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 (7nearly.) 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 Dwere 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

н
H

B

off the sun's disk at C; the time of doing which, let us suppose to be the same as the calculated duration of the transit as seen from the earth's centre. But during this time, by the rotation of the earth on its axis, the place D is carried eastward to F, where it is at the end of the transit ; so that instead of coming to H, Venus moves only to E in its orbit before it is seen passing off the sun's disk at C, and the transit is ended.

154. Hence it is obvious, that the duration of the transit, as computed for the earth's centre, is shortened by the motion of the place from D to F, by the time it would take Venys to move from E to H. Hence by observing the difference between the computed and observed duration of the transit, we have the time which Venus takes in passing from E to H by the excess of her angular motion over that of the earth; and since this excess is previously known, by turning this difference of time between the computed and observed duration of the traṇsit into degrees and minutes of that excess, we get the number of degrees and minutes between E and H, that is, we get the angle ECH, or DCE. Now the line DF may be readily computed from the latitude of the place and the observed duration of the transit; and may be compared with the semidiameter of the earth. From this comparison would be at

the angle at C, which semidiameter of the earth would subtend ; that is, the sun's parallax. Let this parallax be equal to the angle IAL, subtended by the semidiameter of the earth IL. Here then we have a triangle IAL, of which the angle at A is known, and the angle at I a right angle, and the side IL, equal to the earth's semidiameter, is known; whence may be known the angle at L, and the side AI, which is the earth's distance from the sun.

seen

once

a

155. Having obtained the absolute distance of the earth from the sun, and the relative distances of all the planets being previously known, their absolute distances may

be at once ascertained. For, as the relative distance of the earth is to its absolute distance, so is the relative distance of any planet to its absolute distance.

In what has been said of the method of finding the parallax of the earth, and thence the distances of the planets from the sun, none of the difficulties of its execution appear. Incredible pains were taken by astronomers in making accurate calculations, and in providing the means for numerous and accurate observations, previous to the transits of 1761 and 1769. The skilful and scientific of Europe were scattered over the habitable globe, for the purpose of observing this phenomenon under circumstances as various as possible. Some went to India, others to America ; some to the north of Europe, others to the south. The truth was arrived at by vast labour in comparing an almost endless variety of observations, made at different places; correcting the probable error of one observation by the probable opposite error of another observa. tion, thus taking a mean of the whole. For a more full account, the pupil is referred to Ferguson's Astronomy. There will not be another transit of Venus till the year 1874.

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. distance. 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, the attraction is 4 times greater than if four inches apart; for the square of 2 is (2x 2) 4, and the square of 4 is (4x4) 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,