150. The ancients, so far as we know, were quite ignorant of the real distance of the earth from the sun, The solution of this problem baffled the skill and mocked the toil and industry of astronomers for ages; and it was not till very lately that any certain knowledge was gained on this subject. The first approximation towards the truth was obtained by observing as correctly as possible the precise time when half the moon's visible hemisphere is enlightened. For it will be obvious on a little reflection, that this must be the case when the plane of the circle dividing her dark from her illuminated hemisphere, would pass through the centre of the earth; and this takes place a little before the first quarter and a little after the third quarter. When this is the case, the angle made at the moon by lines drawn to the sun and to the earth, is a right angle: By observing the number of degrees between the moon and sun at this time, the angle made at the earth by lines -drawn to the sun and moon is obtained. And the distance of the moon from the earth is already known. Here then is a triangle, of which two angles and one side are known; and hence the other sides may be obtained, one of which is the distance of the earth from the sun.

151. But no observation can be fully relied on for determining the very moment when half the moon's visible hemisphere is enlightened; that is, when the line, dividing the dark from the light portion of the moon's disk, is a straight line. Some other means was therefore to be devised for ascertaining accurately the real distance of the earth from the sun. Dr. Halley in 1691 devised (the method of finding this distance by observing a transit, (that is, a passing,) of Venus over the sun's disk, hence deducing the sun's parallax. As no transit occurred in his day, he could only call the attention of future astronomers to these phenomena,

when they should occur. A transit took place in 1761, and another in 1769; on both which occasions astronomers went into different parts of the world in order to take observations under a variety of circumstances. But the observations of the latter transit did little more than confirm the result derived from the observation of the former.

152. Before we proceed to show how the parallax of the sun can be obtained from a transit of Venus, it may be useful to state some of the facts and principles respecting the motions and orbits of the planets, which were actually discovered from observation, and most of which were necessary to be known before the sun's parallax could be found.

1st. By observations, astronomers had determined the precise time in which each planet completes its revolution.)

2d. Kepler, by comparing observations, developed this law, viz. The squares of the periodical times of the planets are to each other as the cubes of their distances from the sun. Hence, since the periodical times are known, the relative distances of the planets from the sun are readily found. For example, let the periodical times of Venus and the earth be known, and let us suppose the distance of the earth from the sun to be 10; then say, as the square of the earth's periodical time is to the square of the periodical time of Venus, so is the cube of the earth's supposed distance (10,) to the cube of the distance of Venus (74 nearly.) In the same way the relative distance of the other planets may be obtained.

3d. By observation, the relative angular* motion of Venus and the earth was found; and consequently the

* It may be necessary for the instructer to explain to the pupil the difference between angular motion and absolute motion; that the first is estimated by degrees, as seen from the sun, and the second by miles.

excess of the angular motion of Venus over that of the earth.

4th. Observation had enabled astronomers to determine the position of the orbits of Venus and the earth; so that the part or limb of the sun might be known, over which Venus would appear to pass at any particular transit; and also the direction and duration of the transit, as viewed from the earth's centre.

153. Let us then suppose the duration of the transit to be computed beforehand, as seen from the centre of the earth. Let S be the sun, BEH part of the orbit of Venus,

and the earth in its orbit. For the greater advantage, let the transit be observed from a place, as D, where the sun will be on the meridian about the middle of the transit. Let us suppose that Venus at B is seen at D as entering on the sun's disk at A, If the place D were stationary with regard to the earth's centre, Venus must move by the excess of her angular motion over that of the earth, from B to H, before

it would appear to

F

BOOK II.

PHYSICAL ASTRONOMY.

Attraction.

156. There is one property common to every particle of matter in the universe, viz. (it tends to every other particle. However near, or however remote from each other, still they all tend to each other, in a greater or less degree. This universal tendency constitutes what is called the principle of universal gravitation or attraction. If a stone be flung into the air, it comes to the ground. The tendency, which causes it to fall, is gravitation (It is precisely the same as weight. When a body is said to weigh a pound, the meaning is, that the tendency of that body to the earth is equal to the tendency of another body, called a pound weight. The unknown tendency or gravity of one body is compared with the known tendency or gravity of another; and as the unknown exceeds or falls short of the known, it is said to weigh more or less than a pound. So of any number of pounds.

157. But this tendency or gravitation is not uniform. It is varied by one and only one circumstance, viz. dis-, tance. Two particles close together are more strongly attracted towards each other, than if far apart. But this attraction varies according to a certain known law. (It decreases as the square of the distance increases.) For example, if two particles be two inches apart, thè attraction is 4 times greater than if four inches apart; for the square of 2 is (2 × 2) 4, and the square of 4 is (4 × 4) 16; and 16 is four times greater than 4. The very fact that attraction or gravitation operates in this manner, proves that it can never entirely cease; for two bodies can never be infinitely distant.

158. When there is no distance between two or more particles, they adhere and form a distinct body; which attracts and is attracted, like a single particle. But as every particle in this body attracts every particle out of it, just as much while they adhere as if they were separate, it follows that one body attracts all others more or less according to the number of particles it contains ; that is, its solid contents. (If a stone be flung into the air, it falls to the earth, because the solid contents of the earth exceed those of the stone. But the earth also is at the same time drawn towards the stone, and actually moves towards it. If the solid contents of the stone and of the earth were equal, that is, if these bodies were equally heavy, they would meet half way. If the solid contents of the stone exceeded those of the earth, as much as those of the earth exceed those of the stone, the earth would fall to the stone, just as the stone does to the earth. Hence all attraction of bodies is mutual; and greater or less, according to their solid

contents.

159. If two unequal bodies be drawn towards each other by mutual attraction the distances of the points, where they would meet (called the centre of gravity) from the points whence they set out, will be inversely as their solid contents. For example, if a body of 40 pounds, and a body of 10 pounds, move to each other in a straight line, the body of 10 pounds will move 4 times faster than that of 40 pounds; so that if the distance be 100 yards, the centre of gravity is 80 yards from the point where the body of 10 pounds set out, and 20 yards from the point where that of 40 pounds set out. Whence it follows, that if the weight of each body be multiplied into its distance from the centre of gravity, the product is the same. (10×80-800, and 40×20=800.) This is universally true, and affords an easy method of finding the centre of gravity of two