To obtain precise views of the motions of the heavenly bodies, it is necessary to be able to assign precisely the place in which they are. This is done by means of several imaginary lines or circles, supposed to be described upon the surface of the sphere. These circles are divided into degrees, minutes, and seconds. The great circle of the sphere, QE, which is perpendicular to the axis of the world, and of course 90° distant from either pole, is called the equator. The smaller circles which the stars describe in consequence of their apparent diurnal motions, are called parallels, because they are parallel to the equator. The equator divides the heavenly sphere into two equal parts, the north and south; but, to be able to assign the position of the stars, it is necessary to have another circle passing through the poles, and cutting the equator perpendicularly; this is called the meridian, which is supposed to pass through the poles, and also directly over the head of the observer M, and the point N exactly opposite to that. The first of these points is called the zenith, and the second is denominated the nadir. The meridian divides the circles described by the stars into two equal parts, and when they reach it they are either at their greatest height above the horizon, or they are at their least height. The situation of the pole is readily found, it being precisely half way between the greatest and least height of those stars that never set. Since HMO, the visible part of the heavens, contains 180°, and it is 90° between the pole P, and the equator EQ; if, therefore, we take away P E from the semicircle HMO, there remains 90° for the other two arcs PH and EO, that is, the elevation of the pole and the equator, are together equal to 90°, so that the one being known, and subtracted from 90°, the other also is found. Hence it is known, that "the elevation of the pole at any place, is the complement of the elevation of the equator:" or what that elevation wants of 90°. Hence also the "elevation of the equator is equal to the distance from the pole P to the zenith M ;" for the elevation of the equator is the difference between that of the pole and 90°. When we travel towards the north, we perceive that the north pole does not remain stationary, but rises towards the zenith, in proportion to the space that we pass On the contrary, it sinks just as much when we travel towards the south, VOL. I.

over.

earth is not plane, as would appear to a su perficial observer, but curved.

The heavenly bodies appear to describe a complete circle round the earth every 24 hours; but besides these motions which are common to them all, there are several which possess motions peculiar to themselves. The sun is farther towards the south during winter than during summer; he does not therefore keep the same station in the heavens, nor describe the same circle every day. The moon not only changes her form, diminishes and increases, but, if she is observed in relation to certain fixed stars, it will be found that she proceeds to the eastward, making progress every day, till in about a month she makes a complete tour of the heavens. There are eight other stars which are continually changing their place; sometimes they seem to be moving to the westward, sometimes to the eastward, and sometimes they appear stationary for a considerable time: these are called planets. There are other bodies which appear only occasionally, move for some time with very great velocity, and afterwards advance beyond the regions visible to us: these are comets, of which one is now (November, 1807), apparent. The greater number of the heavenly bodies always retain the same, or nearly the same relative distance from each other, and are, on that account, called fixed stars.

OF THE FIGURE AND MOTION OF THE EARTH.

The earth, as we have observed, was long considered as a large circular plane, spreading out on all sides to an indefinite distance; but it is now ascertained that it is of a spherical figure, nearly resembling that of a globe. The evidence for this fact is decisive, without having recourse to scientific principles, by considering that the cele brated navigators Magellan, Sir Francis Drake, Lord Anson, and captain Cooke, have all at different times sailed round the earth. They set out from European ports, and, by steering their course westward, arrived at length at the very place from whence they departed, which could not have happened, had the earth been of any other than a spherical or a globular figure. This form is also apparent, from the circular appearance of the sea itself, and the circumstances which attend large objects when seen at a distance on its surface. For Dd

when a ship goes out to sea, we first lose sight of the hull or body of the vessel, see fig. 4; afterwards that of the rigging; and at last can discern only the top of the mast, which is evidently owing to the convexity of the water, between the eye and the ob. ject; for otherwise the largest and most conspicuous part would be visible the longest. Another proof is taken from the shadow of the earth upon the face of the moon, during the time of a lunar eclipse; for the moon, having no light but what it receives from the sun, and the earth being interposed between them, the moon must either wholly or in part become obscure. And since in every eclipse of this kind, which is not total, the obscure part always appears to be bounded by a circular line, the earth itself, for that reason, must be spherical; it being evident that none but a spherical body can, in all situations, cast a circular shadow.

It is not ascertained who was the first person that asserted the figure of the earth to be spherical, but the opinion is of very great antiquity. For when Babylon was taken by Alexander the Great, it was known that the philosophers in that city had been long in the habit of calculating eclipses, which they could not have accomplished without a knowledge of the true fi gure of the earth. Thales, who flourished six centuries before the birth of Christ, predicted, according to the testimony of Herodotus, an eclipse of the sun. Hence it should seem, that in those early days, the globular figure of the earth had been by the learned investigated and credited. This being known, its magnitude would also soon be discovered: the solution of this apparently difficult problem engaged the attention of many great men about the same period; and though the measures which they have given are wide of the truth, and even very different from one another, yet this may be imputed to the inaccuracy of their instruments, and the want of mathematical knowledge rather than to the impractica bility in the thing itself. Without, how ever, entering upon this subject, we may observe, that the universe in general, as well as the solar system in particular, are in some measure connected with the motion of the globe that we inhabit. By the universe may be understood the whole frame of nature, to the utmost extent of the creation, and by the solar system is meant, that portion of it which comprehends the s, planets, satellites, and comets.

Of

this system the sun is supposed to be in the centre, round which there are eleven planets continually revolving.

If we can form a notion of the manner in which the earth moves, we shall easily conceive the motions of all the rest of the planets, and by that means obtain a complete idea of the order and economy of the whole system. And in order to this, nothing more is necessary than to consider the common appearances of the heavens, which are constantly presented to our view, and attend to the consequences. For since it is well known that the sun and stars appear to move daily from east to west, and to return nearly to the same places in the heavens again in twenty-four hours, it follows that they must really move, as they appear to do, or else that we ourselves must be moved, and attribute our motion to them: it being a self-evident principle, that if two things change their situation with respect to each other, one of them, at least, must have moved. But if this change be owing to the revolution of the stars, we must suppose them to be endowed with a motion so exceedingly swift, as to exceed all conception; since it is now known, by calculations founded on the surest observations, that their distances from us are so immense, and the orbits they have to run round so prodigiously great, that the nearest of them would move, at least one hundred thousand miles in a minute. Now as nature never does that in a complicated and laborious manner, which may be done in a more simple and easy one, it is certainly more agreeable to reason, as well as to the power and wisdom of the Creator, that these effects should be produced by the motion of the earth; especially as such a motion will best account for all the celestial appearances, and at the same time preserve that beautiful simplicity and harmony which is found to prevail in every other part of the creation. And this argument will appear still more forcible, if we compare the vast bulk of the celestial bodies with the bulk of the earth. For it is now well known, that the sun is above a million of times larger than the earth; and from the best modern observations it appears, that many of the stars are at least equally large. It is much more probable, therefore, that the earth revolves round its axis, with an easy natural motion, once in twenty-four hours, than that those immense bodies should be carried from one place to another, with such incredible swiftness. Nor is it any objection to this

and sometimes they go behind it. That their orbits are within that of the earth is evident, because they are never seen in opposition to the sun, that is, appearing to rise from the horizon in the east when the sun is setting in the west, which is another proof that the earth is not the centre of celestial motions. On the contrary, the orbits of all the other planets surround that of the earth; for they sometimes are seen in opposition to the sun, and they never appear to be horned, but always nearly or quite full, though sometimes Mars appears a little gibbous, or somewhat deficient from full.

Since all the planets move round the sun in elliptical orbits, the sun itself is situated in one of the foci of each ellipse. That focus is called the lower focus. If we sup. pose the plane of the earth's orbit, which passes through the centre of the sun, to be extended in every direction as far as the fixed stars, it will mark out among them a great circle, which is the ecliptic; and with this the situations of the orbits of all the other planets are compared. The planes of the orbits of all the other planets must necessarily pass through the centre of the sun; but if extended as far as the fixed stars, they form circles different from one another, as also from the ecliptic; one part of each orbit being on the north, and the other on the south side of the ecliptic. Therefore the orbit of each planet cuts the ecliptic in two opposite points, which are called the nodes of that particular planet, and the nodes of one planet cut the ecliptic in planes different from the nodes of another planet. A line passing from one node of a planet to the opposite node, or the line in which the plane of the orbit cuts the ecliptic, is called the line of nodes. That node where the planet passes from the south to the north side of the ecliptic is called the ascending node, and the other is the descending node. The angle which the plane of a planet's orbit makes with the plane of the ecliptic is called the inclination of that planet's orbit. Thus fig. 2, Plate II. where F represents the sun, the points A and B represent the nodes, and the line AB the line of nodes formed by the intersection of the planes of the orbits C and D. The angle EFG is the angle of inclination of the planes of the two orbits to each other. A line drawn from the lower focus of a planet's orbit (viz. where the sun is) to either end of the conjugate axis of its orbit, (which line is equal to half the transverse axis) is called the mean distance of the planet from the sun. But

according to some, the mean distance is a mean proportional between the two axes of that planet's orbit. The distance of either focus from the centre of the orbit is called its eccentricity. The two points in a planet's orbit which are farthest and nearest to the body round which it moves are called the apsides; the former of which is called the higher apsis, or aphelion; the latter is called the lower apsis, or perihelion. The diameter which joins these two points is called the line of the apsides. When the sun and moon are nearest to the earth, they are said to be in perigee. When at their greatest distance from the earth they are said to be in apogee. When a planet is situated so as to be between the sun and the earth, or so that the sun is between the earth and the planet, then that planet is said to be in conjunction with the sun. When the earth is between the sun and any planet then that planet is said to be in opposition. It is evident that the two inferior planets must have two conjunctions with the sun, and the superior planets can have only one, because they can never come between the earth and the sun. When a planet comes directly between us and the sun, it appears to pass over the sun's disc, or surface, and this is called the transit of the planet. When a planet moves from west to east, viz. according to the order of the signs, it is said to have direct motion, or to be in consequentia. Its retrogade motion, or motion in antecedentia, is when it appears to move from east to west, viz. contrary to the order of the signs. The place that any planet appears to occupy in the celestial hemisphere when seen by an observer supposed to be placed in the sun, is called its heliocentric place. The place it occupies when seen from the earth is called its geocentric place.

The planets do not move with equal velocity in every part of their orbits, but they move faster when they are nearest to the sun; and slower in the remotest part of their orbits; and they all observe this remarkable law, that if a straight line be drawn from the planet to the sun, and this line be supposed to be carried along by the periodical motion of the planet, then the areas which are described by this right line and the path of the planet are proportional to the times of the planet's motion. That is, the area described in two days is double that which is described in one day, and a third part of that which is described in six days, though the arcs or portions of the