(382.) The time in which any of the inferior planets will return into a given fituation, may be eally known. Compute the diurnal heliocentric motions of Venus and of the Earth: the difference

of thefe motions is the diurnal motion of Venus from the Earth, or the quantity by which Venus would be feen to recede from the Earth every day by a spectator placed in the Sun : thus the mean motion of Venus is every day about 59 minutes and & feconds; the difference is 37 minutes. Therefore, As 37 minutes is to 360°, or to 21,600 minutes, fo is one day to the time wherein Venus, having left the earth, recedes from her 360 degrees; that is, to the time wherein the returns to the earth again, or the time between two conjunctions of the fame kind.

(383.) The calculations of the times are here made according to the mean or equable motions of the planets: and is therefore called a mean conjunction: but because Venus and the Earth are really carried in elliptic orbits, in which their motions are fometimes fwifter and fometimes flower, the true conjunctions may happen fome days either fooner or later than what thefe rules will give. The time of the true conjunction is to be computed from that of the mean conjunction in the following manner. Find by aftronomical tables the places of Venus and the Earth in the ecliptic, from which we shall have the distance of the two as feen from the Sun; compute alfo for the fame time the angular motions of these two planets for any given time, fuppofe fix hours; the difference of these two motions will give the accefs of Venus to the earth, or her recefs from it in fix hours. As this difference is to the arc between the places of Venus and the earth at the time of a mean conjunction, fo is fix hours to the time between the mean conjunction and the true. This time added to, or fubtracted from, the time of the mean conjuction, according as Venus is in antecedence or confequence from the earth, hows the time of their true conjunction.

(384) As to the conjunctions, oppofitions, direct and retrograde motions, &c. of the fuperior planets, they depend on the combinations of their motions with that of the earth, and are more frequent in Saturn than in Jupiter, and in Jupiter than in Mars, but most frequent of all in Herfchel; because the flower the motion of the planet is, the fooner the earth will overtake it, fo as to have it again in any given fituation.

(385.) Thus, fuppofe Saturn to be in conjunc. tion with the fun in V, if he were to ftand ftill for one year, then he would again be in conjunction in ; but as he goes on flowly, according to the order of the figns, about 12° annually, the earth must go through almott 13° more than an entire revolution; to that there will be almost a yer and 13 days, between any conjunction between the Sun and Saturn, and the conjunction immediately following. As Jupiter moves in his orbit with greater velocity than Saturn, the Earth muft have a proportionably larger space added to the year; and as Mars moves (wifter till, the time betwixt any two of bis conjunctions must be ftiil Jonger. The time when a fuperior planet will return into any given fituation, may be found by the methods already laid down for the inferior

planets; and the true conjunctions, &c. may be found in the fuperior planets as in the inferior. SECT. II. Of the VELOCITY, FIGURE, MOTIONS, &c. of the EARTH,

(386.) The Earth is 95,173,000 miles from the fun, and goes round in 365 days 5 hours 49 minutes, from any equinox or folftice to the fame again; but from any fixed ftar to the fame again, as feen from the fun, in 365 days 6 hours 9 minutes; the former being the length of the tropi cal year, and the latter the length of the fideral, It travels at the rate of 68,000 miles every hour; a motion, which, though upwards of 140 times fwifter than that of a cannon ball, is little more than half as swift as Mercury's motion in his or bit. The earth's diameter is 7970 miles; and by turning round its axis every 24 hours from weż to eaft, it causes an apparent diurnal motion of all the heavenly bodies from eaft to weft. By this rapid motion of the earth on its axis, the inhab tants about the equator are carried 1042 mies every hour, whilft thofe on the parallel of Loncea are carried only about 580, befides the 68,co miles by the annual motion above mentioned, which is common to all places whatever.

(387.) A variety of circumftances afford the cleareft evidence, that the earth is of a glob figure. 1. When we are at fea on board a fh, we may be out of fight of land, when the land is near enough to be visible, if it were not hid from our eye by the convexity of the water. Thes let ABCD, fig. 10 Plate XVII, reprefent a por tion of the globe of the earth. Let M be the top of a mountain; this cannot be feen by a perior on board the ship at B, because a line drawn from M to his eye at E is intercepted by the convexity of the water: but let the fhip come to C, then the mountain will be visible, because a line y be drawn from M to his eye at E. II. The higher the eye, the farther the view will be extended. It is very common for failors from the top of the maft of a flip to difcover land or fhips at a much greater diftance than they can do when they ftand upon deck. III. When we ftand on shore, the highest part of a fhip is vifible at the greatest de tance. If a fhip is going from us out to fea, we fhall continue to fee the maft after the hull or body of the fhip difappears, and the top of the A will continue to be feen the longeft. If a hip s coming towards us, the top of the maft comes firft in view, and we fee more and more til! at t the hull appears. If the furface of the sea weri flat plain, a line might be drawn from any of fituated upon it, as the fhip D, fig. 11. to the eye, whether placed high or low, at A or B. la this cafe, any object upon the earth or fea wed be visible at any diftance which was not to gat as to make the appearance of it too faint, er tus angle under which it appears too finall, to x feen by us. An object would be visible at the fame diftance, whether the eye were high or Not the higheft, but the largest, objects we be visible to the greateft diftance, to that w should be able to fee the hulk of a ship farther than the maft.

(388. IV. Several navigators, fuch as FadeMagellan, Sir Francis Drake, Lord Anies,

and D, and B be the real place of the ftar, its apparent place would be at A to an obferver at N. (398.) The apparent place B is always in the plane of aberration, drawn through the way of the obferver NF, and the line NA drawn from the obferver to the real place of the ftar; for AB being parallel to NF, is in the plane ADNF. The angle BNA or NAD is the angle of aberration; by the quantity of this angle the ftar is depreffed, in going towards it; or raifed in going from it. In the triangle AND; AN: ND::S.ADN:S.NAD; and AN and ND being given; the S.NAD the aberration will be as the SADN. Becaufe AN is 10300 times greater than ND; the S.NAD does not differ from its arch or angle; whence, the angie of aberration NAD or ANB is always as the fine of the angle ADN, or ANF, which are nearly equal, and which may be called the angle of the EARTH'S WAY. Hence the angle of aberration ANB is greateft, when AN is perpendicular to ND; and becomes nothing, when ANF is nothing. Since AN is to ND, as radius to 20"; when AN is perpendicular to ND, the angle NAD or ANB will be 20", which is the greatest it can be. In other cafes, as radius to S. angle of the earth's way ANF:: fo 20", to the aberration, anfwering to that angle; which angle is always taken in the plane of aberration ADNF.

(399.) In Plate XVII. fig. 13. let BCDE be the earth's orbit, S the fun, A or Q a ftar, N any place of the earth in its orbit. Through the ftar A draw the circle AI perpendicular to the plane of the ecliptic, and draw KSBH, and ESC perpendicular to it, or parallel to the tangent at B. Draw the tangent Nd, and draw NI towards the ftar, and make NI to Nd as the velocity of light to that of the earth, or as ro300 to 1, and draw dI which leads to the apparent place of the ftar; and fuppofe DA, SA parallel to dI, NI; then DA will alfo lead to the apparent place of the ftar. Draw SFG perpendicular to SN, or parallel to Nd. Then will INd be the plane of aberration. This plane continually changes its fituation, revol. ving round the fun in a year along with the tangent Nd. Since AS, SF are parallel to IN, Nf, ASF is equal to INf, and ASF is equal to the angle of the earth's way. Hence the plane ASF may be taken for the plane of aberration, which continually turns round the line AS, as the earth revolves about the fun; the line SF being always in quadrature with the earth at N.

(400.) Let the earth be at E, then the plane of aberration ASB will be perpendicular to the ecliptic; and the angle of the earth's way ASB is the leaft that it can be, and the angle of the aberration the leaft. Whilft the earth moves to B, the angle of the earth's way, and of aberration increafes, and at B the plane of aberration is ACS, and the angle of the earth's way ASC, a right angle, which is the greateft it can be; therefore the angle of aberration is the greateft poflible. While the earth moves to C, the angles of the earth's way and aberration decrease again, and at C are the leaft; and in moving to K they increafe again to K, where they are greateft. From K to E they diminish again, where they are leaff.

(451.) It is evident then, that whilft the earth is at E moving towards N, the star's apparent

place is at c lower than A; at B moving towards F, it appears at forward. When the earth is at C, the ftar appears at c above A. And when the earth is at K, the ftar is feen at k, having gone backward. Hence the apparent place of a ftar defcribes a fmall ellipfis in a year, about the true place of the ftar in its centre, whofe tranfverfe axis is parallel to the ecliptic; and leffer axis perpendicular to it. This ellipfis is beke, answering to places of the earth at B, C, K, E. And the points k, c, k, e, answer refpectively to the points C, K, E, B, where the plane of aberration cuts the ecliptic, being 90 degrees before the earth, or go de grees behind the fun.

(402.) The ftrongeft objection, that can be made against the earth's moving round the fun like the other planets, is, that, in oppofite points of the earth's orbit, its axis, which always keeps a parallel direction, would point to different fixed stars; which is not found to be fact. But this objection is easily removed, by confidering the immenfe diftance of the ftars in refpect of the dia meter of the earth's orbit; the latter being no more than a point when compared to the former. If we lay a ruler on the fide of a table, and alerg the edge of the ruler view the top of a fpire at ten miles distance; then lay the ruler on the oppofite fide of the table in a parallel fituation to what it had before, and the fpire will fill appear along the edge of the ruler; becaufe our eyes, even when aflifted by the beft inftruments, are incapable of diftinguifhing fo fmall a change at fo great a diftance. As the apparent places of the ftars, therefore, correfpond with this theory, the motion of the earth and the motion of light are both determined.

(403.) In fact, we find that the fun, and thofe planets on which there are vifible spots, tur round their axes: for the spots in general move regularly over their disks, allowing for the va riations already taken notice of. Hence we may reafonably conclude, that the other planets, on which we fee no fpots, and the earth, which is likewife a planet, have fuch rotations. But being incapable of leaving the earth to view it at a dis tance, and its rotation being fimooth and uniform, we can neither fee it move on its axis as we co the planets, nor feel ourfelves affected by its me tion. Yet there is one effect of fuch mother, which will enable us to judge with certainty whe ther the earth revolves on its axis or not.

(404.) All globes which do not turn round the axes, will be perfect spheres, on accourt of the equality of the weight of bodies on their furfaces; efpecially of the fluid parts. But all globes, which turn on their axes will be oblate fpheroides; that is, their furfaces will be higher or farther from the centre in the equatorial than in the polar regions: for, as the equatorial parts more quickett, they will recede fartheft from the axis of motion, and enlarge the equatorial diameter. That our earth is really of this figure, is demonftrable from the unequal vibrations of a pendulum, and the u qual lengths of degrees in different latitudesSince then, the earth is higher at the equator ta at the poles, the fea, which naturally runs dow ward, or toward the places which are nearch the centre, would run towards the polar regions, and

leave the equatorial parts dry, if the centrifugal force of thefe parts, by which the waters were carried thither, did not keep them from returning. The earth's equatorial diameter is 36 miles longer than its axis.

(405.) It is found that bodies near the poles are heavier than thofe towards the equator, becaufe they are nearer the earth's centre, where the whole force of the earth's attraction is accumulated. They are also heavier, because their centrifugal force is lefs, on account of their diurnal motion being flower. For both these reasons, bodies carried from the poles towards the equator gradually lofe their weight. Experiments prove, that a pendulum, which vibrates feconds near the poles, vibrates flower near the equator, which flows that it is lighter or lefs attracted there. To make it ofcillate in the fame time, it is found neceffary to diminish its length. By comparing the different lengths of pendulums fwinging feconds at the equator and at London, it is found that a pendulum must be 2 lines (or 12th parts of an inch) fhorter at the equator than at the poles.

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(406.) A perfon on the earth can no more be fenfible of its undisturbed motion on its axis, than one in the cabin of a fhip on smooth water can be fenfible of the fhip's motion, when it turns gently and uniformly round. It is therefore no argument against the earth's diurnal motion, that we do not feel it; nor are the apparent revolutions of the celeftial bodies every day, a proof of the reality of these motions; for whether we or they revolve, the appearance is the very fame. A perfon looking through the cabin windows of a fhip, as ftrongly fancies the objects on land to go round when the ship turns, as if they actually did fo.

(407.) The other common objections against the earth's motion on its axis, are easily answered. Some imagine, that if the earth turns eaftward, as it certainly does, if it turns at all, a ball fired perpendicularly upward in the air, fhould fall confiderably weftward of the place it was projected from. This objection will be found to have no weight, if we confider that the gun and bail partake of the earth's motion; and therefore the ball, being carried forward with the air as quick as the earth and air turn, muft fall down on the fame place. A ftone let fall from the top of a mainmaft, if it meets with no obstacle, falls on the deck as near the foot of the maft when the fhip fails as when it does not.

(408.) As for thofe fcriptural expreffions which feem to contradict the earth's motion, this general answer may be made to them all, that, The fcriptures were never intended to inftruct us in philofophy or aftronomy; and therefore on those fubjects, expreflions are not always to be taken in the literal fenfe, but for the most part as accommodated to the common apprehenfions of mankind. Men of fenfe in all ages, when not treating of the fciences purpotely, have used common language; and it would be abfurd to adopt any other in addreffing the majority of mankind.

(409.) The annual motion of the earth has been effectually confirmed by an argument drawn from the progreffive motion of light; and from the fame confideration the truth of the diurnal motion may be completely established.

(410.) In confequence of the progreffive motion of light, the apparent place of a fixed ftar is east of its true place, and the difference is proportional to the cofine of the ftar's declination; this difplacement of the fixed stars has changed, becaufe of the preceflion of the equinoctial points Therefore, if the diurnal revolution of the heavens were a real motion, the whole heavens must have changed their appearance; and the respective positions of the stars must be very different now, from what they were in the time of Hipparchus. A ftar which is now near the vernal equinox must have changed its apparent diftance, at leaft 5° from another ecliptical ftar which is 60° eaft from it. Nay it is highly probable, that no zodiacal star could be ever vifible; fuch would have been the direction that the rays of light must have taken, because of their own proper motion being compounded with that of the ftar, whofe velocity must have been exceedingly great, by reafon of its diftance from the poles of the motion. But fince no fuch remarkable displacement of the ftars has been observed, we may conclude, that the cause which would have produced it, has no existence; and that the revolutions of the heavens is not a real, but only an apparent motion.

(411.) The ANNUAL and DIURNAL MOTIONS of the earth, together with the different lengths of days and nights, and all the beautiful variety of feafons, depending on those motions, may be thus illuftrated.

(412.) In PLATE XVII. fig. 1. let FGHI be the earth, O its centre; and let it revolve about an axis perpendicular to the plane of the figure, in the order IFGH; that is, from weft to caft. Let A be the fun, draw AFOHC, and GOI perpendicular to it; let a fpectator be at I; then face the tangent at I (which reprefents the horizon) will be parallel to AFH, and A at an immenfe distance; they will nearly meet in A, and the fun at A will be rifing in the horizon at 1. As the earth moves round, the spectator is carried towards F, and the fun at A feems to rife higher and higher; and when the fpectator is arrived at F, then the fun is at the higheft. As the earth ftill turns round, and the fpectator is carried from F towards G, the fun appears to defcend, as if it moved towards D; and when the spectator is arrived at G, then the fun appears in the tangent at G; that is, in the horizon at G; and therefore the fun is fetting. Afterwards, all the time the spectator is moved through GHI, the fun appears under the horizon, till it comes at I, where the fun feems to rife again.

(413.) Thus it is evident, that while the spectator is carried through the illuminated half of the earth IFG, it is day light; at the middle point F, it is noon-day; at the dark hemifphere GHI it is night; and at H, it is midnight. And thus the viciflitude of day and night appears, by, the rotation of the earth about its axis. What has been faid of the fun, is equally true of the moon, or any ftar placed at A. And therefore all the celestial bodies feem to rife and fet by turns, one after another, according to their various fituations. For let A, B, C, D) be four stars: when the spectator is at I, the star A rifes; and when at G, it fets. When the spectator is at F, B rifes; and

when

when it is at H, it fets. When he is at G, Crifes; and when at I, it fets. When the fpectator is at H, D rifes; and when at F, it fets.

(414.) Hence it is the very fame thing, as to the diurnal motions, WHETHER THE EARTH MOVES uniformly about its axis, while the HEAVENS STAND STILL; or whether the HEAVENS MOVE uniformly round, while the EARTH STANDS STILL; the phænomena being exactly the fame either way. For whether the fpectator move uniformly in the arch IF, from weft to eat, whilft A is fixed; or A moves uniformly in the arch AD, from eaft to weft, whilft I is fixed; the fame angle will be defcribed, and therefore the altitude of A, above the horizon will be the fame either way.

SECT. III. Of the SEASONS.

(415.) To explain the caufes of the various feafons, fee PLATE XVII. fig. 2. and fupply in the middle of the dark circle ENQA. Let Y

be the earth's orbit, and S the fun. This orbit is fo fmall in respect to the distance of the fixed stars, that the fame afpect of the heavens will appear, whether a man be placed in the earth or in the fun. If the earth be at , a fpectator will fee the fun in ; when the earth comes to 8, he will fee the fun in m; and the fun will appear to have moved throughm. Whilft the earth is moving to II, the fun will feem to pass through m; and a perfon in the earth obferves the fun to go through the fame fpace in the heavens, that a fpectator at the fun would fee the earth go through and as he is not fenfible of the earth's motion, he afcribes that motion to the fun, which in reality is unmoved. Hence, because the relative motion is the fame, whether of the two is moved, and all effects are the fame as to their places; aftronomers generally fuppofe the fun to move along the ecliptic, defcribing its orbit round the earth at rest.

(416.) Let NEAQ be the earth, NA be its axis, N the north pole, A the fouth; EQ the equinoctial, and PR a parallel of latitude pafling through any place. Draw a plane G I perpendicular to S, which divides the illuminated hemifphere from the dark one. The axis NA is inclined to the plane of the ecliptic or earth's orbit, in an angle of 66 degrees: and during the earth's motion in its orbit, the axis always remains in a parallel pofition, or pointing to the fame ftar. The earth alfo moves uniformly round this axis; and defcribes equal arches in equal times. Now let the earth be at ; in this pofition, the circle dividing the light and dark hemispheres pafies through the poles N and A, and divides all the parallels as PR into two equal parts; therefore any point in that parailel, as the earth revolves round, will flay as long in the light hemifphere as in the dark; that is, the days and nights are equal. As it moves to m, the pole N comes into the light hemifphere, by reafon of the oblique pe fition of the axis NA; and as it proceeds to and 9, the light hemifphere reaches farther and farther beyond N, till coming to, it is at the fartheft, reaching to G, and making the arch NG 23 degrees, the complement of Ny S, or 66} degrees. Then the

(417.) In the oppofite or fouthern hemisphere the days have been decreafing, and are at the fhorteft when the earth is at : for all para!! to E Q have their greater part in the dark lemi sphere. If through the point G a parallel be d fcribed, this parallel is called the ar&ic circk; and all the space contained therein is illuminated, and there is no night, when the earth is at 9. Fr the fame reason, the space within a parallel drawa through I, will be all dark, and all is night there. If a parallel be drawn through B, where Sc the arch N E, that parallel is called the trop Cancer; and then the fun will shine perpendicular upon the inhabitants in that parallel. This is the fummer feafon for those that are in the hemifph a ENQ, and the winter for thofe that live in EAC and fince E Q is equally divided by the circk (1 light and darkness G I, the days and nights are aways equal under the equinoctial.

(418) While the earth moves through as

to, the circle of light and darkness com s nearer and nearer to the pole N, the angle N G, and confequently B E grows lefs and let, till they vanish in ; then the circle of light and darkness paffes again through the poles N and A bifecting all the parallèls as PR; and the days and nights are again cqual, all over the earth.

(419.) While the earth moves through Y, 3. II, too, the fun feems to go through, m, 4, to and the circle feparating light and nefs falls fhort more and more of the north po N, and goes further and further beyond the to th pole A; whence the parallels cut by that cine will have the greater part in the dark in the north hemifphere; but in the fouth hemifphere, the greater part will be in the light: and it is winter to the northern hemisphere ENQ, the days borg at the fhorteft; and fummer to the fouthern mifphere E AQ, their days being at their long". Within the parallel drawn through G, there w be no day whilft the earth is at ; and ir te parallel drawn through I, there will be no nigh At the pole A it will be day for 6 months, a. the pole N it will be night for 6 months; jus contrary of what happens when the earth is In this pofition, if a parallel be drawn through as the fun will thine perpendicular to the earth a that parallel, and it is called the tropic of Comm corn; and a parallel drawn through I is called the antardic circle.

(420.) When the earth moves from on thrach and up to again; it is evident the cine parating light and darkness draws nearer andr er to the poles N and A, by which the light 24 dark parts of the parallels become nearer a Që lity, and fo to the days and nights. Therder, a the north hemifphere ENQ, the days are ch ing; and in the fouth hemifphere they are dec ing: and the days and nights become equal 2 every place, when the earth arrives at

(421.) In this manner are the feveral for