furface that do not change their places; every other point describes a circle greater as it is farther diftant from thofe fixed points or poles.

In the heavens, therefore, there must be two points, PQ, fig. 3, pl. 2, that appear fixed, wherein à ftar can have no apparent motion; thefe points are determined in the heavens, by prolonging the axis of the earth; these are the poles of a great circle of the celeftial sphere, formed in the heavens by continuing the plane of the terrestrial equator, and all the ftars will appear to turn round these two poles.

Thus the axis pq, of the earth peqz, fig. 3, pl. 2, are the poles of a great circle ETZ of the celeftial fphere, formed in the heavens by continuing the plane of the terreftrial equator e z z, and all the ftars will appear to turn round the two poles P, Q, or rather round the axis P Q. Let P reprefent the north pole, Q the fouth pole.

If through the center of the earth C, and any point m on it's furface, a right line Cm be fuppofed prolonged to the heavens, the extremity M of that right line will, by the earth's diurnal rotation, defcribe the celeftial parallel LM ML, anfwering to the terreftrial parallel 1mm1 of the point m. And if CM be fuppofed to be prolonged on the other fide to the heavens in T, then T will defcribe in the heavens a parallel TT V V equal to the parallel LM MI., anfwering to, and having the fame declination with the terrestrial parallel ttuu.

Hence it follows, 1. That the plane of the celeftial parallel L M M L, and that of the correfpondent parallel Immil, are fimilar elements of a cone, whofe axis is the fame as that of the earth, and whofe vertex C is at the earth's center. Therefore the plane of a celeftial parallel cannot be the

Jame

fame with it's correfponding terreftrial paralleľ only the plane (EZZ) of the celestial equator is the fame with the plane ezz of the terrestrial equator.

2. When in the earth's diurnal rotation a star paffes through the observer's zenith, the parallel of that ftar correfponds with the observer's terrestrial parallel; that is to fay, the celeftial parallel is as far diftant from the celeftial equator, as the terreftrial parallel is from the terreftrial equator: for then the line of the obferver's zenith is a right line drawn from the earth's center through the obferver's eye, terminating at the ftar, and is the line that defcribes the ftar's parallel in the heavens.

If therefore the arc M Z, the diftance of the ftar M from the celeftial equator be measured, it gives alfo the meafure of the arc m z, the obferver's diftance from the terreftrial equator. Therefore the arc of the obferver's distance from the terreftrial equator, is equal to the declination of the flar that paffes through bis zenith. So that if it be a fixed far, and the obferver changes his place, the different declinations of the ftars that pafs through his zenith at the various places he comes to, will fnew how much he approaches to, or recedes from the equator.

It follows, laftly, that any place on the terref trial fphere may be reprefented by it's correfponding zenith point in the heavens. For the celeftial parallel paffing through that point, reprefents the terreftrial parallel of the place, and the declination of the celeftial parallel measuring the diftance of that place from the equator; alfo the great circle of the celeftial fphere defcribed from that zenith as a pole, denotes the plane of the horizon of that place, and the particular phenomena of a place on the earth may be explained, by denoting that place

na

no otherwife than by it's zenith in the hea

vens.

OF THE ANNUAL MOTION OF THE EARTH.

It is owing to the industry of modern aftronomers, that the annual motion of the earth has been fully evinced; for though this motion had been known to, and adopted by many among the ancient philofophers, yet they were not able to give their opinions that degree of probability, which is attainable from modern difcoveries, much less the evidence arifing from thofe demonftrative proofs, of which we are now in poffeffion. I fhall, therefore, enumerate fome of the reafons which induce aftronomers to believe that the earth moves round the fun, and then explain further the nature of this motion, which is calculated to afford us the useful and delightful variety of the feafons, the mutual allay of immoderate heat and cold, and the fucceffive growth and recruit of vegetation.

On the fuppofition of the earth's motion, the celeftial motions become incomparably more fimple, and free from thofe looped contortions which must be fuppofed in the other cafe, and which are not only extremely improbable, but incompatible with what we know of motion.

This opinion is alfo more reafonable, on account of the extreme minuteness of the earth, when compared with the immenfe bulk of the fun, Jupiter, and Saturn; and there are no known laws of motion, according to which fo great a body as the fun can revolve about fo fmall a one as the earth.

The fun is the fountain of light and heat, which

The whole of what is faid under this head, may be beautifully illuftrated by the armillary sphere.

which it darts through the whole fyftem; it ought, therefore, to be in the center, that it's influence may be regularly diffufed through the whole heavens, and communicated in juft gradations to the whole fyftem.

When we confider the fun as the center of the fyftem, we find all the bodies moving round it, agreeable to the univerfal laws of gravity; but upon any other confideration we are left in the dark.

The motion of the earth round the fun accords with that general harmony, and univerfal law, which all the other moving bodies in the fyftem obferve, namely, that the fquares of the periodic times are as the cubes of the diftances; but if the fun moves round the earth, that law is deftroyed, and the general order of fymmetry in nature interrupted.

The annual motion of the earth is inconteftibly proved by obfervation, a motion having been difcovered in all the fixed ftars, which arifes from a combination of the motion of light with the motion of the earth in it's orbit.

It will be clearly fhewn in it's place, that Venus and Mercury move round the fun in orbits that are between it and the earth; that the orbit of the earth is fituated between that of Venus and Mars; and that the orbits of Mars, Jupiter, &c. are exterior to, and include the other three.

OF THE APPARENT MOTION OF THE SUN, ARISING
FROM THE EARTH'S ANNUAL MOTION ROUND it.

As when a perfon fails along the fea coaft, the fhore, the villages, and other remarkable places on land, appear to change their fituation, and to pafs by him; fo it is in the heavens. To a fpectator upon the earth, as it moves along it's orbit, or fails as it were through celeftial space, the fun, the pla

nets,

nets, and the fixed ftars, appear to change their places.

Apparent change of place is of two forts; the one is that of bodies at reft, the change of whofe place depends folely on that of the fpectator; the other is that of bodies in motion, whofe apparent change of place depends as well on their own motion, as on that of the fpectator.

I fhall firft confider only that apparent change which takes place in those which are at reft, and which is owing wholly to the motion of the earth; and fhew that the fun, when feen from the earth, will appear to move in the fame manner, whether it revolves round the earth, or whether the earth revolves round the fun.

Let us fuppofe the earth at reft, without any motion of it's own, and let the fun be supposed to revolve round it in the orbit ABCD, fig. 1, pl. 4, and let EFGH be a circle in the concave sphereof the ftarry heavens; as the fun moves in the order of the letters ABCD in it's orbit, it will appear to a fpectator on the earth to have defcribed the circle EFG H. When the fun is at A, it will appear as if it was among the fixed ftars that are at É; when it is at B, it will appear among the fixed fars at F; when at G, among those at H; and when it is at D, it will appear among the fixed ftars at G. Indeed, the fixed ftars and the fun are not seen at the fame time; but I have flewn, that we may tell in what part of the heavens the fun is, or what fixed ftars it is near, by knowing thofe which are oppofite to it, or come to the fouth at midnight. Therefore, if we find that any fet of ftars, as those at G for inftance, come to the fouth at midnight, we may be fure that they are oppofite to the fun; and confequently, if we could fee the ftars in that part of the heaven where the fun is, we thould find them to be those at F.

Secondly,