liars, of which is fomewhat brighter, and th,e other fomewharnbsp;Cfs bright than the given one. � I place, (he fays) eachnbsp;^ar, inftead of giving its magnitude, into a ftiort feries,nbsp;ionllrucled upon the order of brightuefs of the neareftnbsp;proper ftars. For inftance, to exprefs the luftre ofnbsp;quot;nbsp;nbsp;nbsp;nbsp;1 fay CDE. By this Ihort notation, inftead of re-

� ferring the ftar D to an imaginary uncertain ftandard, I �quot;ifer it to a precife and determinate exifting one. C isnbsp;^ ftar that has a greater luftre than D; and E is anothernbsp;lefs briffhtnefs than D. Both C and E are neighbour-'�'g ftars, chofen in fuch a manner that I may fee them atnbsp;'�oe fame time with D, and therefore may be able tonbsp;Compare them properly. The luftre of C is in the famenbsp;^ manner dfcertained by B C D j that of B by ABC j andnbsp;the brightnefs of E by DEF j and that of F bynbsp;EFG.�

Of ihe fixed Stafs.

Coma Berenicis -Carnelopardalus -Mons Menelaus -Corona Borealis -terpens - - nbsp;nbsp;nbsp;-

Taurus Ponia-towflci Cyra -Cuipecula etnbsp;Anfer -^^gittanbsp;^quilanbsp;Celphinus -Cygnusnbsp;Cquuleus -Cacerta , -Cegafus --Andromeda - -

Centaurus - -Lupus - - -Quadra Euclidis Triangulum Au-ftrale -nbsp;nbsp;nbsp;nbsp;-

Ara - - -Telefcopium -Lorona Auftralis E* avo - _ -^ndus - - -J^icrofcopiumnbsp;^ftans Hadleia-nus - - - .nbsp;Qrus . - - ,nbsp;Toucan - - �nbsp;�Tcis Auftralis

The whole number of ftars, as reckoned in the Preceding lifts, amounts to 3186. But the nakednbsp;can feldom diftinguifti a third part of that num-J in more favourable climates fome perfonsnbsp;can diftinguifti more ftars, in certain conftella-than thofe which have been ftated in the lifts.

^Tion.

Befides the feparate ftars, a fharp eye in a clear night may obferve a few whitilh fpots called neluUtnbsp;but a moft, remarkable broad and much extendednbsp;whitiQi track may be obferved at all times in thenbsp;heavens. This is called, from its whitenefs, thenbsp;galaxy, via la�iea, or milky way. This remarkablenbsp;zone is irregularly extended, and varies in breadthnbsp;from 4� to 20�. It paffes through Calfiopeia, Per-feus, Auriga, the foot of Gemini, Orion�s Club, partnbsp;of Monoceros, the tail of Canis major, throughnbsp;Argo Navis, Robur Carolinum, Crux, and the feetnbsp;of the Centaur : beyond which it divides into twonbsp;parts 5 its eaftern branch paffes through Ara, thenbsp;tail of Scorpio, the eaftern foot of Serpentarius, thenbsp;bow of Sagittarius, Scutum Sobiefcianum, the feetnbsp;of Antinous and Cygnus. Its weftern branch paflesnbsp;through the upper part of the tail of Scorpio, thenbsp;right of Serpentarius and Cygnus, and ends it*nbsp;Cafliopeia.

Such are the objefts which may be difcerned by the naked eye in the region of the fixed ftars; bubnbsp;by the afliftance of the telefcope, the number, thenbsp;beauty, and the variety of wonderful objedls is itgt;'nbsp;creafed to an aftonifhing degree; and much mot^nbsp;fo in proportion to the power of the telefcope.nbsp;immenfe quantity of new ftars is difcovered. Sevei^^nbsp;ftars, v/hich appear as fingle ftars to the naked ey^�nbsp;and even through ordinary telefcopes, when vi^^nbsp;with higher powers, appear to be double, or trebk'nbsp;or quadruple, amp;c. viz. are found to be two or thre^�

more ftars, fo near to one another as to appear, through ordinary telefcopes, as a fingle ftar ¹. Theynbsp;alfo moftly found to havCs peculiar colours, ornbsp;'��fits, fo that one flat will be of a greenilh tint,nbsp;another of a reddifli, or bluilh, amp;c. f. The num-of nebulse that can be difcovered by the aflif-^^nce of a powerful telefcope, amounts to fomenbsp;^houfands f. The via ladlea, and feveral of the ne-are found to confift of an aftonilhing numbernbsp;apparently fmall ftars, fituated very clofe to eachnbsp;�ther; fo much fo, that in a fmall part (as of aboutnbsp;degree in diameter) of fome of thofe nebuls,nbsp;of the via laftea, there appears to be a greaternbsp;humber of ftars than can be feen by the naked eye innbsp;whole celeftial fphere.

It is remarkable that though the ftars appear '^aftly to differ from one another in apparent gran-as they certainly do in point of brilliancy ; yetnbsp;'�^eir apparent diameter cannot be meafured; for theynbsp;always look like incommenfurable points; and ifnbsp;'^hen viewed through certain telefcopes, they feem tonbsp;a fenfible diameter j that effedl arifes fromnbsp;imperfedlion of the telefcope, fince it increafes

a Herculisj S' Lyrse; � Geminorum; 7 Androme-� ft Cygni j and a great many more, are double ftars j ^ 1'yras, is treble � Orionis, is quadruple, amp;c. amp;c.

quot;I See Herfchel�s catalogues of double ftars and nebul� 'h ihe Philofophical Tranfadtlons.

and decreafes in proportion as the telefcope is more or lefs perfeft, and according to its adjuftment.

This obfervation, together with their total defi' ciency of parallax, fliews the- moft incomprehenfiblenbsp;diftance at which even the neareft of the fixed ftarsnbsp;muft be fituated.

That the ftars ftiine not by refledled or borrowed light, like the planets j but by being felf luminous,nbsp;like the fun, may be eafily and fatisfadorily concluded from the following confideration. The apparent fize of the ftars is certainly fmaller than thatnbsp;of the fatellites of Jupiter or of Saturn; tljeir dif-tances from us are likewife incomparably greater thannbsp;thofe of the fatellites ; but thofe fatellites cannot benbsp;feen by the naked eye, and feme of them even require moft powerful telefcopes; therefore, if thenbsp;ftars fhone by reflecting the light of the fun, as thenbsp;fatellites do, they ought to be much lefs vifible thaanbsp;the fatellites ; which is not the cafe. We may therefore fafely cohclude, that the fixed ftars are felf Iti-minous like the fun. They probably are of the faro^nbsp;nature, and equally large, if not larger. And fin^^nbsp;fuch immenfe bodies, fo far removed from us as Wnbsp;be moftly out of our fight, could not be intendednbsp;for bur ufe, nor to interfere with the folar fyftem i '*�nbsp;is moft likely that they are the funs, or the centres�nbsp;of as many fyftems, and that a number of planets andnbsp;comets isi revolving round each ftar, from

may advance our conjedture a ftep farther, and '^uppofe that poffibly fome of the comets of eachnbsp;fyftem, which move in very cxcentric orbits, may,nbsp;their aphelia, come within the attractive power ofnbsp;^ome other ftar or fun, fo as to pafs from one fyfteminbsp;another; and thus form a fort of communicationnbsp;between the different fyftems; but as there is nonbsp;^*id to conjecture, let us return to matter of faCt.

Though the flats are called fixed, as they are in ^Ornparifon to other celeftial bodies ; yet they muftnbsp;*^ot be confidered as perfectly immoveable and unchangeable. Indeed the little movements, to whichnbsp;��hey have been obferved to be fubjeCt, mull: not benbsp;corrfidered as their proper movements ; for'theynbsp;to be accounted for upen the motion of thenbsp;c^rth, the motion of light, amp;c. as will be flrewn innbsp;��he fequel j but independent of motion from theirnbsp;�^cfpeCtive fituations, feveral changes have unquef-��onably been obferved amongft the flats, and probably a great many more will liereafter be obferved ;nbsp;the accurate catalogues of the fizes, appearances,nbsp;fituations of the flats which have been latelynbsp;�^^de, and the powerful infiruments that are now innbsp;^^*^3 will enable the aftronomers to difeover the moilnbsp;^j^�nute variations of fize, of brilliancy, and of fitua-

^ 1 wo liars of the fecond magnitude, which were trnerly vifible in the flern of the confiellation yirr

of the emperor Ocho, a new ftar appeared in CafTio-peia, which difappeared fome time after. In the year i6co, Kepler obferved,a new ftar in thefwan�snbsp;breaft, which remained vifible during feveral years;nbsp;bat it became invifible from the year 1660 till thenbsp;year 1666, when it was again obferved in the verynbsp;fame place by Hevelius, as a ftar of the fixth magnitude. A ftar in the neck of the whale has the remarkable property of appearing and difappearingnbsp;alternately. Other ftars appear to have their fize otnbsp;brilliancy increafe and decreafe periodically. A ftatnbsp;of this fort is in Hydra, another in Cygnus, and anbsp;moft remarkable one, called Hlgol, is in Meduja'snbsp;head. This Algol feems to have a period of 2nbsp;days and 21 hours, during which it varies from thenbsp;fize of the fecond magnitude to that of the fourth iitnbsp;about hours, then returns to the former fize it*nbsp;the fame time, and retains that fize for the reftnbsp;of the above-mentioned period. Such periodica^nbsp;changes in the brightnefs of ftars, may probably b�nbsp;owing to their performing periodical rotations rouoftnbsp;their axes, and to their having fpots on fomenbsp;of their furfaces j fo that when that part happens tt*nbsp;be turned towards us, the ftar muft appearnbsp;bright than at other times. After the fame manne*quot;nbsp;the entire difappearance and reappearance of certai**nbsp;ftars may perhaps be accounted for.

If the reader wifh to learn the fituation of tb� conftellations, and the names of the moft remarkable

liars, or to find the particular ficuacions of ^^rtain liars, we mull refer him to the catalogues,nbsp;to the celeftial atlalTes of Flarnlleed, Bode, andnbsp;^'^Hers. A competent knowledge of the fame may,nbsp;however, be obtained by means of a common ce-^^ftial globe, which being duly fituated and reflifiednbsp;the particular time of making the obfervation,nbsp;indicate the fituation of the liars with fufficientnbsp;^'^curacy; fo that the learner, having fituated thenbsp;�lobe (according to the precepts which will benbsp;8'ven hereafter) in an open place and a ferenenbsp;*^'ght, when the moon does not lliine, by lookingnbsp;any particular conllellation or liar on the uppernbsp;of the globe, and imagining that a llraight line,nbsp;from the centre of tlie globe, and through thenbsp;B�ven liar or conllellation on the furface of thenbsp;�^ohe, be extended as far as the heavens, he willnbsp;*'^adily find the real ftar or afiemblage of liars innbsp;*-^''at identical fpot, which is pointed out by the im-^S'nary line*.

In this part of the world the moll cop/picuous ^onllellations, and therefore the bell for a learner tonbsp;quot;^^g'n with, are the Great Bear and Orion; and fromnbsp;diredlion of the principal liars of thofe conltel-

lations, he may, by referring to the globe,, learn the contiguous ftars, then tbofe which are farthernbsp;off, and fo forth. The Great Bear is undoubtedlynbsp;the moft ufeful, becaufe for this part of the earthnbsp;it never lets. Oi ion is vifible in the winter time. tO'nbsp;wards the fouth, and the arrangement of its ftars i*nbsp;fo remarkable, that once known, it is not afterwardsnbsp;eafily forgotten.

[ 221 3

Here it muft be obferved, that the fpedtator B the right line which joins the centre of thenbsp;and the celeftial body H ; therefore he feesnbsp;^ body perpendicularly over his head, and in thenbsp;^ m.anner (viz. againft the fame ftar), as if henbsp;It from the centre of the earth ; whereas this isnbsp;the cafe with the fpedlator at A, or with a fpec-f t fituated any where elfe upon the furface of thenbsp;^tth. Now the difference between the true place

of a celeftial body (meaning the place which it feefflS to have when viewed in the diredtion of the centranbsp;of the earth¹), and the place which it feemsnbsp;have in the celeftial fphere, when viewed from anynbsp;other part of the furface of the earth, is called bynbsp;the aftronomers the parallax of that body. Other'nbsp;wife, in general terms, the parallax of an objeft isnbsp;the difference between the places, that objedl is rC'nbsp;ferred to in the celeftial fphere, when feen at thenbsp;fame time from two different places within thatnbsp;fphere; or it is the angle under which any two place�nbsp;in the inferior orbits are feen from a fuperior planer�nbsp;or even from the fixed ftars.

In the abovementioned figure, N is the true plac^ of the body H; O is its apparent place; and the arcnbsp;ON is its parallax. It is evident that the nearriquot;nbsp;the body H comes to the vertical line CZ,nbsp;fmaller its parallax becomes; for when the bodynbsp;in that vertical line as at h, the two lines, viz. tb^rnbsp;which paffes through A, and the body h, as alfo tba^nbsp;which paffes through C, and the fame body h, coiC'nbsp;eide; and of courfe, when the bedy is in the vertic^r^

I'he ftuatioiis of celeftial objefts are calculated aiwaf¹ W'ith rei'ped to the centre of the earth, and in all the p^'^'nbsp;cepts that are given for the folution of aftronom'cal P¹�¹�'nbsp;blems, the diftances and fituations of celeftial objeifts-�'�¹nbsp;always reckoned from their centres ; hence the place vvhicbnbsp;a celeftial objeA feems to have when viewed from the ceiitr�nbsp;of the earth is called its true place.

or in the zenith j it cannot have any parallax, the cont^'ary, when the body is at I, v'z. in thenbsp;^^tizcn of the fpeftator A, then it has the greateftnbsp;P^raliax 0 :�: becauie the place of obfervation A,nbsp;�'h',, rface or i.he earth, is then the fartheft pof-fible ^pom the other place of obfervation b, which isnbsp;the diredlion of the centre C.

It is alfo evident that, cateris paribus, the farther ^ celeftial body is from the earth, the fmaller itsnbsp;P^tallax muft be; thus the body P, which is farthernbsp;*�001 the earth AB^, than the body H, has its pa-N p, evidently fmaller than the parallax ON,nbsp;the body H.

^ith refpefb to the meafure of the above-men-^*otied parallax, it muft be obferved that the pa-quot;^^Hax N O of the body H, is the difference of the ^**gles ZCH and ZAH; that is, of the angles ZGNnbsp;^**d ZAO j which difference is equal to the anglenbsp;�^^C, or NHO ; for the external angle ZAH, ofnbsp;triangle AHC (Euclid�s Elements, B. I. prop,nbsp;is equal to the two internal and oppofite anglesnbsp;and ACH ; therefore AEIC is the differencenbsp;^�ween the two angles ZAH and ACH, or ZCH;

this angle AHC (which is equal to NHO) ^Cafures, or is itfclf called, the parallax of the bodynbsp;that fituation. AHC then is the angle undernbsp;the femidiameter AC of the earth appears tonbsp;fituated at the celeftial body H. The angle,nbsp;*t;h the diameter of the earth�s orbit would fubtend

to an eye fituated in a celeftial object, is called th^ parallax of the great orbit.

From whac has been faid above, the following ufeful theorem is eafily derived �, viz. the fine of tbtnbsp;parallax is to the fine of a celeftial body's anguU^nbsp;diflance from the vertex as the fiemi-diameier of thtnbsp;earth is to the diflance of that body from the centre 4nbsp;the earth. Thus the fine of the angle AHC isnbsp;the fine of the angle ZAH, as AC is to CH. Fo*quot;nbsp;the fides of plane triangles are as the fines of the op'nbsp;pofite angles; hence in the triangle AHC, the fii^�nbsp;of the angle AHC is to the fine of the angle CAf^nbsp;(or ZAFI), as AC, the femidiameter of the earth�nbsp;is to CH, the diflance of the body H from F*nbsp;Therefore, if the parallax of a celeftial body,nbsp;that body is at any given diflance from the vert^^�nbsp;be known, we can eafily find by the theorem,nbsp;parallax at any other diflance from the vertex.

It alfo follows from the preceding explanation� I ft, that when bodies are at unequal diftances fro^^nbsp;the centre of the earth, the fines of their paralla^^^nbsp;are reciprocally as thofe diftances; zdly, that vvh^^^nbsp;the bodies are at equal diftances from the centre 0nbsp;the earth, the fines of their parallaxes are as the fio'Jnbsp;of their apparent diftances from the zenith;nbsp;3dly, that when the bodies are at unequal dift^^^^^^nbsp;both from the centre of the earth and fromnbsp;zenith, then the fine of the parallax of one body ^nbsp;to thfit of another body, in a ratio compounded ^

inverfe ratio of the diftances from the centre of the earthj and the diredt ratio of the fines of thenbsp;apparent diftances from the 2enith.

The general effect of the parallax of a celeftial body is to let that body appear nearer to the horizonnbsp;than it really is; therefore, in order to deduce thenbsp;Proper places of celeftial objeefts from the obferva-tions, it is neceftTary to deduft the effefts of the pa-t^llax ; for the relative fituations of celeftial objeftsnbsp;^te always reckoned with refpedt to their centresnbsp;to the centre of the earth ; whereas the obfer-'^^dons cannot always be made in the diredion ofnbsp;^he centre of the earth.

The effed of the parallax being greater in proportion as the objed is nearer to the earth, it follows *^hat the moon which is the neareft to us, is fubjed tonbsp;^ greater parallax than any other celeftial body, andnbsp;^^^t parallax varies according to the different alti-and different diftances of the moonj then fincenbsp;fituation of the moon muft be afeertained fofnbsp;'^^rious ufeful aftronomical purpofes, thofe variousnbsp;Parallaxes of the moon are calculated, and arc fet innbsp;^^hles, which are to be met with in nautical alma-ephemerides, amp;c. The horizontal parallaxnbsp;the moon varies from about 6\' 32'', to 53'

obi

Befides the neceffity of allowing for the effefts of parallax in effimating the exaft altitudes of celef-tial objeflsj the afcertaining of parallaxes anfwersnbsp;another very effential purpofe in aftronomy, viz.nbsp;they are ufeful for finding the dimenfions andnbsp;principally the diftances of the celeftial bodiesnbsp;from the' earth j as alfo the dimenfions of theirnbsp;orbits.

When the diftance' of a celeftial body from the earth is known, its horizontal parallax, and hence itsnbsp;parallax at any altitude, may be eafily found ; for innbsp;the right-angled triangle ACI, fig. 10, Pl.XXVlU-three parts being known (viz. the femi-diameter oinbsp;the earth AC, the diftance of the body C I, andnbsp;the angle A, which is a right angle), the ang!^nbsp;AIC, which is the horizontal parallax of the bodynbsp;I, is eafily found, by trigonometry j alfo, if we hav^nbsp;the parallax, We may eafily determine the diftanccnbsp;of the celeftial body from the centre of the earth Jnbsp;for in that cafe the three angles and the fide AC oinbsp;the fame triangle being known, the fide or diftancc

not to exceed 14.quot;, and of courfe very difficult to obferved with certainty.

Hitherto we have mentioned the effedt of the parallax with, refpefl: to the altitude only of a celeftial and have ffiewn that in confequence of thatnbsp;parallax, the body always appears to be fomewhatnbsp;lower than it really is, except when it ftands in thenbsp;'^^rtical line, or in the zenith. But it muft benbsp;obferved, that if the apparent place of a celeftialnbsp;relatively to the zeniiji, is different from itsnbsp;r^al place, the apparent relative fituation of the famenbsp;body^ with refpeft to other circles, muft alfo be dif-^'^rent from its real fituation; viz its apparent longi-ft'd�, latitude, right alcenfion and declination, muftnbsp;different from its real longitude, latitude, amp;c. ornbsp;Iroin the longitude, latitude, amp;c. it would have, ifnbsp;*'� 'vere viewed from the centre of the earth. Nownbsp;^be difference of longitude obferved from the centrenbsp;in the diredion of the centre) of the earth, whichnbsp;oalled the true longitude, and that feen from fomenbsp;^ffier point of the furface of the earth, is called thenbsp;h^^'allax of longitude �, the difference between the la-'�'mde, as obferved from the centre, and that ob-

0 furface of the earth, is called the �parallax of afeenftonand laftly, the difference betweennbsp;^be declination, as obferved from the centre, and

that obferved from the furface of the earth, is called the parallax of declination.

Refractioist, as has been explained in' the third volume of thefe Elements, is the bending of the raysnbsp;of lighti which is occafioned by their pafling obliquely from one medium into another naedium of 3nbsp;different refraftive power.

The atmofphere, which furrounds the earth, is 3 refraftive medium, and of courfe the rays of lightnbsp;which fall obliquely upon it, are bent by it; therefore the celeftial objects which are neceffarily feef*nbsp;through part of the atmofphere, muft appear to benbsp;in fituations different from their real places, unlefsnbsp;they be in the zenith ; for in that cafe the rays ofnbsp;light which come from the celeftial bodies to outnbsp;eyes, fall not obliquely, but perpendicularly, upoOnbsp;the atmofphere ; in which cafe they fuffer no bending or refra�lion. It naturally follows that the lowernbsp;the fituation of the body is, the greater, deterisnbsp;rihus, muft its refra�fion be; for the rays of lightnbsp;fall more obliquely upon the atmofphere.

Were the atmofphere of an uniform denfity, the ray, which fell obliquely upon it, would be bent onlynbsp;at its entrance into the atmofphere, and would afte*quot;nbsp;wards proceed ftraight through it j but as the atrno' ,nbsp;fphere is increafing in denfity in proportion as itnbsp;approaches the furface of the earth, therefore thenbsp;ray of light is continually bent more and more as it

approaches the earth, fo as to become a curve line AB, fig. II, PI. XXVIII.; and fince to a fpec-^tor at B, upon the furface of the earth, the objefb Cnbsp;appear in the direftion which the ray of lightnbsp;Cab has, when it enters the eye at B ; thereforenbsp;objedl, which really Hands at C, muft appear, innbsp;^onfequence of the refraiftion, to Hand at D.

The refraflive power of the atmofphere varies According to its gravity, to its temperature, and tonbsp;humidity; therefore the real quantity of refrac-^�on rnuft be deduced from the compound effe�lsnbsp;Pfall thofe caufes.

appears therefore that the celeftial bodies are *^ut of their real places, not only in confequence

R.3

of the parallax, but likewife in confequence of the refrattion of the atmofphere ; and that the parallaJ^nbsp;caufes them to appear lower than they really are.�nbsp;whilft the refraftion makes them appear higher thannbsp;their real places ; therefore, in order to determinenbsp;their real from their apparent places, a correftionnbsp;for the effe�l of refraftion is alfo to be applied;nbsp;and for this purpofe the rcfraflions for different altitudes, at a mean ftate of the atmofphere, are calculated and ftated in a table, called the table efnbsp;fraBions in altitude.

Befides the refraftion in altitude, there are fontquot; other forts of refratlion, the nature of which willnbsp;be eafily underflood from what has been faid withnbsp;refpedl to the different forts of parallax, in fhorbnbsp;if the effeft of the refraftion caufes a body to appea!quot;nbsp;in a place different from its real place, it follo�^'^nbsp;that the apparent fituauon of that body with refpe*^nbsp;to other circles, muft be different from its real fitu^'nbsp;tion j viz. in confequence of the refraflion, thenbsp;longitude, latitude, right afcenfion, and declination^nbsp;of that body, muft differ from its apparent long'quot;nbsp;tude, latitude, amp;c. and thofe differences conftiton-^^nbsp;or are called, the rejraSion of longitude, the refrabf '^�^�^nbsp;of latitude, the refratiim of right afcenfion, and the t't'nbsp;fraSiion of declination.

The quantity of refradfion for every degtee o altitude in a mean ffate of the atmofphere, is fheWOnbsp;by the follov/ing table, which confifts of two 00nbsp;himns repeated. The firft column contains the

app^r^^''

the Aberration of Light. . nbsp;nbsp;nbsp;231

apparent altitudes, and the fecond fliews the cor-I'efpondent refradion, or the quantity which muft be fubtradled from the apparent altitude of the ce-^^ftial objedt. Thus when a celeftial body appearsnbsp;^0 be 36 degrees above the horizon, you will findnbsp;^gainft 36 degrees of apparent altitude in the table.

18quot;; which means that the refradtion makes the objedl appear 1' 18quot; higher than it really is; hencenbsp;^bat quantity muft be fubtradled from 36�, and thenbsp;*'emainder 35� 58' 42quot;, is the altitude of the objedlnbsp;corredled of the effedt of refradlion.

The

The horizontal refradion varies from 31' to The refraftions for other altitudes are alfo variabkinbsp;but lefs and lefs in proportion as they recede fromnbsp;the horizon. In confequence of the caufes whichnbsp;have been mentioned above, namely, the temperature, gravity, amp;c. the refradtion is greater in colcinbsp;weather and cold climates than in warmer; it i*nbsp;generally greater in the morning than in the eveningjnbsp;�cc. In confequence of the refradlion, the fungt;nbsp;planets, ftars, amp;c. begin to appear when they arenbsp;aftually below the horizon.

A very remarkable effedl: of the refradlion of the atmofphere is known under the name ofnbsp;(creptjculum), and it is the light which we perceivenbsp;when the fun is adlually feveral degrees below thenbsp;horizon; in which cafe it is evident that if the ray�nbsp;of light, which proceed from the fun, were notnbsp;bent by the atmofphere, they could not pofliblfnbsp;reach us; that light, therefore, which we recei'f^nbsp;from the fun, either before its rifing or aftefnbsp;its fetting, and in confequence of the refrafti''^nbsp;power, as alfo the refleftion, of the atmofpherejnbsp;is the twilight. At a mean the twilight begif�nbsp;to appear in the morning, or ceafes to appc^'quot;nbsp;in the evening, when the fun is about 18quot; below the horizon. Whatever increafes or decreafe�nbsp;the refradfive power of the atmofphere, will�nbsp;courfe, increafe or decreafe the duration of the twi'nbsp;light, vi^. will caufe the twilight to begin when th^nbsp;fun is more or lefs than 18� below the horizon-Thus, fateris -paribus, the twilight in cold climates

9 nbsp;nbsp;nbsp;'nbsp;nbsp;nbsp;nbsp;bfts

longer than in warmer climates. When the during the night, does not defcend below thenbsp;horizon more than 18�, as is the cafe w'ith this iflandnbsp;in the fummer time, then the twilight lafts all night,nbsp;it is faid that there is no night. Within the polarnbsp;circle, the fun in confequence of the refraftion ofnbsp;atmofphere, efpecially in that cold climate, begins to make its appearance fome days before itnbsp;^^nght to appear according to its real fituation.nbsp;�According as the fun either in its riling or in itsnbsp;i'^Cting is a longer or a Ihorter time in percurring thenbsp;*8� below the horizon, which arifes from the dif-^^tent obliquity of its courfe, fo the twilight beginsnbsp;^noner or later before fun rife, and continues longernbsp;Ihorter after fun fet. Hence, in this country, thenbsp;twilight is longer in the fummer time than in thenbsp;'''inter; hence alfo, ceteris faribus^ the twilightnbsp;longer in higher latitudes than near to thenbsp;^'luator.

T' HE Aberration is an apparent movement of the which was difcovered towards the beginningnbsp;^i^the-laft century, by Dr. Bradley, then aftronomernbsp;rphis apparent movement is the compoundnbsp;of the progreffive motion of light, and of thenbsp;*^otion of the earth in its orbit; in confequence ofnbsp;each fixed liar appears in the courfe of onenbsp;to defcribe a fmall ellipfe, whofe greater axisnbsp;about 40quot;.

In order to comprehend the caufe of this apparent Movement, let E, fig. 13, Plate XXVIII. be a liar,

from which a ray of light proceeds towards us, and confider this ray as a fmall body moving from E tonbsp;B. Let A B be a portion of the earth�s orbit; fornbsp;inftance of aoquot;, and let CB reprefent the fpace per-curred by the light whilft the earth has moved front'nbsp;A to B; lb that the fmall body or particle,of lightnbsp;is at C, when the earth is at A;'and both at,thenbsp;fame time arrive at B. Thus CB and AB reprefentnbsp;the refpeflive velocities or the light and of the earthnbsp;in aoquot; of time. Draw CD equal and parallel tonbsp;AB, and complete the parallelogram DCAB-Then, agreeably to the principles of the compofj'nbsp;tion and refolution of forces (fee the firft volumenbsp;of this work), the velocity of light CB may be con-fidered as the refult of two velocities in the directions' CD and CA; of which the velocity CD, beingnbsp;in the fame dire�lion, and equal in quantity to thenbsp;velocity of A B of the earth, cannot be perceived gt;nbsp;for the eye of aii'obferver on the earth cannotnbsp;be ftruck by a body which moves with the fame velocity and in the fame direction as the eye itfelfonbsp;therefore that part of the velocity of light whichnbsp;in the direftion C A, is what affefts the eye of thenbsp;obferver; and hence we perceive the ftar in the di-redlion AC or BD, which is parallel to AC. Thennbsp;the angle CBD is called the aberration. In fhorbnbsp;CBD is the angle by which a ftar feems to be removed from its true place, in confequence bothnbsp;the progreflive motion of light, and of the motionnbsp;of thC� earth in its orbit.

ThB

This compound efFed; being rather difficultly, ^otnprehended by beginners, I ffiall fubjoin Dr.nbsp;Bradley�s own explanation, which places the phaeno-�^^non in a different light¹. Thedoftor imaginednbsp;fig. 12, Plate XXVIII. to be a ray of lightnbsp;falling, perpendicularly upon the lineBDj that, ifnbsp;the eye be at reft at A, the objedt muft appear jnnbsp;the direftion AC, whether light be propagated innbsp;t'nre, or inftantaneoufly. But if the eye be movingnbsp;^tom B towards A, and light is propagated innbsp;tirtie, with a velocity that is to the velocity of thenbsp;^ye as CA to BA, then light, moving from C to A,nbsp;quot;'hilftthe eye moves from B to A, that particle ofnbsp;�t, by which the objed will be difcerned, when thenbsp;^ye comes to A, is at C when th� eye is at B.nbsp;Joining the points B, C, he fuppofed the line CBnbsp;be a tube, inclined to the line B D in the anglenbsp;^BC, of fuch a diameter as to admit but one par-^'^le of light. Then it was eaiy to conceive, thatnbsp;^he particle of light at C, by which the bbjed muftnbsp;feen, when the eye as it mbves along, arrives atnbsp;�^5 would pafs through the tube B C, if it be in-^^�ned to BD in the angle DBC, and accompaniesnbsp;eye in its motion from B to A; and that itnbsp;^�old not come to the eye placed behind fuch anbsp;�^obe, if it had any other inclination to the line BD.

inftead of fiippofing CB fo fmall a tube, we Imagine it to be the axis of a larger tube 5 then, fornbsp;fame reafon, the particle of light at C would

not pafs through that axis, unlefs it is inclined to BD in the angle CBD. In like manner, if thenbsp;eye moved the contrary way, from D towards Ajnbsp;with the fame velocity, then the tube muft be inclined in the angle BDC. Although, therefore,nbsp;the true, or real place of an objeft is perpendiculatnbsp;to the line in which the eye is moving, yet thenbsp;place will not be fo, fince that, no doubt, muft benbsp;in the direction of the tube; but the difference between the true and apparent place, will be, cateri^nbsp;faribus, greater or lefs, according to the differentnbsp;proportion between the velocity of light and that ofnbsp;the eye. So that if we could fuppofe that light wasnbsp;propagated in an inftant, then there would be nOnbsp;difference between the real and vifible place of annbsp;obje�l, although the eye were in motion; for in thatnbsp;cafe, AC being infinite with refpeft to AB, thenbsp;angle ACB, viz. the difference between the truenbsp;and vifible place, vanifhes. But if light be propa'nbsp;gated in time, it is evident, from the foregoingnbsp;confiderations, that there will be always a differencenbsp;between the real and vifible place of an objed:, un'nbsp;lefs the eye is moving either diredly towards ornbsp;from the objed:: and, in all cafes, the fine of thenbsp;difference between the real and vifible place of thenbsp;objed: will be to the fine of the vifible inclinationnbsp;of the objed to the line in which the eye is moV'nbsp;ing, as the velocity of the eye is to the velocity 0^nbsp;light.

��Qund the fun annually, and the velocity of light be ^0 the velocity of the earth�s motion in its orbit, asnbsp;^000 to I, that a ftar really placed in the very polenbsp;�f the ecliptic, would, to an eye carried along withnbsp;earth, feem to change its place continually j andnbsp;^cgledting the fmall difference on account of thenbsp;Earth�s diurnal revolution on its axis, would feem tonbsp;^cfcribe a circle round that pole, every way diftancnbsp;from it 31'; fo that its longitude would be variednbsp;through all the points of the ecliptic every year,nbsp;hut its latitude would always remain the fame. Itsnbsp;fight afcenfion would alfo change, and its declination, according to the different fituations of the fun,nbsp;'''ith refpecl to the equinoctial points, and its appa-tent diftance from the north pole of the equator,nbsp;'I'ould be 7' lefs at the autumnal than at the vernalnbsp;^'luinox.

The greateft alteration of the. place of a ftar in the pole of the ecliptic, or which, ineffedl, amountsnbsp;to the fame thing, the proportion between the velo-'^'ty of light and the earth�s motion in its orbit being;

^Uown, it will not be difficult, he obferves, to find quot;ihat would be the difference, upon this account,nbsp;etween the true and apparent place of any othernbsp;friif at any time; and, on the contrary, the differencenbsp;between the true and apparent place being given,nbsp;^he proportion between the velocity of light and thenbsp;^^rth�s motion in its orbit may be found.

^ow, fince the apparent declination of the ftar, Called �Y' Draconis, on account of the fucceffive

propagation of light, would be .to the diameter of the.little circle which a ftar would feem to defcribonbsp;about the pole of the ecliptic, as 39quot; to 40'',4; thenbsp;half of this is the angle ACB'. This, thereforegt;nbsp;being 2oquot;,2, AC will be to AB, that is, the velocity of light will be to the velocity of the eycnbsp;(which in this cafe may be fuppofed the fame as thenbsp;velocity of the earth�s annual motion in its orbit)nbsp;10210 to I.; from vvhence it will follow, that lighi^nbsp;moves as far as from the fun to the earth in 8', 12quot;*nbsp;This, Dr. Bradley obferves, is very probably thenbsp;truth, becaufe it is a medium between 7 and iigt;nbsp;which were the times which it had before been fup'nbsp;pofed to take up, according to different obfervatlonsnbsp;of the eclipfes of Jupiter�s fatellites. Comparingnbsp;his obfervations on other ftars, he afterwards con'nbsp;eluded that light is propagated from the fun to thenbsp;earth in 8h 13' ; and the near agreement of his ob-fervations induced him to think that this fuppofi'nbsp;tion could not differ fo much as a fecond of ^nbsp;degree from the truth; fo that the time which ligh^nbsp;fpends in pafling from the fun to us may be detef'nbsp;mined by thefe obfervations within 5quot;, or lO�nbsp;which is fuch a degree of exablnefs as we cannbsp;never hope to attain from the eclipfes of Jupiter snbsp;fatellites.

� The near agreement of the refiilt of Dr. Brab' ley�s obfervations on the light of the ftars, whic^nbsp;we have all the reafon toTuppofe that they fliine bynbsp;their own luftre, with the refult of Mr. Roemer s

^bfervations on the light of the fatellites of Jupiter, quot;'bich (bine by refledting the light of the fun, notnbsp;confirms the progreffite motion of light, butnbsp;bkevvife fhews that the velocity of light is the famenbsp;^^fore as after refledlion.

The aberration arifing from the compound mo-bon of light and of the earth, does alfo affedl the P^snets, and the fun �, and though it be very little;

in nice computations of occuUations and other P*'oblems, this aberration muft be calculated front �nbsp;known velocities of light, the Velocity and di-of the earth, and the diftance of the planetnbsp;queftion. The fun�s aberration in longitude isnbsp;'�'^nfiantly 20quot;; for the earth moves through thatnbsp;^P3ce in 8quot; 7% which is the time employed bynbsp;%ht in paffing from the fun to us.

quot; Dr. Bradley, by his continued obfervations the ftars, perceived each year the period of thenbsp;aberrations confirmed, according to the rules henbsp;lately difcovered ; but befides this, he foundnbsp;year to year other differences, the confi-^^'quot;ation of which led him to another brilliantnbsp;d'lcovery, that of the nutation of the earth's axis.nbsp;b's is a kind of libratory motion of the earth�snbsp;by which its inclination to the plane of thenbsp;'^'^bptic is continually varying backwards and for-quot;'^tds, hy a fmall number of feconds. The wholenbsp;^^tent of this change in the inclination of thenbsp;or, which is a confcquence of it, in the

apparent declination of the ftars, is about i and the period of the change is little more than nin^nbsp;years; or, the fpace of time from its letting outnbsp;from any point and returning to the fame again�nbsp;about 18 years an^ 7 months, being the fame aSnbsp;the period of the moon�s motions, on which in'nbsp;deed it chiefly depends, being the efedl of thenbsp;inequalities of the joint adtion of the fun and moonnbsp;upon the fpheroidical figure of the earth, by whichnbsp;its axis is made to revolve with a conical motion�nbsp;fo that the extremity of it defcribes a fmall ellipfis�nbsp;having its diameters 19quot;,!, and i4',2, each revO'nbsp;lution being performed in the time above-mentioned. This is a natural confequence of thenbsp;Newtonian fyftem of univerfal attradlion, and hadnbsp;been hinted at by fome, ever fince the publicationnbsp;of the Principa.� ¹

Thus we have pointed out the differene app^' rent movements of the ftars, and have flievvnnbsp;that they arife from the parallax, from the refraction of the atmofphere, from the progreflive rnO'nbsp;tion of light, and from the movements of thenbsp;earth. Yet it mull; be acknowledged, that indc-

Mr. Gregory�s Aflronomy, Chap. XXII. For ther information on the fubjecl of the nutation, feenbsp;Phi�ofophical Tranfaefions for 1784. Dr. Mafkelyn� ¹nbsp;. Aftronomical Obfervations, 1776; and De lanbsp;nbsp;nbsp;nbsp;^

pendent of thofe apparent movements, fome of �he fixed ftars have been found to have a propernbsp;though exceedingly fmall motion. The prefentnbsp;ftate of aftronomical knowledge cannot well ac-�^ount for this movement; perhaps the ftars ornbsp;^hole fyftems, though immenfely diftant fromnbsp;�ach other, may alfo have a mutual tendency ornbsp;^ttradtion j perhaps a congeries of fyftems, or thenbsp;quot;'hole aflemblage of them all, may turn round anbsp;Common centre of attraction} but we muft leavenbsp;thofe fpeculations to pofterity.

According to the common or vulgar fignification, the day and the night, meannbsp;refpedively the time of the fun�s remaining abovenbsp;the horizon, and the time of its remaining beloWnbsp;it. For the fake of diftinftion, this day is callednbsp;the artificial day. The natural day is the time employed by the fun in its apparent motion all roundnbsp;the earth, from one meridian and to the fame again.nbsp;This time is divided into 24 hours j each hour isnbsp;divided into 60 minutes; each minute into 60 fc'nbsp;conds; each fecond into 60 thirds, amp;c. Whennbsp;the intervals of time are longer than one day, thefnbsp;may be reckoned by the number of days, and partsnbsp;of a day, or by certain aflemblages of days toge'nbsp;ther, with odd days and parts of a day. Thofe af-femblages of days are called weeks, months, yeartynbsp;cycles, periods, ^c.

The 24 hours, or 24 parts, of a natural da/� are not always equal to the 24 parts of anothernbsp;natural day j or, in other words, the fun does not

always

always employ the fame time in its apparent motion the earth, from a given meridian to the famenbsp;�Sain, This, as has been explained in the preced-chapters of this volume, arifes from the earth�snbsp;^��bit being elliptical, from the earth�s axis being in-^^'ned to the plane of the ecliptic, and from the pre-�^eflion of the equinoxes. But independent of thenbsp;tbeory, the inequality of natural days is clearly ma-*^'fe(l:ed by means of the well known machines,nbsp;'�^lled clocks, regulators, time-keefers, chronometers,nbsp;longitude watches ; for by obferving the fun�snbsp;over the meridian each day, it will be foundnbsp;^bat the fun�s centre comes to the meridian fome-��'^es before and fometimes after the lapfe of fuchnbsp;^4 hours, as are fhewn bv the going of the clock,nbsp;chronometer; but the mean natural days, viz.

fi-jat are between the longeft and the (liortefr, precifely equal to the 24 hpurs of the clock ;nbsp;^^^ce thefe are called hours of true or mean time,nbsp;the 24 equal parts of mean days.

'That upon the v;hole, well regulated chronome-*�^*'5, are equable meafures of time, is proved by '�^^ir agreeing among thernfelves, which they donbsp;quot;'�thin a trifling difference of a fecond or two, andnbsp;quot;'bich difference may be afcertained by the motionnbsp;^bthe fun itfelf,,or by the time of its arrival to the .nbsp;'^'^bdian; for as that time, whether longer or fliorternbsp;the period of 24 hours of mean time, has beennbsp;'�i^kulated from theory, and being meafured by thenbsp;^�Ock at the time of the fun�s tranfit, the obferver

will eafily perceive whether the clock indicates the fame excefs or defeft from the 24 hours of meannbsp;time, as has been obtained by calculation, and is re-giftered in moft almanacks. This excefs or defc^inbsp;which muft be added to or fubtrafted from the 24nbsp;hours of mean time, or fuch as are Ihewn by a wellnbsp;regulated chronometer, in order to obtain the realnbsp;length of a natural day, is called the equation 4nbsp;time i and it fometimes amounts to feveral minutes-

Thq natural day is either eivi/ or ajironomical ^ different commencement of the civil day has beennbsp;adopted by different nations. The Britifh, Frencbjnbsp;Dutch, Spaniards, and others, begin the civil dafnbsp;at midnight} the ancient Greeks, Jews, Bohemian^�nbsp;Silefians, with the modern Italians and Chinefe;nbsp;begin it at fun-fetting j the ancient Babylonians?nbsp;Perfians, Syrians, and modern Greeks, begin it a'-fun-rifing.

The aftronomical day at any place commence^ when the fun�s centre is on the meridian of th^^nbsp;place, and its 24 hours are reckoned from i tonbsp;and again from i to a fecond 12; diflinguilhingnbsp;the firfl 12 by the initial letters P. M. which me^*^nbsp;pfi meridiem or in the afternoon-, and the fecondnbsp;hours by the initials A. M. which mean ante Hfd'nbsp;ridiem, or in the forenoon. Aftronomers,' howeve'quot;?nbsp;generally reckon through the *4 hours from no'^'^nbsp;to noon ; fo that what is commonly called thenbsp;of 10 in the morning of April the 6th, is called hfnbsp;the aftronomers the 22d hour of April the 5^^'* �

and 3 o�clock in the morning of October the 20th, is ^^prelTed by the aftronomors, Oftober the 19th,nbsp;^S^ and fo forth.

The fun�s daily motion in longitude, which is ^eafured by an arc of the ecliptic, or its daily mo-*�'00 in right afeenfion which is meafured by thenbsp;^Orrefpondent arc of the equator, being nearly equalnbsp;59' 8'/, it follows that the above-mentioned agronomical day is meafured by the fum of the wholenbsp;^^oator (viz. 360�), and an arc of it equal to thenbsp;*On�s daily motion in right afeenfion (viz. 59' 8quot;),nbsp;^^ich fum is equal to 360�, 59', 8' . For at the endnbsp;nf a diurnal rotation of the earth, which obferva-nons (hew to be equable, the meridian comes to thenbsp;^^me ftar or point of the ecliptic at which it ftoodnbsp;no the preceding noon j excepting the very fmallnbsp;'difference which arifes from the preceflion of thenbsp;'^oinoftial points; whereas the fun, during thatnbsp;P^dod, has removed from that ftar or point of thenbsp;^'^ffptic to another, which has a greater right afeen-ffon by 59', %quot; �, therefore he muftdeferibe fuch annbsp;�ffditional arc befides a whole circle, in order to re-^nrn to the fame meridian j hence a fidereal day,nbsp;'''ffich is the interval between two fucceflive returnsnbsp;fame ftar, to the fame meridian, is fhorternbsp;a mean folar day by 3 minutes and 56 fecondsnbsp;time, which 3�, 56�, is the time employed bynbsp;fun in percurring the additional arc of 59', 8quot;;nbsp;that the mean folar day is 24 hours, whilft thenbsp;R 3nbsp;nbsp;nbsp;nbsp;fidereal

fidereal day is 23'�, 56�, 4�, according to the clock, which fhews mean time.

The folar days are equal, or the mean folar days take place when the fun�s daily motion in right afcen-fion is 59', 8quot;, which takes place about the 15th ofnbsp;April, the 15th of June, the ift of September, andnbsp;the 24th of December; fo that at thofe times thenbsp;fun and the clock, or the fun-dial and the clock,nbsp;agree very nearly, and of courfe no equation isnbsp;wanted; at other times the fun-dial and the clocknbsp;difagree more or lefs, and an equation is required�nbsp;This equation is greateft about the ift of Novem'nbsp;ber, when it amounts to l�quot;, 14�.

It is evident, from what has been faid above, that in feveral aftronomical obfervations the equation ofnbsp;time, befides the other corredions for parallax, rO'nbsp;fradlion, amp;c. muft be^duly attended to.

I need not inform the reader of the names and of the number of days which form a week.

A months properly fpeaking, is the time of a lunS' tion, or the period of time taken up by the moon i'�nbsp;performing its courfe in the zodiac. Another monthjnbsp;which more properly is the ajironomical month, an*^nbsp;js nearly equal to the above, is the time in whioknbsp;the fun moves along one fign of the ecliptic. ^nbsp;civil month confifts of a certain number of daV��nbsp;which number, however, is not always the fa�^nbsp;for every month, nor the fame in all countri^�'nbsp;The names of the twelve months, together

number of days in each, as are at pre-in life among the greateft number of clvi-nations, are fo well and fo commonly known, nothing more needs be faid about them in thisnbsp;place.

What the fidereal, the folar, the anomaliftic, the civil years, are, has been already fhewnnbsp;another place ; but in order to prefent all thole.nbsp;*^cafures of time in one point of view, we ftiallnbsp;briefly repeat their lengths in this place.

48�, 49%

The fidereal year confifts of 6*', 9�quot;, 12% The anomaUflic year, which is the time employednbsp;% the earth, in going from aphelion to aphelion,nbsp;�^onfifts of 6�', 14�, 2%

The common civil year, alfo called Julian year, fuch is adopted by moft nations, confifts of 365 days;nbsp;every fourth year is called a hiffexjlile or leapnbsp;and confifts of 366 days, viz. one day morenbsp;ti^an the common year j and this day is ufuallynbsp;^dded to the end of February �, excepting, however,nbsp;��1�e laft year of every century, not divifible by four,nbsp;quot;'iiioh is to remain a common year of 365 days. Seenbsp;61 and 62 of this volume.

Th^ lunar year confifts of 12 revolutions of the �^oon, from the fun to the fun again, and it con-taiiis nearly 354^ 8quot;, 48�, 36%

cycle is a perpetual circulation of a certain fixed and determined time. Thus the cycle of the

fun is a revolution of 28 years. In which time the days of the months return again to the fame daysnbsp;of the week j the fun�s place returns to the famenbsp;ligns and degrees of the ecliptic on the fame months'nbsp;and days, fo as not to differ one degree in loOnbsp;years j and the leap-years begin the fame courfenbsp;over again with refped to the days of the week onnbsp;which the days of the months fall. The cycle ofnbsp;the moon, commonly called the golden number, is nnbsp;period of 19 years, in which time the conjunftions�nbsp;oppofitions, and other afpedts of the moon, arenbsp;within about an hour and a half of being the fame a�nbsp;they were on the fame days of the months 19 yearsnbsp;before. The indiSlion is a revolution of 15 yearsgt;nbsp;ufed only by the Romans for indicating the time�nbsp;of certain payments made by the fubjedls of tb�nbsp;Republic, It was eftablifhed by ConflantinCinbsp;A. D. 312,

The year of our Saviour�s birth, according the vulgar mra, was the 9th year of the folar cyck,nbsp;the firft year of the lunar cycle; and the 3i2tbnbsp;year after his birth, was the firft year of the Romannbsp;indidtion. From this w'e may eafily find the cof'nbsp;refpondence between the fubfequent cycles.

The olympiads confifted each of four years, anlt;l the mode of reckoning by olympiads was ul^d bynbsp;the Greeks. The firft olympiad began 775 yea^nbsp;(according to other chronologifts 777 years) bC'nbsp;fore the birth of our Saviour.

points or commencements of the numeration of years have been adopted. Some reckoned from the fup-pofed time of the creation of the world. Thenbsp;Romans counted from the building of Rome ; thfenbsp;'I'urks reckon from the flight of Mahomet, callednbsp;*he hegira, or Turkijh cera; almoft all the nations ofnbsp;Europe and America reckon from the birth of ournbsp;Saviour, and this is called the Chriftian sera jnbsp;^he modern French reckon from the abolitionnbsp;their monarchical government; other nationsnbsp;have ufed other sefas. But of all thofe aeras thenbsp;'Julian period feeml^ to be the moft ufeful, as it in-*^iudes almoft all the other teras or periods. Thisnbsp;Julian period confifts of 798,0 years, which numbernbsp;the produdt of 15,19, and 28, viz. of the Romannbsp;*udi(ftion, of the lunar cycle, and of the folar cycle;

In the following fliort table, 1 ftiall ftate the com-^I^^ncement or the correfpondence of the principal according to the more commonly receivednbsp;Opinion; for the precife times of feveral remarkablenbsp;^'^ents have been differently ftated, and are as yetnbsp;^he fubjecft of controverfyj I muft therefore refernbsp;^he inquifitive reader to the profefled works of chro-nologiftj with refpeft to thofe points.

The Arabian or Turkifli hegira -The PeiTian nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-

WHEN our view of a celeftial body is ob-ftrufted by the interpofition of another oeleftlal body, or of its Ihadow, the phenomenonnbsp;IS called an eclipje, an occultatioti:, or a tranfit; yetnbsp;Oot quite indifcriminately fo j for the word eclipje isnbsp;itiore particularly applied to the apparent obfcura-don of the fun by the interpofition of the moon between it and the earth; to the obfcuration of thenbsp;^oon. by its coming within the Ihadow of thenbsp;^arth j and to the obfcuration of the fatellites ofnbsp;�ther planets by their coming within the fhadowsnbsp;�f their refpeftive primaries. The word occultationnbsp;more commonly'applied to the difappearance ofnbsp;^he flars or planets, occafioned by the interpofitionnbsp;the moon. The word tranfit is more commonly ufed to denote the palfage of the inferiornbsp;P'anets, Venus and Mercury, over the difc ofnbsp;fun.

Of all thofe phenomena, the ecliples of the fun and of the moon, are by far the moll ftriking,nbsp;nnd have at all times excited the fears of the vulgar,

and

and the diligent attention of th� moft enlightened part of the human fpecies. The prefent improvednbsp;ttate of aftronomy has brought all the particulars,nbsp;which relate to eclipfes, occultations, and tranfits,nbsp;within the limits of calculation, whence the times,nbsp;durations, and quantities of thofe phenomena maynbsp;be foretold with wonderful accuracy.

Having elfewhere fhewn the general nature of eclipfes, we fhall, for the fake of perfpicuity, colle�lnbsp;in this chapter all the moft efiential particulars relative to thofe phenomena, in order that the readernbsp;may fee the fubje�l under one point of view.

As the light of the fun falls upon the earth, a fhadow of the latter muft be extended in thenbsp;heavenly fpace behind it; and this fhadow is conical, becaufe the fun is larger than the earth. Butnbsp;on the fides of this converging or conical fhadow,nbsp;there is a diverging fhadow, the denfity of whichnbsp;dccreafes in proportion as it recedes from thenbsp;fides of the former conical fhadow; this, which isnbsp;ufually called the penumbra, is occafioned by thenbsp;partial obftruftion of the fun�s rays in the places adjacent to the denfe conical fhadow. Thus, in fig. Unbsp;Plate XXIX. the rays of the fun ASB, falling uponnbsp;the earth ETF, are intercepted by it, whence thenbsp;conical fhadow E F C is formed, from no part ofnbsp;which the fun can be feen ; but adjoining to and allnbsp;round this cone, there is the diverging iinperfelt;3:nbsp;fhadow or penumbra EFHG, from any part ofnbsp;which a portion only of the fun can be feen ; and

tHat portion of the fun�s difc is larger according as the place is farther from the conical fhadow EFC,nbsp;hence the penumbra decreafes in intenfity j thus atnbsp;0^ the portion zy B of the fun can only be feen,nbsp;but from R, the portion'is feen ; whichnbsp;portions are determined by drawing ftraight linesnbsp;from the given places to the fun and along the fur-' face F of the earth. The conical fliadow EFC ofnbsp;the earth is extended much farther than the diftancenbsp;of the moon, but not near fo far as the nearefl;nbsp;planet which is Mars; therefore the moon alonenbsp;?an come within that fhadow.

Now let O P be a portion of the moon�s orbit i then as the moon, in its motion from the weft towards the eaft, viz. from O towards P, enters thenbsp;penumbra at O, it begins to be partly obfcured onnbsp;its eaftern fide ; the obfcuration gradually proceedsnbsp;towards the weftern fide of the moon, and.increafesnbsp;intenfity ; the moon then comes within the conical fhadow EFC, at which time the obfcuration isnbsp;Steateft. After this, it begins to emerge out ofnbsp;tbe conical fhadow EFC, with its eaftern fide, andnbsp;It proceeds it becomes gradually more and morenbsp;illuminated, until the end of the eclipfe, viz. untilnbsp;tbe moon is got quite out of the penumbra at P.

it rnuft be obferved, that the moon is never Perfectly eclipfed; or, in other words, during annbsp;^'^lipfe, we never lofe fight of the moon entirely,nbsp;^''en when fhe is at L, in the middle of the conicalnbsp;Ibadow EFC j but in that fuuation flie appears of a

dark dull red colour, which is owing to the requot; fraftive power of'the earth�s atmofphere (the famenbsp;which produces the twilight), in confequence ofnbsp;which Ibme of the fun�s rays which pafs clofe to thenbsp;furfacfe of the earth, and through its atmofphere, arenbsp;bent or refradted by the latter, fo as to enter the conenbsp;EFC, and in fome meafure diminilh the perfedtnbsp;darknefs which it would have if the earth had nonbsp;atmofphere.

By infpedling fig. i, and by attending to the above explanation, the following particulars willnbsp;be eafily comprehended. An eclipfe of the moo^fnbsp;can only happen at the time of full moon, whennbsp;the fun, the earth, and the moon, are in the famenbsp;ftraight line} but on account of the inclination ofnbsp;the moon�s orbit to the earth�s orbit, an eclipfe cannot take place at every full moon. It can only takenbsp;place when the full moon happens to be in one ofnbsp;the nodes of the moon�s orbit, or fo near it, as thatnbsp;the moon�s latitude does not exceed the fum of thenbsp;m.oon�s apparent femidiameter and the femidiameternbsp;of the earth�s fliadow, where it meets the moon�snbsp;orbit. And according as that latitude is more otnbsp;lefs, or nothing, fo the eclipfe may be partial^ totaUnbsp;or central.

The quantity of the moon�s difc which is eclipfe*^ (and the fame thing muft be underftood of the difquot;.nbsp;of the fun in a folar eclipfe), is expreffed by twelf^^^^nbsp;parts, called digits^ of that difc, viz. the difcnbsp;fuppofed to be divided by twelve parallel lines: then

Of Eclipjes, Occultations, ^c. nbsp;nbsp;nbsp;255

Half the difc is edipfed, the quantity of the edipfe is faid to be fix digits; if one twelfth part is obscured, then the quantity of the edipfe is faid to benbsp;one digit, and fo forth. And when the diameternbsp;the lhadow, through which the moon muft pafs,nbsp;greater than the diameter of the moon, thennbsp;quantity of the edipfe is faid to be more than 12nbsp;'i'gits; thus, if the diameter of the moon is to thenbsp;'Siameter of the fhadow as 4 to 5, then the quan-hty of edipfe is faid to be equal to 15 digits j fornbsp;4 : 5 : : 12 : 15.

The edipfes of the moon are vlfible alike from fuch parts of the earth as have the moon abovenbsp;horizon at that time ; but they are not feen atnbsp;very fame time from places which differ in longi-^�de; for inftance, if a place B be 15 degrees weft-�'^ard of another place A, the obferver at the latternbsp;place A, muft fee the commencement or the end ofnbsp;edipfe an hout later than the obferver at B, be-Caufe on account of their difference of longitudenbsp;''�Hen it is 10 o'clock at B, it is 11 o�clock at A, ornbsp;quot;Hen it is 11 at B, it muft be � 2 at A, amp;c. Hence,nbsp;H^onn attentive obfervations, made at two differentnbsp;Peaces, of the commencement, or of the end of thenbsp;^clipfe, or of the arrival of the flradow at any par-'�tular fpot of the moon ; the difference of longitudenbsp;cfween thofe two places may be determined,

quot;S he moon always enters the fhadow with its ^^ftern fide, and comes out of it with the famenbsp;^�ftern fide foremoft; for the proper motion of th�

moon being fwifter than that of the earth�s fliadoquot;^� the moon approaches the fliadow from the weft, andnbsp;paffes through it with its eaftern fide forempfcnbsp;leaving the ftiadow weftward.

The duration of a lunar eclipfe is various, but never exceeds two hours. In order to calculate thenbsp;time, duration, and quantity of an eclipfe, the fo^'nbsp;lowing particulars muft be known, and thefe arenbsp;obtained from the almanacks and other aftronorni'nbsp;cal tables.

The true time of the moon�s oppofition, for the particular place for which the computation of thenbsp;eclipfe is intended.

^ever be entirely involved in the lhadow of* the ^oon, becaufe the moon is much fmaller than thenbsp;^^nh, and the fhadow of the moon, being conical,nbsp;^be fcftion of that cone at the diftance of the earthnbsp;confiderably fmaller than the difc of the moon,nbsp;l^hus, in fig. 2, Plate XXIX. the rays of the funnbsp;ASB, being intercepted by the moon CLD, formnbsp;^be conical fhadow CDG, which falling upon thenbsp;hirface of the earth ETF, entirely deprives the por^nbsp;*^ion / 0 of the fun�s light, and of courfe the inhabitants of that portion will have a total eclipfe of thenbsp;bln, the eclipfe being central at n. Beyond thenbsp;^enfe conical fhadow CGD, there is the invertednbsp;Cone of the penumbra CDEF, which is occafionednbsp;by the moon�s intercepting a part only of the fun�snbsp;J'ays from thofe places which fall within the penum-bral cone, and are out of the denfe fhadow CDG ;nbsp;^bus from Z, the portion YYB of the fun can onlynbsp;be feen ; confequently the inhabitants of the partsnbsp;and zE, or of the zone which goes all roundnbsp;^be denfe fhadow, will have a partial eclipfe, thenbsp;S^antity of which, for any particular place, is morenbsp;lefs, in proportion as that place is nearer to thenbsp;c^enfe fhadow i O, or nearer to the borders EF ofnbsp;*-be penumbra.

Knowing the diameters of the fun and moon, as the diftances of the fun from the moon andnbsp;bom the earth, at the time of the conjundlion ; thenbsp;Extent of the conical fliadow, and the diameter ofnbsp;of its feftion at the furface of the earth may benbsp;cafily calculated ; or it may be drawn upon papernbsp;IV.nbsp;nbsp;nbsp;nbsp;s snbsp;nbsp;nbsp;nbsp;with

with confiderable accuracy, by taking the proper-* ttonal dimenfions from a fcale of equal parts. Nownbsp;from fuch computations made at different fituationsnbsp;of the moon with refpeft to diftance, it appearsnbsp;that, when the moon is at its greateft diftance--from the earth (that diftance varying from 56nbsp;to 64 femidiameters of the earth) the apex ofnbsp;the conical fhadow CDG does not reach the earth,nbsp;as is (hewn in fig. 3, Plate XXIX.; but thenbsp;penumbra EF only falls upon the furface of thenbsp;earth; therefore the eclipfe will be partial all overnbsp;the fpace EF ; but with this difference, that whilftatnbsp;one place within EF, the inhabitants lofe fight ofnbsp;one part of the fun, at another place the inhabitantsnbsp;lofe fight of fome other part of that luminary, asnbsp;may be eafily conceived by infpeding the figure.nbsp;Thofe who happen to be at the centre H of the penumbra, will lofe fight of the middlemoft part kk ofnbsp;the fun, and a ring of light all round the moon, ornbsp;only the circular edge of the fun will at that time benbsp;feen. The eclipfe is then faid to be annular.

So far we have deferibed the various phenomena as if at the time of an eclipfe the fun, the mooivnbsp;and the earth, remained in the fame line for an/nbsp;length of time; but fince that is not the cafe, aridnbsp;fince the proper motion of the moon, is muc^nbsp;quickerquot; than that of the fun, therefore the followingnbsp;particulars neceffarily take place.

The eclipfe of the fun alvrays begins fomevvherf on the weftern half of the fun�s dife, and ends 3tnbsp;the eaftern ; for tlie moon moves in that dire�lio� *

fo does the lliadow move upon the furface of �he earth; fo that thofe parts of the earth which arenbsp;*�gt;ore weftwardj will fee the eclipfe fooner than thofenbsp;quot;'hlch are more eaftward. Since the lhadow of thenbsp;'^oon, and even the penumbra, is at all times muchnbsp;^Haller than the half of the earth�s furface, the famenbsp;*^cllpfe of the fun can never be feen by a wholenbsp;^emifpherical furface of the earth; and according asnbsp;different places on that furface are lefs or morenbsp;^iftant from the line, which paffes through the centresnbsp;the fun and of the moon, fo the inhabitants ofnbsp;^iiofe places fee the eclipfe either partial or central,nbsp;not at all; and the particular quantities of thofenbsp;appearances, or the digits eclipfed, may be determined by computation, from the knowledge of thenbsp;diameters of the fun and moon, their diftances, thenbsp;diftance of the moon�s node from the conjundion,nbsp;�^d the particular fituation of the place on the fur-^�ce of the earth. With refped to the time whennbsp;eclipfe of the fun is to take place, for it doe snotnbsp;mke place at every new moon, the calculation maynbsp;conduded in a manner fimilar to that ufed fornbsp;eclipfes of the moon ; the particulars that arenbsp;f'��'ncipally requifite, and which muft be extradednbsp;^^m the aftronomical tables, are the true time ofnbsp;conjundion ; the longitudes both of the fun andnbsp;the moon; the latitude of the moon, with its bori-�tontal parallax, and its horary motion; the apparentnbsp;di^nrieters of the fun and the moon; and the fun�snbsp;t*tary motion. But with refped to the particular

mode of performing the neceflary calculations, I muft refer the ingenious reader to the.works writtennbsp;profefledly upon the fcience of aftronomy*; and fhallnbsp;only add a few other particulars, which deferve to benbsp;remarked with refpeft to folar eclipfes,

� The middle of a folar eclipfe will not be at the fame time in all places on the fame meridian j fotnbsp;the parallax of longitude will be different in differentnbsp;latitudes. The excefs of the apparent diameternbsp;of the moon above that of the fun in a total ecfipfejnbsp;is fo fmall, that darknefs feldom continues morenbsp;than four minutes in the latitude of London. Itinbsp;moft folar eclipfes, the moon�s dife is covered withnbsp;a faint light, which is attributed to the refledion ofnbsp;the light from the illuminated part of the earth,nbsp;total eclipfes of the fun, the darknefs is fometirnesnbsp;fo great as to render vifible the planets that arcnbsp;above the horizon, and ftars of the firft and lecon^nbsp;magnitude. In fuch eclipfes the moon�s limbnbsp;feen furrounded with a ring which appears muchnbsp;brighter and whiter near the moon�s body thannbsp;at a diftance from it; this ring in all refpeds re'nbsp;fembles the appearance of,an enlightened atrnofphere^nbsp;viewed from a diftahice ; but whether it belongs tonbsp;the moon or the fun, is not entirely decided, though

*� See Ftainftead�s Method in Sir Jonas Moore�s Syftea* �f Mathematics, Vol. I. Keill�s Agronomical Ledure*�nbsp;Fergujbn�s Aftronomy, Vince�s Aftronomy, and'Gregory *nbsp;Aftronomy, on the Subjed of Eclipfes.

former.

With refpedt to the number of ecUpfes of both itiminaries, it may be obferved, that there cannotnbsp;fewer than two, nor more than feven, in onenbsp;year j the moll iifual number is four, and it is rarenbsp;�O have more than fix. The reafon is obvious; for nnbsp;^he fun pafles by both the nodes of the moon'snbsp;Orbit but once in a year, unlefs he pafs by one ofnbsp;in the beginning of the year, in which cafe h^nbsp;'^i'lpafs by the fame again a little before the end ofnbsp;the year.

quot; Since the nodes move backwards 19^ � every year, they would fliift through all the points of thenbsp;ecliptic in 18 years and 225 days; and this wouldnbsp;he the regular period of the return of the echpfes,nbsp;any complete number of lunations were performed in it, without a fraflion; but this is notnbsp;the cafe. However, in 223 mean lunations, afternbsp;the fun, moon, and-nodes, have been once in a linenbsp;t'f conjunftion, they return fo nearly to the famenbsp;ftate again, that the fame node, which was in con-Jtindlion with the fun and moon at the beginningnbsp;t*f thefe lunations, will be within 28' 12quot; of thenbsp;hne of conjundlion, when the laft of thefe lunationsnbsp;Completed; and in this period there will be a re-gular return of eclipfes, till it be repeated about 40nbsp;t'oies, or* in about 720 years, when the line ofnbsp;^he nodes will be 28 x40 from the conjundtion,nbsp;will, confequcntly, be beyond the ecliptic limits;

this is called the Plinian period, or Caldean faros j it contains, according to Dr. Halley, 18 Julian years,nbsp;17quot;� 43quot;'gt; 20�} or, according to Mr. Fergu-fon, 18 years, ii'�, y**, 42,quot;�, 44�. In an intervalnbsp;of 557 years, ai'�, i8\ nquot;', 51�, in which therenbsp;are cxadtly 6890 mean lunations, the conjunftionnbsp;or oppofitlon coincides fo nearly with the node, asnbsp;not to be diftant more than i If therefore, tonbsp;the mean time of any folar or lunar eclipfe, we addnbsp;this period, and make the proper allowance for thenbsp;intercolary days, we fhall have the mean time ofnbsp;the return of the fame eclipfe. This period is fonbsp;very near, that in 6000 years it will vary nonbsp;more from the truth, than 8 I minutes of a degree*.�

After what has been faid above concerning the cclipfes of the moon, we need not fay much withnbsp;refpeft to the eclipfes of the fatellites of the othernbsp;planets; for they muft evidently be calculated afternbsp;the fame manner, and the calculations muft benbsp;cftablilhed upon fimilar particulars �, as far, however, as may be obtained, confidering that ournbsp;knowledge of the irregularities of the movements ofnbsp;�hofe fatellites is as yet imperfeft.

In calculating the times of the eclipfes of the fatellites of Jupiter, which indeed are, befides thenbsp;moon, the only cclipfes of fatellites that are no-

t�ced, an allowance proportionate to the diftance the planet from the earth, muft be madenbsp;on account of the progreffive motion of light,nbsp;3s we have elfewhere noticed; but befides thisnbsp;oaufe, it has been obferved, that when viewednbsp;different perfons and through different te-Jofcopes, the eclipfes of the fatellites of Jupiter donbsp;not appear to take place exadly at the fame time';

reafon of which is, that as the fatellite is pro-greffively or gradually obfcured when it enters the fhadow of the planet, and gradually enlightenednbsp;'vhen it emerges from that fhadow, its difappear-3nce in the former cafe, and its reappearance innbsp;latter cafe, muft be feen fooner or later, ac-Oording to the goodnefs of the telefcope and thenbsp;3cutenefs of the obferver�s fight. This caufe ofnbsp;otror in obfervation, cannot be remedied withoutnbsp;sfcertaining the power of the telefcope, amp;c. fromnbsp;^'^ual experiments, and making a fuitable allowance.

The theory of eclipfes is not a fubjedt of ufe-lefs curiofity j but feveral effential advantages are ^^rived from it. From the various phenomena ofnbsp;eclipfes of the fun and moon,- we derive anbsp;Confirmation of the figures and fizes of thofe bo-as alfo of the earth. All the eclipfes, par-bcularly thofe of the moon, and of the fatellitesnbsp;Jupiter, which happen much more frequently,nbsp;of very great ufe for determining the longi-s 4nbsp;nbsp;nbsp;nbsp;tudes

tildes of places on the furface of the earth. We may laftly addj that the knowledge of eclipfes hasnbsp;been of great chronological utility, as the precifenbsp;times of feveral remarkable events have been af-certained by calculating backwards the times ofnbsp;eclipfes, which have been faid in hiftory tonbsp;have accompanied, preceded, or followed thofenbsp;events.

The occultation of the fixed ftars by the moon, and their reappearance, are alfo of great ufe fotnbsp;determining the longitudes of places upon thsnbsp;furface of the earth. Their difappearance is fonbsp;fudden, that the time of it may be obferved withnbsp;great accuracy. The only difficulty which attends the fubjedl of occultations, is, that thenbsp;movements of the moon cannot be entirely calculated with all the precifion which might be de-fired; yet it muft be acknowledged, that th^nbsp;tables of thofe movements have of late been wonderfully corredted ; fo that the occultations as art;nbsp;now dated in the nautical almanack, and elfe'nbsp;where, may be depended upon as being fufficientlfnbsp;ufeful for the purpofe of determining the longi'nbsp;tildes of different places. For Inftance, fuppof*^nbsp;that the occultation of a certain ftar by the mooojnbsp;is, according to calculation, to take place atnbsp;o�clock, P. M. Greenwich time j but being ob-ferved from another fituation, and making the oe-ceffary allowances, according to the precepts, ir

found to take place at half paft eleven, the copclu-fion in the laft mentioned fituation is 7 | degrees ^aft of Greenwich 5 for (by converting the timenbsp;^nto fpace at the rate of 15� per hour), the halfnbsp;^our is equivalent to 7 f degrees; and at a placenbsp;'^hich is 7 I degrees eaftward of another it muft-11 I o�clock, when at the latter it is only ii.nbsp;Thofe ftars whofe latitude does not exceed 6%nbsp;36', north or fouth, may fuffer an occultation fromnbsp;the moon, fuch as may be obferved from fome partnbsp;tgt;f the furface of the earth ; but their occultationsnbsp;ttiay be obferved from all parts of that furface whichnbsp;^ave the moon above the horizon, when their latitudes do not exceed 4�, 32''¹.

With refpedl to the tranfits of Venus and Mercury over the difc of the fun, we have eifewhere ^ewn that they cannot take place at every con-JUnftion, becaufe the orbit of Venus makes annbsp;^Ugle of 3�, 23', 35'', and that of Mercury makesnbsp;angle of 7� with the ecliptic ; in confequence ofnbsp;'''hich either of thofe planets cannot be feen overnbsp;difc of the fun, unlefs at the time of conjunc-the. planet be fo near its node as that its geo-^^ntric latitude be lefs than the apparent femi-^'ameter of the fun.

See the method of making the yttlculation for an oc-'^ultation, in Vince�s Aftronomy, or in Gregory�s Aftro-homy.

The chief ufe of the obfervations of thofe tran-fits, which do not frequently happen, efpecially that of Venus, is to determine the diftance of thenbsp;fun from the earth, or its parallax; from which andnbsp;the well known analogy between the periods andnbsp;the difiances of the planets, the diftances of allnbsp;the planets may be determined, as has alreadynbsp;been done¹.

For the method of calculating tranfits, and otlier pat' ticulars relative to them, the reader mayconfult almofianfnbsp;of the late writers on aftronomy.

Th E number of aftronomical inftruments which have, aC various times, been con-bived for a variety of aftronomical purpofes j thenbsp;'^iprovements which they have received from timenbsp;^ time, particularly of late years, and in this coun-^*�7� would form the contents of a curious hiftory,nbsp;^^ch indeed as might be both agreeable and ufefulnbsp;^ fcientific perfons; but fuch an hiftory cannotnbsp;^ expected, nor indeed is required in an elemen-work like the prefent; yet it would be im-Ptoper to let the reader remain perfeftly unac-^tJainted with thofe inftruments, by the ufe ofnbsp;^*^ich moft of the foregoing particulars have beennbsp;^terrtiined, or may hereafter be verifiedi I fhallnbsp;^^^refore briefly fubjoin a competent defcription ofnbsp;principal inftruments that are at prefent ufed bynbsp;^fttonomers, and fhall, at the fame time, add verynbsp;more than the mere definitions of fuch othernbsp;**^ftrutnents as are cither not efientially neceflary,nbsp;that are too common to need a defcription.

The

The principal inftruments for a fixed obferva-tory, are a large fixed quadrant, or a circular divided inftrument, chiefly for meafuring vertical angles gt; a tranfit inftrument; an equatoreal inftrti'nbsp;ment �, a chronometer, or regulator j one or morenbsp;powerful telefcopes; a fixed zenith telefcope, and anbsp;night telefcope.

The quadrant, or quarter of a circle, divided intlt;a 90�, and each degree fubdivided into minute*nbsp;or fmaller parts, has been made of various fizes gt;nbsp;fome of them having a radius even of 8 or 9 otnbsp;more feet in length. When thofe quadrants do no^nbsp;exceed one or two, or at moft three feet in radio*/nbsp;they are generally fixed upon their particular (land*/nbsp;which are furniflred with various mechanical, contrivances, that are necelTary to place the plane of ch*^nbsp;quadrant perpendicular to the horizon, and for allnbsp;the other neceflirry adjuftments. But large quadrants are fixed upon a ftrong wall by meansnbsp;proper clamps j hence they have'been commonlynbsp;called mural quadrants, and are fituated in thenbsp;of the meridian of the obfervacory. In eithernbsp;thofe quadrants an index, which reaches from tl�^nbsp;centre to the edge of the arch, moves roundnbsp;centre, or round a Ihort axis which palTes throughnbsp;that centre, fo as to be moveable with its extremii^ynbsp;all round that arc, and thus point out on the di^*'nbsp;fions of the arch, the angle which it forms withnbsp;horizon, or with the vertical line, in anynbsp;fituation. This index carries a telefcope, throog

�Which the obferver looks at any particular objeft, whofe altitude he wifhes to determine.

Fig. 4, Plate XXIX. reprefents a pretty fimple conftruftion of a fmall moveable quadrant, andnbsp;fig. 5, reprefents a mural quadrant. Of the quadrant, fig. 4, CEB, is the arch divided into 90�,nbsp;2nd generally fubdivided into fmaller divifions, fuchnbsp;2s half degrees, or third parts of each degree, amp;c.nbsp;The centre of the arch is at A, and the whole is con-*^elt;hed together by means of ftrong metallic bars, asnbsp;ihewn between the letters ABC in the figure, in thenbsp;Centre A, a ftiort axis is fixed perpendicular to thenbsp;plane of the inftrument, and to the upper part ofnbsp;dais axis is fattened the index AD, which carries thenbsp;^^lefcope. This index generally has a fmall lateralnbsp;Ptojeftion, as at E, upon which the nonius is marked,nbsp;fiy which means the minutes or fmaller parts ofnbsp;each'degree may be difeerned *. The ferew P,nbsp;^ornmonly called the tangent /crew, with a nutnbsp;^fiat may be fattened to any part of the arch BC,nbsp;ficrews likewife into the extremity of the index,nbsp;is ufeful for moving the index gently or morenbsp;^'^curately than by the immediate application of thenbsp;^2nd to the index itfelf.

Since the index is fufpended at one end, viz. at if the other end D happens to be difengagednbsp;the ferew P, that lower end D of the index

will naturally come down to C, on account of own weight, and that of the telefcope. Now, idnbsp;order to avoid this tendency downwards, an armnbsp;y of brafsor iron, is frequently affixed to the uppernbsp;part of the index, which carries the leaden weight Z�nbsp;fufficienc to balance the weight of the index and te-kfcope; fo that by this means, even when difen-gaged from the fcrew P, the index will remain ihnbsp;any fituation in which it may be left. The wholenbsp;frame ABC is fupported upon a ftrong vertical axisnbsp;FS, the lower part of which turns into the pedefta^nbsp;QKw�, and carries an index S.v, which moves upon thenbsp;divided horizontal circle Q^, fixed to the pedeftahnbsp;This ferves to fix the plane of the quadrant in anfnbsp;azimuth that may be required. The lower part ofnbsp;the pedeftal has three claws, with a fcrew m it*nbsp;each ; by which means the axis FS may be fet trulfnbsp;perpendicular. The plummet AO, fufpended at Agt;nbsp;ferves to ffiew when the edge AC of the inftrumentnbsp;is truly perpendicular, or when the firft divifion ofnbsp;the arch at C is exadly in the vertical which palk*nbsp;through the centre A of tne quadrantal arc Bnbsp;The weight I of the plumm.et generally moves in ^nbsp;glafs of water, which is fixed upon the arm GK gt;nbsp;the objedl of which is to check the vibrations of th�nbsp;pendulum; which otherwife would he eafily movo^nbsp;by every breath of air, and would continue to rno''^nbsp;for a confiderable time after. I omit to mentionnbsp;lehfes or microfcopes that are applied to readnbsp;divifions at E, and at or to fee the coincidence of

P^Ufnmet-Hne, with a dot marked upon the arc C, as matters that need no particular defcrip-��cn.

In the eye-tube of the telefcope ADj there are ^^rtain {lender wires, placed in the focus of thenbsp;^ye-lens, and perpendicular to the axis of the te-^cfcope, which enable the obferver to diftinguifhnbsp;�^ore accurately when an objed, that is feen throughnbsp;telefcope, reaches the axis of the telefcope, ornbsp;'t is more commonly called, the line of collima-amp;c. Now when the ftars or planets are ob-�^rved at night, thofe wires in the eye-tube cannotnbsp;^ feen; therefore, to render them vifible, an armnbsp;wire is fixed occafionally at the end of the te-^^fcope, which arm holds a fmall piece of ivory ornbsp;z, fet aflant to the axis of the telefcope; for

jfjj-Q jufjg qP the telefcope will ^'^able the obferver to diftinguifh the wires at thenbsp;time that he beholds the celeftial objeft.

inftrument like the above, excepting that it no ftand; and its index is prevented fromnbsp;^^ding on account of its great length, by means ofnbsp;^^tallic bars d, f hy c. This inftrument is firmlynbsp;^ tipo;t a wall exaftly in the plane of the meri-of the obfervatory, for which purpofe it has

This undoubtedly is the principal inftrument of an obfervatory ; for by obierving the times by tho

dock, of the arrival of any celeftial objedt to the meridian, the right afeenfion of that objeft is balt;lnbsp;immediately ; and its declination is (hewn at thenbsp;fame time by the index of the quadrant upon thenbsp;divided arch ; deduding the inclipation of thenbsp;equator, which is given by the latitude once afeef'nbsp;tained of the obfervatory. It '\s by this means th^��nbsp;exad catalogues of the places of the fixed ftars ha'^^nbsp;been made.

The principal defeds of thofe quadrants are th� diange of fhape, which they frequently fuffer froi^nbsp;the weight and ftrels of their own parts, and th^nbsp;�difficulty of determining the error which is intrO'nbsp;duced amongft the divifions of the arch from th^^nbsp;change of fhape.

Principally with a view of remedying thofe feds, the late improved date of mechanics hasnbsp;troduced whole circles inftead of quadrants;nbsp;thefe are fixed upon their own particularnbsp;quite independent of a wall. The index, withnbsp;telefcope, of thofe circular inftrum�nts is as longnbsp;the diameter of the divided circle, and hasnbsp;nonius divifions at its two extremities, whichnbsp;to the like divifions on two oppofite parts ofnbsp;circle, provided the inftrument be exad; other^^^

their pointing to diffimllar divifions, they in-ftantly manifeft the incorreft ftate of the divifions, �r the derangement of the parts of the inftru-rtienr.

1 lhall not fubjoin a particular defcription of fuch Circular inftruments, firft, becaufe it is not effentiallynbsp;'^eceflary for our prefent purpofe; and, fecondly,nbsp;becaufe it would take up more room than we cannbsp;Conveniently allow it in this work. A very goodnbsp;defcription, by the Rev, F. Wollafton, of an excellent inftrument of this fort made by Mr. Cary,nbsp;IS to be found in the fecond part of the volume ofnbsp;^he Philofophical Tranfadtions for the year 1793.

The trunfit inftrument confifts of a telefcope of ^ny convenient length, fixed at right angles to annbsp;horizontal axis, which axis is fupported at its twonbsp;Extremities; and the inftrument is generally fituated,

that the line of collimation of the telefcope may ttiove in the plane of the meridian. The ufe of thisnbsp;inftrument is to obferve the precife time of thenbsp;Ecleftial bodies paflage acrofs the meridian of thenbsp;^bfervatory.

f ig. 6, Plate XXIX. exhibits a tranfit inftrument. Nm is the telefcope, in the eye-tube of whichnbsp;^ ^y em of parallel wires, fuch as is reprefented atnbsp;^ I is fituated in the focus of the eye-lens. FE isnbsp;i^he horizontal axis, in the middle of which thenbsp;telefcope is fteadily fixed; fo that by moving thenbsp;telefcope, the axis is forced to turn round its twonbsp;^^tremities E and F, which reft in the notches of

tt74 Of the Aj�ronomical InJlrumentSt

two chick pieces, T, S, of bell metal, fuch as are delineated feparately, and magnified at N. H*nbsp;and III. Thofe pieces are generally fixed uponnbsp;two pillars, either of call; iron, or, which isnbsp;better, of ftone, as are fhewn in the figure �, andnbsp;they are conftru�led fo as to be fufceptible of anbsp;fmall iriOtion by means of Aides and fcrews,nbsp;viz. the piece T backwards and forwards, and thenbsp;piece S upwards and downwards; by which meansnbsp;the axis EF of the inftrument may be fer, andnbsp;caufed exadlly horizontal, to move perpendicular tonbsp;the plane of the meridian. In order to verify thenbsp;firft of thofe requifites, viz. to fee whether the axisnbsp;is truly horizontal, the long fpirit-level P CFis fillquot;'nbsp;pended upon it by means of the metallic branchesnbsp;P O, and QJR �, and the fituation of the bubble innbsp;it will immediately fltew' whether the axis be trulynbsp;horizontal, or which way it inclines, and of courfenbsp;where it muft be raifed or deprefiied. The othefnbsp;requifite, viz. whether the axis be perpendicular tonbsp;the plane of the meridian, or nor, may be vcrifi^^^-by various means, the beft of which is by o'oferv^'nbsp;tions on thofe circumpolar ftars, wiiich never go below the horizon of the obfervatory. Thus, obfer''^nbsp;the times by the clock, when a circumpolar ftar, leennbsp;through the telefcope NM, croffes the meridiannbsp;both above and below the pole; and if the timesnbsp;defcribing the eafiern and weftern parts of its circo'^nbsp;are equal, the telefcope is then in the plane ofnbsp;meridian, confequently the axis E F is perpendicti-

lar to that plane; otherwife the notched pieces

,3nd S, which fupport the extremities E, F, of the mud be moved accordingly, or until uponnbsp;�tgt;fervation it be found that the above-mentionednbsp;of the ftars� lemi-revolutions be equal¹.

The cylindric extremity F is perforated, and the P^tforation paffes through the half of the axis, andnbsp;^'Caches the infide of the telefcope; that fide of thenbsp;^^lefcope tube, which is exadly facing F, being alfonbsp;Perforated. Within the faid tube, and diredlly op-Pofite to the perforation of the end F, a plane re-^e^lor, or a flat piece of ivory, is fixed, making annbsp;^'�gle of 45�, with the axis of the telefcope, andnbsp;^^ving an hole through it large enough to admit allnbsp;rays paffingfrom the objed-glafs to the eye-glafsnbsp;the telefcope.

^Vhen flars or other celeffial objeds are to be '^bferved in the night time, a fmall lantern Y is feenbsp;'^Pon a ftand juft before the perforation of the ex-^'^^mity F, fo as to throw the light within the axis,nbsp;upon the flant refledor within the tube of thenbsp;^^kfeope, whence it is refleded upon the wires innbsp;*�^6 eye-tube M, and renders them vifible. Bynbsp;Placing the lantern nearer to, or farther frorn the

When the inftrument has been once fo adjufted, a ^^rlc may be made upon a houfe, or rock, or poft, at foinenbsp;ranee from the obfervatory, fo that when viewed throughnbsp;telefcope, this mark may appear to be in the diredion ofnbsp;^xis of the telefcope 5 by which means the corred fitua- -�t of the inftrument may afterwards be readily verified.

extremity F, the obferver may illuminate the wires fufficiently for the purpofe, and not toonbsp;much.

To the other extremity E, of the axis, a divided circle, or fometimes a femi-circle, is fixed� which turns with the axis; the index being fixednbsp;to the pillar which fupports the axis. Sometime^nbsp;the fituation of thofe parts is reverfed; viz. thenbsp;circle is faftened to the pillar, or to the brafs piecenbsp;v/hich fupports the axis, and the index is faflenednbsp;to the extremity E of the axis. The ufe of thisnbsp;circle is to place the telefcope in the diredlion ofnbsp;any particular celeftial body, when that body crofiesnbsp;the meridian ; which inclination is equal to the col-latitude of the place, more or lefs the declination ofnbsp;the celeftial body, according as that declination isnbsp;north or fouth.

The equatorial injrument is not fo generally be found in aftronomical obfervatories ; yet, whconbsp;properly conftrufted, it anfwers feveral ufeful po'�'nbsp;pofes; it ferves almoft inftead of all other inftr*^'nbsp;ments, and faves a good deal of calculationnbsp;feveral cafes ; hence the portable equatorialnbsp;ftruments, have frequently, been called prtablenbsp;fervatories.

The principal parts of an equatorial inftrumcoh are an axis fixed in a proper frame, fo as tonbsp;parallel to the axis of the world, and to turn roundnbsp;its two extremities, as if it were the axis ofnbsp;earth upon its two poles. A circle divided inlt;^^

degree�'

*^egrees, and llkewife into 24 equal parts or hours, '''ith the fubdivifions, Sre, is fixed perpendicularlynbsp;and about the middle of the axis. Therefore,nbsp;circle is in the plane of the equator, and it is onnbsp;^his account that the Inftrument has been called annbsp;^iuatorial. Upon the fame or principal axis therenbsp;another circle, or a femi-circle, which moves innbsp;plane of the axis, confequently perpendicular tonbsp;equatorial circle. This vertical circle carriesnbsp;telefcope, and is called the declination circle.nbsp;^ow if a celeftial body move in the equator, thennbsp;file declination circle mull be fet at 0�; viz. thenbsp;telefcope is fet parallel to the equatorial circle; andnbsp;^'Jtning the whole inftrument round its principalnbsp;^^is, fo far from the meridian as the celeftial bodynbsp;queftion is from it, you will fee that objefbnbsp;^'�'eitly through the telefcope. But if the givennbsp;^Qdy have any declination, viz. if it be not ex-in the equator, then the declination circle withnbsp;|he telefcope muft be fet accordingly, amp;c. Such,nbsp;*�* ftiort, are the principal parts of an equatorialnbsp;''iftrument for a fixed obfervatory, where thofenbsp;P^tts are adapted to mafonry work, or to othernbsp;^eady ftipports. But a portable equatorial muftnbsp;fome other parts, which are neceflary fornbsp;^^dlifying it according to the latitude of any re-^^ired place, for holding the whole machinenbsp;^adily, amp;c. ; hence it is furniftied with a ftand,nbsp;horizontal circle with fpirit levels, amp;c. I donbsp;T 3nbsp;nbsp;nbsp;nbsp;not

2^8 Of the JJironomical Injlruments,

not attempt' to delineate or to defcribe all the ufes of an equatorial, as our limits do not admitnbsp;of it.

Various arrangements of the above-mentioned parts have been adopted by various artifts ; but thenbsp;beft inftruments of the fort, both portable and (otnbsp;a fixed obfervatory, were unqueftionably contrivednbsp;and executed by that great mechanical genius, thenbsp;late Mr. JelTe Ramfden. A Ihort deferiptioonbsp;of his portable equatorials was fome years agonbsp;publilhed by itfelf, and has been tranferibed ionbsp;various diftionaries of arts and fciences. Thenbsp;beft large inftrument of the kind, as far as I know�nbsp;which was likewife conftrufted by Ramfden for Sirnbsp;George Shuckburgh, is now in the poffeflion of thenbsp;fame, who has publilhed a very accurate defeription�nbsp;and a delineation of it in ,the Philofophical Tranfquot;nbsp;aftions for the year 1793.

Of ail the different forts of chronometers, ot time-keepers, a pendulum-clock, when properlynbsp;conftruded, is undoubtedly capable of the greateftnbsp;accuracy; it being liable to fewer caufes. of oh'nbsp;ftrudlion or irregularity; therefore fuch machio^*nbsp;are moft recommendable for an obfervatory.nbsp;fituation of this clock muft be near the quadrant�nbsp;and near , the tranfit inftrument; fo that the ohnbsp;ferver, whilft looking through the telefcope ofnbsp;of thofe inftruments, may hear the beats of the clo^^-

I nee�

I need hardly obferve with refpeft to telefcopes, they are of very great ufe in an obfervatory.nbsp;Indeed a telefcope for the fame can never be toonbsp;Eood or too large j and it fhould be furnilhed withnbsp;*i^icrometers, with different eye-pieces, amp;c.; but

a large inftrunnent of that fort is not eafily ma-'^aged, nor is always required, fo there fhould be f'vo or three telefcopes of different fizes and different powers in every obfervatory. With refpe�tnbsp;^0 the conflruftion of telefcopes enough has beennbsp;f^id in the third volume of this work ; but I fhallnbsp;'^nly obferve in this place, that one at leaft ofnbsp;telefcopes ought to be fixed upon' an axisnbsp;Hich may move parallel to the axis of the earth jnbsp;fnr in this conftrudtion the celeftial bodies may,nbsp;'''ith the telefcope, be eafily followed in theirnbsp;�Movements, as the hand of the obferver is, innbsp;^hat cafe, obliged to move the telefcope in one di-''^ftion only.

A pretty good telefcope, placed truly vertical in ^n obfervatory, is likewife a very ufeful inftru-'^fnt; as the aberration of the flats, latitude ofnbsp;^he place, amp;c. may be obferved and determined bynbsp;ufe of fuch an inftrument, with great eafe andnbsp;Accuracy.

The night telefcope is a fhort telefcope, which '^^gnifies very little j but it colledts a confiderablenbsp;Quantity of light, and has a very great field ofnbsp;''^lew; it therefore renders vifible feveral dim objeifis,nbsp;''^l^ich cannot be difeovered with telefcopes of con-

fiderably greater magnifying powers ; and hence ic is very ufeful for finding out nebula, or fmalinbsp;comets, or to fee the arrangement of a great numbernbsp;of ftars in one view.

The principal inftruments that are at prefent ufed for marine aftronomy, or for the purpofes of navigation, are that incomparably ufeful inftrumentnbsp;called Hadley's Jextanf, or quadrant, or o�lant; ^nbsp;portable chronometer; and a pretty good telefcope-With thofe few inftruments, the latitudes, longitudes, hours of the day or night, and feveral othernbsp;problem's ufeful to navigators, may be accuratelynbsp;folved. The defeription and the various ufes ofnbsp;Hadley�s fextant, may be found in all the works onnbsp;navigation of the laft 30 or 40 years, as alfo in allnbsp;the modern didtionaries of arts and fciences. Inbsp;fliall not fay any thing with refpeeft to other inftruments of lefs efiential ufe; fuch as a zenith fedlor,nbsp;an equatorial fefbor, an equal altitude inftrument?nbsp;fun-dials, amp;c.*

* With refpeit to fun-dials, I muft not omit to recommend the ufe of what is called the univerfal ring-dial, to thofe gentlemen who, in travelling, wifli to fet their watchesnbsp;within four or five minutes of common time, for commonnbsp;purpofes; which in moll country places, where even thenbsp;church-clock is much out of the true time, cannot be eafilfnbsp;accompliflred. The ring-dial when properly cenftruclctl?nbsp;and from four to fix inches in diameter, is eafily ufed in anynbsp;part of the world; is a cheap, very portable, and durable in-llrumentand, when the.fun fhines, it fhews the time of th^nbsp;day within lefs than five minutes; allowing for the equationnbsp;of time, which is Hated in almoll every almanack. , .

^ nbsp;nbsp;nbsp;Uncle�s

Under the title of aftrononnical machines, fome 'Writers doalfo reckon orreries, planetariums, globes,nbsp;Machines for fliewing eclipfes or tranfits, amp;c. butnbsp;thofe only ferve to illuftrate the theory of aftronomy,nbsp;3nd as fuch they are undoubtedly of ufc in a ledlurcnbsp;*�0001, or to inftruft novices. For this purpofe Inbsp;'vould give the preference to a pair of globes ; fornbsp;thefe are neither very expenfive, nor eafily put outnbsp;Qf order j and are, at the fame time, ufeful for thenbsp;Solution of a great many problems, as will be fhewnnbsp;'tl the next chapter.

An orrery is a very fit machine to fhew the fyftem the world, and fome of them have been made atnbsp;^ti enormous expence, with a great complication ofnbsp;quot;'heels and other parts, by which means they havenbsp;'tnitated the principal movements of the celeltiainbsp;bodies; but even the beft of them fall very fhort ofnbsp;feal accuracy; and of courfe they are quite unfit fornbsp;^he purpofes of calculating the future fituations ofnbsp;the ccleftial bodies. With refpefl to the defcrip-''on of orreries, planetariums, amp;c. I muft refer thenbsp;teader to the w'orks of other authors, efpecially tonbsp;^^fgufon�s Aftronomy, and to his Lectures; as alfonbsp;the various tradis of Benjamin Martin.

C ^82 3

TW O globes, one to reprefent the c�leftiat fphere, and the other to reprefent the furfacenbsp;of the earth, are commonly made for the purpofe o(nbsp;inftrufting ftiidents in aftronomy and geography*nbsp;They are made of various fizes, and have been va-lioufly mounted in frames furnilhed with magneticnbsp;needles, and a variety of extra pieces, intended bynbsp;the workmen to anfwer different purpofes, Thofcnbsp;which are delineated in fig. 7 amp; 8, Plate XXIX.nbsp;of the moft ufual form, and fuch as are quite fufS-cient for the purpofe of illuftration, and for the fc'nbsp;lution of the problems which may be expedted to benbsp;folved by m.eans of the globes. And here I muftnbsp;once more requeft the reader to recolledl: that thenbsp;circles, poles, amp;c. which are either delineated upon�nbsp;or annexed to the frames of thofe globes, are by 0�nbsp;means exifting in nature; but they are ideal circle^�nbsp;or lines, or points, or zones, which are of ufe o^lynbsp;for expreffing our ideas, or meafures, amp;c. On the

of land and water. In the heavens we perceive the fon, the moon, the fixed ftars, the planets, andnbsp;Oow-and then a comet; which bodies are undoubtedly at different diftances from us; but fince tonbsp;Common fight they appear to be all equally diftant,nbsp;therefore they are delineated upon the furface of anbsp;globe; and, if conveniency would allow it, theynbsp;Ought to be delineated on a concave fphericalnbsp;lurface.

With refpeft to the aftronomical problems, which tTouft be folved by calculation, or by the ufc of in-Htuments, I iliall add in the note a few of them onlynbsp;that are of more common ufe and lefs operofe. Itnbsp;'''ould be impracticable to infert a complete collection of fuch problems in this work, and thenbsp;teader, who is defirous of going deeper into thenbsp;Icience of aftronomy, will find abundance of themnbsp;1^ the works written profelTedly upon that fcience,nbsp;Ihch as Dela Lande�s, De la Caille�s, Vince�s, Gregory�s, and others (I).

(l.) I. To find the Meridian of the Place of Obfervation, or to draw a Meridian Line.

A line drawn from the floor of a room or elfewhere, and^ the plane of the meridian, fo that the rays of the funnbsp;Coming along the edge of a window, or through a hole innbsp;^he adjoining wall perpendicularly above one end of the line,nbsp;be upon, that line whenever the fun is in the meridian

2^4 nbsp;nbsp;nbsp;7'he XJJe of the Glebes,

The {lands, with the frames which fupport the globes, are fo fimple, and fo evident in the figure.

at noon, is of great ufe for redlifying a globe, for fituating a moveable quadrant in certain cafes, for regulating a common watch, amp;c.

The eafieft method of delineating it is as follows;� On an ho-rizontal plane defcribe three or four concentric circlesnbsp;and placing a convenient ftand near tliofe circles, let a plummet, as BC, fig. g, Plate XXIX. confifting of a thread, withnbsp;3 leaden (hot at its lower extremity, be fufpended from a pro-jedlion AB of the faid (land, fo that its lower extremity C maynbsp;be juft over, but not touch, the common centre of the circles.nbsp;A knot muft be made Ibmewhere, as at K, in the thread ofnbsp;this pendulum. When the fun fhines in the morning, ob-ferve where the (hadow of the knot K touches one of thenbsp;cirdcs, as for inftance at D, and draw the line D C, viz.nbsp;from the centre C to the mark D. After this time, thenbsp;(hadow of the knot will be found to fall within the circlenbsp;nntil a certain time, after which, viz. in the afternoon, it willnbsp;again approach that circle. Now when you find that thenbsp;(aid (hadow falls upon the fame circle, as at F, marknbsp;�hat place, and draw another line CF from the centre C tonbsp;it. Laftly, bifed the angle DCF, and the line of divifionnbsp;CE is the meridian line, or line in the plane of the meridiannbsp;�f th� place gt; for the projedlion of the (hadow of CK uponnbsp;the horizontal plane, is longer or (horter, according to thenbsp;various elevations of the fun; confequently it muft benbsp;equally long when the fun is at equal altitudes, viz. equallynbsp;uiftant from the meridian. Therefore the middle fituatioOnbsp;CE between the two fituations DC, FC, muft be thenbsp;tiue meridian line. This operation proceeds upon the fup'

and the Solution of Pfohkins. nbsp;nbsp;nbsp;285

is to require no particular defcripdon. Each of thofe ftands iupports, and is firmly fixed to, the

broad

Pofition that the fun is equally high above the horizon, at '^qual times from noon, which is not exaftly the cafe, be-lt;^aufe the fun is continually changing its declination; yetnbsp;^hat change is riot fo great as to occafion any fenfible errornbsp;'It the above-mentioned operation. The beft time of thenbsp;y^ar for drawing a meridian line is about Midfummer ; thenbsp;�laily or hourly change of the fun�s declination at that time,nbsp;being very little.

When a meridian line has thus been drawn, another me-f'dian line, in a more convenient fituation near the fame place, 'quot;ay be eafily drawn. Thus fufpend a thread and plummetnbsp;Jult over the fouth end of the known meridian line, and taf-Pend another plummet over the fouth end of the intendednbsp;'quot;eridian line. When the fun fhincs, let an obfcrv�r givenbsp;quot;otice when the ftiadow of the firft mentioned plummet linenbsp;^alls exa�tly upon the known meridian line, and at the famenbsp;'quot;ftant let another perfon mark two points in the fiiadow ofnbsp;*be fecond pendulum, viz. upon the plane where thatnbsp;'''her fhadow is projedled. Then a line drawn through thofenbsp;marked points, is the other meridian line fought. Anbsp;�quot;Pridian line thus drawn, may be correifted by repeating thenbsp;^hove-mentioned operation at other opportunities.

To find the Latitude of the Place of Qhfervation., and con~ fiequently the Elevation of the Pole for that Place.

means of a quadrant, find th'e fun�s apparent meridional �^'itude; viz. the greateft altitude above the horizon that thenbsp;does reach on the day of obfervation j and in order to

deduce

broad circular piece H 6, which reprefents the horizon. M.m is a brafs circle, which fits two notches

made

deduce the true altitude from this, which is the apparent altitude, you muft apply the following corretEfions, viz. ift. If you have obferved the altitude of the fun�s upper or lowernbsp;limb, you muft accordingly add or fubtrad the fsmi-diameternbsp;of the fun�s difc (which is given in the nautical almanacknbsp;for every day) fo as to have the altitude of the fun�s centre,nbsp;zdly, Subtract the refradlion correfpondent to the obfervednbsp;altitude; and, 3dly, add the fun�s parallax in altitude (whichnbsp;particulars are to be had from the nautical almanack, andnbsp;from the tables requifite to be ufed with it, from whichnbsp;fome of the following problems are taken), and the refult isnbsp;the corredl meridional altitude of the fun�s centre. Subtractnbsp;this corredted altitude from 90�, and the remainder is thenbsp;true diftance of the fun�s centre from the zenith ; which isnbsp;to be called north or fouth, according as the zenith of thenbsp;place is north or fouth of the fun�s centre. Take the fun�snbsp;declination for the day of obfervation, out of the almanack�nbsp;obferving if it be north or fouth declination. Then if thenbsp;zenith diftance and^the declination be both north or bot^*nbsp;fouth, add them together; but if one be north, and the otbetnbsp;fouth, fubtradl the lefs from the greater; and the fom in thenbsp;firft cafe, or the difference in the fccond cafe, is the latitudenbsp;of the place, of the fame name with the greater, viz. northnbsp;or fouth.

In correfling the apparent or obferved altitude, fome othet corredion is fometimes neceffary to be applied, which ntu^nbsp;be derived from the nature of the inftrument with which th^nbsp;altitude is taken; for inftance, if the obfervation be loa�

with an Hadley�s fextant, and an artificial horizon, you otu

tak�

^3de in the horizon H h. It is fixed perpendicu-larly to it, and may be moved vertically, fo that any

'ake the half of the angle which is fubtended at the eye by the Ian and by its refledfed image. If you oblerve the altitude atnbsp;and make ufe, according to cuftom, of the apparent ho-''�Zon or boundary of the fea, you muft fubtradf what is callednbsp;dip of the horizon (the quantity of which is found in thenbsp;fable requifite to be ufed with the nautical almanack}; fornbsp;^'^cording as the deck of the fhip is more or lefs elevatednbsp;�bove the furface of the fea, fo the horizon appears to benbsp;fnore or lefs deprefled.

The fun�s femi-diameter, which mull be fubtraded -nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;0�nbsp;nbsp;nbsp;nbsp;15' 51quot;

the fum, viz. 53� 37' 33quot;) is the correded elevation, ''^bich being fubtraded from 90�, leaves the north zenithnbsp;biftance equal to -nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;36� 22' 27quot;

their fum is the north latitude of the of obfervation, viz. -nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;- 50� 55' 37quot;

283 nbsp;nbsp;nbsp;Ufe of the Globes,

part of it may be placed above the horizon; onc half always remaining below the horizon. Thenbsp;globe is furnifhed with an axis, tlie extremities ofnbsp;which, or poles, N, S, pafs through two focketSinbsp;or holes, made in the brafs circle M m j and as thenbsp;globe may be turned round that axis, and of courfenbsp;any part of its furface may be fituated under the

brafs

III, To find the Latitude of the Place from the ohfiervt^ meridional Altitude of a fixed Star.

The meridional or greateft altitude of a ftar above th� true horizon, is to be obferved in the fame manner as thenbsp;altitude of the fun; but as the fixed ftars have no apparefi*'nbsp;diameter, nor any fenfible parallax, therefore the only cof'nbsp;reftion that can be applied to the apparent, in order to oh'nbsp;tain the corredled altitude, is the effedt of refradlion,nbsp;proceed as has been faid in the preceding problem, viz. fob'nbsp;traft the corrected altitude from 90�, and the remaindernbsp;the zenith diftance, which is north or fouth, accordingnbsp;the zenith is to the north or to the fouth of the ftar at th�nbsp;time of obfervation. Take the ftar�s declination out ofnbsp;tables requifite, amp;c. obferving whether it be north or footb*nbsp;Then if the zenith diftance and declination be both northnbsp;both fouth, add them together; but if one be north, and tb�nbsp;other fouth, fubtradl the-lefs from the greater, and the fongt;nbsp;difference will be the latitude of the place of obfervation*

Example. The meridional altitude of the ftar Procyf^ was obferved at fea with an Pladley�s fextant, and it app^^*^^nbsp;to be 77� 27' 15quot;, the zenith of the place being

brafs circle M m therefore this circle is called the itniverjal meridian, or the brazen meridian, in diftinc-don from the meridians which are delineated on the

*he ftar, and the height of the obferver�s eye being 22 feet shove the furface of the tea.. What was the latitude ?nbsp;Apparent meridional altitude of Procyon -nbsp;nbsp;nbsp;nbsp;77�nbsp;nbsp;nbsp;nbsp;27'nbsp;nbsp;nbsp;nbsp;15 '

22 feet of the obferver�s altitude, fubtracf 0� nbsp;nbsp;nbsp;4'nbsp;nbsp;nbsp;nbsp;28quot;

snd there remains the true altitude of Pro-cyon - nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;= 77� 22' 34quot;

true fouth zenith diitance of Procyon = i2� nbsp;nbsp;nbsp;37'nbsp;nbsp;nbsp;nbsp;26'quot;

quot;Phe declination of Procyon, which being north, mult be fubtradted -nbsp;nbsp;nbsp;nbsp;- 5�nbsp;nbsp;nbsp;nbsp;39 '

^d the remainder, viz. 6� 50' 47quot;, is the latitude fouth the fhip at the moment of taking the liar�s meridionalnbsp;slcitude.

This ufeful problem may be folved various ways, of which ^nwever I Ihall fubjoin fuch only as are lefs operofe.

With a fixed inftrument, fuch as a quadrant oratranfit-in-^^tument duly fituated in the plane of the meridian, the exact **'ne of apparent noon may be readily afcertained; for younbsp;*'^6d only obferve, when the centre of the fun is exadlly innbsp;axis of the telefcojie. Alfo other times of the day, or ofnbsp;VoL. IV.nbsp;nbsp;nbsp;nbsp;unbsp;nbsp;nbsp;nbsp;the

ajo nbsp;nbsp;nbsp;'The Ufe of the Globes,

furfacc of the globe itfelf, and which are the meridians of thofe places only over which they a?e drawn.

The

the night, may be afeertained by obferving the meridian fage of fome fixed ftar or planet, whofe diftance from the figt;^nbsp;is known.

Though to ohferve the arrival of the fun�s centre to the axis of the telefcope may at firfi: fight appear to be an operation fufficicntly fimple; yet as the pradlitioner will pt�'nbsp;bably meet with fome difficulty, I fliall add the follovyif�nbsp;diredtioris :

In the eye-tubes of the telefcopes of quadrants, circulat inftruments and tranfits, there always are certain perpen^i'nbsp;cular and parallel wires (generally five), by means of whichnbsp;the time of the approach of the fun�s limb may be accuratelynbsp;obferved; whence the time of the fun�s centre being in thenbsp;meridian may be determined. This time muff be eftimatc*!nbsp;by means of a clock or chronometer ; or, in othernbsp;the obferver is to find what hour, minute, fecond, andnbsp;of a fecond, is fliewn by the clock when the fun�s centrenbsp;upon the meridian; then, by applying the equation ofnbsp;for- that day, in which the obfervation is made, he will afee*^nbsp;tain whether the clock is right, or how much it deviatesnbsp;�nean time. In order to make the obfervation, fet the tenbsp;lefcope of the tranfit-inftrument io the proper altitude,nbsp;the altitude which the fun muft have at noon on that da)�nbsp;and which is had by taking the fum or difference of thenbsp;latitude of the place and the fun�s declination for thatnbsp;according as they are of the fame or of different denornit*^nbsp;don. Then a few minutes before noon apply / �

and the Solution of Prohlems. nbsp;nbsp;nbsp;291

The brazen meridian, being of a confiderable thicknefs, cannot reprefent a real meridian, whichnbsp;is nor more than a line 5 therefore one furface or

one

(defended by a dark glafs) to the telefcope, and wait till you fee the firft limb of the fun enter it; which will be apparently on the weft fide, becaufe thofe telefcopes, being of thenbsp;aftronomical kind, invert the objefts. When this happens,nbsp;let your affiftant attend to the watch ; and, when the firftnbsp;limb of the fun touches the firft wire, bid him mark the fe-Cond and part of a fecond, which is fhewn by the watch ;nbsp;and which muft be fet down in the firft column of a papernbsp;that contains five columns, ready ruled for the purpofe. Henbsp;rnuft then prefix the minute, and attend again to the watch.nbsp;When the fun�s firft limb arrives at the fecond wire, bid himnbsp;again to mark the fecond, amp;c, which muft be fet down innbsp;the fecond column of the paper, and after having prefixed thenbsp;tninute, he muft attend again to the watch. And in thisnbsp;ttianner the times, when the fun�s firft limb arrives at everynbsp;tgt;ne of the wires, muft be obferved and noted down in itsnbsp;proper column. The times when the fecond limb arrivesnbsp;^t each of the five wires muft be obferved in the fame man-*ter, and written in the proper columns under thofe of thenbsp;If the wires in the focus of the telefct)pe be fo dif-Pofed, that there is not time to obferve the firft limb at allnbsp;five wires, before the fecond limb arrives at the firftnbsp;''��re, the obfervation of the firft limb at the fifth wire muftnbsp;omitted ; and, in this cafe, the obfervation of the fecondnbsp;^'rnb at the firft wire may be omitted alfd, as it will be ofnbsp;ufe.

The mean of the times, when the two limbs of the fun at the middle wire, will be the time of apparent noonnbsp;U2nbsp;nbsp;nbsp;nbsp;by

29 2 nbsp;nbsp;nbsp;Uje of the Globes.,

one fide only of it muft be confidered as the merr-dian j and, in faft, the holes for the extremities of the axis are not made in the middle of the thickneis

by the watch j and if the wires are equi-diftant (as they ought to be), the mean of the two times, when the firft limbnbsp;was at the firft wire, and the latter limb at the fifth wire, willnbsp;alfo be the time of noon. Alfo the mean of the two times,nbsp;when the firft limb was at the fecond wire, and when thenbsp;latter limb was at the fourth wire, will be the time of noon.nbsp;Likewife the mean of the times when the firft limb was atnbsp;the fourth wire, and the latter limb was at the fecond wire,nbsp;will be the time of noon. If the firft limb was obferved atnbsp;the laft wire, and the latter limb at the firft, the mean of thefcnbsp;two obfervations willalfo be the time of apparent noon : andnbsp;the mean of all thefe refults, if they differ as they moft likelynbsp;vril), is the time of apparent noon by the watch. This done,nbsp;take the equation of time for the dayof obfervation from thenbsp;almanack,, and add or fuhtratft it, according as is mentionednbsp;in the almanack, to the above-mentioned noon time, and thenbsp;difference of the refuk from the 12 o�clock hour is thenbsp;acceleration or retardation of the watch. Thus,, if by tirenbsp;obfervation of the tranfit the apparent noon be at I 2gt;' 3' bynbsp;the watch, and the equation to be fubtraefted is 2'30quot;,nbsp;muft fubtracl 2' 30quot; from 12'' and the remainder is i2*nbsp;0' 30'', which (hews tliat the watch is 30' too fall.

'I'he above-deferibed obfervation may be performed by finglc perfon without any affiftant, provided he has a clocknbsp;fo near the inftrument as to hear the beats of its penduIuiH�nbsp;and count the feconds whilft he is looking through the tc'nbsp;lefcope 5 for he will have quite time enough to mark doWi^

and the Solution of Prohkms, nbsp;nbsp;nbsp;293

the circle M m, but by means of two projedlions of brafs, they are made fo as to be even with thenbsp;above-mentioned furface. This fame furface of the

brafs

A fecond method of finding the time of the day when the latitude and longitude of the place of obfervation, the fun�snbsp;declination at noon, and its altitude as taken by a quadrant,nbsp;at any time, are known, is as follows:

Correff the obferved altitude for the effe�ls of refradion and femidiameter of the fun (according as the altitude of itsnbsp;Upper or lower limb has been obferved), fubtradl the naturalnbsp;fine of the corredled altitude from the natural fine of thenbsp;meridian altitude (the meridian altitude of the fun is thenbsp;firm or the difference of the colatitude of the place and thenbsp;fun�s declination, according as they are of the fame or ofnbsp;different denomination )i find the logarithm of the remainder,nbsp;to which add the logarithmic fecant of the latitude of thenbsp;place, and the logarithmic fecant of the fun�s declination ;nbsp;their firm, rejedling 20 from the index, muff be fought for innbsp;table XVI. of the table requifite to be ufed with the nauti-t^al almanack, under logarithmic rifing, and the time cor*nbsp;tefponding to it, is the apparent time from the nearelt noon,nbsp;quot;'hen the fun�s altitude was obferved; confequently, if thenbsp;uhfervation be made in the forenoon, the time, thus found,nbsp;muft be taken from 24 hours, and the remainder will benbsp;the appare.nt time from the noon of the preceding day.

Example. On the 5th of March 1780, in the afternoon, *u latitude 16� 24' north, and longitude 138quot; eaft, the altitude of the fun�s lower limb was obferved to be 47� 8'nbsp;What was the apparent time when the obfervationnbsp;quot;fts made ?

end the Schtion of Problems. nbsp;nbsp;nbsp;295

^dian, towards each pole; the other two quadrants 3re reckoned from the poles towards the other in-terfedtion m, with the equator. When the globe is

redtified

Whofe logarithm is - nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;� -nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;4)^7823

which add the logarithmic fecant of the declination -nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-'nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;10,00223

I^ejea 20 from the index of the fum, and the remainder, 4,29850, muft be fought for in table XVI. of the re-^uifite tables, under the column of logarithms rifing, andnbsp;againfl: ic you will find the correfpondent time, which is thenbsp;hijie of making the obfervation, viz. 2^ 27' 2quot;.

It has been mentioned in the preceding chapters of this Volume, that the longitude of one place from another may benbsp;afcertained by various methods. Thofe methods may benbsp;*^�duced to four, viz. it may be afcertained, ift, by obfervingnbsp;time of an eclipfe of a fatellite of Jupiter; but this cannbsp;be done on land, when fuch eclipfes take place, and thenbsp;'Veather is fufficiently clear j 2dly, by obfervations made atnbsp;time of an eclipfe of the fun or of the moon;

refiified for experiment, this divided fide is ufually turned towards the eaft, and the north pole, Ny towards the real north.

The

means of a time-lceeper or chronometer; and 4th!y, by lunar obfervations, viz. by obferving thediftance of the moon fromnbsp;the fun or from fome fixed flar; which two Jaft methods maynbsp;be ufed alinoft at all times.

Refpedting the firft and feepnd method, enough has been faid in the preceding chapters. With refpedl to the fourth,nbsp;wiiich is the moft difficult and operofe, J muft refer the readernbsp;to the modern aftronomical works, and efpecially to the tablesnbsp;requifite to be ufed with the nautical almanack, where benbsp;will find the luriar method clearly and corredlly dc-feribed�nbsp;whilfi: I fhall only briefly deferibe the third method, viz.nbsp;the ufe of a time-keeper.

� If a chronometer or time-keeper be regulated to ke^P mean time exactly, and be fet to the mean time at the m�'nbsp;ridian of one of the two places, whofe difference of longitudenbsp;is required; for inftance, be fet to mean time at the meridisPnbsp;of Greenwich obfervatory. It is evident that fuch a chrO'nbsp;nometer will continue to fhew the mean time at that m�'nbsp;ridian as long as it continues to go at the fame rate, vvhat'nbsp;ever place it may be carried to ; confequently, if a watchnbsp;regulated, be kept on board a fliip, it will always (hew d'�nbsp;mean time at the firft meridian. Hence, if the meannbsp;be found in the fhip, under any other meridian, by the pf�nbsp;ceding problem, the difference between it and the time fhe'''*'nbsp;by the chronometer, when the fun�s altitude was obfer'^� �nbsp;being turned into degrees and minutes, at the rate of i5nbsp;an hour, will be the longitude of the place where thenbsp;altitude was obferved.�nbsp;nbsp;nbsp;nbsp;jt

and the Solution ef Prohkms. nbsp;nbsp;nbsp;297

The horizon H-6, which is generally of wood �hovered with paper, has its upper fide dividednbsp;'vith feveral circles j the innermoft of whichnbsp;is divided into 360�; then come the twelve fignsnbsp;of the zodiac, difiinguilhed by their names andnbsp;charafters, and each fign is divided into 30quot;.

It is not, however, abfolutely iiecelTary that the chrono-*^ieter fliould either be fet precifely to mean time at the firft �Heriaian, or be regulated to keep exadly rhean time ; bothnbsp;�Of which might, perhaps, be difficult, or, at leaft, tediousnbsp;to effect. The only thing which is abfolutely requifite in anbsp;tvatch, to render it equal to the talk of finding the longitude,nbsp;h, that it will go uniformly at fome known rate; for in-ftance, that it will accelerate or retard its going by a fecondnbsp;or two, or more, every day; which acceleration or retardation is commonly called the rate of the watch, and beingnbsp;itnown, the mean time at the firft obfervatory may benbsp;ittiown by the chronometer, as well as if that machinenbsp;Slewed that mean time exaamp;ly. Thus, if the watch accelerates 10quot; each day, three days after the fetting of thenbsp;chronometer, 1 know that the noon at the meridian, wffiercnbsp;the chronometer was fet, is when that machine fliews iz**nbsp;and 30quot;.

The few problems which are given in this note, are intended merely to give the ftudentan idea of fuch operations. If he wilhes to proceed farther in the fcience of praflicalnbsp;^ftronomy, he is referred to the recent works written pro-fefledly on the fcience, and which have been frequentlynbsp;ft'^oted in the preceding pages of this volume. A completenbsp;fet of all the neceffary aftronomical problems, together withnbsp;their demonftrations and examples, being abfolutely incompatible with the limits of this work.

Next to this circle there is the calendar, viz. the names of the twelve months with the divifions ofnbsp;the days correfpondent with the figns of the zodiac.nbsp;The outermoft circle contains all the points of thenbsp;com pafs, and the winds as they are denominated bynbsp;the feaiTten.

On the meridian and round the north pole Ngt; there is a circle C faftened to the meridian. Thisnbsp;is called the horary circle, and is divided into twicenbsp;twelve hours; the 12th hour at noon being on thenbsp;upper part of the meridian ; and the 12th hour atnbsp;night being on the lower fide of the meridian ofnbsp;towards the horizon. The extremity of the axis atnbsp;N prqjedls a little above the plane of this horarynbsp;circle, and carries an . index, which turns with thCnbsp;globe when the globe is turned round its axis, andnbsp;indicates the hours, or how much a given part of th�nbsp;iurface of the globe is removed from the meridian 5nbsp;fince the time of a whole revolution is divided intbnbsp;24 equal parts or hours.

^0 fhew the altitude of an objedl on the furface of globe; and hence it is called the quadrant ofnbsp;^^titude.

There frequently is another appendage to the S�obes, which Is called the Jemic'ircle of fofition. Itnbsp;a pretty flender wire, whofe extremities are fixednbsp;the points of north and fouth on the horizon, fonbsp;^^at the wire or femicircle can be moved freely fromnbsp;horizon to the meridian, and may be raifed tonbsp;^f^y pofition.

The principal circles marked upon the furfaces the globes, and which, having already been de-^cribed, need only be mentioned, are the following,nbsp;the equator, divided into 360�, the numerationnbsp;^ornmencing at the vernal ihterfeftion �with thenbsp;^'^liptic, which croffes the equator at the vernal andnbsp;the autumnal equinoftial points, viz. firft degreenbsp;Aries, and firft degree of Libra. The eclipticnbsp;divided into 12 equal parts or figns, and each fign

If on each fide of the ecliptic we add a broad P^ne of about 8�, we have the zodiac, and this isnbsp;^�^tially drawn upon the celeftial globe, with itsnbsp;^ ^ i^onftellations.

quot;The two tropics, viz. that of Cancer being on northern, and that of Capricorn on the fotithernnbsp;*'^'1 of the globe.

N'ear the poles are feen the two polar circles, viz. north, or the ardtic polar circle, near the north

Befides thofe, there are other circles, which how-^ ever are not common to both the globes. Thus thenbsp;celeftial globe has the two colures and the circlesnbsp;latitude ; it has alfo the conftellations with the ftatsnbsp;reprefented in their proper fituations and magoi'nbsp;tudes. The terreftrial globe has the meridians, thenbsp;parallels of latitude, and the rhumbs; it has alfo thenbsp;reprefentations of countries, coafts, iflands, feas,nbsp;generally the tracks of the moft renowned circunnu�'nbsp;vigators. The principal problems which may henbsp;folved by means of the globes, are g,s follows ;

I. particular place upon the terrejlrial globe bti^^ given, to find its latitude and longitude.

Turn the globe round its axis, until the place comes juft under the brazen meridiannbsp;(viz. under the edge of its divided fide, whichnbsp;, rnuft always be underftood when the meridiannbsp;mentioned), and the degree of the meridian whi^^nbsp;is juft over the place (meaning the degrees ofnbsp;two quadrants, which are numbered from the eft^�nbsp;tor) is the latitude fought; and it is north ornbsp;according as it is on jthe northern or on the fouth^*^^^nbsp;fide of the equator. . At the fame time the degree ^nbsp;the equator, which is juft under the brazen rperi^^^'��nbsp;is the longitude of the place in queftion.nbsp;nbsp;nbsp;nbsp;.

B. In old globes, the longitude is reckoned the ifland of Ferro, one of the Canary Iflands.nbsp;prefent the longitude on the globes that are madenbsp;this country, begins to be reckoned from the me-^'dian of the Royal Obfervatory at Greenwich.

The latitude and longitude of a place being given^ to find that place on the terreflrial globe.

This is the reverfe of the preceding problem, is eafily folved. Find on the equator the knownnbsp;'^^grce of longitude, and turn the globe fo as tonbsp;that degree juft under the brafs meridian;nbsp;find the degree of the given latitude upon thenbsp;'^�^ridian, obferving whether it be north or fouthnbsp;^titude, and exactly under it you will find the placenbsp;^ueftion.

If the latitude of the place be north, elevate the pole as many degrees above the horizon H h.nbsp;I^the latitude be fouth, elevate the fouth pole abovenbsp;horizon an equal number of degrees; for ac-^j^tding to the lower or higher latitude of any par-'�''^^lar place, fo does the pole appear to be higher ornbsp;at that place. The degrees of this elevationnbsp;pole are counted upon the meridian. Thusnbsp;figure, the north pole is elevated 51� abovenbsp;^ horizon, the globe being reftified for the latitude

London.

Turn

Turn the globe till the given place comes to tl'^ meridian ; and that part of the meridian, -which isnbsp;over it, and which is 90� diftant from the horizon 0^nbsp;either fide, reprefents the zenith. To this point olquot;nbsp;the meridian the quadrant of altitude muft benbsp;tened, which ferves to folve certain problems tha*^nbsp;will be defcribed hereafter. Laftly, turn the whol�nbsp;frame of the machine, fo that the north pole be di'nbsp;refted towards the real north, and of courfenbsp;fouth fide towards the real fouth. Then the gln^^^nbsp;is fituated jull as the real earth is fituated with ff'nbsp;fpe�l to the given place. In order to place thenbsp;ftrument duly north and fouth, a magnetic needlenbsp;affixed to fome globes j bur you muft then allow 1�'�

IV. Two f laces being given upon the fur face of globe, to find their difi�rence of latitude and dif^^'nbsp;ence of longitude.

Turn the globe until one of the places cotn^^ under the brazen meridian, and mark the degree ^nbsp;latitude which is juft over it, obferving whethernbsp;be north or fouth; then turn the globe untilnbsp;ether place comes under the meridian, andnbsp;likewife the degree of this place�s latitude.nbsp;if both thofe latitudes be north, or both fo^'^ ^nbsp;their difference is the difference of latitude betw^^^nbsp;the two places 1 but if one he fouth and the other not �

�when one of the places is under the meridian, mark the point or degree of the equator, which is'at thenbsp;fame time under the equator; then turning the globenbsp;Until the other place comes under the meridian,nbsp;naark likewife the point of the equator which is cutnbsp;by the meridian; and the number of degrees whichnbsp;He between thofe two marks, is the difference ofnbsp;longitude fought.

If this number of degrees be turned into time at the rate of 15� per hour, you will have the difference between the apparent time at thofe places; fornbsp;inftance, if the difference of longitude be 35% thennbsp;the difference between the apparent times at the twonbsp;places is 2 hours and 20 minutes; fo that whennbsp;b is noon at one of thofe places, it muft be 2 o�clocknbsp;and 20 minutes in the afternoon, or 2 hours andnbsp;^0 minutes before noon, at the other place, accord-tug as the latter is eaftward or weftward of thenbsp;former. But this difference of apparent time maynbsp;be had likewife by the horary circle C ; for ifnbsp;quot;'hen one of the places is under the meridian, younbsp;place the index at the 12th hour on the horarynbsp;'^'fcle, and then turn the globe until the other placenbsp;'^omes under the meridian, you will find the indexnbsp;^�refted to the proper difference of time. Thusnbsp;tu the above-mentioned inftance the index will

found directed cither to j**, 40�*, or to 2*�*

The eafieft and general way of performing thi* operation is by leparating the quadrant of altitudenbsp;from the meridian, and applying it to the two plate�nbsp;on the furface of the globe. Then the numbernbsp;degrees which are Ihewn by that quadrant tonbsp;between the two places, being converted into mile�nbsp;at the rate of 69^ miles per degree, will give thenbsp;diftance in miles between the two places. Shoul*^nbsp;the two places be farther afunder than the quadrani^

. can reach, the operation may be performed by rneafurements, viz. make a mark fomewhere bt'nbsp;tween the two places, and as nearly as you cannbsp;their diredtion ; then apply the quadrant, and tak� �nbsp;the diftance between one of the places and the matkjnbsp;and in the fame manner take the diftance between�nbsp;the mark and the other place. Then the fum of tho*^nbsp;two diftances is evidently the diftance betW�eennbsp;two places.

Find on the wooden horizon the given � of the month, and in the circle of the figns which'nbsp;clofe to it, you will find the degree of the fig^nbsp;refpondent to it: now find that degree of that

the ecliptic, which is marked upon the globe, ^nd that is the place of the fun for the given day;nbsp;quot;^here you may make a mark, or fix a bit of papernbsp;by means of a bit of wax, as this will be ufeful fornbsp;the folution of other problems.

If you move the globe until the above-mentioned t�larked place of the fun comes under the meridian,nbsp;then the number of degrees which are found on thenbsp;brazen meridian to be between it and the equator, isnbsp;the declination of the fun for that day, and it isnbsp;tiorth or fouth, according as the marked place isnbsp;the northern or on the fouthern fide of thenbsp;^uator,

If you reftify the globe for any particular place, 3nd then turn it until the marked place of the funnbsp;t^omes to the meridian, the number of the degrees,nbsp;quot;'hich are Ihewn by the meridian to be between thenbsp;horizon and that marked place of the fun, is thenbsp;�Meridian altitude of the fun for that place on tiienbsp;Siven day.

^II. To find the time of fun-rifing, and of fun fetting, at any given place, and for any given daynbsp;of the year.

Find and mark the fun�s place in the ecliptic for day given (by die preceding problem). Rec-the glube for the latitude ol the given place;nbsp;^'^d turn the globe fo as to bring the fun�s placenbsp;the mieridian. In this fituation keep the globenbsp;'�OL. ly. gt;nbsp;nbsp;nbsp;nbsp;Xnbsp;nbsp;nbsp;nbsp;Ready

fteady, and direft the index of the horary circle to the 12 o�clock hour; then turn the globe until thenbsp;fun�s place comes to the horizon on the eaftern fidenbsp;of the machine, and the index of the horary circlenbsp;will point to the hour and part of the hour, at whichnbsp;the fan will be feen to rife gt;on that day from thenbsp;given place. If you turn the globe until the fun�snbsp;place cornes to the horizon on the weftern fide ofnbsp;the machine, the index of the horary circle willnbsp;fliow the time of fun fetting for the day and place it^nbsp;queftion j whence you have the length of the day.

VIII. I'� find the beginning and the end of the twtUghi for any place and day given.

Find the latitude of the place, and redlify th^ globe (by problem ift and 3d) ; put the index ofnbsp;the horary circle to the 12th hour, tlic fun�s placenbsp;being in the m.eridian j then take the point of thenbsp;ecliptic oppofite to the fun�s place, and turn thenbsp;globe weftward, as alfo the quadrant of altitude, tillnbsp;the point oppofite to the fun�s place cuts the qo^'nbsp;drant of altitude in the 18� above the horizon. Theonbsp;the index on the horary circle will fhew the tin^^nbsp;when twilight begins in the morning. If you tak^nbsp;the point oppofite to the fun, and bring it to th^nbsp;eaftern hemifphere, and turn it until it meets witknbsp;the 18 th degree on the quadrant of altitude, the inde?^nbsp;will Ihew when the twilight ends in the evening.

Reflify the globe for the latitude of the place ; bring the folfticial point of that hemifphere (viz.nbsp;the firft point of Cancer, if the place have north latitude ; or the firft point of Capricorn, if the plac�nbsp;have fouth latitude) to the eaftern part of the horizon, let the index to the 12 o�clock hour at noon ;nbsp;turn the globe until the folfticial point comes to thenbsp;�Weftern fide of the horizon j and the hours paftecinbsp;over by the index give the length of the longeft daynbsp;or night at that place. The complement of whichnbsp;time to 24 hours, is the length of the fliorteft daynbsp;or ftiorteft night,

Find the latitude of the place on the brazen me-tidian; turn the globe, and obferve the two points Of the ecliptic that pafs under the above-mentionednbsp;^ogree of the brazen meridian. Then feek Q)r thofenbsp;points of the ecliptic in the circle of the twelve fignsnbsp;that are marked upon the horizon H h, and againftnbsp;them you will find the days of the month in whichnbsp;the fun will be vertical to the .given place.

XI. nbsp;nbsp;nbsp;any given time to find all thofie places ofi thenbsp;earth where the Jun is then rifing or Jetting, andnbsp;where it is noon or midnight.

Find the place where the fun is vertical at the given time �, redlify the globe for the latitude ofnbsp;that place, and bring the place to the meridian.nbsp;Then all thofe places, that are in the weftern halfnbsp;of the horizon, have the fun rifing, and thofe whichnbsp;are in the eaftern half of the horizon, have the funnbsp;fctting; thofe who are under the meridian above thenbsp;horizon have noon or the fun culminating, and thofenbsp;who are under the meridian below the horizon,nbsp;have midnight j thofe who are above the horizon,nbsp;have day, and thofe who are below it, have night�

XII. nbsp;nbsp;nbsp;A place being given within either of the polarnbsp;circles, to find the time when thefun begins to be feen,nbsp;and when it departs from that place ; alfo how longnbsp;he will continue to he feen, and how long he willnbsp;abfent from that place.

� Re�tify the globe for the latitude of the place; turn it, and obferve what degrees in the firft andnbsp;fecond quadrants of the ecliptic are cut by the northnbsp;point of the horizon (the latitude of the place beingnbsp;fuppofed to be north). Find thofe degrees in thenbsp;circle of the figns on the horizon, and their cor-

refponding days of the month; and all the time between thofe days the fun will not fet in thatnbsp;place.�

Again, obferve what degree in the third and fourth quadrants of the ecliptic will be cut by thenbsp;fouth point of the horizon, and the days anfwering;nbsp;then th.e fun will be quite abfent from the givennbsp;place during the intermediate days j that day in thenbsp;third quadrant fhews when he begins to difappear ;nbsp;and that in the fourth quadrant fhews when he begins to fhine in the place propofed.�

XIII. �The latitude of the place, and the day of the month, being given, to find the fun's declination, meridian altitude, right afcenfion, amplitude, obliquenbsp;afeenfion, afcenfional difference; and thence the timenbsp;of rifing andfetting, with the length of the day andnbsp;night,

� Reftify the globe for the latitude of the place, and noon (viz. bring the place under the meridian);nbsp;then the degree of the meridian over the fun�s placenbsp;is the declination. The meridian altitude is fhewnnbsp;by the degree the fun is above the horizon, and isnbsp;equal to the fum or difference of the colatitude andnbsp;declination. The fun�s right afcenfion is thatnbsp;degree of the equator which is under the meridian.�

� Bring the fun�s place to the eaftern part of the horizon ; then the amplitude is that degree of thenbsp;horizon which is oppofite to the fun. The obliquenbsp;ftfeenfion is that degree of the ^equator which is cutnbsp;by the horizon. The afceiffional difference is thenbsp;difference between the right and oblique alcenllons.nbsp;The afcenfional difference converted into time, willnbsp;give the time the fun rifes before or after the hournbsp;of fix, according as his amplitude is to the northwardnbsp;or fouthward of the eaft point of the horizon.�

XI V. 'The latitude of the place, day of the month, and the funs altitude being given,, to find the azimuth,nbsp;and hour of the day.

Redfify the globe for the Lititude of the place j bring that place under the meridian ; fix the indexnbsp;to the 12 o�clock hour at noon j and fix the clampnbsp;of the quadrant of altitude to the zenith. This donenbsp;turn the globe, and move the quadrant of altitudenbsp;until the fuq�s place coincides vyith the given altitudenbsp;on the graduated edge of the. quadrant; then thatnbsp;edge of the quadrant will cut the degrees of azimuth on the horizon H h, reckoned from the.nbsp;north; and at the fame time the index will Ihew thenbsp;hour of the dav on the horary circle.

XV. To difpoje the celejlial globet Jo as to Jhew th%^ aElual appearance of the heavens at any given timenbsp;and place.

Reftify the celeftial globe for the latitude of the place., Take the place of the fun for the givennbsp;time, and bring it to trSi meridian; alfo fet the indexnbsp;to the twelfth hour on the horary circle ; then turnnbsp;the globe until the index points to the given hour ;nbsp;then the globe will be fituated like the celeftialnbsp;fphere, and every ftar upon the globe will point to-'Vards the real ftar in the heavens. The ftars whichnbsp;are in the eaftern half of the horizon, are rifing;nbsp;thofe in the weftern half, are fetting; and thofe whichnbsp;are under the meridian, are culminating. If thenbsp;quadrant of altitude be fet to any given ftar, it willnbsp;fliew the altitude of that ftar, and its lower extremitynbsp;'''ill fhew the azimuth of that ftar upon the horizon.nbsp;If you turn the globe quite round, you will eafilynbsp;perceive thofe ftars which are within the circle of perpetual apparition, as alfo thofe which are within thenbsp;limits of perpetual occultation,viz. thofe which nevernbsp;Eu below the horizon, and thole which never rifenbsp;^bove the horizon, of the given place.

The celeftial globe reprefents the fixed ftars; but planets cannot be delineated upon it, becaufe thenbsp;X 4nbsp;nbsp;nbsp;nbsp;lattcf

latter are always fhifting their places amongfl: the former. Therefore, when the planets are to be re-prefented for any particular time, they mufc benbsp;ftuck on occafionally; ,viz. little round pieces ofnbsp;paper, each having the mark or character of ^nbsp;particular planet on one fide, and a bit of waJtnbsp;on the other (the philofophical inftrument makersnbsp;fell papers with the charafters of the planets readynbsp;ftamped for this purpofe) are lightly fiurk uponnbsp;the globe in their proper places, which places at?nbsp;given in the ephemeris for every day of the year ?nbsp;then if you perform the preceding problem, yo^nbsp;will have the reprefentaion of the planets in theirnbsp;proper places, as well as of the ftars.

Place one extremity of the quadrant of altitude upon one of the poles of the ecliptic, viz. tha^nbsp;pole which is nearer to the given ftar ; and let it�nbsp;graduated edge fall upon the given ftar. Thennbsp;the number of degrees which the quadrant fbe'vsnbsp;to be between the ecliptic and that ftar, is the lati'nbsp;tude �f the fame. The longitude is the degree on.nbsp;the ecliptic, which is cut at the fame ti.me by th^nbsp;quadrant of altitude.

meridian i then the degree of the meridian, which juft over it, is its declination; and the degree ofnbsp;the equator, which is cut by the meridian in tha?nbsp;htuation, is its right afcenfion.

XlX. To find when a given filar rifes,fets, or culminates on any given filace and day of the year.

Reftify the globe for the latitude of the place,: bring that place to the meridian, and fet the index tonbsp;the 12 o�clock hour at noon. Then move the globenbsp;t^ntil the given ftar coincides with the horizon onnbsp;the eafte'rn fide, and the index will fhew the time ofnbsp;tts rifing. If you turn the globe until the fame ftarnbsp;t^oincides with the horizon on the weftern fide, thenbsp;mdex will fhow the time of its fetting, and if younbsp;bring the ftar to the meridian, the index will fhewnbsp;the time of its culminating.

The meridian altitude of the ftar, as alfo its ob-afcenfion and afcenfional difference, are found the fame manner as for the fun. See problem

PARTY.

A FEW particular fubjefts, ufeful to the ftu-dent of natural philofophy, but which could with propriety, be inferced in the precedingnbsp;Relumes, will form the contents of the prefent ornbsp;part of this work; which, therefore, will benbsp;''^lt;ded into fedlions that are quite unconne�lednbsp;each other. The fubjeft of aeroftadon willnbsp;c briefly treated of in the firft feftion. The nextnbsp;tel *nbsp;nbsp;nbsp;nbsp;abridgment of fads and conjeftures

_ ^dve to meteors, and to the fall of ftones from the ofphere. The third fedtion will exhibit a com*nbsp;uon of weights and meafures. The laft fedtion

- oontam feveral additional fadts, difeoveries, ob-�^oons. Sec. relative to the different branches of Of philofophy, which have either been made,nbsp;to notice, fubfequent to the printing of the

TH E art of flying, or of imitating the feather^� tribe, has long been the objedl of earn^^nbsp;defire amongft men. The fanciful ideas ofnbsp;the tales of amulement, the pretended difcovet'^*nbsp;of impoftors, and the projedts of mechanicians,nbsp;lative to this art, have not been deficient innbsp;age, and almoft in every country. Cars, artifi^-�nbsp;birds, wings, and other mechanifms for fly�^'^

^avendifh, and others, fuggefted, fome time before above-mentioned year, the pradicability ofnbsp;^^ttning machines fufficient to elevate conliderablenbsp;�^^ights into the regions of the atmofpherc, Mr.nbsp;^avendhh was the firft who afeertained the fpecificnbsp;gravity of hydrogen gas, (then called inflammablenbsp;^'r) and found it to be a vaft deal lighter thannbsp;^tinimon air. His experiments on this fubjed arenbsp;Priblilhed in the Philofophical Tranfadions for thenbsp;1766. In confequence of this difeovery, itnbsp;'''as natural to conclude, that if a large bladder, ornbsp;or envelope, were filled with hydrogen gas,nbsp;^trd that if the weight of the envelope added to thatnbsp;'^f the contained gas, did not exceed the weight ofnbsp;^ri equal bulk of common air ; the apparatus wouldnbsp;*bount up into the atmofpherc for the fame rcafon,nbsp;in the fame manner as a cork would rife fromnbsp;bottom towards the furface of the fea, fup-Pofing the cork were left at liberty in the formernbsp;Pkce.

t)r. Black of Edinburgh thought of filling the ^^^antois of a calf with hydrogen gas, for the purpofenbsp;fhewing at his ledures that fuch a body wouldnbsp;^^cend into the atmofpherc ; but he never put thenbsp;P''ojed to the tefl of adual experience,nbsp;�iarly in the year 1782,1 made the firft attemptsnbsp;elevate a bag full of hydrogen gas into the am-�^�it air, and an account of my experiments wasnbsp;at a meeting of the Royal Society on the 20thnbsp;'^Oune 1782.

The weight of hydrogen gas, the mean welgW of atmofpherical air, and the weight of the fubflanc�nbsp;of which the vefl�l or bag is to be formed, beinSnbsp;afcertained, it is eafy from thofe particulars' to determine by calculation, the dimenfions of a vefl�l�nbsp;which, when filled with hydrogen gas, might benbsp;lighter than an equal bulk of common air j for th^nbsp;furfaces of fimilar bodies are as the fquares of the'*�nbsp;fimilar fides, or of their diameters, whilft their ca*nbsp;pacities are as the cubes of thofe fides or diarnC*'nbsp;ters; fo that if the diameter of the globe Anbsp;0. feet, its contents will be equal to j cubicnbsp;nearly, and its furface will be equal to 6 fquarenbsp;nearly; but if we increafe the diameter, ofnbsp;globe, for inftance, we make it 4 feet, thennbsp;contents or capacity wilt be 8 times what it was b^'nbsp;fore, and its furface will be only 4 times whatnbsp;was before; hence, let the thicknefs or weight ^nbsp;the fubftance, which forms the bag, be whatnbsp;may, by increafing the diameter of the globe, 0^^nbsp;may always render it fo that, when filled with hy

6 nbsp;nbsp;nbsp;ali

thofe precautions, I found the largeft and lighteQ: thofe prepared bladders to be fomewhat too heavynbsp;^or the purpofe. Some fwimming bladders of fifhesnbsp;quot;'ere allb found too heavy for the experiment; nornbsp;Could I ever fucceed to make any durable light ballsnbsp;blowing hydrogen gas into a thick folution ofnbsp;gums, thick Varnilhes, and oil paint. In fliort,nbsp;^oap-balls, inflated with hydrogen gas, were the onlynbsp;'�flings of this fort which I could fucceed to elevatenbsp;�oto the ambient air j and thefe, as far as I know, arenbsp;firft fort of air balloons that were ever con-ftrufted.

After thofe trials I endeavoured to make bags or Walloons of the fineft fort of China paper, and tonbsp;*fgt;fiate them with hydrogen gas. The fize of thofenbsp;^ags was fuch, that had it been pcffible to fill themnbsp;quot;'ith the gas, they miift have undoubtedly afcendednbsp;*fito the atmofphere ; but I had the mortification tonbsp;that though common air did not, yet the hydro-Sen gas pafled through the pores of paper exactlynbsp;^�ke water through a fieve. After a variety of fimi-trials, being at lafl; tired with the expence andnbsp;^cfs of labour, I deferred the profecution of fuchnbsp;^^periments to a future opportunity, and contentednbsp;^yfelf with giving an account of my attempts tonbsp;Royal Society.

^ Not long after this, news^ was received from �'^nce of the fucccfs which had attended an expert-of a fimilar nature made at Avignon, by Stephennbsp;^cntgolfier �, but the bag was not filled with

hydrogen gas. It was filled with air rarefied by heat, which of eourfe was lighter than an equal bulknbsp;of common air, of the ufual temperature.

It is faid that the two brothers, Stephen and John Montgolfier, began to think on the experiment ofnbsp;the aeroftatic machine as early,as the middle ornbsp;latter end of the year 1782. The natural afcenfionnbsp;of fmoke, and of the clouds in the atmofphere, fug'nbsp;gefted the firft idea; and to imitate thofe bodies, ornbsp;to enclofe a cloud in a bag, fo that the latter migk*-be elevated by the buoyancy of the former, was thenbsp;firft projedl of thofe celebrated gentlemen,

Stephen Montgolfier, the eldeft of the two brO' thers, made the firft aeroftatic experiment at Avig*nbsp;non, towards the middle of Novembernbsp;The machine confifted of a bag of fine filk, in th^nbsp;fliape of a parallelopipedon, open on one fide, tb^^nbsp;capacity of which was equal to about 40 cubic fe^*^'nbsp;Burning paper, applied to its aperture, fervednbsp;rarefy the air, or to form the cloud ; and, whennbsp;ficiently expanded, the machine afeended rapidlynbsp;the ceilinsr of the room. Thus the original hif'

covpry was made, which was afterwards confirm^ � improved, and diverfified by different perfonsnbsp;different parts of the world.

As foon as the news of Mr. Montgolfier�s fucccf^ ful experiment reached Paris, the fcientific perfu'^*nbsp;of that capital, juftly concluding that a fimil^rnbsp;periment might be made by filling a bag with h/;

iwppofition. A fiibfcription for �efray�ng the ex-pencesi which might attend the accompliihmenr of the projeft, was immediately opened �, perfons ofnbsp;^11 ranks ran with eagernefs to fign their names, andnbsp;d'-e neceffary fum was fpeedily raifed. Meffrs. Roberts were appointed to conftruft the machine, andnbsp;Mr. Charles, profeflor of experimental philofophy,nbsp;t^'as appointed to fuperintend the work.

The obftacles, which oppofed the accomplifli-ttient of this firft attempt, were many; but the� tWo principal difficulties were to produce a largenbsp;Quantity of hydrogen gas, and to find a fub-^ance fufficiently light to make the bag of, andnbsp;the fame time imperrrieable to the gas. 'Atnbsp;^^0: they conftrudted a globular bag of a fort of lllknbsp;Ruff, called lutejlring; which, in order to render'nbsp;impervious to the gas, was covered with a certainnbsp;''arnifhj faid to confift of diffolved elaftic gum (ca-^'Jtchouc). The diameter, of this bag (which, fromnbsp;ball-like fnape, was called.a balloon, and gave the'nbsp;�^snne ,of dr-balloons to thofe miachines in general)nbsp;J2 feet 2 inches French, or about 13 feetnbsp;^^gliffi. It had only one aperture, like the necknbsp;a bladder, to which a ftop-cock was adapted.

The attempts to fill this bag commenced on the '�d of Auguft 1783, But the operators met withnbsp;difficulties and difappointments, from inad-^^ttences, want of materials,

See. fo much foj that the accomplifhment of the periment, viz. the adtual afeent of the balloon, didnbsp;nor take place before the 26th of the fame month-, On the morning of that da)', the inflated balloon,nbsp;having a fitiall cord faftened to its neck, was pC'nbsp;mitted to rife only to the height of about 100 feet;nbsp;but at five o�clock in the afternoon of the 27th,nbsp;balloon was difengaged from its faftenings, innbsp;Camp of Mars, and rofe majeftically in the at'nbsp;mofphere before the eyes of a great many thoufandnbsp;Ipedtators, and amidft a copious fhower of rain.nbsp;about two minutes time it rofe to the height of aboul^nbsp;3123 feet. After remaining in the atmofphere opifnbsp;I of an hour, this balloon fell in a field near Gonep^nbsp;a village about 15 miles from Paris. Its fall wasnbsp;attributed to a rupture that was found in it, andnbsp;was reafonably imagined that the expanfion ofnbsp;hydrogen gas, when the balloon had reached a mu^^nbsp;lefs denfe part of the acmofphere, had burftnbsp;When this balloon went up, it was found uponnbsp;to be 35 pounds lighter than an equal bulk ofnbsp;mon air.

Thus in the years 178-2 and 1783, it was afe^'^ tained that bags full of hydrogen gas, or of raren^nbsp;common air (either of which is lighter than cofgt;anbsp;mon air in its ufual (late), would afeend into thenbsp;mofphere, and that they might take up confideranbsp;weights. The principal experiments and impr�'^*nbsp;rnents that were made in purfuance of thofenbsp;vei'ies, will be mentioned in the next chapters;

It will be previoully neceflary to make the following remark j namely, that this difcovery, though in it-felf very remarkable, is far from amounting to thenbsp;art of flying. The only efleft that an aeroflaticnbsp;rnachine can produce, is to elevate, and to keepnbsp;fufpended, a certain weight in the atmofphere;nbsp;but with refpeft to its progreflive motion, it cannbsp;Only follow the courfe of the wind 5 nor has anynbsp;method been difcovered by means of which the balloon may be caufed to deviate from that eoitrfe innbsp;any ufeful degree.

SOON after the fuccefs of the firfl; attempt, the Montgolfiers repeated the experiment in thenbsp;open air, and with bags of different fizes ; but theifnbsp;firft grand and public exhibition in the prefence ofnbsp;a very refpeftable and numerous affembly, was madenbsp;on the 5th of June 17 83, with an aeroftatic machinenbsp;or bag that meafured 35 feet in diameter. Thenbsp;machine inflated by the rarefied air, afcended to Rnbsp;confiderable height, and then fell at the diftance ofnbsp;7668 feet from the original place of afcenfion-This experiment was defcribed and recorded withnbsp;great accuracy j and accounts of it were immO'nbsp;diately forwarded to the court of France, to thenbsp;academy of fciences, and alrnofl as far as literarynbsp;and entertaining correfpondence could reach. Th^nbsp;youngefl Montgolfier, arriving at Paris not longnbsp;after the above-mentioned public exhibition, wasnbsp;invited by the Academy of Sciences to repeat hisnbsp;Angular aeroftatic experiment; in confequence tifnbsp;which invitation, that gentleman began to conftrodf

the expence of the academy. But while this operation was going-on, and as a fuccefsful experiment v/ith an inflammable air balloon, had already beennbsp;performed on the 27th of Augufl:, the projeft ofnbsp;making balloons became general, and thofe whonbsp;wifhed to make the experiment on the fmalleft fcale,nbsp;foon calculated the neceflary particulars, and foundnbsp;that the performance of the experiment was far fromnbsp;being cither difficult or expenfive. The baron denbsp;Beaumanoir, at Paris, by the fuggeftion of a Mr.nbsp;Defchamps, was induced to try gold-beater�s fkin,nbsp;and foon m.ade a balloon by glueing feveral piecesnbsp;of chat fkin together. This balloon was no morenbsp;than 19 inches in diameter; it was of courfe eafllynbsp;filled with hydrogen gas, and on the iith of Sep-,nbsp;tember 1783, it mounted with rapidity into the at-mofphere.

In confequence of this experiment of the baron, feveral perfons endeavoured to make balloons ftillnbsp;ftnallerthan his, and fome fucceeded to make themnbsp;of not more than fix inches in diameter, whichnbsp;'Weighed between 30 and 40 grains. Thefe werenbsp;filled with the utmoft facility, and ferved wellnbsp;onough to fhew the experiment in a room ; but asnbsp;they were neceflfarily formed of fldns extremely fine,nbsp;oonfequently more porous than the ufual thick�rnbsp;fi^ins, the gas foon efcaped from them, and the di-ttiinutive balloons hardly floated longer than a mi-ttute or two.

y 3 nbsp;nbsp;nbsp;Mr. Mont-

Mr. Montgolfier, having completed his large aeroftat, agreeable to the defire of the academy�nbsp;made a private experiment with it on the eleventhnbsp;of September, which fucceeded, On the followingnbsp;day another experiment was made with the fame,nbsp;before the commiflaries of the academy, and a vaftnbsp;number of other fpedlators; but this experiment,nbsp;in confequence of a violent fhower of rain, was attended with partial fuccefs j and the aeroftat wasnbsp;thereby confiderably damaged,

Another fimilar machine was fpeedily conftrufted by the fame Mr. Montgolfier, with which the experiment was performed at Verfailles on the 19th ofnbsp;September, before the royal family of France, andnbsp;an innumerable concourfe of ijpedators. The preparation for filling the machine with rarefied air con-fifted of an ample fcaffold, raifed fome feet abovenbsp;the ground; in the middle of which there was a wellnbsp;or chimney, about 16 feet in diameter; in the lowernbsp;part of which, near the ground, the fire was made.nbsp;The aperture of the aeroftat was put round thenbsp;chimney or well, and the reft of it was laid dowtinbsp;over the well and the furrounding fcaffold.. As foonnbsp;as the fire was lighted, the machine began to fwelhnbsp;acquired a convex form, ftretched itfelf on every-fide, and inn minutes time, the chords beingnbsp;cut, the machine afeended, together with a wickernbsp;balket or cage, which was fattened to it by meansnbsp;of a rope, and in which a fneep, a epek, and ^

duck had been placed. Thefc were the firft.. animals that ever afcended with an aeroftatic machine. The apparatus rofe to the height of aboutnbsp;1440 feet, and remained in the atmofphere duringnbsp;8 minutes j then fell at the diftance of about 10200nbsp;feet from Verfailles, with the animals fafe in thenbsp;bafket.

After the fuccefs of this experiment with the animals, amp;c., and when ten months had fcarcelynbsp;clapfed fince Mr. Montgolfier made his firft experi-ttient of this fort, Mr. Pilatre de Rozier publiclynbsp;offered himfelf to be the firft adventurer in thenbsp;aewly invented machine. His offer was accepted,nbsp;^is courage remained undaunted, and on the 15thnbsp;of Oftober 1783, he actually afcended into the at-ntofphere, to the aftonifhment of a gazing multimode, The aeroftat with which he afcended, wasnbsp;of an oval ftiape, its height being about 74, andnbsp;mts horizontal diameter 48 feet. The aperture ornbsp;lower part of the machine had a wicker gallerynbsp;about 3 feet broad, with a baluftrade both withinnbsp;without, about 3 feet high. The inner diameternbsp;'^f this gallery, and of the neck of the machine whichnbsp;Paffed through it, w�as nearly 16 feet. In the middlenbsp;*^f this aperture an iron grate, or br;azier, was fup-Ported by means of chains, which came down fromnbsp;^be fides of the machine. In this conftruftion, whennbsp;'�be machine was up in the air, with a fire lighted innbsp;^be grate, it was eafy for a perfon who ftood in thenbsp;S^llery, and had fuel with him, to keep up the fire

y 4 nbsp;nbsp;nbsp;in

in the opening of the machine, by throwing tiie fuel on the grate through port-holes made in thenbsp;ficck of the machine. By which means the machine might be kept up as long as the perfOn ionbsp;its gallery thought proper, or till he had fuel tonbsp;fupply the fire with.

After this Mr. de Rozier repeated the experiment with the fame and with other fimilar machines, and his fuccefs fliewed to the world that' human beings might fafely afcend with thofe machines. In facV, the experiment was afterwardsnbsp;repeated by a variety of people of both fexes; andnbsp;it is remarkable, that in thofe aerial excurfions, ntgt;nbsp;giddinefs, nor ficknefs was experienced by thenbsp;travellers.

The firft aerial voyage, with an inflammable ah balloon, was performed fubfequent to the above-m.entioned experiment, viz. on the ifi: of Decern'nbsp;her 178J. Mr. Charles and Mr. Robert, whonbsp;conftrufted the firft balloon of this fort, as has beennbsp;mentioned in this chapter, were the firft adveri'nbsp;turers. Tiie balloon was globular, its diametetnbsp;being | feet. xV net went over the upper he-mifpbere, and was faftened to a hoop, which wentnbsp;round the middle of the balloon. From this hoopnbsp;ropes proceeded, and w'erc faftened to a boat whicitnbsp;fwLinga.few feet below the balloon. In order tonbsp;prevent the burfting of the machine by the expanfloonbsp;of the gas, in an elevated region, a valve was m^ad^nbsp;on the upper part of it, which, by pulling a firing�

Would open and let out part of the gas. There Was likewife a long filken pipe, through which thenbsp;balloon was filled.

The apparatus for filling it confifled of feveraj Wooden calks placed round aJarge tub full of water,nbsp;every one of which had a long tin tube,which terminated under a vefiel or funnel, that was inverted intonbsp;the water of the tub. A tube then proceeded from thisnbsp;funnel, and communicated with the balloon, whichnbsp;flood juft over it. Ir�n filings and diluted fulphu-ric acid were put into the cafks; and the gas whichnbsp;Was extricated from thofe materials, pafled throughnbsp;the tin tubes, then through the water of the tub,nbsp;and, laftly, through the tube of the funnel into thenbsp;balloon.

When Meflfs. Charles and Robert placed them' felves in t.he boat, they had with them proper philO'nbsp;fophical inftruments, provifions, clothing, and fomenbsp;bags full of fand, by way of baliaft. With this pre^nbsp;Paration they afeended at -J after one o'clock^, Atnbsp;'^be time they went up, the thermometer, Fahrenheit�s fcale, ftood, at 52�, the mercury in the baro-�^eter ft�od at 27 inches, from which tliey deducednbsp;their altitude to be nearly 6'o yards. During thenbsp;t^fl of their voyage, the mercury in the barometernbsp;ffioved generally between 2� inches, and 27,655nbsp;fifing and falling according as part of the baliaftnbsp;thrown our, or fome gas efcaped from thenbsp;^^floon. The thermometer flood generally between

57%

Soon

Soon after their afcent, they- remained ftationary for a (hort time; then they went horizontally, in thenbsp;direction of N. N. W. They crofled the Seine, andnbsp;paffed over feveral towns and villages, to the greatnbsp;aftonifliment of the inhabitants, who did not expectnbsp;to fee fuch a fpe�lacle, and who had perhaps nevernbsp;heard of this new fort of experiment. This deli-�nbsp;cious a�rial voyage lafied one hour and threenbsp;quarters. At laft they defcended in a field nearnbsp;Nejle, a fmall town, about 27 miles diftant fromnbsp;Paris; fo that they had gone at the rate of aboutnbsp;jmiles per hour, without feeling the lead; inconvenience ; and the balloon underwent no other alteration,nbsp;than what was occafioned by the dilatation and coiU'nbsp;tra�lion of the gas, according to the vicifTitudes ofnbsp;heat and cold. '

The fuccefs of the experiments, which have been already defcribed, fpread a univerfal enthufiafmnbsp;throughout Europe, and tlie aeroftatic experiments*nbsp;both in the diminutive, and in the large way, werenbsp;foon undertaken in different countries. The firftnbsp;experiment of this fort was fhewn in London on tn^nbsp;25th of November 1783, with an inflammable ah'nbsp;balloon of 10 feet in diameter, by Count Zam'nbsp;beccari, an Italian gentleman. The firft a�'riafnbsp;voyage undertaken in England, with an infiamma,'nbsp;ble air-balloon, of 33 feet in diameter, madenbsp;oil fiik, was performed by Mr. Lunardi, anochetnbsp;Italian, on the 15th of September 1784,

DurirS

During the above-mentioned and the three following years, the daily papers, and other periodical publications, gave frequent accounts of aerialnbsp;Voyages having been performed in various parts ofnbsp;Europe, and even in America. The fmall inflam-��table air-balloons were exhibited at public le�lures,nbsp;almoft in every private affembly. Small aerofta-bc machines of fine paper, to be elevated by rarefiednbsp;^ir, were publicly fold in great plenty, fome of themnbsp;fven for the trifling price of a Angle Ihilling; andnbsp;3s thefe formed a pretty fpeclacle in the night time,nbsp;ou account of the burning combuftjble which wasnbsp;appended to their aperture for the purpofe of rarcfy-the air, a great many of them were every nightnbsp;Een to move over London, in the diredtion of the

'vind.

The Ample conftrudlion of thofe diminutive aero-ll^tic machines for rarefied air, is as follows. Pieces that fort of fine paper, which is fold in Londonnbsp;^uder the name offan paper, or filver paper, are cutnbsp;an oblong fhape, gradually tapering at the twonbsp;^^tremities. Thofe pieces are ftuck together fuc-'^^flively, edge to edge, fo as to form a globularnbsp;P3per bag. Part of this globe is then cut off fo asnbsp;leave a circular aperture of about, 10 or 12 inchesnbsp;diameter, to the edge of which a fine iron or brafsnbsp;is adapted by way of ftrengch, and is fixed bynbsp;b^�ning and palling a little of the edge of the papernbsp;ftVer Two flraight and pretty thin iron wires

are alfo to be placed acrofs each other in the above* mentioned aperture, and their extremities arenbsp;cd to the circular wire, which goes round thenbsp;ture. This crofs of wire ferves to fupport thelbebnbsp;viz. in the middle of it a ball of fpun wool isnbsp;�lfo by means of fine iron wire, which whennbsp;experiment is to be performed, muft be foakednbsp;fpirit of wine, or in fplrit of turpentine, andnbsp;lightedj whilft'an afiiftant holds the balloon (whk^nbsp;need not be larger than a yard in diameter) bynbsp;top. The combuflion Immediately fwells the ballo��nbsp;with rarefied- air, and when this has takennbsp;the affiftant relinquifiies his hold, and the ballo^'^nbsp;mounts, amp;c.

The aeroftatic experimjents, originally iind^'quot;' taken for mere curiofity, foon became the obj^'^nbsp;of gain, and aimoft all the aerial voyages were r'f�nbsp;dertaken for the lake of profit. Perfons enti*quot;^^^nbsp;unacquainted wdth any branch of natural phd'-^quot;nbsp;fophy, offered to make aerial voyages, and tonbsp;form experiments in the atmofphere, for whi�'^nbsp;they were not in the leail qualified, and with gt;'''nbsp;ftruments, of which thc7 did not underftandnbsp;life.

In confequence ofthis pradlice, the aerial voy^g^�� though nvmnerous, have not however been prodult;^*nbsp;tive of much information. Yet the variety ofnbsp;tions, of machines, and of accidental, circumfta*�^^^�nbsp;added to the cbfervacions of able perfons, have

^^oubtedly fliewn a variety of fa6ls which defervg �he attention of the philofophcr. Therefore omittingnbsp;particular account of al! the ufelefs voyages, Inbsp;lhall only mention thofe which have been attendednbsp;^''ith any particular and remarkable occurrencenbsp;^hat tnay appear capable of ettabiifhing fome ufe-^1 faft, or to remove fome preconceived ob-*

_ The Abb� Bertholon feems to have been the firft perfon who made ufe of fmall balloons for exploringnbsp;^he eleftricity of the atmofphere, which muft be anbsp;''ery ufeful m.ethod, particularly in calm weather,nbsp;'*^1160 eled�trical kites cannot be raifed. He raifednbsp;feveral air-balloons, to which long and flender wiresnbsp;'*\'ere attached ; the lower extremity of the v/ire be*nbsp;*tig faftened to a glafs ftick or other infuiated dand,nbsp;''hereby he obtained from fuch wires eleclricitynbsp;Enough to fhew its kind, and even fparks.

On the 13th of January 1784) an aeroftatic ma-�^hlne, of about 37 feet in height, and so in diameter, was launched from the caftle de Pifan^qn^ near Pomans, in Dauphin�. It rofe v/ith furprifing velocity, and as the wind was north, it went fouth-'quot;'ard; but when the machine had afeended to thenbsp;height of about 1300 feet, it went back towards thenbsp;t^orth, and iniefs than five minutes time itafcend�dnbsp;to the height of above 6000 feet. In lefs than teanbsp;ttiinutes it fell at the diftance of nearly four-miles.

This experim.entj and indeed the fimilar fuccefs many others, fhews that tiiere frequently are in

the atm�fphere currents of air in different, and ibmetinnes quite oppofite, diredions ; this, however^nbsp;is far from being always the cafe. If different currents could always be met with at different height*nbsp;above the furface of the earth, the method of guide-ing balloons would be extremely eafy ; for thenbsp;aerial traveller would have nothing more to do thannbsp;to place himfelf in the favourable current, which henbsp;may do by throwing out either fome ballad: or forn.snbsp;inflammable gas, according as he wilhes to go highernbsp;or lower.

The largefl: aeroftatic machine ever made, and filled with rarefied air, was launched at Lyons on th^nbsp;19th of January 1784, with not lefs than fevennbsp;perfons in its gallery, amongfl: whom were Jofepl^nbsp;Montgolfier, and Pilatre de Rozier. The heightnbsp;of this machine was about 131 feet, and its horizon'nbsp;tal diameter about 104. Its weight, when it afeend'nbsp;ed, including paffengers, gallery, amp;c. was abon^nbsp;16co pounds.

teeded eaft-fouth-eaft, afcending, at the fame time� Until it was at leaft 1000 yards high.

The effect which was produced on the fpedtators by this fpedtacle, is deferibed as the moft extraordinarynbsp;that was ever occafioned by any produdtion of human invention. It was a mixture of the ftrangeffnbsp;nature imaginable. Vociferations of joy, fhrieks ofnbsp;fear, expreffions of applaufe, the found of martialnbsp;inftruments, and the difeharge of mortats, producednbsp;an effedl more eafily imagined than deferibed. Somenbsp;of the fpectators fell on their knees, and others elevated their fuppliant hands to the heavens; femenbsp;Women fainted, and many wept; but the confidentnbsp;travellers, without (hewing the leaft appearance ofnbsp;fear, were continually waving their hats out of thenbsp;gallery.

At about 15 minutes after the afeent, the wind ffifted again; but it was fo feeble that the machinenbsp;ftood almoft ftaticnary for about four minutes.nbsp;Idnfortunately about this time a rent was made innbsp;the machine, which occafioned its defeent; and whennbsp;came within 600 feet of the ground, its velocitynbsp;quot;'as confiderably accelerated, it is faid that no lefsnbsp;than 60000 perfons, befides the Marechauff�e, rannbsp;to the fpot, with the greateft apprehenfion for thenbsp;hves of the adventurous aerial travellers. Theynbsp;quot;^ere immediately helped out of the gallery, andnbsp;Stickily no perfon had received any hurt, except Mr.nbsp;Montgolfier an infignificant fcratch. The machinenbsp;torn in feveral places, befides a vertical rent of

upwards of 50 feet in length j which clearly fliew5 how little danger, is to be apprehended from the uftnbsp;of thofe machines, cfpecially when they are properlynbsp;conftrufted and judicioufly managed.

On the 5th of April 1784, Meffrs. de Morveaii, and Bertrand,' at Dijon, afeended with an inflammable air-balloon, Which, according to their barometrical obfervations, feems to have reached thenbsp;extraordinary height of 13000 feet^ when the coldnbsp;was fo great, that the thermometer flood at 25�.

On the 15th of July, the duke de Chartres, the two brothers Roberts, and another perfon^ afeendednbsp;with an inflammable air-balloon, from the park ofnbsp;St. Cloud, at 52 minutes paft feven in the morning-This balloon was of an oblong fornn, its-dimenfionsnbsp;being 55 feet by 34. It afeended with its greateflnbsp;extenfion nearly horizontal; and after remainino- innbsp;the atmofphere about 45 minutes, it defeended at ^nbsp;fmall diflcance f'-oin its place of afeenfion. Rut the 'nbsp;incidents that occurred during thiaa�rial excurflonjnbsp;defeiwe particular notice, as nothing like it had hap'nbsp;pened before to any of the aerial travellers. Thl^nbsp;machine contained an interior fmall balloon, filk�'^nbsp;v/ith common air; by whidi tn'eans it was fuppof^'*^nbsp;that they might regulate the afeent and thenbsp;of the machine, without any lofs of the hydrogtf'nbsp;gas, or of baliaft. The boat was furnifiied with ^nbsp;helm and oars, that were intended to guide,the tn?-'nbsp;chiru?, but which were m this, as well as in every oth�^'^nbsp;fimilar, attempt found to be quite ufelefs.

On the level of the fea, the mercury m the baro-tneter flood at 30,25 inches, and at the place of afcenfion it flood at 30,12. Three minutes afternbsp;its afcenfion, the balloon was loft in the clouds, andnbsp;the aerial voyagers loft fight of the earthy being involved in a denfe vapour. Here an unufual agitation of the air, fomewhat like a whirlwind, in a mo-tnent turned the machine three times from the rightnbsp;to the left. The violent fhocks which the adventurers fufFered, prevented their ufing any of thenbsp;means prepared for the diredlion of the machine;nbsp;and they even tore away the filk fluff of which thenbsp;helm was made. Never, faid they, a more dreadful feene prefented itfelf to any eye, than that innbsp;�which they were involved. An unbounded oceannbsp;of ftiapelefs clouds rolled beneath, and feemed tonbsp;forbid their return to the earth, which was ftill in-vifible. The agitation of the balloon became greaternbsp;^ery moment. They cut the cords which heldnbsp;the interior balloon, which confequently fell on thenbsp;bottom of the external balloon, juft upon the aperture of the tube that went down to the boat, andnbsp;flopped up that communication. At this time thenbsp;thermometer was a little above 44�. A guft ofnbsp;^'�ind from below drove the balloon upwards, to thenbsp;Extremity of the vapour, where the appearance ofnbsp;fun fhewed them the exiftence of nature ; butnbsp;tiQw both the heat of the fun, and the diminifliednbsp;^-nfity of the atmofphere, occafioned fuch a dilatation of the gas, that the burfting of the balloon

was apprehended ; to avoid which, they introduced a flick through the tube, and endeavoured to remove the inner balloon, which flopped its aperturenbsp;within the external balloon ; but the dilatation ofnbsp;the gas prefled the inner balloon fo forcibly againftnbsp;that aperture, as to render every attempt ineffedlual.nbsp;During this time, they continually afcended, untilnbsp;the mercury in the barometer flood not higher thannbsp;24,36 inches, which (hewed their height above thenbsp;furface of the earth to be about 5100 feet. In thefcnbsp;dreadful circumftances they thought it necelTary tonbsp;make a hole in the balloon, in order to give exit tonbsp;the gas; and accordingly the duke himfelf, with onenbsp;of the fpears of the banners, made two holes in thenbsp;balloon, which opened a rent of about feven or eightnbsp;feet. In confequence of this, they then defeendednbsp;rapidly, feeing at firfl no objedl either on earth or ii^nbsp;the heavens �, but a moment after, they dilcoverednbsp;the fields, and that they were defeending flraight intonbsp;a lake, wherein they would inevitably have fallen�nbsp;had they not quickly thrown over about 60 poundsnbsp;weight of ballafl, which occafloned their corningnbsp;down at about 30 feet beyond the edge of the lake*nbsp;Notwithftanding this rapid defeent, none of the fo^*'nbsp;adventurers received any hurt; and it is remarkable�nbsp;that out of fix glafs bottles full of liquor, whichnbsp;Amply laid down in the boat, one only was foon^nbsp;broken.

In .the courfe of the fummer 1784, two perfons� viz, one in Spain, and another near Philadelphia^

America, were very nearly lofing iheir lives by going Up with rarefied-air machines. The form�r, on thenbsp;fth of June, was fcorched by the machine takingnbsp;fire, and was hurt by the fubfequent fall, fo that hisnbsp;life was long defpaired of. The latter, havingnbsp;afcended a few feet, was wafted by the wind againftnbsp;the wall of a houfe, and fome part of the machinerynbsp;Was entarrgled utjder the eaves, from which he couldnbsp;not extricate it. At laft the great afcenfionalnbsp;power of the machine broke the ropes or chains,nbsp;and the man fell from the height of about 20 feet.nbsp;The machine prefently took fire, and was confumed. �nbsp;I lhall now relate one of the moft remarkablenbsp;Serial voyages that were ever made with an aeroftaticnbsp;tnachine. It is the crofling of the Englilh channelnbsp;in an inflammable air-balloon of 27 feet in diameter.nbsp;The enterprifer of this dangerous voyage was Mr.nbsp;Blanchard, an intrepid Frenchman, who had alreadynbsp;nrade five other aerial voyages with the very famenbsp;Walloon, both in France and in England. Mr.nbsp;Blanchard is remarkable for having made a greaternbsp;�^umber of aerial voyages in England, in France,nbsp;3nd elfewhere, both before and after the crofTing ofnbsp;fhe Engllfh channel, than any other enterprifernbsp;��ecorded in the hiftory of aerofiation. The onlynbsp;^ial worth remarking which Mr. Blanchard appears to have made in his aerial excurfions, isnbsp;file ineffedlual ufe of oars, wings, amp;c. for di-

On Friday the 7th of January 1785, being a fine clear morning, after a fliarp frofty night, and thenbsp;wind being about N. N. W. though hardly perceptible, Mr. Blanchard, accompanied by Dr. Jeffries,nbsp;an American gentleman, departed in the old balloonnbsp;of 27 feet diameter, from Dover Caftle, diredlingnbsp;their courfe for the French coaft. Previous to thenbsp;departure, the balloon, with the boat, containingnbsp;the two travellers, feveral neceffaries, and fome bagsnbsp;of fand for ballaff, were placed within two feet ofnbsp;the brink of the perpendicular cliff before the caftle.nbsp;At one o�clock the intrepid Blanchard defired thonbsp;boat, amp;c. to be pufhed off; but the weight beingnbsp;too great for the power of the balloon, they w'erenbsp;obliged to throw out a confiderable quantity ofnbsp;ballad, in conf�quence of which they at lad rofenbsp;gently and majedically, though making very littlenbsp;v/ay, with only three bags of ballad of ten poundsnbsp;weight each. At a quarter after one o�clock,nbsp;barometer, which on the cliff dood at 29,7,nbsp;fallen to 27,3 j and the, weather proved finenbsp;warm. Dr; Jeffries deferibes with rapture thonbsp;profpedl which at this time was before theirnbsp;The country to the back of Dover, interfpe^f^*^nbsp;with towns and villages, of which they could couo^nbsp;37, made a beautiful appearance. On the othernbsp;fidp the breakers, on the Goodwin Sands,

formidable. Upon the whole, they enjoyed a view perhaps more extended and diverfified than wasnbsp;ever beheld by mortal eye. The balloon was muchnbsp;diftended, and at 50 minutes paft one o�clock itnbsp;Was defcending, in confequence of which they werenbsp;obliged to throw out one bag and a half of fand-They were at this time about one third of the waynbsp;from Dover, and had loft diftindl fight of the caftle.nbsp;Not long after, finding that the balloon was defcending very faft, all the remaining ballaft was thrownnbsp;over, as alfo a parcel of books, in confequence ofnbsp;which the balloon rofe again. They were now atnbsp;about half way. At a quarter paft two o�clock thenbsp;fifing of the mercury in the barometer (hewed thatnbsp;they were defcending; in confequencee of whichnbsp;the remaining books were thrown into the fea. Atnbsp;25 minutes after two, they w'erc at about three-fourths of the way, and an enchanting view of thenbsp;French coaft appeared before their eyes; but thenbsp;lower part of the balloon was collapfcd, owing to thenbsp;lofs or condenfation of the gas, and the machine wasnbsp;defcending, which obliged them to throw overnbsp;ptovifions for eating, the oars or wings of the boar,nbsp;^fid other articles. � We threw away,� faid Dr.nbsp;y^ffries, � our only bottle, which, in its defcent,nbsp;caft out a fteam like fmoke, with a rulhing noife;

' and when it ftruck the water, we heard and felt the (hock very perceptibly on our car and balloon.� But the balloon ft ill approaching the fea,

they began to ftrip and caft away th�ir clothes. They even intended to fallen themfelves to thenbsp;eords and cut the boat away, as their laft refource;nbsp;but at this critical point, they had the fatisfadlion tonbsp;obferve that they were rifing j their dillance fromnbsp;the French Ihore, which they were approachingnbsp;very fall, was about four miles. Fear was now va-nilhing apace j the French land Ihewed itfelf everynbsp;moment more beautiful, more diftindl, and morenbsp;extended; Calais, and above 20 other towns andnbsp;villages, were clearly dillinguilhed. Exaftly at threenbsp;o�clock, they paffed over the high grounds aboiii^nbsp;midway between Cape Blanc and Calais and it i*nbsp;remarkable that the balloon at this time rofe verynbsp;fall, and made a magnificent arch; probably owingnbsp;quot;to the heat of the land, which rarefied in fome mea'nbsp;fure the hydrogen gas. At lall they defcended asnbsp;low as the tops of the trees in the forell of GuinneS)nbsp;and opening the valve for the efcape of the gas, thefnbsp;foon after defcended fafe to the ground, after havingnbsp;accomplilhed an enterprife which will probablynbsp;recorded to the remotell pollerity.

The following is the melancholy account of a'�^ experiment which was attended with the death nnbsp;two aerial adventurers, one of whom was Mr-Rozier, the firll p�rfon that ever afeended with annbsp;aerollatic machine.

*hc air, formed a plan of combining the two fpecies of aeroftatic machines, from which he expefted tonbsp;J�ender their joined buoyancy more lading, and ofnbsp;oourfe more ufeful. His plan was to place an inflammable air-balloon at top, and to affix to it, bynbsp;Orleans of ropes, a rarefied aar-balloon, fo that a fpacenbsp;of fcveral feet might intervene between flie two.nbsp;The paflenger or pafiengers were intended to takenbsp;their places in the gallery of the lower machine,nbsp;whence they could regulate the fire, and might, bynbsp;a proper management of the fuel, eleva.te or deprcfsnbsp;the whole, w'ithout the neceffity of lofing any inflammable gas from the upper balloon.

Accordingly this plan was put in execution. The tipper or the inflammable air-balloon was of varnifh-ed filk, lined with a fine membrane, like goldbeaters� fkin. The other aeroftat was of ftrongnbsp;linen. On the 15th of June 1785, at feven o�clocknbsp;tn the morning, every thing being ready, Mr.nbsp;�*ilatre de Rozier and a Mr. Romain, placed them-felves in the gallery of the aeroftat, wnth plenty ofnbsp;ftiel, inftruments, and other neceflary articles; andnbsp;tofe in the atmofphere. The machine feemed tonbsp;take the beft poffihJe direiftion, but the wind beingnbsp;both feeble and fhifting, they changed their direftionnbsp;^tvo or three times ; but when they were at a confi-flerable height, and not above i of a mile from thenbsp;place of afcenfion, the machine appeared to be innbsp;flames, and prefently the whole was precipitated

down to the ground. The unfortunate adventurers v/ere inftantly killed, their bones disjointed and dreadfully mangled by the tremendous fall.

How the inflammable air took fire, is varioufly conjedtured; but it is natural to fuppofe, that thenbsp;fparks of fire mull; have flown from the lower to thenbsp;upper or inflammable air-balloon. On the ground,nbsp;the bag of the upper balloon was in great mea-fure burned or fcorched j that of the lower wasnbsp;entire.

Omitting the various uninterefting, though not numerous, aerial voyages undertaken in various partsnbsp;of the world, during the 17 years fubfequent to thenbsp;above-mentioned dreadful accident of Pilatre denbsp;Rozier and Mr. Romain, I lhall only add the account of two aeroftatic experiments lately performer^nbsp;in England by Mr. Garnerin, a French -aeronaut-The firft of thofe is remarkable for the very greatnbsp;velocity of its motion; the fecond for the exhibitionnbsp;of a mode of leaving the balloon, and of defeendinflnbsp;with fafety to the ground.

On the 30th of June 1802, the wind being ftroijg� though not impetuous, Mr. Garnerin and anothefnbsp;gentleman alcended with an inflammable air-ballootinbsp;from Ranelagh-gardens on the fouth-weft of ho^'nbsp;don, between four and five o�clock in the afternoon�nbsp;and exaftly in three quarters of an hour they dCquot;nbsp;feended near the fea, at the diftance of four mik�nbsp;from Colchefter. The diilance of that place frngt;^

Ranelagh is fixty miles; therefore they travelled at the aftonifhing rate of 80 miles per hour. It feemsnbsp;that the balloon had power enough to keep them upnbsp;four or five hours longer, in which time they mightnbsp;have gone fafe to the continent; but prudence induced them to defcend when they faw the fea notnbsp;far off.

The Angular experiment of afcending into the at-t�iofphere with an inflammable air-balioon, and of defcending with a machine called a parachute (thenbsp;breaker of a fall, or of a Jhock) was performed by Mr.nbsp;Garnerin on the sift of September 1802. He af-cended from St. George�s Parade, North Audleynbsp;Street, and defcended fafe into a field near the Small-Pox Holpital at Pancras.

The balloon was of the ufual fort, namely, of oiled filk, with a net, from which ropes proceeded,nbsp;^hich terminated in, or were joined to, a Anglenbsp;^�ope at a few feet below the balloon. To thisnbsp;^ope the parachute was faftened in the followingnbsp;�Planner.

The reader may eafily form to himfelf an idea of *His parachute, by imagining to fee a large umbrellanbsp;�f canvas of about 30 feet in diameter, but deftitutenbsp;^f the ribs and handle. Several ropes of about 30nbsp;^^et in length, which proceeded from the edge ofnbsp;parachute, terminated in a common joining,nbsp;from which fhorter ropes proceeded, to the extre-�^�'ties of which a circular balket was faftened, and

in this baOcet Mr. Garnerin placed himfelf. Now the fingle rope, which has been faid above to proceed from the balloon, paffed through a hole in thenbsp;centre of the parachute, alfo through certain tinnbsp;tubes, which were placed one after the other in thenbsp;place of the handle or flick of an umbrella, and wasnbsp;laflly faftened to the bafket; fo that when the balloonnbsp;was in the air, by cutting the end of this rope nextnbsp;to the bafket, the parachute, with the baflcet, wouldnbsp;be feparated from the balloon, and, in falling downwards, would be naturally opened by the refiflancenbsp;of the air. The ufe of the tin tubes was to letnbsp;the rope flip off with greater certainty, and tonbsp;prevent Its being entangled with any of the othernbsp;ropes, as alfo to keep the parachute at a diftancenbsp;from the balket.

The balloon began to be filled at about two o�clock. There were 36 caflis filled with ironnbsp;turnings, and diluted fulphuric acid, for theprodnc-tion of the hydrogen gas. Thefe communicatednbsp;with three other caflts or general receivers, to eachnbsp;of which was fixed a tube that emptied itfelf int�nbsp;the main tube attached to the balloon.

At fix, the balloon being quite full of gas, and the parachute, amp;c. being attached to it, Mr.nbsp;nerin placed himfelf in the bafket, and alcendcdnbsp;majeftically amidfl the acclamations of innumeraonbsp;fpedlators. The weather was the clearefl andnbsp;fanteft imaginable ; the wind was gentle and abot^

�^eft by fouth j in confequence of which Mr. Gar-nerin went in the direftion of about eafh by north. In about eight minutes time, the balloon and parachute had afcended to an immenfe height, and Mr.nbsp;Garnerin, in the bafket, could fcarcely be perceived.nbsp;While every fpecfator was contemplating the grandnbsp;fight before them, Mr. Garnerin cut the rope, andnbsp;in an inftant he was feparated from the balloon,nbsp;trufting his fafety to the parachute.

At firfb, viz. before the parachute opened, he fell with great velocity gt; but as foon as the parachute was expanded, which took place a fewnbsp;iTioments after, the defcent became very gentle andnbsp;gradual. In this defcent a remarkable circumftancenbsp;Was obferved ; namely, that the parachute with thenbsp;appendage of cords and bafket, foon began to vibrate like the pendulum of a clock, and the vibrations were fo great, that more than once the parachute, and the bafket with Mr. Garnerin, Teamednbsp;to be on the fame level, or quite horizontal, whichnbsp;Appeared extremely dangerous: however, the extent of the vibrations diminiflied as he came prettynbsp;t^ear to the ground. On coming to the earth,nbsp;Mr. Garnerin experienced Tome pretty ftrongnbsp;ibocks, and when he came out of the baflcet, henbsp;quot;'as much difcompofed ; but he foon recoverednbsp;bis fpiiits, and remained without any materialnbsp;hurt.

As foon as the parachute, amp;c, was feparated from the balloon, the latter afcended with great rapidity,

If it be alked, what ufe can be made of the p^' rachute, we can only anfvt'er, that it may be ufednbsp;as a precaution j viz. it may be attached to a balloon j and, in cafe the balloon Ihould take fire ornbsp;burft, the aeronaut might defcend by the affiftancenbsp;of the parachute.

For farther particulars relative to the difcovery of aeroftatic machines, and of the various aerialnbsp;voyages made foon after that difcovery, as alfo fo^quot;nbsp;the praftical part of the fubjecl, fee my Hiftorynbsp;and Pradice of Aeroftation.

CHAP. in.

Twenty years are now fully elapfed fincc the aeroftatic machines were firft invented.nbsp;The experiments in this new branch of natural phi-lofophy have been frequently repeated, and oftennbsp;diverfified. Few accidents have happened ; but anbsp;vaft nunqber of aerial voyages have perfe�lly fuc-^eeded j and if it be confidercd that moft of the ad-''^enturers have been perfons little, if at all, fldllednbsp;�ft philofophy or mechanics, we may with morenbsp;propriety wonder that a greater number of difa-greeable accidents has not happened.' The fimila-�fty with which a vaft number of fuch experimentsnbsp;been 'performed, might enable the hiftorian tonbsp;f^efcribe a great many aerial voyages with the verynbsp;^^rne words, faving the change of date, and of a fewnbsp;�fh(.T unlnterefting particulars ; we have, therefore,nbsp;^^lecled for the preceding chapter, fuch experi-as were attended with more remarkablenbsp;��f^fults, whence the reader may derive a Corn-Patent idea of the whole fubjeft; and, in order

to affift as much as poflible the formation of an idea fufRciently comprehenfive of aeroftation in general?nbsp;we fhall fubjoin a ftatement of the moft remarkablenbsp;particulars that have been deduced from the refultsnbsp;of experiments.

Two forts of aeroftatic machines have been dif-covered, viz. one to be filled with rarefied common air; the other to be filled with hydrogen gas (in-flammable air). The efFedl of thofe machines is tonbsp;lift up a certain weight into the atmofphere, whereinnbsp;they rile to a greater or lefs height, according as tije/nbsp;are more or lefs light than an equal bulk of commonnbsp;air. The firft fort may be filled either by applyingnbsp;a fire clofe to its aperture, only before it goes upgt;nbsp;hich introduces a quantity of heated and rarefie�^

air into the machine ; or by adapting a fire-place to the neck of the machine, wherein the fire maynbsp;continued. In the firft cafe; the aeroftat remain*nbsp;only a fhort time in the atmofphere, viz. until thonbsp;enclofed air cools, and becomes nearly of the fr,m^nbsp;temperature as the circumambient air. In the fecononbsp;cafe the machines remain in the air as long as th^nbsp;fire is continued in the fire-place. The inflamrna'nbsp;ble airvballoons remain in the air as long as anbsp;cient quantity of gas remains within them, whichnbsp;amounts in general to feveral hours, according to thenbsp;quality of the ftiifF which forms the envelope.

machines, is by no means fo light as an equal bu of hydrogen gas; hence, in order to fupport a gi

Weight, an aeroftatic machine, with rarefied air, l�iufl; be larger than one with the gas. In order tonbsp;fupport a fingle man of a mean fize, a machine ofnbsp;the firft fort ought to be about 30 feet in diameter jnbsp;of the latter fort it will juft do if the diameter be 20nbsp;feet.

In the atmofphere, the machine is at reft with re-fpeft to the furrounding air; hence it moves with that air; and hence the aeronauts feel no wind, nornbsp;^ny difturbance whatever, excepting in the above-baentioned cafe of the duke of Chartres; fo muchnbsp;fo, that they hear their leaft whifpers with greatnbsp;diftinftion, and it is remarkable that they feel nonbsp;ficknefs or giddinefs.

Several attempts have been made to direft the aeroftatic machines out of the direftion of the wind;nbsp;hut the contrivances have not met with any ufefulnbsp;The oars or wings, or fuch other mecha-^iftns, intended to let the balloon move in a direction either contrary or oblique to that of the wind,nbsp;have a very trifling effeft; for inftance, in a per-ftlt;ft calm, by the managem.ent of the above-men-boned wings, the miachine might perhaps be movednbsp;the rate of about half a mile per hour; then ifnbsp;'�he balloon, with a moderate breeze, move in anbsp;'�Attain direftion at the rate of about 30 miles pernbsp;hour, it is evident that the adlion of the wings, whennbsp;iiianaged by one or two ftrong men, can hardlynbsp;'�^bfe the defleflion of the balloon from the di-'^tiion of tire wind in any fenfible or ufeful degree.

What is the ufe, and what is the advantage, whicfi the human fpecies has derived, or is likely toderive^nbsp;from the ufe of fuch machines, is an importantnbsp;queftion, to which as much attention fliould be pai^^,nbsp;as the ftate of the fubje�l will admit of. Duringnbsp;the firft five or fix years after the difcovery, aero-ftatic machines excited an unparailelled enthufiafn^nbsp;throughout the civilized part of the world j perfon�nbsp;of every rank eagerly fought to learn, to fe^�nbsp;and to promote, the new difcovery. Liberal fub'nbsp;fcriptions have afllfted the enterprifers in almol^nbsp;every part of Europe and elfewhere; and perhapsnbsp;an indifferent eye was never turned away from th^nbsp;exhibition of aeroftatic experiments; yet indepcf�'nbsp;dent of the pleafure which arifes from a view or fro^nbsp;the performance of fuch experiments, the hum^f*nbsp;fpecies has not derived any real advantage fromnbsp;fubject of aeroftation. The expence, the time, an*^nbsp;the trouble, w'hich attend the conftrudlion, and th^nbsp;ufe of aeroftatic machines, will perhaps ever prevef*^nbsp;their being ufed as vehicles for travellers, efpeciai^l^nbsp;confidering that they can only move in the dit^'^nbsp;tion of the wind, which is frequently unfavourabquot;^�nbsp;and always uncertain. Neverthelefs in certain calquot;^�nbsp;the ufe of balloons might be not only advantage�'^quot;�nbsp;but the only one prafticable. During the latenbsp;on the continent, it is Paid that the Frenchnbsp;great ufe of balloons for reconnoitring the pofi^*�^nbsp;of the adjacent country, or of the armies of ^nbsp;enemies. For this purpofe, an inflamma.ble

tgt;aibon, juft fufficient to hold a fingle perfon, was fadened by a {lender cord, and was permitted to rifenbsp;not higher than three or four hundred -feet, fromnbsp;vvhich elevation the obferver could eafily form a plannbsp;of the country, or army, amp;c.

With refpeft to philpfophical experiments in the atmofphere, little has been done by means of balloons ; nor can much be expedted to be done, unlefsnbsp;perfons of real knowledge and ability be employe'dnbsp;and alTifted in the enterprife.

It has been generally obferved by aeronauts, that during the abfence of the fun, the cold in the uppernbsp;fegions is confiderable; but the diredi rays of thenbsp;fnn produce much heat, which is rendered morenbsp;likely by confidering that the air about the aeronautnbsp;and balloon, is refpedlively at reft,' and cannotnbsp;dilTipate the heat, as the wind does with refpedt tonbsp;^ perfon who ftands on a mountain. The cold ofnbsp;dte atmofphere increafes, ceteris 'paribus, with thenbsp;'ncreafe of diftance from the earth j but the greateftnbsp;^^ight, to which aeronauts have afeended, thoughnbsp;precifely known, feems to be about 16000nbsp;wet. They feldom fpeak of having felt any uneali-^�efs vv^ith refpedt to relpiration, or other animalnbsp;^'Jndtion*

I v/as told of a magnetic experiment faid to have ^^en made by three gentlemen, who afeended withnbsp;inflammable air-balloon from the vicinity ofnbsp;London, on the 3d of June 1785. They obfervednbsp;^hat a magnet, when in the atmofphere, would notnbsp;'quot;0-. IV.nbsp;nbsp;nbsp;nbsp;A Anbsp;nbsp;nbsp;nbsp;hold

hold nearly as much weight as it did when it flood as ufual on the furface of the earth.

Relative to the conftruclion of aeroftatic iria' chines, the following particulars may be of ufe tonbsp;thofe who are defirous of performing fuch experiments.

machines, may be found almoft every, where ano a moderate rate, their ufe may juftly be reco*�*^nbsp;mended for experiments, efpecially where the rn^nbsp;terials neceflary for the other fort of balloons cannbsp;be procured.

, The inflammable air-balloons are confiderably rtiore expenfive. Nothing has been found morenbsp;advantageous for their envelopej than oiled, or rather varnifhed filk; which is by no means a cheapnbsp;article, efpecially in England. Refpefting the pro-duftion of the gaSi the only method pra�licable fornbsp;this purpofe, is to ufe the iron turnings, which maynbsp;be had at various iron manufadlories, and dilutednbsp;fulphuric acid. I do not proceed to ftate in thisnbsp;place the utniofl quantity of hydrogen gas that anbsp;chemift can extrafl; in his laboratory, from a givennbsp;Quantity of iron and acid; fince that precifion of,nbsp;operation cannot be expedled w�ith large procefTes,nbsp;Eich as are neceflary to fill a balloon in the open air,nbsp;and with a coarfe apparatus; but I lliall ftate one ofnbsp;the mofl economical operations for filling a balloon,nbsp;quot;'hich came to my notice when Mr. Blanchard madenbsp;aerial excurfion with a balloon of only 20 Frenchnbsp;beet (about 21 Englifh) in diameter, from whiclinbsp;the reader may judge of fimilar operations. Thatnbsp;balloon was completely filled by the ufe of looonbsp;pounds w'eight of iron turnings, and 1250 poundsnbsp;''�^ight of fulphuric acid. The iron, however, wasnbsp;^oo much, and 900 pounds weight of it might havenbsp;Sufficed. The capacity of that balloon was 4849nbsp;^tibic feet, Englifh meafure. The apparatus for thenbsp;operation of filling it canfifled of only four caflks,nbsp;^^ch having a tube which communicated with anbsp;'Common receiver inverted in water, whence the gasnbsp;conveyed into the balloon, which was fufpendednbsp;A A 2nbsp;nbsp;nbsp;nbsp;over

over it. The capacity of each cafk was 120 gallons. The operation lafted between 10 and 11 hours.

Notwithftanding the much greater expence an(J trouble which attend the conftrudion and the fillingnbsp;of this fort of balloons, it mull be acknowledgednbsp;that they are by far the molt ufeful and moft pleafantnbsp;aerial vehicles. Once full, they require very littlenbsp;attendance; and, by a proper management of thenbsp;ballaft, the aeronauts may keep them up for a con-fiderable time. A balloon of this fort, not abovenbsp;36 feet in diameter, if properly conftrufted, proper'nbsp;ly filled, and dexteroufly managed, might keep nPnbsp;in the atmofphere two perfons of moderate weightnbsp;perhaps longer than 30 hours�time fufficient, withnbsp;a pretty good wind, to crofs the whole continent 0nbsp;Europe.

[ 357 ]

SECTION IL

General and frequent obfervation fliewsf that fogs, mifts, dews, rain, fnow, and hail,nbsp;fall more or lefs copioufly from the atmofpherenbsp;Opon the furfacc of the earth j and that all thofenbsp;bodies confxft of the fame fubftance, namely, water,nbsp;either in the ftate of fteam, or of fluid water, or,nbsp;laftly, under a congealed form.

Though we cannot rightly underftand the mecha-tiical operation by which water is converted into va.^ Pour, and vice verja, yet it is in general known,nbsp;that water reduced into vapour, afcends in the at-ttiofphere, and forms the clouds; alfo that after-quot;'ards the clouds are refolved into water, which,nbsp;according to its quantity, and according to the various temperatures or other dates of the atmofphere,nbsp;'^^fcends, under various forms, on the furface of thenbsp;^arth.

The eledlricity, which experiments fliew (as has mentioned in the, preceding volume) to benbsp;Produced at the time of the converfion of water intonbsp;A A 3nbsp;nbsp;nbsp;nbsp;vapour,

vapour, and likewife at the converfion of vapour into water, feems fufficient to account for t,he thuti'?nbsp;der and 1'gktning, which pretty often accompany thenbsp;clouds. But independent of thofe effc�ts, therenbsp;have been obferved in the atmofphere two othernbsp;forts of phenomena, which the prefent ftate of phi'nbsp;lofophical kn�wledge is not fufficient to explain;nbsp;nor can even offer an hypothefis fufficiently plaufiblenbsp;for their explanation. I mean, firft, thofe luminousnbsp;apparitions generally known under the name ofnbsp;meteors 5 and, adly, the ftony fubftances which atnbsp;various times are faid to have fallen on the furfac?nbsp;of the earth.

The concurrence of feveral obfervations feems to ffiew, that there is a confiderable connedion between thofe phenomena, and it is on this accounfnbsp;that a compendious examination of both has bee^nbsp;placed in this fame fedion.

TH E fudden apparition and fliort duration of luminous bodies in the Hcy, of different fize,nbsp;and generally of quick motion, feems to have beennbsp;obferved from time immemorial for we find accounts of fuch apparitions in a variety of ancientnbsp;authors, who, according to the different fliapes ofnbsp;thofe phenomena, gave them the names of faces, ornbsp;or flammee, amp;c. and in latter times they arenbsp;denoted by the different names of Jheoting-ftars, hallsnbsp;fire, or meteors.

Not much information can be derived relative to diof� phenomena from ancient accounts, which arenbsp;tnoftly too fhort and incorrect; or they are involvednbsp;myftery, and diftorted by exaggerated expref-hons; but the obfervations of latter times, efpe*'nbsp;^�ally thofe which come within our remembrance,nbsp;afford much more fatisfaftory information. Thenbsp;magnificent meteor of latter times, was feennbsp;the 18th of Auguft 1783 j and as I had the goodnbsp;fortune to obferve it from a moft eligible fituation.

viz. from the terrace of Windfor caftle j I fhall tran-fcribe the account which I fent to the Royal Society} from which the reader may form a competent ideanbsp;of meteors in generah I jfhall then fubjoin the ob-�nbsp;fcrvations made on other meteors, whence the fimi'nbsp;larity or the diffimilarity of particular-circiimftancesnbsp;may be eafily feen,

The following account was formed from the con-' curring obfervations ofa few intelligent friends withnbsp;whona I then happened to be in company, everynbsp;one of whom made fome particular remark.

On the evening of the i8th of Auguft 1783, were ftanding upon the north-eafl: corner of th^nbsp;above-mentioned terrace. The weather was calin^nbsp;and agreeably warm j the flcy was ferene, exceptingnbsp;very near the horizon, where a hazinefs juft pr^^nbsp;vented the appearance of the flars. A narrovv'�nbsp;ragged, and oblong cloud ftood on the north-weftnbsp;fide of the heavens, reaching from the extremity 0^nbsp;the hazinefs, which rofe as high as 18 or 20 degreesgt;nbsp;and ftretching itfelf for feveral degrees towards th^nbsp;call, in a direftion nearly parallel to the horizon*nbsp;It was a little below this cloud, and confequentlVnbsp;the hazy part of the atmofphere, about the N�nbsp;W. I W. point of the compafs that this luminot^^nbsp;meteor was firft perceived, Some flalhes ofnbsp;bent light, mpeh like the aurora borealis, were fitftnbsp;obferved on the northern part of the heavens, whi^^nbsp;were foon perceived to proceed from a roundhh itJnbsp;rpiootis body, nearly as big in diameter as the fe'^�

diameter of the moon, and almoft flationary in the above-mentioned point of the heavens. It was thennbsp;about 25 minutes after nine o�clock in the evening.nbsp;This ball at firft appeared of a faint bluifli light,nbsp;perhaps from being juft kindled, or from its appearing through the hazinefs; but it gradually in-creafed its light, and foon began to move, at firftnbsp;afeending above the horizon in an oblique direftionnbsp;towards the eaft. Its courfe in this direiftion wasnbsp;Very fhort, perhaps of five or fix degrees; afternbsp;�which it direfted its courfe towards the eaft, and,nbsp;moving in a diredlion nearly parallel to the horizon,nbsp;reached as far as the S. E. by E. point, where itnbsp;finally difappeared. The whole duration of thenbsp;meteor was half a minute, or rather lefs ; and thenbsp;altitude of its track feemed to be about 25� abovenbsp;the horizon. A Inert time after the beginning ofnbsp;its motion, the luminous body pafled behind thenbsp;above-mentioned Tmall cloud, lb that during thisnbsp;paflage we obferved only the light which was eaft innbsp;the heavens from behind the cloud, without aduallynbsp;feeing the body from which it proceeded for aboutnbsp;the fixth or at moft the fifth part of its track j butnbsp;as foon as the meteor emerged from behind thenbsp;cloud, its light was prodigious. Every objedl appeared very diflin�l; the whole face of the countrynbsp;511 that beautiful profpedl before the terrace, beingnbsp;inftantly illumined. At this moment the body ofnbsp;the meteor appeared of an oblong form; but it pre-(cntly acquired a tail, and foon after it parted into

feveral

feveral fmall bodies, each havl�g a tail, or elonga-and all moving in the fame diredlion, at fmall diftance from each other, and very little behind the principal body, the fize of which was gradually reduced after this divificn. In this form thenbsp;whole meteor moved as far as the S. E. by E. point,nbsp;where, the light decreafi-ng rather abruptly, the wholenbsp;difappeared.

During the phenomenon, no noife was heard by any of our company, excepting one perfon, whonbsp;imagined to have heard a crackling noife, fomethingnbsp;like that which is produced by fmall wood whennbsp;burning. But about lo minutes after the difap-pearance of the meteor, and when we were juft'nbsp;going to retire from the terrace, we heard a rumblingnbsp;noife, as if it were of thunder at a great diftance,nbsp;which, in all probability, was the report of thenbsp;meteor�s explofion ; and it may be naturally imagined that this explofion happened when the meteotnbsp;parted into fmall bodies, viz. at about the middle ofnbsp;its track.

Now if that noife was really the report of the explofion, which happened at the above-mentionednbsp;place ; the diftance, altitude, courfe, and other pat'nbsp;ticulars relating to this meteor, mull be very nearlynbsp;fuch as are exprelTed in the following lift ; they being calculated with mathematical accuracy upon thenbsp;preceding particulars, and upon the fuppofition thatnbsp;found travels at the rate of 1150 feet peVnbsp;But if the noife jsve heard was not that of

meteor�s explofion, then the following refults riiuft be confidered as quite ufelefs and erroneous.

cattle nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;130 miles.

heavens nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;550 mijes.

Such is the account which I wrote the day after the appearance of the meteor; and it is remarkablenbsp;that the above-mentioned particulars were almoftnbsp;entirely confirmed by various other accounts of thenbsp;fame meteor, which were afterwards either fent tonbsp;the Royal Society, or inferred, in different publications.

Thofe accounts, which were fent from various parts of this ifland, as alfo from the continent, confirmed, as nearly as can be expefted, the above-mentioned refults refpedting its fize, velocity, elevation, and explofion, over Lincolnfhire j but thisnbsp;meteor mutt have certainly had its origin muchnbsp;farther north than we imagined; and indeed, on

account of the intervening cloud, it v/as impoffible for us to perceive it at an earlier part of its courfe.nbsp;It is alfoprobable that itmufthavegone ortermlnatednbsp;at a much greater diftance than it appeared to us; fornbsp;as its light diminillied until it vanifhed, we muftnbsp;naturally have loft fight of it fooner than thofe whonbsp;flood farther fouth on the continent. The various accounts feem to eftablilh, that its courfe commencednbsp;beyond the northern extremity of this iftand, probably fomewhere ever the northern ocean. Itnbsp;pafled a little weilward of Perth, and perhaps anbsp;little caftward of Edinburgh: it proceeded over thenbsp;fouth of Scotland, Northumfoerland, the bilhopricnbsp;of Durham, Yorkfliire, Liheoinftsire, over which itnbsp;feemed to have deviated gradually to the weftward?nbsp;and in the courfe of that deviation, to have fuffere^nbsp;the burfting or partition. It then paiTed over Cana*nbsp;bridgeflftre, Eftex, and the Straits of Dover, entering the continent probably not far from Dunkirkinbsp;where, as well as at Calais and Oftend, it wa?nbsp;thought to be vertical. It was feen at Bruflels�nbsp;Paris, Nuits in Burgundy, and, it is faid, evennbsp;Rome. Upon the whole it muft have deferibed ^nbsp;track upwards of looo miles in about half a nai'nbsp;nute; an aftoniflaing rate of going, vaftly fwift^*'nbsp;than the motion of found.

Such are the particulars of this magnifi^^*-��^^ meteor, which undoubtedly was one of the larg^^�nbsp;and with which feveral other accounts may

I am unwilling to aflert, though I have no particular rcafon to deny, that the large meteors, fuch as we have defcribed, and thofe which are commonly called fliooting-flars, have a common origin.nbsp;Or are of the fame nature, and difter only in fize.nbsp;Our utter ignorance of their nature, and the want ofnbsp;accurate obfervations, do not enable us to form anynbsp;other diftindion. It appears then, that the number ofnbsp;meteors is immenfe 5 for the lliooting-ftars, or thenbsp;meteors of tha fmalleft fize, are to be feen in plentynbsp;every clear night. Some of them are fo fmall as tonbsp;be accidentally feen only through tclefcopes, othersnbsp;are vifible to the naked eye that happens to be di-reded to that part of the fky; whilft others, bynbsp;rafting more or lefs light, excite attention, and arenbsp;remarked.

The apparent fize of thofe meteors is various; but their apparent motions, vdicn they happen tonbsp;dired their courfe nearly at right-angles to thenbsp;fpedator, feem not to differ much : whence we maynbsp;Conclude that they are nearly at equal diftances from,nbsp;the earth; and of courfe they muft adually differ innbsp;fize. This point, however, is much in want ofnbsp;Confirmation, and it might be wiflied that three ornbsp;four obfervers, in a pleafant autumnal evening,nbsp;^ere fituated at certain diftances (for inftance 10 ornbsp;miles) from each other, and would endeavournbsp;^0 remark the altitudes of all the Ihooting-ftars they

faw, together with the time of their appearance. The altitude may be eafily afcertained by obfervingnbsp;the ftars over or near which the meteor paffes, andnbsp;by referring it to a common celeftial globe, redifiednbsp;for the latitude of the place and time of the appari tion, amp;c. By this means the altitudes above thenbsp;furface of the earth, of thofe diminutive meteorsjnbsp;might in great meafure be afcertained. With refpeftnbsp;to large meteors, whofe altitudes have been prettynbsp;well eftimated, it is remarkable that they have beennbsp;found to be nearly at the fame height. A meteofnbsp;mentioned in the'5 iff volume of th^ Philofophicalnbsp;Tranfaftions, feems to have attained the height ofnbsp;nearly 50 miles. In the a�ts of the Academy ofnbsp;Sciences at Paris, for 1771, a meteor is defcribednbsp;which was fcen on the 17th of July 1771.j andnbsp;was reckoned to have been 54 miles high whennbsp;began, and 27 when it exploded. The greateft al'nbsp;titude of the meteor of the i8th of Auguft 178.?�nbsp;was about �56 miles with refped: to fize; a regionnbsp;where the air is at lead joooo times rarer than nc^'�nbsp;the earth.nbsp;nbsp;nbsp;nbsp;�

This fame meteor of the i8rh of Auguft, certainly one of the largeft �, fome accounts, hoV'^'nbsp;ever, make mention of a few larger meteors havifcrnbsp;been feen; but it muft be obferved that the da2nbsp;zling light of fuch bodies always tends to impf^^*nbsp;the mind of the obferver with an enlarged idea 0nbsp;their fizes.

, nbsp;nbsp;nbsp;pillars�

pillars, barrels, paper kites, amp;c. amp;c. which fliews that they muft really be of different forms; yet itnbsp;is evident that moft of thofe varieties muft arife fromnbsp;the different pofitions of thofe bodies with refpedtnbsp;to the obfervers. Their moft ufual form is nearlynbsp;globular, generally having a fort of tail or elongation, which is of various lengths in different meteors,nbsp;and ciiangeable in the very fame meteor. Somenbsp;meteors feem to preferve their ftiapes during theirnbsp;appearance, others change it, and frequently theynbsp;are divided, or burft, into fmaller bodies. Thenbsp;fame meteor has been fometimes obferved to burftnbsp;more times than once during its appearance. '

At the time of the apparent burfting, a hollow found, like that of diftant thunder, or a much Iharpernbsp;found, has often been heard ; and fome of the meteors that have come nearer to the earth, have beennbsp;attended with a hiffing, or a fort of rattling noife,nbsp;during the greateft part of their courfe.

The colour and fplendour of meteors vary con-fiderablyin different meteors, as alfo in the fame meteor throughout its courfe. In general it is white, v\'ith a fhade of blue. Their luftre has fometimesnbsp;exceeded that of the moon, and it is related thatnbsp;meteors have been feen even in the broad day-light,nbsp;^nd full fun-ffiine.

The duration of the appearance of meteors has hardly ever exceeded half a minute i and it is oftennbsp;fo inftantaneous as to be barely perceptible.

the furface of the earth, or that fomething hard ha� fallen from them, has been afferted in various ac-'nbsp;counts 5 amongft which I fhall tranfcribe the following, which is very circumftantially related by Johnnbsp;Lloyd Williams, Efq. in the Philofophical Tranf-adlions for 1802. . This'gentleman being in India,nbsp;and having heard of an extraordinary phenomenonnbsp;which had juft happened, made particular inquiriesnbsp;concerning it. �� The information,� he fays, � Inbsp;obtained was, that on the 19th of December 1798,nbsp;about 8 o�clock in the evening, a very luminousnbsp;meteor was obferved in the heavens, by the inhabitants of Benares, and the parts adjacent, in th^nbsp;form of a large � ball of fire; that it was accompanied by a loud noife, refembling thunder; and thatnbsp;a number of ftones were faid to have fallen from ibnbsp;near Krakhut, a village on the north fide of thenbsp;river Goomty, about 14 miles from the citynbsp;Benares.

� The meteor appeared in the weftern part 0^ the hemifphere, and v/as but a fhort time vifiblt^'nbsp;it was obferved by feveral Europeans, as well as na'nbsp;tives, in different parts of the country.

� In the neighbourhood of Juanpoor, about i* miles from the fpot where the ftones are faid to hav^nbsp;fallen, it was very diftindly obferved by feveralnbsp;ropean gentlemen and ladies; whodeferibed it �nbsp;large ball of fire, accompanied with a loud rumbliflSnbsp;noife, not unlike an ill difeharged platoon ofnbsp;quetry. It was alfo feen, and the noife heard,

Various perfons at Benares. Mr. Davis obferved the light come into the room where he was, throughnbsp;a glafs window, fo ftrongly as to projeft fliadowsnbsp;from the bars between the panes, on a dark-colourednbsp;carpet, very diftindlly; and it appeared to him asnbsp;luminous as the brighteft moon-light.

� When an account of the fall of the ftones reached Benares, Mr. Davis, the judge and magi-ftrate of the diftrift, fent an intelligent perfon tonbsp;make inquiry on the fpot. When the perfon arrived at the village near which the ftones were faidnbsp;to have fallen, the natives, in anfwer to his inquiries, told him, that they had either broken to pieces,nbsp;or given away, to the Tefleldar (native colledlor) andnbsp;others, all that they had picked up; but that henbsp;might eafily find fome in the adjacent fields, wherenbsp;they would be readily difeovered (the crops beingnbsp;then not above two or three inches above thenbsp;ground), by obferving where the earth appeared tonbsp;be recently turned up. Following thefe directions,nbsp;he found four, which he brought to Mr. Davis:nbsp;moft of thefe, the force of the fall had buried, according to a meafure he produced, about fix inchesnbsp;deep, in fields whlc'i feemed to have been recentlynbsp;Watered ; and it appeared from the man s qeferip-tion, that they muft have lain at the diftance of aboutnbsp;loo yards from each other.

� What he further learnt from the inhabitants of ihc village, concerning the phenomenon, was, thatnbsp;�bout 8 o�clock in the evening, when retired to

their habitations, they obfcrved a very bright lights proceeding as from the fky, accompanied with anbsp;loud clap of thunder, which was immediately followed by the noife of heavy bodies falling in thenbsp;vicinity. The firft circumftance which attradhednbsp;their attention, was the appearance of the earthnbsp;being turned up in different parts of their fields, asnbsp;before-mentioned, where, on examining, they foundnbsp;the ftones.

� At the time the meteor appeared, the fky was perfedlly ferene; not the fmalleft veftige of a cloudnbsp;had been feen fince the i ith of the month, nor werenbsp;any obferved for many days after.

� Of thefe ftones, I have feen eight, nearly per-fed, befides' parts of feveral others, which had been broken by the poffeflbrs to diftribute among thenquot;nbsp;friends. The form of the more perfedl ones, ap'nbsp;peared to be that of an irregular cube, rounded o�*nbsp;at the edges j but the angles were to be obferved onnbsp;moft of them. They were of various lizes, froonnbsp;about three to upwards of four inches in their largc^^nbsp;diameter j one of them meafuring 4 ^ inched'nbsp;weighed two pounds and la ounces. In appearancenbsp;they were exadlly fimilar x externally, they werenbsp;covered with a hard black coat or incruftatio^�nbsp;which in fome parts had the appearance of varndh�nbsp;or bitumen ; and on moft of them^ were fraiftu'�^^'nbsp;which, from their being covered with a nnatteCnbsp;fimilar to that of the coat, feemed to have been

other�

othw, and to have pafled through fome medium, probably an intenfe heat^ previous to their reachingnbsp;the earth. Internally, they confifted of a numbernbsp;of fmall fpherical bodies, of a flate colour, embedded in a whitifli gritty fubftance, interfperfednbsp;with bright Ihining fpicute, of a metallic or pyriti-Cal nature* The fpherical bodies were much hardernbsp;than the reft of the ftone: the white gritty partnbsp;readily crun\bled, on being rubbed with a hardnbsp;body j and, on being broken, a quantity of it attached itfelf to the magnet, but more particularlynbsp;the outfide coat or cruft, which appeared almoftnbsp;wholly attraftablc by it.�*

It feems from this account, that the meteor confifted of a large body, which burft at the time when the report was heard, and that its fragmentsnbsp;fell to the earth.�The principal remarks, whichnbsp;have been made concerning thofe and other ftonynbsp;fubflances, faid to have fallen from the fky, will benbsp;found in the following chapter.

The writings even of the remotefl; antiquity, the verbal traditions of moft nations, and various circumftantial accounts of modern times, aflertnbsp;that ftones, or ftony and metallic concretions ofnbsp;various fizes, have, at different times, fallen fromnbsp;heaven upon the furface of the earth.

Ignorance and fuperftition have frequently attributed a facred charadler to thofe extraordinary ilories; but fince fuperftition and impofture arcnbsp;nearly allied, and as the formation of fuch folidnbsp;bodies in the fky is utterly unaccountable in thenbsp;prefent ftate of philofophical knowledge, the fal^nbsp;of thofe celeftial ftones, though generally believednbsp;by the vulgar, has been as generally difbelieved bynbsp;the learned, part of the human fpecies.

Every fingle account of this fort might perhaps be rejedted without impropriety j but the repeatednbsp;affertions of a great many authors in almoft everynbsp;age ; the accounts of recent cafes of this fort that

at this very time, who have been examined and interrogated with all the formality and Gircumftantial minutenefs that fcepticifm could demand ; and,nbsp;above all, the ftrong evidence which arifes fromnbsp;the chemical analyfis of various ftones of this fort,nbsp;which have been colle�led at different times, and innbsp;moll diftant countries, are more than fufficient tonbsp;eftablifh the general fa�l in the minds of impartialnbsp;perfons; and only leave for pofterity the duty ofnbsp;examining with the greateft attention, and of recording with minutenels, all the circumftances thatnbsp;may attend future cafes of this fort; whence thenbsp;origin and the nature of fuch wonderful phenomenanbsp;may be fatisfadorily inveftigated.

We are much indebted to Edward King, Efq.¹ and to Dr. Chlodni f, for having collefled a greatnbsp;number of accounts relative to this fubjcft, and fornbsp;having ably compared them with each other; andnbsp;We arc principally indebted to Edward Howard,nbsp;Efq. for a careful analyfis of various Hones faid tonbsp;have fallen from heaven.

The fall of alhes, and even of red-hot ftones in the vicinity of volcanos, at the time of an eruption,nbsp;are fo evidently owing to the eruption, that no doubt

Sec his Remarks concerning Stones faid to have fallen from the Clouds, both in thefe Days, and in ancient Times,�¹nbsp;London, 1796.

t See his Tra�l concerning the fuppofed Origin of the Mafs of Iron found by Dr, Pallas in Siberia.�Riga, 1794.

can be entertained concerning the faft. The ignited matter, accompanied with very denfe fmoke, is feennbsp;to rife from the crater of the volcano, and is pro-jedted into the air, even to the perpendicular heightnbsp;of fcveral miles ¹ ; the thick, dark fmoke forms anbsp;cloud of vapKjur and afoes, which is extended by thenbsp;wind in its diredtion, over a great extent of country,nbsp;Ibmetimes amounting to feveral hundred miles;nbsp;upon which it drops afoes f, and in the neareft partsnbsp;even ftones of different fixes, according to the various diftances. But independent of thofe evidentnbsp;volcanic produdtions, the ftones of confiderable fize,nbsp;which are faid to have fallen at different times,nbsp;foem to have a different origin j firft, becaqfe theynbsp;have frequently fallen at immenfe diftances fromnbsp;any volcano j and, fecorfoly, becaufe thofe falls havenbsp;moftly happened at times when no volcanic eruptionnbsp;was known to have taken place. It is not improbable, however, as Mr. King leems to conjedture,nbsp;that fometimes, when an extenfive cloud of afhes,nbsp;or earthy and pyritous particles, has been projedtednbsp;from a volcano, and has been driven by the wind

See Sir William Hamilton�s Account of an Eruption of Mount Vefuvius, in the PhilofophicalTranfadtions for 1795?nbsp;page 91 and 9?.nbsp;nbsp;nbsp;nbsp;¹

t At an eruption of y�fuvius, anno 471, the afhes went almoft all over Europe, and in plenty even to the citynbsp;Conftantinople. Carolus Sigonius, and Marcellinus Comes�nbsp;make exprefs ipention of that great eruption.

to a great diftance, thofe particles may have undergone an effervefcence', a combuftion, and a fubfe-quent agglutinatlonj which formed the ftone. The fads, however, do not always feem to admit of fuchnbsp;a fuppofition. But before we attempt to aflert ornbsp;to refute any hypothefis, it will be proper briefly tonbsp;mention fome of the latefl: and beft attefted fads ofnbsp;this nature j which I ftiall moftly tranfcrtbe from thenbsp;above quoted work of Mr. King.

� The well known and celebrated Cardan, in his book De Varietate Rerum, lib. 14, cap. 7 a, tells us,nbsp;that he himlelf, in the year 1510, had feen laonbsp;ftones fall from heaven 5 among which one weighed,

120 and another 60 pounds; that they were moftly of an iron colour, and very hard, and fmelt of brim-ftone. He remarks, moreover, that about threenbsp;o�clock, a great fire was to be feen in the heavens;nbsp;and that about five o�clock the ftones fell down withnbsp;a rulhing nolfe,�

� It is related by Dr. Halley (Philofophical Tranfadions, 34O. that on the aift of Maynbsp;1676, a fire ball was feen to come from Dalmatia,nbsp;proceeding over the Adriatic fea; it pafled obliquelynbsp;over Italy, where a hilling noile was heard; it burftnbsp;S.S.W. from Leghorn, with a terrible report, and thenbsp;pieces are faid to have faien into the fea,\vith the fame

fort of noife as when red-hot iron is quenched or ex-ftngullhed in water. Its height was computed to be I'ot lefs than 38 Italian miles ; and it is faid to have

The Abb� Stutz, afliftant in the imperial cabinet of cUriofities at Vienna, in a hook printed at Leipficnbsp;in 1790, deferibes two ftones faid to have fallen fromnbsp;the clouds; one in the Eichjledt country in Germany,nbsp;and� another in the Bechin circle in Bohenhia, in Julynbsp;1753. He alfo deferibes two more which were f�ennbsp;to fall not far from Agram, the capital of Croatia iunbsp;Hungary; concerning which, he relates that thenbsp;biflrop of Agram caufed feven eye-witnelfes to benbsp;examined Upon oath, and the fubftance of their evidence is, � that about fix o�clock in the afternoonnbsp;of the 26th of May 175 f, there was.feen towardsnbsp;the eaft, a kind of fiery ball, which, after it had burftnbsp;into tv/o parts, with a great report, exceeding thato^quot;nbsp;a cannon, fell from the Iky, in the form and appearance of two chains entangled in one another; whichnbsp;was attended with a loud noife, as if a great man/nbsp;carriages rolled along. After this a black fmokenbsp;was feen, and a part of the ball feertled to fall in tU�nbsp;arable field j on the fall of which to the ground ^nbsp;Hill greater noife was heard, and a fliock was pc'quot;'nbsp;ceived fomewhat like an earthquake.

� This piece was afterwards foon dug out of th^ ground, which had been particularly noted tonbsp;plain and level, and ploughed juft before; but wherenbsp;it was now found to have made a grert fiflure, o'quot;nbsp;cleft, an ell wide, whjlft it finged the earth on chenbsp;lides.

The other piece, which fell in a meadow, was alfo dug up, and v/eighed 16 pounds,�

The ftone which fell in the Eichftedt country, as rnentioned in the preceding page, is faid to confiftnbsp;of afh-grcy fand, agglutinated together, and intermixed with fine particles of native iron, and withnbsp;particles of yellowilh brown iron ochre. In flioPt,nbsp;it feems to confift of filiceous fand and iron. Itsnbsp;hardnefs is not very great. Its furface is coverednbsp;all over with a folid malleable coat of native iron,nbsp;like a blackilh glazing, about two lines thick,nbsp;which was fuppofed to be quite free from fulphur.nbsp;The whole exhibited evident marks of having beennbsp;expofed to fire.

The teftimony of the fall of this ftone is as follows : A labourer at a brick-kiln, in winter, when the earth was covered with fnow, faw it fall downnbsp;out of the atmofphere immediately after a violentnbsp;clap of thunder. He inftantly ran to the Ipot to takenbsp;gt;t out of the fnow ; but, finding he could not effeftnbsp;it on account of its heat, he was obliged to waitnbsp;tintil it cooled. The diameter of this ftone was aboutnbsp;lialf a foot. It was covered all over with a blacknbsp;�^oat like iron.

quot; It is related in the Hiftory of the Academy of. Sciences 1769, p. ao, that three malTes fell downnbsp;quot;'ith thunder, in provinces very diftant from onenbsp;^tiother; and which were fent to the Academy innbsp;*769. They were fent from Maine, Artois, ' zndnbsp;^oteniin i and it is affirmed, that, when they fell, a

hifling was heard; and that they were found hot. All three were like one ahother j all three were pfnbsp;the fame colour, and nearly of the fame grain j andnbsp;fmall metalhc and pyritical particles could be diftin-guiflied in them; and, externally, all three were covered with a hard ferruginous coat; and, on chemical invefligation, they were found lo contain ironnbsp;and fulphur.�

� On the 13th of September 1768, about half an hour after four in the afternoon, there was' feen neatnbsp;the caftle cf Luce in Maine, a tempeftuous cloud;nbsp;from which w'as heard an explofion of thunder, likenbsp;the firing of a cannon, but without the appearancenbsp;of lightning: there was then heard a remarkablenbsp;whizzing noife in the air ; and fome perfons travelling, on looking up, faw an opaque body de-fcending in a curved line, v;hich fell in a green patchnbsp;�f ground near the high road to Mons. They ahnbsp;ran inftantly to the fpot, and found a kind of ftone�nbsp;one half of which was buried in the foil, and whichnbsp;was fo burning hot, that they could not polfiblynbsp;touch it.

� For, firft, the fall of four (tones is precifcly flfcertained; one of which was of an irregular figure,nbsp;with a point like that of a diamond, weighing 5 ^nbsp;pounds, and had a vitriolic fmell. And anothefnbsp;weighed 3 f pounds, was black on the outfide, asnbsp;from fmoke; and, internally, feemed compofefinbsp;of matter of the colour of aflies, in which were per-ceived fmall fpots of metals, of gold and filver.

� And befides thefe, Profeffor Soldani of Sien*'' was fhewn about 15 others, the 1'urfaces of whichnbsp;were glazed black, like a fort of varnilh; refiftclt;inbsp;acids, and were too hard to be fcratched with th�'nbsp;point of a penknife.

� Signior A. Montauli, who faw the cloud as he was travelling, deferibed it as appearing much abo'^enbsp;the common region of the clouds, and as beii��nbsp;clearly difeerned to be on fire ; and becoming whit^*^�nbsp;by degrees, not only where it had a communie*'nbsp;tion, by a fort of Ifream of fmoke and lightning�nbsp;�with a neighbouring fimilar cloud, but alfo, at 1*^�nbsp;in two-third parts of its whole mafs, which wasnbsp;ginally black. And yet he took notice, that itnbsp;not affedled by the rays of the fun, though theynbsp;full on its lower parts. And he could difeern ** '*�nbsp;were the bafon of a fiery furnace in the cloud,nbsp;a whirling miotion.nbsp;nbsp;nbsp;nbsp;^

� This curious cbferver gives an account all^* a ftone, which he was alTured fell from the clouds ^nbsp;the feet of a farmer, and was dug out of thenbsp;into which it had penetrated; and he faysgt; dr**'

'vas about five inches long, and four broad, nearly fquare, and polifhed ; black on the furface, as ifnbsp;finoked, but within like a fort of fand ftone, withnbsp;Various fmall particles of iron, and bright metallicnbsp;ftars.�

Other ftones are defcribed by him, which w'erc faid to have fallen at the fame time, were triangular, and terminated in a fort of pyramidal or conicalnbsp;figure j and others were fo fmall as to weigh notnbsp;tftore than one ounce.

In the year 1795, a ftone of remarkable large fize Was faid to have fallen from heaven, near the If^oldnbsp;Cottage, York��xrt, which ftone was afterwardsnbsp;exhibited in Londen. The account of its fall isnbsp;3s follows :

� In the afternoon of the 13th of December 1795-, *iear the Wold Cottage, noifes were heard in the airnbsp;various perfons, like the report of a piftol, or ofnbsp;�uns at a diftance at fea, though there was neithernbsp;^fiy thunder or lightning at the time; two diftineftnbsp;^oncuflions of the earth were foid to be perceived,nbsp;^'^d a biffing noife was alfo affirmed to be heard bynbsp;perfons, as of fomething paffing through thenbsp;J and a labouring man plainly faw (as we are told)nbsp;fomething was fo paffing, and beheld a ftone,nbsp;it feemed, at laft, (about to yards diftant fromnbsp;ground) defeending, and ftriking into thenbsp;^�'ound, which flew up all about him ; and, in fall-foarks of fire feemed to fly from it.

� Afterwards he went to the place, in company with others, who had witneflTed part of the phaeno-mena, and dug the ftone up from the place, wher�nbsp;it was buried about 2i inches deep.

*' It fmelt (as it is faid) very ftrongly of fulphur� �when it was dug up; and was even warm, andnbsp;fmoked. It was found to be 3c inches in length�nbsp;and 28 \ inches in breadth ; and it weighednbsp;pounds.�

This ftone, as it was exhibited, appeared to havc a dark, black cruft, with feveral concave imprelTionsnbsp;on the outlide, which muft have been made befot^nbsp;it was quite hardened �, juft like what is related con'nbsp;eerning the crufts of thofe ftones that fell in Italf¹nbsp;Its fubftance was not properly a granite (as dlt;t'nbsp;fcribed in the printed account that .was diftributed) gt;nbsp;but a fort of grit-flone^ compofed (fomewhat like th^nbsp;ftones faid to have fallen in Italy) of fand and alh^^'nbsp;There were in it a great many pyritous partid^^�nbsp;and fome fmall rufty fpecks, perhaps decompd^nbsp;pyrites. It did not effervefce with acids. It fee^^^nbsp;that, this excepted, fuch kind of ftones havenbsp;been found in any part of England.

From the above and other fimilar accounts, �which might hereto be annexed ¹, the general fa6tnbsp;of ftones having aftually fallen from the fky, feemsnbsp;to be eftabliflied beyond the poffibility of a doubt.nbsp;On account of the explofion, which generally attendsnbsp;their fall, thofe ftones have often been called thunder-fionesj or thunder-bolts-, and it is vulgarly and pretty generally believed, that every clap of thunder is attendednbsp;with the fall of a ftone. But a wide diftinftion muftnbsp;be made between the above-mentioned phenomenanbsp;and the common thunder and lightning, which arenbsp;the effefts of eledtncity difcharged from the clouds ;nbsp;and which have nothing to do with the fall of ftones.nbsp;Yet it muft be obferved, that fometimes the twonbsp;fpecies of phenomena are combined, and take placenbsp;both at the fame time, as may be gathered from thenbsp;preceding accounts; and the prefent ftate of knowledge does not enable us to make a due diftindtionnbsp;between them. The laft account of the precedingnbsp;chapter, deferibing the fall of ftones near Benares,nbsp;and the circumftanccs which have attended fimilarnbsp;phenomena, feem to indicate that every meteor.

Befides the above quoted works of Mr. King and Dr. ^hladni, the reader will find fimilar accounts in Falconet�snbsp;Papers upon Boetilia, inferted in the Hijl. dcs Infcriptions ctnbsp;^dles Lettres; Zahn's Specula Fhyfico-Mathematica Hlfio-^�gt;na ; La Fftea Satterrtinea di Giacinto Gemma j and Mr.nbsp;Howard�s elaborate and fatisfadtory Paper in the-Philofophi-Tranfaiftions for the year 1802.

fuch as have been defcribed in that chapter, is owing to the formation, or ignition, of fomething folidjnbsp;which moves with wonderful rapidity, mofliy throughnbsp;the regions of the atmofphere vaftly above the ufualnbsp;clouds, and which, befides the hiffing noife thatnbsp;moftly accompanies Its courfe, generally burfts withnbsp;one or more explofions, and laftly falls down uponnbsp;the furface of the earth in a few or in a great man)'nbsp;pieces. It Teems, how�ver, that the fall of the ftonCrnbsp;which fell in Yorkfhire, was not attended with anynbsp;luminous appearance.

Whence do thofe meteors or folid bodies derive their origin and their motion ? is the great defidera�-turn; the important queftion, which the prefent ftatcnbsp;of knowledge does not enable us to anfwer, any mof^nbsp;than by the fuggeftion of hypothefes. A brief ftatC'nbsp;ment of thofe hypothefes will conclude this chapter jnbsp;but previous to this, if will be nccefiary to adducenbsp;what may be called the ftrongeft evidence of fn^^nbsp;ftones having really fallen from the fky, viz. tb^^nbsp;evidence which arifes from their chemical analyb^�nbsp;and their general external charadters.

The mineralogical defcription of the ftones Benares, the ftones from Yorkfhire, one ofnbsp;ftones from Italy, and a ftone from BohemiaJ ^nbsp;faid to have fallen from the fity, as given by Cou^�-de Bournon, is inferted in Mr. Howard�s papernbsp;the Philofophical Tranfaftions for 1802, fromnbsp;in addition to what has been already mentionednbsp;the preceding accounts, ^ it appears, tliat all m

j[tonesgt;

ftones, whatever their fize may be, are entirely covered with a thin cruft of a deep black colour, un-lefs they have been broken in their fall or otherwife; for, in this cafe, the furface of the broken fide has nonbsp;cruft. Their {�rhce is quite deftitute of rnetallicnbsp;glofs, and is fprinkled with afperiries. Whennbsp;broken, their interna! texture is granulated, refem-bling, more or lefs, a coarfe grit-ftone. By the ufenbsp;of a lens, their component particles feem to be ofnbsp;four fpecies, the proportion of which fcems to vary anbsp;little in the different fpecimens. Thofe ingredientsnbsp;are, ift, A great abundance of grey or browniftinbsp;globules of different fizes, which may be eafilynbsp;broken in all directions j their fraflure is conchoid,nbsp;with a fmooth, fine, compact, and fomewhat gloffynbsp;furface ; their hardnefs is fuch as to afford a fewnbsp;faint fparks when ftruck with fteel ; 2d!y, A granulated martial pyrites, of a reddifh yellow colour,nbsp;but black when powdered. This fubftance, whichnbsp;is irregularly diftributed through the mafs of thenbsp;ftone, is not attraftable by the magnet; 3d!y, Smallnbsp;particles of iron in a perfedl metallic ftate, whichnbsp;I'ender the whole ftone attradlable by the magnet;nbsp;4thly, A fubftance of an earthy confiftence, andnbsp;'''hitifti' grey colour, which feems to cement andnbsp;^nite the other three ingredients, and from whichnbsp;the others may be eafily feparated with the pointnbsp;a knife, or even with the nail.

quot; The black cruft with which the furface of the ftone rs coated, although it is of no great thicknefs,nbsp;V0L..IV.nbsp;nbsp;nbsp;nbsp;c cnbsp;nbsp;nbsp;nbsp;emits

emits bright Iparks, when ftruck with fteel: it may be broken by a ftroke with a hammer; and feemsnbsp;to poflefs the fame properties as the very attradablenbsp;black oxide of iron. This cruft is, however, likenbsp;the fubftance of the ftone, here and there mixed withnbsp;Imall particles of iron in the metallic ftate: theynbsp;may eafily be rendered vifible, by pafling a file overnbsp;the cruft, as they then become evident on accountnbsp;of their metallic luftre.�

Thofe which have a greater fpecific gravity, evi' dently contain a greater quantity of iron.

The firft ftone of this fort, that was chemically analyzed by the French Academicians, was found opnbsp;the 13th of September 1768, yet hot, by perfoo*nbsp;who faw it fall, as has been faid in the precedio?nbsp;pages.

Another ftone of the fame nature, but little diff^^' ing in appearance, was analyzed by Mr. Barthol*^'nbsp;who found that 100 parts of the ftone contaiP^

2 parts of fulphur, ao of iron, 14 of magno^'^� 17 of alumine, 2 of lime, and 42 of filicoo*^^nbsp;earth.

of the four diftinft bodies which form the ftones from Benares, and afeertained the following particulars : The external coat contains a good deal ofnbsp;iron attraftable by the magnet, and fome nickel,nbsp;which form its principal components. The fliiningnbsp;or pyritous particles, irregularly dilTeminated throughnbsp;the Hone, being carefully feparated and analyzed,nbsp;were found to contain 2 parts of fulphur, io| ofnbsp;iron, nearly i of nickel, and 2 of extraneous earthynbsp;matter. The globular bodies contained 50 parts ofnbsp;filica, 15 of magnefia, 34 of oxide of iron, and 2 �nbsp;of oxide of nickel. Laflly, the earthy matter, whichnbsp;formed the cement or matrix for the other fub-ftances, was found to contain 48 parts of filica,

The Hone from Siena, on being analyzed, was found to contain 70 parts of filica, 34 of magnefia, 52 of oxide of iron, and 3 of oxide ofnbsp;nickel.

The ftone from Yorkfirire was found to contain 75 parts of filica, 37 of magnefia, 48 of oxide ofnbsp;iron, and 1 of oxide of nickel.

The ftone from Bohemia w�as found to contain 25 parts of filica, 9 | of magnefia, 23 | of oxide ofnbsp;iron, and i of oxide of nickel.

The great fimilarity which the chemical analyfis, and a careful examination of the mineralogical ornbsp;apparent formation of thofe ftones, fhew to exiftnbsp;among fpecimens colledled at different times, and

brought from various parts of the world fo very remote from each other, undoubtedly is the ftrongeft proof of their being different from common minerals;nbsp;and of their owing their origin to the fame generalnbsp;caufc. The mineralogifts, who have examined them,nbsp;find themi d ifferent from any other fort of mineralogicalnbsp;fubftance ever defcribed by the writers on thatfubjed.nbsp;Thole fads alone feem to convey perfed convidionnbsp;concerning the accidental defcent of thofe ftonesnbsp;upon our globe; but a careful examination of allnbsp;the circumftances, the fimilarity of the accounts, asnbsp;given by various perfons of different nations, andnbsp;unknown to each other, who could not poffibiy accord in a falfe account j the nature of thofe ftones,nbsp;and tlie ancient accounts related by a variety of credible authors, or handed down, by tradition; allnbsp;thofe circumftances, I fay, when duly confidered,nbsp;feem to eftablifh the general fad of the fall, amp;c.nbsp;beyond the poffibility of doubt. We fliall thereforenbsp;conclude this fubjed with a concife ftatement of thenbsp;moft rational hypothefes that have been offered ionbsp;explanation of thofe phenomena.

Unwilling to force upon the reader any particular hypothefis concerning meteors and the fall of ftonesjnbsp;I have confined the preceding chapter to the formernbsp;of thofe fubjeds, and the prefent to the latter only inbsp;yet, by the laft account in the preceding chapter�nbsp;and by various accounts in the prefent, the readernbsp;muft naturally, remark the great connedion whichnbsp;appears to exift between the two phenomena-gnbsp;nbsp;nbsp;nbsp;WithotJt

Without attempting to decide definitively upon the fubjedt, we may neverthelefs place the hypotheticalnbsp;part of both phenomena under one point of view.nbsp;The vague opinions entertained by the ancients, ofnbsp;theuftones coming from the fun or the moon, neednbsp;not be formally refuted.

It was Doctor Halley�s opinion, that a ftratum or train of inflammable vapour, gradually raifed fromnbsp;the earth and accumulated in an elevated region,nbsp;fuddenly took fire at one end, and the fucceflive inflammation of the ftratum, like the inflammation ofnbsp;a train of gun-powder, produced the apparent motion as it were of a ball of fire which conftituted thenbsp;meteor ¹. But the leafl examination of the differentnbsp;parts of this hypothefis, will readily manifefl its im-perfedtions.

In a differtation on this fubjedt by Profeffor Clap, of Yale College, in New England, we find a fup-pofitlon, that the bodies which form the meteors,nbsp;may be folid bodies revolving round the earth, asnbsp;the comets revolve round the fun, and now andnbsp;then fome of them coming fo near as to fall uponnbsp;it. This hypothefis feems, at firft fight, to be attended with apparent improbability �, yet a littlenbsp;confideration may perhaps render it more intelligiblenbsp;to the fpegulative philofopher, and more applicablenbsp;to the explanation' of the phenomena.

390 Of the Stony Bodies which are Jaid

With refped to thofc phenomena I am inclined to propofe the following explanation. Imaginenbsp;that a revolving body moves round the earth withnbsp;a velocity fomewhat like that of the moon, or ofnbsp;the earth in its orbit; alfo fuppofe that the attractive force in proportion to the centrifugal, is rathernbsp;ftronger than that which is required to keep thenbsp;revolving body in the fame immutable orbit; andnbsp;that confequently the faid body mufl move in anbsp;fort of fpiral, coming continually nearer and nearernbsp;to the earth. Now when this body comes withinnbsp;a certain part, however rare, of the atmofphere,nbsp;with its immenfe velocity, the fri�tion it fuffersnbsp;may poffibly heat it to the degree of incandefcence,nbsp;checking at the fame time its centrifugal force,nbsp;which confequently increafes the gravitating or at-traftive power. The great heat, which the bodynbsp;acquires in confequence of the fridlion, producesnbsp;two natural effefts. In the firft place, it partlynbsp;melts or vitrifies the external furfice, which formsnbsp;the common black cruft of the body (viz. thenbsp;black cruft of the ftones faid to have fallen fromnbsp;the Iky); and, fecondly, by expanding unequallynbsp;the parts of the body, caufes it to break with ex-plofion, in the fame manner as ftones often do in ^nbsp;common fire.

The greateft objeftion to this hypothefis feerns to be, that the revolution of fo many bodies roundnbsp;the earth as are neceftirry to form all the meteorsj

The fuppofition that meteors are the efFed of, or nothing more than, a feparate quantity ofnbsp;ele�lrlc matter, though, at firfl: fight, may appearnbsp;to be warranted by certain electrical phenomena,nbsp;is, on mature confideration, liable to very great ob-je�lions.

I lhall ladly fubjoin Mr. King�s hypothefis concerning the fall of ftones at Siena in Italy.

This very learned gentleman eftabliflies his fup-pofition^ upon a careful examination of all the cir-cumftances that feemed to be at all concerned with that wonderful phenomenon. He remarksnbsp;tliat the fpace of ground within which the ftonesnbsp;fell, was from three to four miles; that the phenomenon took place the very day after the great eruption of Vefuvius, which is not lefs diftant from Sienanbsp;than 200 miles, and that Vefuvius is fituated to thenbsp;fouth of the fpot; whereas the cloud came from thenbsp;north, about 13 or at moft 18 hours after the eruption. Mr. King then briefly mentions his formernbsp;obfervations on the formation of ftones and rocks,nbsp;cither by the means- of fire or of water; after whichnbsp;he fays, � It is alfo well known, that a mixture ofnbsp;quot; pyrites of almoft any kind, beaten fmall, andnbsp;� mixed with iron filings and water, when buriednbsp;quot; in the ground, will take fire, and produce a fortnbsp;quot; of artificial volcano j and furely then, wherever a

� any time become mixed together, ,as flying duft � or aflies, and be by any means condenfed togC'*nbsp;� ther, or comprefied, the fame efFcd might benbsp;� produced, even in the atmofphere and air.

� Inftead, therefore, of having recourfe to the � fuppofition of the cloud in Tufeany having beennbsp;� produced by any other kind of exhalations fromnbsp;� the earth, we may venture to believe, that an im-� menfe cloud of afhes, mixed with pyritical dulfjnbsp;and with numerous particles of iron, having beennbsp;�� projeded from Vefuvius to a mofl: prodigiousnbsp;� height, became afterwards condenfed in its de-� feent, took fire, both of itfelf as well as by meansnbsp;of the eledric fluid it contained, produced manynbsp;� explofions, melted the pyritical, metallic, and ar-� gillaceous particles, of which the afhes were com-� pofed j and by this means had a fudden cryftalH'nbsp;� zation and confolidation of thofe particles takennbsp;� place which formed the flones of various fiz^snbsp;� that fell to the ground �, hut did not harden tblnbsp;clayey afhes Jo rapidly as the metallic particles cryjl^^'nbsp;� lized-, and therefore gave an opportunity fornbsp;� prejfwns to be made on the furfaces of fome of thenbsp;�f flones as they fell, by means of the impingingnbsp;� the others*.�

[ 393 3

SECTION HI.

CHAPTER I.

TH E fluctuating nature of the bulks of all forts of bodies, fuch as are within our grafp, thenbsp;general cxpanfion and contraction which arife fromnbsp;heat and cold, the Ihrinking and warping whichnbsp;are the effeCts of the evaporation and abforption ofnbsp;fluids, and the lofs of matter from the furfaces ofnbsp;moft bodies, ariflng from friCtion, or abrafion, render it extremely difficult to form a certain invariablenbsp;length or ftandard meafure, of any fort whatever,nbsp;with which other extenfions may, in future, benbsp;compared.

] t is true that feveral ftandard meafures of glafs, of brafs, of iron, or of other metal, that are nownbsp;preferved in diverfe public and private repofitoriesnbsp;for the regulation of meafures and weights in civilnbsp;economy, when duly examined, are found to agree

fo well with each other, as that the error or difference feldom amounts to the thoufandth part of the whole; and Inch difference would indeed be toonbsp;trifling to deferve notice, were it not for the accumulation of the error which takes place when that mea-fure comes to be repeated a great number of times.nbsp;Thus, if I meafure a certain extenfion with a footnbsp;ruler, which ruler is one thoufandth part of a footnbsp;deficient, or Icfs than the real ftandard, it i,s evident that when I havemeafured looo feet with fuchnbsp;ruler, my meafurement is one foot lefs than the truth.nbsp;Now fuch error would be of very great confequencenbsp;in a variety of cafes

On the above-mentioned accounts, and becaufe it is not eafy to fend an accurate ftandard meafurenbsp;from place to place, wherever it may be wanted, ornbsp;to prevent its being loft or broken by accidents innbsp;procefs of time, various plans have been propofednbsp;for forming a ftandard meafure at any time j or,nbsp;other words, plans have been propofed for inftruftingnbsp;a perfon how to form, or to determine, the meaftn^nbsp;of a foot, or of a yard, or of any other given denO'nbsp;ruination by means of words only, viz. withoutnbsp;actually Ihewing him that meafure.

Of the different plans which have been propo^^ for this purpofe, two are undoubtedly the beft,nbsp;thofe I {hall endeavour briefly to explain.

ift. The length of the pendulum which vibrates leconds, has long been ufed for a ftandard'of mea-fure; for if you fallen a leaden ball, or any othernbsp;Weight to a flexible thread, and, having fulpendednbsp;the upper part of the thread to a nail, you caufe itnbsp;to vibrate; and, by obferving with a clock or watch,nbsp;you count the vibrations, and lengthen or Ihortennbsp;tile thread, until that pendulum performs 60 vibrations in one minute, or 3600 vibrations in one hour ;nbsp;then the length of that pendulum, in the latitude ofnbsp;London, will be little more than 39,1 Englilhnbsp;inches. In any other latitude the length of thenbsp;pendulum that vibrates feconds, muflt be longer ornbsp;Ihorter than 39,1 inches, according as the place isnbsp;nearer to one of the poles, or nearer to the equatornbsp;of the earth ; but the quantity by which the pendulum muft be Ihortened or lengthened, in order thatnbsp;it may vibrate feconds in any given latitude, maynbsp;he eafily calculated *; hence that pendulum or anbsp;pendulum that vibrates any other afcertained numbernbsp;of times in a minute, may be ufed as a ftandard ofnbsp;tneafure in any known latitude. But the inaccuracynbsp;to which this method is liable, arifes principallynbsp;htom the difficulty of meafuring the precife diftance-between the real point of fufpenfion, and the centrenbsp;^f ofcillation of the pendulum,

In order to obviate in great meafure the errors to which the above-mentioned method is liable, the

Of the Standard Meafurt.

late ingenious Mr. Whitehurft contrived a machine, or piece of clock-work, having a pendulum with anbsp;moveable centre of fufpenfion, whence it mightnbsp;be lengthened or fhortened at pleafure, and whichnbsp;of courfe might be adjufled fo as to vibrate anynbsp;number of times in a given interval of time.nbsp;then propofed to ufe as a ftandard of meafure, notnbsp;the length of the whole pendulum, but the difference of the lengths of the fame pendulum, when it

* A Table, (hewing how much a pendulum which vibrate* feconds at the equator, would gain every 24 hours in different latitudes, and how much the pendulum need to b�nbsp;lengthened in thofe latitudes in order to vibrate feconds.

performed a certain number of vibrations in one hour, and when it performed another certain numbernbsp;of vibrations like wife in one hour; by which meansnbsp;the above-mentioned fources of error would in greatnbsp;iiieafure be obviated*.

After the death of Mr. Whitehurft, Sir George Shuckburgh Evelyn refumed the fubjeft, and, being poflefied of the very fame machine which Mr.nbsp;Whitehurll had conftrudted, he made all the experiments which that machine was capable of performing; and at laft he came to the followingnbsp;conclufion, which ,we have already tranferibed innbsp;the fecond volume of this work. �It appears,�nbsp;he fays, � that the difference of the length of twonbsp;quot; pendulums, fuch as Mr. Whitehurft ufed, vi-quot; brating 42 and 84 times in a minute of meannbsp;quot; time in the latitude of London, at 113 feet above

the level of the fea, in the temperature of 60% quot; and the barometer at 30 inches, is equal tonbsp;quot; 59gt;^935^ inches of the parliamentary ftandard;nbsp;� from whence all the meafures of fuperficies andnbsp;*' capacity are deduciblef.�

adly. The other method, which was lately prac-^'fed by the French Academicians, for determining ^0 invariable ftandard meafure, is to ufe a certain

398 nbsp;nbsp;nbsp;Of the Standard Meajure.

portion of the whole circumference of the earth. For this purpbfe the extent of feveral degrees ofnbsp;the meridian, are actually meafured with any givennbsp;ruler, from which meafurement it is eafy to calculate the extent of the whole meridian j that is, ofnbsp;the whole circumference of the earth; then a certain portion of that circumference is to be ufed as 3nbsp;ftandard meafurej for inftance, if that circumferencenbsp;fhould be found equal to one million times thenbsp;above-mentioned ruler, then the millionth part ofnbsp;that circumference, or that identical ruler, maynbsp;be the ftandard meafure. Should a nation, or ^nbsp;perfon in any other country, and at any diftance ofnbsp;time, wifli to form a ftandard meafure equal tonbsp;the above, they muft adually meafure fome degrees of the meridian with any ruler at pleafure}nbsp;whence they may calculate the number of luch

rulers that are equal to the whole circumference 0 the earth ; laftly, taking the thoufandth part of th^��nbsp;extent, they will have the ftandard meafure as abovO'nbsp;Now', the French Academicians have taken th*-^nbsp;forty millionth part of the whole circumference ^nbsp;the earth for their ftandard meafure, they ha'''^nbsp;formed rulers, or fcales, exaftly equal to thatnbsp;which they call metre, and which, by a careful cornnbsp;parifon, with accurate fcales of Engllfh inches,

amp;c. at the temperature of 62�, has been found eq'^'^ to ^9,371 Englifh inches*.

In fhort, the inch of ftandard Englifli meafure, iz of which form a foot, amp;c. and with which allnbsp;other meafures are compared, is an extenfion which,nbsp;if it be multiplied by 59589353, the product isnbsp;equal to the difference of the lengths of twonbsp;pendulums, one of which vibrates 42, and thenbsp;other 84 times in a minute of mean time, at thenbsp;temperature of 60�, and, in the latitude of London,nbsp;113 feet above the level of the fea*. Or the above-mentioned Englifli inch is an extenfion, which, ifnbsp;multiplied by 39,3715 the produft is equal to anbsp;French metre, 40 millions of which (at the temperature of 6a� Fahrenheit�s thermometer) arenbsp;equal to the whole meridian or circumference ofnbsp;the earth,

Having fhewn in the preceding chapter ho''^ to determine the length of anEnglifhinch, ornbsp;number of inches, we lhall now proceed to ftate thfrnbsp;meafures of other denominations that are ufed in thisnbsp;ifland, by fhewing the number of inches to whichnbsp;they are equal; thus, from the following table,nbsp;appears that 12 inches make a foot; that 3^nbsp;inches, or 3 feet, make a yard; that 198 inchesnbsp;equal to 16i feet, or to 5 \ yards, or to one rod�nbsp;that 7920 inches are equal to 660 feet, or to 22OJnbsp;or to 40 poles (otherwife called rods) or to oncnbsp;furlong, amp;c.

One degree of a great circle of the earth is commonly reckoned equal to 691 miles, or to 365640 feet.

45 nbsp;nbsp;nbsp;20nbsp;nbsp;nbsp;nbsp;5nbsp;nbsp;nbsp;nbsp;. linbsp;nbsp;nbsp;nbsp;I

Inches, Links of Feet. Yards. Poles, Chains. Mile, a Chain.nbsp;nbsp;nbsp;nbsp;or Rods.

792 nbsp;nbsp;nbsp;100nbsp;nbsp;nbsp;nbsp;66nbsp;nbsp;nbsp;nbsp;22nbsp;nbsp;nbsp;nbsp;4 I

63360 nbsp;nbsp;nbsp;8000nbsp;nbsp;nbsp;nbsp;5280nbsp;nbsp;nbsp;nbsp;1760nbsp;nbsp;nbsp;nbsp;320nbsp;nbsp;nbsp;nbsp;80nbsp;nbsp;nbsp;nbsp;I

The heights of horfes are generally meafured by hands. A hand is equal to 4 inches.

461448^600 27878400 3097600 102400 2560 640 I IV,nbsp;nbsp;nbsp;nbsp;D Dnbsp;nbsp;nbsp;nbsp;Lineal

402 Of Britijh Meqf^s and Weights.

Lineal Scotch Meajures.

Inches. Linksof Feet. Ells. Falls,or Chains. L.Rood.M* a Chain.nbsp;nbsp;nbsp;nbsp;Short

Square Scotch Meajures.

- Ccrrefpondence between Englijh and Scotch Meajures-

24,8 Englifh yards are equal to one Scotch chain. One Englilh mile is equal to 71 Scotch chains.nbsp;6150 Square Englifh yards are equal to a Scotchnbsp;acre.

one

The ftandard of lineal meafures being once afcer-tained, a ftandard weight is thereby eafily determined} for if you take a body of a uniform fubftancc, and of afty given dimenfions, the weight of thatnbsp;body will ferve for the ftandard weight. Thus it hasnbsp;been determined, that a cubic inch of pure diftillednbsp;water, when the barometer is at 29,74 inches, andnbsp;the thermometer at 66�, weighs 252,422 parliamentary grains, 5760 of which make orie poundnbsp;troy¹.

There are three forts of weights principally ufed in Great Britain ; namely, froy weights j Avoirdupois, or Avoirdufoize, weight j and Apothecariesnbsp;weight-, but the Troy pound, confifting of 5760nbsp;grains, as mentioned above, is confidered as the beftnbsp;integer to adopt as the ftandard of weight.

viz. According to the ftandard weights made by Mr. Harris, Aflay Mafter of the Mint, under the orders of thenbsp;Houfe of-Commons in, the year 1758, which are kept innbsp;the fame cuftody with Mr. Bird�s Scale of Length, and appear to have been made with great care, as a mean refultnbsp;ftom a great number of comparifons of the old weightsnbsp;in the Exchequer, Philofophical Tranfaiftions for I79^gt;nbsp;page 173.

1 pound Avoirdupois is equal to 1,21545 pound Troy, or to i pound 11 penny weights andnbsp;20 grains Troy¹.

The Troy weights are ufed for weighing gold, filver, coftly liquors, and a few other articles.

The Avoirdupois weights are ufed in commerce for weighing all kinds of grocery, fruit, tobacco,nbsp;butter, cheefe, iron, brafs, lead, tin, foap, tallow,nbsp;pitch, rofin, fait, wax, amp;c.

The apothecaries and chemifts compound and fell their medicines by the above-mentioned apothecaries weights; but they buy their articles by thenbsp;Avoirdupois weights.

There are a few weights of other denominations ufed in commerce, or In particular parts of England,nbsp;for weighing wool and a few other articles; but fornbsp;thofe we mull refer the reader to the works onnbsp;commerce.

This correfpondence is taken from the experiments �Hade in the year 1744, by Martin Folkes, Efquire, Prefi-�ient, and feveral other gentlemen, members of the Royal

A ftriked bufhel is to a heaped bufhel as 3 to 4, viz.' a heaped bufhel is one-third more than a ftrikednbsp;bufliel.

The avoirdupois weight of a bufhel of wheat, a mean, is 60 pounds; ditto of barley is 50 pounds 5nbsp;ditto of oats is 38 pounds.

� The weight of a pint (or P^^t of a peck) dry meafuce, in avoirdupois ounces, at a mean of wheat,nbsp;is 15 ounces ; of barley is 12 f ounces;, of oats isnbsp;5 } ounces.

nerally

nerally weighs 50 pounds avoirdupois. An heaped bulhel thereof generally weighs 83 pounds avoir-,nbsp;dupois, and 36 bufliels (or one chaldron) weighnbsp;26,67 hundred weight j that is, 298 S pounds avoirdupois.

The following table fhews what number of mca-fures of one denomination make up one of another denomination, as alfo the number of cubic inches tonbsp;which each meafure is equal. Thus, for inftance, itnbsp;fhews that the capacity of one barrel is equal to 34nbsp;gallons, or to 136 quarts, or to 272 pints, or tonbsp;9588 cubic inches, according to the country meafure ; alfo it fhews that 35 | cubic inches are equalnbsp;to a pint, 2 pints are equal to a quart, 4 quarts arenbsp;equal to a gallon, Stc. The like explanation muftnbsp;be applied like wife to the table of wine meafures,nbsp;as alfo to that of the Scotch liquid meafures. Beernbsp;meafure for London is 36 gallons to the barrel.nbsp;Ale meafure for ditto is 32 gallons to the barrel.nbsp;Beer and Ale meafure for the country is 34 gallonsnbsp;(viz. a mean between the, two former) to thenbsp;barrel.

231 cubic inches make one gallon wine meafure by a�l of parliament 5th of Cb Anne; but the ftandardnbsp;gallon^ at Guildhall, contains only 224 cubjcnbsp;Inches,

quot;Xhe Jlirling Jug, containing one Scotch pint, is the original ftandard of all liquid and dry meafures,nbsp;and of all weights in Scotland. It contains 103,404nbsp;cubic inches. When accurately filled with the waternbsp;of Leith, the water weighs 3 pounds and 7 ouncesnbsp;pf Scots Troy (equal to 55 ounces, or to 26180nbsp;Englifh Troy grains); fo that one ounce weighsnbsp;476 Englifh Troy grains.

By the a�l of Union, the barrel for Englilh country meafure of 34 gallons, the capacity ofnbsp;which is 9588 cubic inches, is reckoned equalnbsp;to 12 Scots gallons, making 9926,7 cubicnbsp;inches.

[ 410 3

PREVIOUS to the late French revolution, the principal lineal meafures of that nation werenbsp;lines, inches, feet, and toifes 11 lines are equal tonbsp;one inch; i2 inches make one foot j and 6 feetnbsp;make one toife.

The Paris a?-pent confifts of 100 fquare perches i each is 18 Paris feet lineal meafure, viz. 324 fquarenbsp;feet, which, multiplied by 100, gives 32400 fquarenbsp;Paris feet (or 36720 fquare Englilh feet) for thenbsp;arpent �, that is, in round numbers, about 4- of thenbsp;Englilh acre. But according to the mejure royale, ^nbsp;perche has 22 feet of lineal meafure, and confe'nbsp;quently is 484 fquare feet, which, multiplied bynbsp;100, gives 48400 fquare Paris feet (or 5485313^nbsp;Englilh feet) to the arpent. This arpent is abovenbsp;I J EngliQi acre. But the former arpent of 3240�nbsp;feet was the meafure ufed about Paris.

The cubic Paris foot or inch is to the cubic Englifh foot or inch, nearly as l,ai to i ; fo thatnbsp;one cubic Paris foot, or inch, is about 14- Englilh.nbsp;cubic foot or inch: hence 5 Paris cubic feet makenbsp;6 Englifh cubic feet. i6 litrons make a hoijfeau 3nbsp;hoijfeaux make one 7ninot; 2 minots make one mine;nbsp;2 mines make one feptier j and 12 feptiers make onenbsp;muid.

The Paris feptier for wheat contains 6912 Paris cubic inches, which are equal to 8363 Englifhnbsp;cubic inches, or 4 Englifh bufhels nearly. Thenbsp;Paris feptier for oats is double the. one for wheat.

72 grains make one grofs, 8 grojfes make one punce, and 16 ounces make one pound. One Frenchnbsp;grain is .very nearly equal to 0,8203 of an Englifhnbsp;troy grain. One ounce poids de marc, which contains 576 French grains, is equal to 472,49 Englifhnbsp;troy grains.

Since the French revolution, all the meafures and quot;Weights of that nation are deduced from the metre,nbsp;which we have already faid to be equal to the 40nbsp;iftillionth part of the whole circumference of thenbsp;earth, and to be equal to 39,371 Englifh inches ;

Thefe new French meafures, as well as the weights, proceed in a decimal order j for inftance,nbsp;the millimetre is the loth part of the centimetre;nbsp;the latter is the loth part of the decimetre, the decimetre is the loth part of the metre, and fo on.nbsp;The numbers which are annexed to the followingnbsp;names of the French meafures, exprefs the numbernbsp;of Englifli inches or Troy grains to which theynbsp;are equivalent.

A litre is nearly equal to 2^ Engllfh wine pints. 14 decilitres are nearly equal to three Engliflinbsp;wine pints.

A decametre is equal to 6 penny weights and *�:44 grains Englifli troy weights, or to 5,65 avoirdupois drams.

A gramrne is the v/elght of a cubic centimetre of pure 'vater at its maximum of denllty.

I HAVE endeavoured in the preceding chapters to give an accurate ftatement of the meaf�fesnbsp;and weights of Great Britain, and of the Frenchnbsp;nation, becaufe thefe have been determined with allnbsp;the accuracy which the prefent ftatc of knowledgenbsp;relative to philofophy and mechanics could fuggeft.nbsp;It is much to be defired, that other nations wouldnbsp;follow their example, aad either eftablifh or makenbsp;known their invariable ftandard, or adopt the mea-fures of one of the above-mentioned nations. Thenbsp;weights and meafures lately eftablilhed by thenbsp;French, are undoubtedly the moft rational in theory,nbsp;the leaft perplexing in praftice, and the moft eafilynbsp;remembered j yet it muft be acknowledged thatnbsp;great innovations of this fort, though evidently fornbsp;the better, are not relifhed by , moft nations. Innbsp;this cafe they might at leaft determine with accuracynbsp;the ftandard of their ancient meafures and weights,nbsp;^nd make kt known to the world for the advantagenbsp;of philofophy and commerce.

In collecting the Hansards of meafures and weights of the principal nations of Europe, I havenbsp;met with a much greater difficulty than I at firftnbsp;expedted. The unfetded ftate of thofe meafures innbsp;certain countries, the variety of meafures ufed innbsp;the fam? country, the difficulty of obtaining diredtnbsp;and authentic information, and the difagreemehtnbsp;between authors who deferibe the meafures and thenbsp;weights of the very fame nation, have prevented thenbsp;making of as complete a ftatement of the generalnbsp;meafures and weights of different nations as mightnbsp;have been vviffied. I have therefore ftated thofenbsp;particulars only which, from the concurrence of thenbsp;moft creditable authors, feem to be beft afeertained.nbsp;In this ftatement the reader will find the value ofnbsp;the different meafures, amp;c. expreffed in Englifbnbsp;meafures and weights.

Sir George Shuckburgh Eyelin, having examined various ancient rules, and having meafured feveralnbsp;ancient buildings, fays, The' mean refult of thefenbsp;� experiments, gave me for the length of the an-� cient Roman foot -nbsp;nbsp;nbsp;nbsp;- ' 11,617 Englifb inches

� rules - nbsp;nbsp;nbsp;- -nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;11,606 ditto.

which is engraven the length of feveral meafures, � from whence I took the following:

quot; The ancient Roman foot=i 'ifizs Englilh inches quot; The modern Roman palm� 8,82 dittonbsp;� The ancient Greek foot � 12,09 ditto*

The ancient Roman mile (by Plinius) tr 4840,5 The ancient Roman mile (by Strabo) - 4903nbsp;The Jiadium of the ancient Romans - 606nbsp;The Jiadium of the Egyptians - -nbsp;nbsp;nbsp;nbsp;- 730gt;8

VOL, IV. nbsp;nbsp;nbsp;EEnbsp;nbsp;nbsp;nbsp;The

The Genoa palm - nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;- -nbsp;nbsp;nbsp;nbsp;-

The Swedilh foot is divided into 12 inches. Th^ Swedilh kannc (which contains 8 quadrantes, eachnbsp;of which contains 12 f Swedilh cubic inches)nbsp;equal to 107,892 Englifh cubic inches. But aOnbsp;Englilh gallon, wine meafure, is equal to 231 cubicnbsp;inchesi therefore the Swedilh kanne is to the Engh^nbsp;gallon as 107,892 to 231 j viz, equal to littlenbsp;than half a gallon.

, nbsp;nbsp;nbsp;9

E 420 3

VoL. III. After the fecond line of the note page 54, add. Though the freezing point of quick'nbsp;filver be �39quot;; yet that metal requires a te(^'nbsp;perature of�45�} in order to alTume its perfelt;^^l^nbsp;folid ftate. . Philofophical Tranfaftions for

Mr. Bouguer, after many trials, concluded, that the light of the fun is about 300000 times greaternbsp;than that of the moon.

Dr. Smith (Optics, Vol. I. Art. 95.) thought that he had proved, from two different confidera-tions, that the light of the full-moon is to our daylight, as one to about 90900, if none of the raysnbsp;incident from the fun upon the furface of the moonnbsp;�Were loft by the irregularities of the latter.

VoL. III. page 115. The experiment, which is defcribed in that page, may be performed with anbsp;fingle refleflor j for if the thermometer be placednbsp;in one of the conjugate foci, and the burning charcoal, or the ice, be placed in the other of chofe foci,nbsp;the fame effedt will take place, but not fo effedually,nbsp;nor at fo great a diftance as when two refledtors arenbsp;nfed.

A remarkable difference is to be obferved between th� radiant heat from the fun, and that from ^ common fire; viz. the former will pafs throughnbsp;^ater, glafs, amp;c. and will hardly heat them j but thenbsp;tadiant heat of a fire, heats thofe fubftances, and isnbsp;^Itnoft entirely flopped by them.

Dr. Hulme, in a fecond paper on the fpontaneous %ht of fifli, amp;c. (Philofbphical Tranfadfions fornbsp;Art. XXI.) relates feveral new expcrinientsnbsp;E E 3nbsp;nbsp;nbsp;nbsp;and

and obl�rvationsj the principal refults of which are contained in the following paragraphs.

� Thefe experiments prove, that objedls which abound with fpontaneous light in a latent ftate, fuchnbsp;as herring, mackerel, and the like, do not emit itnbsp;�when deprived of life, except from fuch parts asnbsp;have been fome time in contact with the air.

� They likewife (hew, that the blaft of a pair of bellows does not increafe this fpecies of light, as i^nbsp;does that which proceeds from combuftion.

� It appears that oxygen gas does not aft upon this kind of light, fo as to render it much more vividnbsp;than it is in atmolpherical air, which is quite con^nbsp;trary to what fome authors have alledged.

It is a remarkable circumftance, that azoti^^ gas, which is incapable of fupporting light fronfnbsp;combuftion, fhould be fo favourable to the fpontan^'nbsp;ous light which is emitted from fifties, as to preferv^nbsp;its exiftence and brilliancy for fome time whennbsp;^lied upon a cork j yet that it fliould prevent thefl^Pnbsp;of the herring and the mackerel from becomingnbsp;minous, and alfo extinguilh the light proceed'*�^nbsp;from rotten wood.

Carbonic acid gas, or fixed air, has alfo an cxtingui/hing property with refpecfl to fpontaneousnbsp;light j but, in general, the light returns, if the ob-jed of experiment be taken out and expofed to thenbsp;open air.

quot; It appears that fulphurated' hydrogen gas ex-tinguifnes fpontaneous Tigln much fooner than carbonic acid gas, and that, in general, the light returns much more flowly when the fubje�t is expofed tonbsp;atmofpheric air.

� Nitrous gas, we obferved to have totally prevented the emiffion of light, and to have quickly extinguilhed that which had been emitted: likewifenbsp;that the luminous objefts which had been under itsnbsp;influence (except the glow-worm) did not experience a revival of their light, when taken out andnbsp;kept for fome time in common air.

quot; A piece of Ihining wood was put under the receiver of an air-pump j the light dlminifhed in proportion as the air was exhaufledj but revived on the re-admittance of the air.

It appears that folar light, when imbibed by Canton�s phofphorus, is fubjedl to the fame laws,nbsp;with refpeft to heat and cold, as the fpontaneousnbsp;light of filhes, rotten wood, and glow-worms, viz.nbsp;lieat difpofes the phofphorus to yield the lightnbsp;tjuickly, but foon exhaufts it; whereas cold pre-

See the fame paper (Philofophical Tranfadions for i8oi, page 426) for an improvement in thenbsp;conftruftion of Canton�s phofphorus.

An ingenious application of the principle mentioned in the above, and a few preceding pages, was lately made by Dr, Wollafton; viz. he ha*nbsp;rendered it capable of meafuring the refra�livenbsp;and difperfive powers of various fubftances. Thenbsp;paper, with the account of thofe improvements, wasnbsp;lately pubiiflred in the Philofophical Ttanfaflions fornbsp;the year 1802. Art. XII. from which I lhall tran-fcribe the following paragraphs.

� Since the range of inclination, within which total refleftion takes place, depends not only on thenbsp;denfity of the refieding prifm, but alfo on the raritynbsp;of the medium adjacent to it, the extent of that rangenbsp;varies with the difference of the denfities of the twonbsp;media. When, therefore, the refradive power of onenbsp;medium is known, that of any rarer mediumnbsp;be learned by examining at what angle a ray of lig^*'nbsp;will be refleded from it.

� In examining the refradive powers of fluids, or of fufible fubftances, the requifite contad is eaftl/nbsp;obtained i but, with folids, which can in few �O-

fiances be made to touch to any great extent, this cannot be effedted without the interpofition of fomenbsp;fiuid, or cement, of higher refradtive power thannbsp;the medium under examination. Since the furfacesnbsp;of a ftratum fo interpofed are parallel, it will notnbsp;effedt the total deviation fo a ray paffing through it,nbsp;and may therefore be employed without rilk of anynbsp;error in confequence.

� Thus, refins, or oil of fafiafras, interpoled between plate-glafs and any other prifm, will not alter the rcfult.

� If, on the fame prifm, a piece of felenite, and another of plate*glafs, be cemented near each other,nbsp;their powers may be compared with the lamenbsp;accuracy as if they were both in abfolute contadbnbsp;with it.

� For fuch a mere comparifon of any two bodies, a common triangular prifm is beft adapted; but,nbsp;for the purpofe of adtual meafurement of refradtivenbsp;powers, I have pi eferred the ufe of a fquare prifm,nbsp;becaufe, with a very fimple apparatus, it fhews thenbsp;fine of refradtive power fought, without the need ofnbsp;any calculation.

� Let A, fig. 14, Plate XXVIII. be a fquare or redtangular prifm, to which any fubftance isnbsp;applied at and let any ray of light, parallel tonbsp;ci, be refradled through the prifm, in the direction bde.

� Then, if e f and ^ ^ be taken proportional to the fines that reprefent the refradtive powers of the prifm,

and of air, fg, which is intercepted between/) and the perpendicular eg will be the correlponding finenbsp;to reprefent the refra�liv,e power of the medium b.nbsp;For, fince e dg (oppofite to ef) is the angle of re-fraftion, efg (oppofite to ed) muft be equal tonbsp;the angle of incidence bdh\ and ef-.fg-.-.bd-.nbsp;dh : : fine of chi : fine of hb d.

� All therefore that is requifite for determining the refraftive power of is to find means of mea-furing the line On this principle the inftrument,nbsp;fig. 15, Plate XXVIII. is conftrudted. On a boardnbsp;ab n fixed a piece of flat deal cd, to which, by anbsp;hinge at d, is jointed a fecond piece de, ten inchesnbsp;long, carrying two plane fights at its extremities.nbsp;At r is a fecond hinge, connefting ef 1^;%^ inchesnbsp;long; and a third at the other extremity of ef, bynbsp;whichis connefted with it. At i alfo is a hinge,nbsp;uniting the radius ig to the middle of ef-, and then,nbsp;fince g moves in a femicircle egf, a line joining e andnbsp;g would be perpendicular to � g.

� The piece c d has a cavity in the middle of itj fo that when any fubftance is applied to the middlenbsp;of the prifm P, it may continue to reft horizontallynbsp;on its extremities. When ed has been fo elevatednbsp;that the yellow rays in the fringe of colours (ob-fervable where perfeft refledtion reminates) are fe^�nbsp;through the fights, the pointy, by means of a verniernbsp;which it carries, Ihews by infpedlion the length ofnbsp;the fine of refradtion fought.

above the ufual mode of examining refraftive powers, are greater than they may at firft fightnbsp;appear.

The facility of determining refraftive powers, is confequently fuch as to render this property of bodies a very convenient teft in many philofophicalnbsp;inquiries. For difcovering the purity of eflentialnbsp;oils, fuch an' examination may be of confiderablenbsp;utility, on account of the fmallnefs of the quantitynbsp;requifite for trial.�

For fuch purpofes, the refractive power of opaque fubftances, which could not be learned by any meansnbsp;at prefent in ufe, may often be defervingof inquiri-.nbsp;For, in the ufual mode, a certain degree of tranfpa-rency is abfolutely neceffary ; but, for trial by con-tafl:, the moft perfect opacity does not occafion thenbsp;leaft inapediment.

�With refpeft to the experiments which Dr. Wol-lafton made with the above-mentioned machine, I muft refer the reader to the paper itfelf.

FINIS.

., ..I:' nbsp;nbsp;nbsp;■;!a;;irf3:;STr'tfcivVvy ;

,' nbsp;nbsp;nbsp;. .nbsp;nbsp;nbsp;nbsp;.,nbsp;nbsp;nbsp;nbsp;r'.i-vi^y quot;s gt;cgt;)p

- • . nbsp;nbsp;nbsp;■nbsp;nbsp;nbsp;nbsp;r;gt;nbsp;nbsp;nbsp;nbsp;'.lir-t'J'jV

INDEX.

Adhefion, of two leaden bullets, ii. 141�of folids, ii. 142. Adjutages, ii. 185�different, their a�ions, ii. 187.

Aerial, fluids, u. zoo�fluids, their expanfibility, ii. 40� telefcope, ii. 277�voyage, the firft, iv. 327.

Aeroftatic machines, difcovery of, iv. 319-,-particulars relative to their c mltruftion, iv. 331. 330. 354.

Air, atmofpherical, ii. 198�neceffary to animal life, to cotti-buftioD, amp;c. ii. 199�its chemical properties, ii. 200.520�

its mechanical properties, ii. 200�its invifibility, ii. 203�� its preffore, ii. 198; 204. 206. 220�its claftkity, ii. 221-i-its compreffibility, ii. 222�table of its expanfion, ii. 273��nbsp;theory of its movements, ii. 280�ufe of its movements, ii.nbsp;402�veflel of a forcing pump, ii. 434�pump^ defcribed, ii.nbsp;465�oxygen, ii. 520�its refiftance, ii. 480, 481, 482�itsnbsp;weight, veliel proper for afcertaining it, ii. 489-�its expanfionnbsp;by heat, iii. 41. 43�^its eleftricity, iii. 437. 442�balloons^nbsp;iv. 321��tbeir powers, iv. 350�their ufe in general, iv. 350.

Alkali, 13, ii. 533, 534�vegetable, 13�foflil, 13�volatile, 13) S34-�fixed, ii. 5. 33.

Altitudes, meafured by the barometer, ii. 248�table of, ii. 258 �the belt method of meafuring them by means of the barometer, ii. 269.

Amplitude, of projeflion, 34!. 350�of projeftion, greatefi# 24.1,�of projeflion, determined,,34.2-�of a jet of fluid, ii.nbsp;196�of a celeftial objefl, iv. 25.

Angle, of elevation in projefling engines, 341. 334�of reflection, how meafured, iii. 163�of incidence and refraftio'�' proportion of their fines, iii. 169�of difperfionor diflipatJO'�'nbsp;iii. 172�of mean refradlion, iii. 172�of deviation, 180-quot;nbsp;fpheric, iv. 38.

INDEX.

Anomaly, iv. 83 � equated, mean, amp;c. iv. 83�excentric, iv. 84.

Apfides, iv. 82, line of, iv. 82�motion of the line of, iv, 83. Aqueous humour of the eye, iii. 244.

Artificial magnets, iii. 513.520. 545. 549�Canton�s, iii. 550. Afcending node, iv. 129.

Afterifins, or conftellations, iv. 36. 207.

Aftronomical, telefcope, iii. 274�inftrutpents, iv. 268�quadrant, iv, 268.

Aftronomy, ii. 6, iv. i.

INDEX.

ii. nbsp;nbsp;nbsp;220. 484�its lienfity and altitude, ii. 226�115 deniitynbsp;different at different diftances from the earth, ii. 227. 229�nbsp;its altitude influenced by the fun and the moon, ii. 242�itsnbsp;flux and reflux, ji. 245, amp;c.�ufes of, ii. 396�eledlrical, iii.nbsp;353-359.400�of the moon, iv. 118.

Atmofpherical, eleftricity, iii. 436�eledricity, laws of, iii. 442 �eleiflrometer, iii. 438.

Attra�lion, 37. 54. ii. ig�proportionate to the quantity of matter, 55�four fort? of, ii. 19�of aggregation, ii. 19. 23.nbsp;�40�of cohefion, ii. 20. 23. 496�of compofition or of affinity, ii. 20.496�of water to glafs, ii. 117. 132�of waternbsp;in capillary tubes, iL 121�amongft other bodies, ii. 132.nbsp;134. 136�of mercury, ii. 133. 135. 138�corpufcular, ii.nbsp;170�between air and water, ii. 410�of eledricity, iii. 336.nbsp;359. 40Z.�magnetic, iii. 513. 516.

Aurora, borealis, ii. 7�Auftralis, ii. 7�fuppofed to be an eledrical phenomenon, iii. 444�affeds the magnetic needle,

Axioms of philofophy, 5�refpeding the declination of the magnetic needle, iii. 538.

Axle, or Axis, 220�in peritrcchio, 231�of a refledor, i�-156�of a magnet, iii. 528 � of a lens, iii. 228�of the world, iv. 22.

Balance, 221, 228�defeds of, 229�of forces, 121�hydroft�' tical, ii. 55.nbsp;nbsp;nbsp;nbsp;�

Balloons, air, iv. 321�their powers, iv. 350�their ufe m g^' neral, iv. 350. 352.

Barometer, or Barofcope, ii. 208�indications of the weather from its various altitudes, ii. 209�its mean altitude, ii.nbsp;its ufe in meafuring altitudes, ii. 232. 248�a regular

INDEX.

ment of, obferved at Calcutta, ii. 256�its conftru�ion various, ii. 456�Ramfden�s, ii. 464.

Battery, eleftrical, iii. 366. 387�voltaic, iii. 474. 482. 486. Benzoic, radical, 13, ii. 16.

ii. nbsp;nbsp;nbsp;70�of air, not mere nothing, ii. 202�indicate the ftrengthnbsp;of fpirits, ii. 202.

Black lead, its ufe in diminiftiing friction, 277�lead, ii. 53*�� objefts, perception of, iii. 259,

Caloric, iz�ii. 15, 16. 516�combined, ii. 518�iii. 9�free, ii. 518�iii. 10�iii. 2�theory of, iii. 3.9�fpecific, tafclenbsp;of, iii. 70�total privation of, iii. 76.

INDEX.

Calorimeter, iii. 8o.

Cannons, 342�experiments with, 354-�proper charge of, 356. Capacities of bodies for caloric�iii. 7. 63. 66. 79�permanent.

Cauftics by refleftion, iii. 155�by refraftion, iii. 220. 236. Celeftial atlas, iv. 17�globe, iv�planifphere, map, or plate-

Centre, of attraftion, 54�of repulfion, 54�of gravity, 58�of gravity how afcertained, 74�of gravity how afcertained bynbsp;the method of fluxions, 78�of gravity of a ftraight line, Stnbsp;�of gravity of a cone, 83�of gravity of an hemifphere, 83nbsp;�of gravity, ufe of, exemplified, 323. 325�of gravity, im'nbsp;proper ufe of, 327�defcent of, ii. 26�of ofcillation, 200�nbsp;201�of ofcillation is the fame as the centre of percuffioO/nbsp;203�of percuflion, 201.

Charge of a Leyden phial, does not difplace the air, iii. 419* Charged eleftrics, iii. 362, 363.

' Charts of magnetic declination, iii. 531.

I N D E Xi

Circle, divifion of, iv. 6�greater and lefler of a fphere, iv. 38 �of vifion refpefting the moon, iv. 12J.

Circles fimple galvanic, iii. 476�the moft adlive, iii. 478,479, 480�have a pofitivc and a negative eledlric fide, iii. 481�nbsp;their aftion, iii. 490.

Clouds, luminous, 8, ii. 8. 404. 410�formation of, ii. 412�are generally eleftrified, iii. 437.

Cold, iii. 3. 10�a privation of caloric, iii. 86�communication of, iii. 89�refledled, iii. 116�produftion of, iii. 118�produced by ventilation, iii. ii8�produced by evaporation, iii.nbsp;119�produced by the application of ice, iii. 122�producednbsp;by the folution of falls, iii. 124�^produced by the expanfionnbsp;of air, iii. 128.

Colours, of light, iii. 172, 173. 180�compounded, iii. 188� by inflexion, iii. 202�of thin plates, iii. 206�Newton�snbsp;theory of, iii. 212�produced by various means, iii. 215�nbsp;prifmatic, marked upon glafs by the force of eleflricity�nbsp;iii. 369.

Combinations, limple, ofconduftors, laws rcfpeflir.g them, iii. 474�of the firft and fecond order, iii. 476.

INDEX.

Comets, �. 6. iv. 19. 189�their parallax, iv. 198�-their nu-deous, iv. zoi �their beards, comas, hair, or tails, iv. 201. Comma, ii. 3^6.

Compafs, mariner�s, iii. 529�different forts of, iii. 562�bell fort of, defcribed, iii. 563, 564,�azimuth, iii. 565.nbsp;Compoiition of forces, 124, 125.

Compreffibility of non-elallic fluids, ii. 21�of air, ii. 222. Condenfer of eleftricity, iii, 424.

Condudors of eleftricity, ii. 519�of heat, ii. 517. iii. 6. 338� eledrics, lift of, iii. 341�for the lightning, iii. 447�combinations of, and their effeds, iii. 474�perfed and imperfeft,nbsp;iii. 474�in magnetics, iii. 550.

Conftellations, iv. 36. 207. ato�-of the zodiac, iv. 37. 210, Contraded vein, ii. 182.

INDEX.

Curves, logarithmic, their principal properties, li, 233�ufeful for illuftrating the various denfities of the atmofphere �nbsp;ii. 233.

Cycloid, I78�its generating circle, 178�-its bafe, 178�its axis, 179�its properties, 179.

Declination ofthe magnetic needle, iii. 514. 530�lines of,iii. 531 �charts of, iii. 531�lift of, iii. 532�hourly, iii. 537�meannbsp;for each month, iii. 537�axioms refpedling it, iii. 338.nbsp;Declination, of celeftial objedts, iv. 32, 43�^of the fun, iv. 43��nbsp;circles of, iv. 44.

Diamond, the hardeft body known, ii. 148 � the body of greateft refraftive power, iii. 178�combuftible, iii. 178.nbsp;Diaphragm, iii. 286.

F � 3 nbsp;nbsp;nbsp;Dipping,

INDEX.

Dipping, of the magnet, iii. 515�-needle, iii. 541. 566�in various places, iii. 544. nbsp;nbsp;nbsp;'

Difcharge of fluids through different apertures, ii. 187�hindrances to it, ii. 189.

Difperflon of light, iii. 172�angle of, iii. 172�by different media, iii. 173. 175.

Diftance, of objefts, how judged of, iii. 257. iv. 5, 7. 42-�� mean of planets, iv. 82.

Diurnal, arch, iv. 49�rotation of the earth and planets, iv. 97 �motion of the moon from the fun,'iv. 128.

Earth, a planet, 6-�dimenfions of, ii. 9. iv. 13�gravitation of, 34�decreafe of its gravitation, 61�divifion of its furfaee,nbsp;10�a great magnet, iii. 546. 555�its figure, iv. u.nbsp;Earthquakes, affedl the magnetic needle, iii. 538.nbsp;Earthen-ware, ii. 532.

Ebbing and flowing wells, ii, 430�of the fea, Iv, 147, 14^-Echo, ii. 399. 344.

Eclipfes of the fun and of the moon,iv, 125, 251. 261�of ^ fatellites of Jupiter, iv, 178. 262.

Ecliptic�

Elafticity, of metallic fubftances, ii. 147�of air, ii. 221�of air, not diminilhed by long continued preffure, ii. 225.

Ele�rical, machine, iii. 337�atmofpheres, iii. 353. 359. 422�battery, iii. 366�machine and apparatus, defcribed,nbsp;iii. 378�experiments, iii. 395�machine of Harlem, iiL 385nbsp;�machine, management of, iii. 395�organs of fifties, iii.nbsp;4SI;

Eledlric, fluid, 12, ii. 15,16.519�appearances,iii. 337�ftiock, ii-. 362�fluid, courfe of, ftiewn by the flame; of a wax taper,

ii. nbsp;nbsp;nbsp;418�jar, iii. 365�well, iii. 399�atmofpheres, iii. 400�nbsp;fluid, courfe of, ftiewn by thedifcharge of ajar, iii. 417.

iii. nbsp;nbsp;nbsp;336. 359�light of, iii. 336. 337�vitreous and refinous,nbsp;iii. 344. 347�theory of, iii: 349�plus, or pofitive, minus, ornbsp;negative, iji. 349�communicated, iii. 352. 361�its effeftsnbsp;upon animals and vegetables, iii. 357. 367�tafte and fmellnbsp;of, iii. 358�its paflage from one body to another, iii. ^53.nbsp;359�its adion on the human body, iii. 376�produdionnbsp;of, iii. 421�how to afcertain the exiftence of a frsall quantitynbsp;of it, iii. 422�produced by melting and coagulation, iii. 429nbsp;�produced by heating or cooling, iii. 431�produced by evaporation, iii. 434�atmofpherical, iii. 436. 442�animal, iii.nbsp;451�produced by the contnfl of metallic bodies and othernbsp;conduftors, iii. 472�its identity with Galvanifm, iii, 508.

Eledlrics, iii. 337�par Je, iii. 338�lift of, iii. 339�charged, iii. 362�coated, iii. 386.

Eledrometer, or eleftrofcope, iii. 346. 389�Canton�s, iii. 390 �-quadrant, iii. 390�-atmofpherical, iii. 438�bottle, iii. 392.

Engines, fire, ii. 436�fcrew for raifing water, ij, 437�compound, 253�cftimation of their powers, 253.

F F 4 nbsp;nbsp;nbsp;Equation,

INDEX,

Equator, of a magnet, iii�528, or equinodlial, iv. 26. 98. Equatorial inllrument, iv. 276.

Evaporation, ii. 403�promoted by the wind,- by agitation, by heat, ii. 404��quantity of, how meafured, ii. 406�in London, ii. 408�^at Liverpool, ii. 408�fafts relative to itj ii.nbsp;411�inchemiftry, ii. 50j�produces eleftricity, iii, 434. 446.nbsp;Evening liar, iv. 67.

Experiments, with the air-pump, ii. 476�eafy to illuftrate the properties of lenfes, amp;c. iii. 235�eleftrioal, iii. 395.nbsp;Expanfion of air, table of, ii. 273�of mercury, table of, ii. 254nbsp;�by heat, iii. 4. 12�of fluids, iii. 26�of aerial fluids, iii. 40nbsp;�of folids, iii. 58.

Fermentation, ii. 554�vinous or fpirituous, ii. 534�*-acetousgt; 5SS�putrid, �.555.

INDEX.

Fire, iii. 3�-engines, ii. 436�places, general rules concerning their conftru�lion, iii. 100.

Fixed, alkali, ii. 533�liars, iv. 29. 206�liars, their dillances, �zes, amp;c. not known, iv. 74�liars, their apparent magni^nbsp;tudes, iv. 206�liars, telefcopic, iv. 207.

Fluids, ii. 2�perfedl, ii. 22�-particles of, ii. 23�different, their preffure againft each other, ii. 42�non-elallic, theirnbsp;adlions When in motion, ii. 99�their compreffibility, ii. 21�nbsp;their motion through holes, pipes, amp;c. ii. 166�theory ofnbsp;their motion, ii. 167�their motion in open channels, ii.nbsp;170�-their motion through apertures, ii. 177�their lateralnbsp;communication of motion, ii. 178�permanently elallic, iLnbsp;200. 518.

Focus, of the rays of heat, iii. 106. 109. 111�of the rays of light, iii. 136�virtual, iii. 134�principal of a convex reflector, iii. 154�-of incident rays, and of reflefted rays, iii. 156nbsp;principal of a concave refleftor, iii. 136�of a lens, iii.nbsp;218. 228�of incident and of refradled rays, iii. 218, virtual,nbsp;iii. 154. 219�of lenfes, how found out, iii. 228, 230,236.

INDEX.

Frogs, their great fufceptibility of eledricity, or of Galvanifm, iti. 462. 464. 490�bell preparation of for Galvanic experiments, iii, 467.

Galvanic; batteries, fee Voltaic batteries�-circles, iii. 476. 478 �circles of the firft order, iii. 479�circles of the fecond order, iii. 480.

Galvanifm, iii. 462�its identity with common eledlricity, iii* 508�probably ufeful in medical cafes, iii. 501.

Gas, ii. 520�various fpecies of, ii. 521�produced by the adlio** of the Voltaic batteries, iii. 501.

INDEX.

Globes, terreftrial and celeftlal, iv. 14. 17. 281�defcription and ufe of, iv. 282�problems to be performed with them,nbsp;iv. 300.

Gravitation, 21. 37�of the earth, 54�decreafe of, 61. Gregorian, telefcope, iii. 284�ftyle, iv. 62.

Gun-powder, fired in vacuo, ii. 540�its force attributed to the expanfion of water, iii. 32.

Hardnefs, 16, ii. 139�of different fubftances,.�. 145, 146. 14S �of metals and femimetals, ii. 147.nbsp;nbsp;nbsp;nbsp;^

Heat, elementary, iii. 9�lift of the effefts produced by certain degrees of, iii. 50�latent, iii. 67�produdlion of, iii. 87. 93.nbsp;97�communication of through fluids, iii. loi�emanationnbsp;of, iii. 104�refie�ion of, iii. 115.

Horizon, fenlible, iv. 19�rational, iv. 20�its eaflern and weftern Tides, iv. 21.

Humid way of performing chemical operations, ii. 312. Hunter�s moon, iv. 136. 140.

Hydrogen, la, ii. 15. 520. 546�gas, ii. 520�gas, its expan.-'' fibility, iii. 40�gas, combuftion of, iii. 83�gas, fulphurated, ii. 521�gas, carbonated, ii. 522�gas, phofphorated, ii. 521nbsp;�gas of marlhes, ii. 522.

Hydrometer, ii. 66�recommended in certain cafes, ii. 71. Hydroftatical balance and apparatus, ii. 55. 70�bellows, ii,nbsp;443-

Hygrometer, or Hygrofcope, ii. 412�-principle of, ii. 418�� De Luc�s, defcribed, ii. 420�its mean height, ii. 423�nbsp;Leflie�s, ii. 423�De SaulTure�s, ii. 429.

Ice, iii. 4�houfes, iii. 122�how produced in India, iii, 123. Jet of fluid, ii. 190. 193�table of the heights of, ii. 195�itsnbsp;amplitude, ii. 196.

Image formed by refraflion, iii. 233�its brightnefs, iii. 234, Impenetrability, 21. 32.

Inclination, of the magnetic needle, iii. 515�of the planetary orbits, iv. 82.

Inclined, planes, defeent of bodies upon, 164�plane, 221. 239. Indiiftion, iv. 248.

Iron

Kite, flying, 8�ele�lrical, defcribeti, iii. 4i).i�eleftrical, laws deduced from the experiments made with it, iii. 443.

Latitude, it-. 40�parallels of,iv. 40�of celeftial objefts, iv. 4J �in what manner is to be afcertained, iv. 285. 288.

Lenfes, iii. 216�various forts of, iii. 317�centres, axes, an' vertexes of, iii. 317�their aberrations or irregularities,nbsp;220, 221�their eflefts, iii. 262�combinations of, iii. 267'.nbsp;Lever, 220. 324.

Light, 12, ii. 15, 16. 516. iii. 133�Defcartes�s theory 133�Newton�s theory of, iii. 134�duration of its impi� .nbsp;upon our eyes, iii. 135�motion of, iii. 136.139,

INDEX.

des of, iii. 137�momentum of, iii. I37-.�refleflion of, iii. 141. 144�incident, iii. 141�infleftion of, iii, T42�pencilnbsp;of, iii. 142�whether material, iii. 321�loft by refledlion,nbsp;how meafured, iii. 165�white in the Iky, iii. 313�zodiacal,nbsp;iii. 313�eleftrical, iii. 336�charafteriftic of the two eledlri-cities, iii. 346�.nbsp;nbsp;nbsp;nbsp;,

Lightning, ii. 8�an eleftrical phenomenon, iii, 436�conduftors for it, iii. 447.

Line, of fwifteft defcent, 195�of direftion, 227. 324�of afpedl, iii. 304�of magnetic declination, iii. 531�of no declination,nbsp;iii. 531�magnetical, iii. 542�or the equator, i\'. 40�of col-limation, iv. 271.

Logarithmic curves, their principal properties, ii. 233�analogous to the denfities of the atmofphere, ii. 233�atraofpheri-cal, ii. 241.

Longitude, in geography, iv. 40�of celeftial objcfls, iv. 45� how found out, iv. 295.

Magnet, iii. 331�affedted by eledlric fiiocks, iii. 370�natural and artificial, iii. 512, 313. 520�ifs armature, iii. 523��nbsp;horfe-fhoe, iii. 523�its attraftion and diredlive power, iii.nbsp;513.524. 549�compound, iii. 549.

Magnetic fluid, 12, ii. 15. 16. 519. iii. 557�properties, iii. 512 ��polarity, iii. 514�poles, iii. 514. 527�meridian, iii. 514

INDEX.

lieedle, i�. 514�iuftruments of three forts, Hi. 562�expert^ merits, iii. 5^7. 525�attradion and repuliion, iii. 516. 525�nbsp;experiments faid to have been made with an air-balloon,

Magnetii'm, iii. 512�communicated, iii. 545. 547. 553�of the earth, iii. 546--theory of, iii. 555.

Magnifying power, of lenfes, iii. 265, 266�of telefcopes afcer* tained, iii. 276. 280. 284. 286. 289�of microfcop�s, iii. 295,nbsp;296, 297.

Maximum of the a�iion of a fluid, on the fails of a- wind-mill, of the rudder of a fttip, amp;c. ii. 111.

Mean, arithmetical and geometrical, ii. 231�temperature of a country, iii. 86.

Meafures, ii. 97�ftandard, iv. 393. 395. 397, 398�Britifti, iv, 400. 407�French, iv. 410�of various countries, iv. 417.

Mercury, 13, ii. 16�table of its expanflbility, ii. 254�1*3 freezing point, iii. 53�amalgam of, with other metals, fom*nbsp;tarnifties, iii. 473�the planet, ii, 5. 528, iv. 170.

Meridian, magnetic, iii. 514�aftron�mical, iv. 23�line, how drawn, iv. 283�uniyerfal or brazen, of globes, iv. 284-

Metallic fubftances, ii., 525. 527�their diflblution, ii. 548,549 fufedby means of eiedlricity, iii. 368, 369. 371. 411,4*�'^nbsp;their adlions upon e.ach other, iii^473.

Metre, French, reduced to Englith meafures, iv. 13. 398.412, Micrometer, iii, 291�mother-of-pearl, iii, 292'�-value of, hownbsp;afcertained, iii. 293�for microfeopes, iii. 298.

Microfcope, iii. 263. 294�folar or lucernal, iii. 295-�Ample, limits of, iii. 295�compound, lii. 296�aquatic, reflefling,nbsp;opaque, Wilfon�s, and rehefting, iii. 298.

Momentum, 46. 49�of Ihots, 341. 358�of the .wind, how afcertained, ii. 45 r.

Moon, ii. 5, 6.�mock, ii. 8�its light affords no fenfible heat, iii. 95. 311�horizontal, iii. 258�its proper movement, iv. 33�its phafes, its cufps, and its firft quarter, iv,nbsp;33�full,,, and its laft quarter, iv. 34�its phafes, motions,nbsp;apparent fize, diftance, fpots, amp;c. iv. m.

Moons or fatellites, ii. 5, 6, iv. 72. iKtoral philofophy, i.-r-its etymology, 2.

Motion, 15.40�abfolute, 15�relative 15,16�of bodies in their defcent towards the earth, 61�accelerative, 61�compound,nbsp;114�reftilinsar, and curvilinear, 134�theory of equablenbsp;motion in. circular orbits, 138�judgment of frequentlynbsp;'�01. ir.nbsp;nbsp;nbsp;nbsp;c Gnbsp;nbsp;nbsp;nbsp;miftakcn.

INDEX.

millaken, iii. 259�in antecedentia, or in confequentia, direiS or retrograde, iv. 83, 84.

Nitrous, gas, ii. 521�acid, ii. 524�produced by the adliott of eleflric Ihocks upon certain gafes, iii. 373.

Nodes, of the planetary orbits, and line of, iv. 81. 129�of orbits of the fatellites, iv. 177.

Non-conduftors of eleftricity, ii. 519�iii. 338�lift of, id- 339' Non-elaftic bodies, 91.

INDEX.

Oil, its ufe for reducing friflion, 277�^its elFefts upon water, ii. 161�ufed by feamen in certain cafes, ii. 162, 163�lightnbsp;volatile, do not produce the fame effeft upon water, as the fatnbsp;oils do, ii. 165�fat or volatile, ii. 552.

Oxigen, 12, ii. 15�air, ii. jzo�quantity necelTary in certain combuftions, iii. 83.

INDEX.

Parallax, of comets, iv. 198�of celeftial objedls, iv. 22z�of latitude, of longitude, of right afcenfion, and of declination,nbsp;iv. 227�of the great orbit, iv. 102.

Pendulum, 174�the length of, when it vibrates feconds, 1.94� compound, iii. 61�ufed as a ftandard of meafure, iv. 395,nbsp;397�its vibrations in different latitudes, iv. 396.

Percuffion, centre of, 201�its fituation afcertained, 207. 209. Perigee, iv. 83. 131.

Phofphorus, 12, ii. 15. 523. iii. 316�Baldwin�s, iii. 318�com-buflion of, iii. 83.

Pipes, tuning, ii. 383�of an Organ, altered by heat and cold� ��s�-�-nbsp;nbsp;nbsp;nbsp;ri.ck,

INDEX.

Fitch, of founds, ii. 354. 337, 358�concert, ii. 383�affefted by heat and cold, ii. 384.

Planets, ii. 5�their charafters, iv, 35. tg*�Ihine by reflefting the light of the fun, iv. 66�primary and fecondary, iv. 73�nbsp;inferior, iv. yg�fuperior, iv. 80�their diameters, periods.nbsp;Sic. amp;c. iv. 162.

Plate, flat glafs, its effe�t with refpeft to refradlion, ii. 226. Platina, 13, ii. 16. 527�attra,dted by the magnet in certainnbsp;cafes, iii. 525,

Poles of the world, iv. 22�of the horizon, iv. 23�-of the earth, iv. 26�of a circle, iv. 39.

PrelTures, 124�on the bottoms or fides of veffejs, containing ^ fluids, ii. 33�centre of, ii, 37.

INDEX.

Prime, condudlor of an eleftrical machine, iii. 37S. 380�con-duftor, pofitive or negative, iii. 399�vertical, iv. 24.

Projedliles, 338�their paths deviate from parabolas, 330. 333 �greateft, 341.

Properties of matter, 2. 4. 10. i6-i-genera], 21��paljive and aftive, ii. 19.

Pump, water, ii. 431�water, ellimate of its power, ii. 433�* forcing water, ii. 434�air, defcribed, ii. 463�Ihort hiftorynbsp;of, ii. 467.

Quadrant, aftronomical, iv. 268�moveable, iv, 269�mural, iv-271�of altitude, iv. 299.

Rain, ii. 8. 298. 404. 410�fafls relative to, ii. 411, 412, 413*� quantity of, ii. 413, 414, 415�gage, ii. 412. 414. 424quot;^nbsp;generally eledlrified, iii. 437. 442--bow, ii. 7, iii. 30!. jC�

INDEX.

Ranges of fhots, 341�method of determining them, 342�are as the charges of powder, 354.

Rays, of heat, iii. 104�reflefted, iii. 106. 115�refrafled, iii. io8�of light, iii. 142�of light from a luminous point, iii.

Refleftion, of light, iii. 141�angle of, iii. 141�lawsof, iii-146�from a flat furface, iii. 147�from a convex furface, iii. 149. 153�from a concave furface, iii. i;o. 154.

Refleftors, iii. 141�of various fhapes, iii. i6i�parabolical, iii. 162�flat, iii. 163.

�of water, glafs, and diamond, iii. 170, 171�increafed a little by heat, iii. 174�table of, in different mediums, iii.

r�of longitude, of latitude, of right afcenfion, and of dedi* nation, iv. 230.

Rivers, ii. ii, 173�permanent ftate of, and thread, of, ii. �proportional lengths of various, ii. 174-�inesjuality of thenbsp;motion of, ii. lyj�ufe of, ii. 177.

Rotation, diurnal of the earth and other planets, iv. 97. Rubber for exciting eleftrics, iii. 337. 379. 386,nbsp;Rules of philofophying, 7,

Screw, 221. '248,, 249�threads of, 249��engins for raifing water, ii. 437.

Sea-water, quantity of fait it contains, iii. 39�its freezing point, i�id�purified by freezing, ffoV.

Security, perfonal, in time of a thunder ftorm, iii. 449; Semicircle of pofition, iv. 299.

Sieve,

sieve, �. 498.

Sounds, ii. 279. '309�ftronger in denfe air, ii. 310�variety of, 310�height of, ii. 311�Ilrength of, ii. 311�quality of,nbsp;ii, 313, 314�.high or low, acute or grave, lharp or flat, ii.nbsp;311�Ample, ii. 314�velocity of, ii. 329�heard fromnbsp;great diftances, ii. 340�tranfmitted through folids, ii. 336nbsp;�refleaion of, ii. 344�mufica), ii. 353�fcak of, ii. 372.nbsp;583. 357�conveyed by the air, ii. 402.

Spark, eleftrical, iii. 336. 335. 366�efFefts produced by it upon animals, .amp;c. iii. 356�upon vegetables,, iii. 357�rarefies

INDEX.

Specific, gravity, ii. 42. 52.�gravity, rules for determining it, ii. 56�gravity, table of, ii. 74�gravity, ufe of, ii. 65�nbsp;attra�lion, ii. 134�caloric, fee caloric,

Stars, ii. 6, iv. 19�fixed, 29, iv. 206�falling, ii. 7�great number of, iv. 213, 214, 215�changes among them, iv,nbsp;217�their peculiar movements, iv. z 17. 241.

Steam, ii. 410, iii. 4�.slaffic, force of, at diffei'ent degrees of temperature, iii. 34.

Stones laid to have fallen from the Iky, iv. 369, 372, amp;c.�their mineralogical defcription, iv. 384�their analyfis, iv. 38�-rnbsp;hypothefes concerning their origin, iv. 388.

Strings of mufical inftruments, lengths of, ii. 373, 373. 383. Strontian, 13, ii. 16. 529. 532.

347-

Syftem of the world, or folar, iv. 64-~variou5 hypothefes concerning it, iv. 69.

Telefcope, dioptric, iii. 274�catadioptric, or reflefling, iii. 274, 282�aftronomkal, iii. 274�aerial, iii. 277�terrellrial,nbsp;iii. 278�-Galilean, iii. 279�night, iii. 280, iv. 279�Gregorian, iii. 384�Calfegrainlan, iii. 287�Herfchel�s, iii.nbsp;z88�zenith, iv. 279,

Tellurite,

Temperature, iii. 10�mean, of a country, iii. 86. 90�mean, of Paris, iii. 90�mean, of London, iii. 91�mean, of pits,nbsp;wells, amp;c. iii. 89.

Theory, of the motion of fluids, not confonant with expert, ments, ii. 166, 167. 170�of heat, iii. 3. 8�of magnetifm,nbsp;iii. 555�of chemiftry, ii. 514�of eleilricity, iii. 415�ofnbsp;univerfal attra�ion, iv. 87.

Thermometers, iii. 13�mercurial, iii. 14. nbsp;nbsp;nbsp;�fpirit, iii. 14�

different, iii. 18, 19. 21�for Ihewing the higheft degrees of heat and cold that have taken place during the abfence ofnbsp;the obferver, iii. 23�for the higher degreec of heat, iii. 43nbsp;, �Afhard�s, iii. 43�Wedgwood�s, iii. 44. 47�extent ofnbsp;their principal fcalcs, iii. 49 �correfpondence of Fahrenheit�snbsp;I and Wedgwood�s, iii. 50�axioms refpedling their indications, iii. 91 �their proper fuuadon, iii. 92.

Time, abfolute and relative, 16�in mufic, how denoted, ii. 580�in limple motion, 49�divifion of, iv. 242�mean, iv.nbsp;243�equation of, iv. 244.

Tones, ii. 356�major and minor, 11.372. 376�names of, ii. 372�principal, ii. 374. 376�of a natural voice, ii. 381�nbsp;tnufical, notation of, ii. 380.

INDEX.

Vibration, 176�of firings, ii. 315. 318. 373�figures, ii. 324� nodes, ii. 325�longitudinal, ii. 322�number of, performednbsp;by mufical firings in one fecond, ii. 360. 362. 364.

INDEX.

Voltaic batteries, iii. 474. 482. 486�their powers, iii. 494� give a weak charge to a common Leyden phial, iii. 497�nbsp;affeft the eleftrometer, iii. 498�r-give fparks, burn combufti-ble bodies; amp;c. iii. 497. 499, amp;c.�their chemical effefls,nbsp;iii. 501. 503.

Water, its decompofition, ii. 541�its formation, ii. 546�^8 boiling point, iii. 31. 34, 35�its expanfion'by cold, iii. 33nbsp;36�freezing, iii. 36, 37, 38�under the receiver of an air-pump, ii. 478�pump, ii. 431, kc Pumf�works at Londonnbsp;bridge, ii. 436�fpouts, ii. 8. 14, 303�bath, ii. 511.

Waves, their'a�lion, ii. 153. 155, 156�their breadth, ii. 135 �their heights, ii. 157�refleaed, ii. 159�on differentnbsp;.fluids, ii. 160.

Weather, glafs, ii. 208�in great meafure indicated by the barometer, ii. 209�indicated in fome meafure by the moon, ii. 218.

Weights, abfolute and relative, ii. 42, 43�Britilh, iv. 405� French, iv. 410. 413�.4 m Herd am, iv. 419.

Wheels, 330, 331�friftion, 278�their moft ufeful figure in certain cafes, 333. 333.

Wind, ii. 8. 279�its various names, velocities, and aftions, ii-287. 290�its more ufual diredlion in particular places, h' 294�eftimates of its force and duration, ii. aSg�trade, ii. 8.

aftion upon founds, ii. 232�table of its force and . velocity, ii. 434�its aftion upon water, oil, amp;c. ii. 157. 160,nbsp;161�gage, ii. 449�pipe, ii. 398.

Year, mean folar, iv. 30. 247�folar and aftral, iv. 56�civil, iv. 59. 247�Julian, or BiHextile, or Leap, iv. 60�Lunar,nbsp;iv. 247�anomaiiftical, iv. 96. 247.

viz. Ceres Ferdinandea, and Pallas, which have been difcovcred fince that ftieet was printed. ,

�� 9, the dimenfions of the earth as given in this page, have been correfted by fubfequent meafurements and calculations, fornbsp;which fee vol. iv. page 13.

-- 187, nbsp;nbsp;nbsp;line 3 from the bottom; inftead of fig. 22, read Jig, 26.

9 ; inftead of rarefaSlion, read condenfation, 95, line 22; inftead of hundred, read thoufatid,

Page 398, line 23 ; inftead of and �which, read and �which at 32� ?� temperature.

'		The Satellites of Saturn.					N
	VII.	VI.	I;	II,	III.	IV.	V.
	d b m s	d h m 8	d h m 1	d h m nbsp;nbsp;nbsp;t	d h m �	1 ** b nbsp;nbsp;nbsp;m *	d b nbsp;nbsp;nbsp;mnbsp;nbsp;nbsp;nbsp;s
Periods - nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;- -	O 22 40 46	I 8 S3 9	I 21 18 27	2 17 41 22	4 12 25 12	IS 22 41 13	79 7 48 0
Diilances in femi-
diameters of Saturn	3\|	3i	41	sf	8	18	54
Ditto in miles - nbsp;nbsp;nbsp;-	107000	135000	170000	217000	to^ooo	704C00	2030000
Apparent diameters of
orbits - nbsp;nbsp;nbsp;.nbsp;nbsp;nbsp;nbsp;.nbsp;nbsp;nbsp;nbsp;.	57quot;	1' 14quot;	1' 27quot;	1' 52''	2' 36quot;	6' 18quot;	17' 4*''

Pegrees of Lailcude.	Time gained in one day, in feconds.	Lengthening in decimals of annbsp;inch, neceffarynbsp;to vibrate feconds.
5�	1.7	0,0016
10	6,9	0,0062
15	15,3	0,0138
20	26,7	0,0246
25	40,8	0,0369
30	57,�	0,0516
35	75,1	0,0679
40	94,3	0,0853
45	114,1	0,1033
50	134-	0,1212
55	�53,2	0,1386
60	171,2	0,1549
65	187,5	0,i6g6
70	201,6	0,1824
75	213.	0,1927
80	221,4	0,2033
85	226,5	0,2050
90	228,3	0,2065

Inches. 12	Feet. I	Ells.	Falls. Furlongs. Miles.
37.2	3.1	1
223,2	18,6	6	. I
8^928	744	240	40 nbsp;nbsp;nbsp;I
71424	5952	1920	320 nbsp;nbsp;nbsp;8nbsp;nbsp;nbsp;nbsp;I

Millimetre -	- nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;-nbsp;nbsp;nbsp;nbsp;0,039371 Eng. in�
Centimetre -	- - - 0^39371
Decimetre -	- - - 3.9371
Metre - nbsp;nbsp;nbsp;-	- - nbsp;nbsp;nbsp;39.371
Decametre -	- - 393.71
Hecatometre	- - 3937.1
Chiliometre	- - 39371.
Myriometre	- nbsp;nbsp;nbsp;393710.
El	igllili ^5iIes. Furl. Yds. Feet. Inches*

�Apparent		Refrac tion.		Apparenf Altitude.		Refrac tion.		Apparent Altitude.	Refrac tion.		Apparent Altitude.	Refrac tion.
O'*	0'	33'	0quot;	5�	0^	9'	54 i	230	z'	hquot;	44�	59quot;
0	S\|3*		10	5	30	9	�!	24	2	7	45	57
0	10^1		22	6	0	8	28	25	2	2	46	55
Q	ijr3o		35	6	30	7	51	26	I	56	47	53
0	20	29	5�	7	jD	7	20	27	I	51	�48 .	51
0	30	28	22	8	0	6	29	28	1	.47	49	49
0	4o!27		0	9	0	5	48:	29	I	42.	50	48
0	5�	25	42	iio	0	5	*5!	30	1	38	52	44 �
	00	24	29	; 1�	0	4'	47 :	31	I	35	54	41
	20	22	15	: 12	0	4	?3 i	32		31	56	38
	40	20		i�3	0	4	3	33		28	58.	35.
2	0	18	35	:I4	0	3	45	34	I	24	60	33
z	20	�7	4	15	0	3	30	35	1	21	65	26
Z	40	'5	45	16	0	3	17	30	I	18	70	21
3	0	'4	36	��7	. 0	3	4	37		16	75	15
3	20	13	34	18	0	2	54	3S		13	80	10
3	40	12	40	'�9	0	. 2	45	39		10	85	5
4	0	I 1	5gt;	:20	0	2	35	4.0	I	8	90	0
4	30	10	48	21	0	2	27,	4'	h	5
				'22	0	2	2�	42		3
				!				43	'I	I

Q ID V f4'

ELEMENTS

PHILOSOPHY.

IN FOUR VOLUMES.

1803.

PART IV.

the

earth.

the

vot. IV.

I nbsp;nbsp;nbsp;At

' OI:

c j nbsp;nbsp;nbsp;form

cf the JVorldy^c, nbsp;nbsp;nbsp;^3

c 4

han4

The

be

of the World, yc. nbsp;nbsp;nbsp;33

feven

lution

D 3 nbsp;nbsp;nbsp;the

meridians

^ y

O is

cf the V/crld, ֒f. nbsp;nbsp;nbsp;5^

tlifoiigb the at!Tiofp!iere, and, of courfe, are lefs ob-ftruded by it, than whea they are more oblique '� �

are

of the World-, nbsp;nbsp;nbsp;55

are between the tropics and the polar circles^ arc Called the tejifperate zcties. Thus the fuiface ofnbsp;the earth is fuppofed to be divided into five

mains E 4

or

[ 64 �]

CHAP. Iir.

The

OfthetrUiSjJ}�mo/lh�Pferygt;^^-

r 4 nbsp;nbsp;nbsp;I*

Of the true Syftem of the Warid, nbsp;nbsp;nbsp;73

axes in the fame diredlion, viz. from eaft to Weft,

millions

[ 79 3

CHAP. IV. nbsp;nbsp;nbsp;\

called

The fame thing may be faid of the other fuperior planets.

path in general of any celcflial body.

The planes of the orbits of all the other planets

, That node, where the planet paffes from the fouth to the north fide of the ecliptic is called the afeend-.

ill

Yelcitivs to tht Plon�fs. nbsp;nbsp;nbsp;^5

C 95 ]

gS nbsp;nbsp;nbsp;Of the Motion of the Earth

VOL. IV.

If

kt

The

I fai*^

I 2 nbsp;nbsp;nbsp;fition

I 4 nbsp;nbsp;nbsp;hepce

every

122 nbsp;nbsp;nbsp;Of the Phajes and Motions

9 nbsp;nbsp;nbsp;When

The

�bout

K a

^thiy�

K 3 nbsp;nbsp;nbsp;^ cidcs

The

Harvefl

150 nbsp;nbsp;nbsp;Of the Tides, (Jc.

moon

in

[ nbsp;nbsp;nbsp;i62nbsp;nbsp;nbsp;nbsp;]

Jl

M 3 nbsp;nbsp;nbsp;The

'phis

M 4 nbsp;nbsp;nbsp;The

� Openings

fun,

earth.

9S 51^ 35�*