zon.

143. Now when the moon is in the horizon, we see intervening objects; but when above the horizon, we do not. Suppose I observe the moon to rise apparently by the side of the trunk of a tree, which I well know to be 200 or 300 rods distant'; and which I also well know is nearly 2 feet in diameter, where it appears in the hori

I see the moon is beyond that tree, and that its apparent diameter is greater than that of the tree; I hence insensibly estimate the diameter of the moon to exceed 2 feet; whereas in the zenith I think it scarce six inches. It is from the same cause, that in looking across water, or an extensive marsh, we always think the distance less than it really is; there being few intermediate objects.

These estimates are made for illustration only. Different people form very different estimates of the apparent diameter of the sun and moon,

D

6

To render this subject more plain the annexed figure is introduced. Let us suppose an observer at E, while the moon passes from the horizon at A through B and C to the zenith D. If the observer considers the moon as passing through a part of a circle, and always at the same distance at B, C, and D, the moon will appear to him always of the same size. But if, while the moon passes from A through the sta- E tions B, C, and D, it appears to him that it passes from A through the stations b, c, and d, it will appear to him less at b, than at A, and less at cand d than at b. Now this last is the true appearance of the moon, while she rises from the horizon A to the zenith D in the cirele ABCD, she appears to us to move in the depressed curve Abcd, thus continually becoming nearer. Thus we attribute to her a variation in size, because there appears to be a variation in her distance,

Sect. V.

of Phenomena arising from the Earth's Magnitude.

PARALLAX.

144. None of the heavenly bodies, unless they be in the zenith, appear to have the same place among the stars when seen from the earth's surface, that they would have, if seen from the earth's centre. To a spectator at G, (PI. VII, fig. 4,) the centre of the earth, the moon at E would appear among the stars at I; but seen from the surface of the earth at A, it would appear at K. The place I is its true place, and K its apparent place; and the difference between them is its parallax, diurnal parallax, or horizontal parallax. As the moon comes above the horizon, say to D, its parallax decreases ; for here it is Ha, less than IK. And when the moon comes to the zenith at F, parallax ceases ; for it appears at Z, whether seen from G or A.

145. The parallax of a heavenly body is less as its distance is greater. If the moon were at e instead of E, its parallax would be n K instead of IK. The moon's horizontal parallax is about 57'; the sun's 8". The distance of the stars is so great, that no parallax can be discovered.

146. Refraction and parallax both make bodies appear where they are not; but refraction elevates them, and parallax depresses them. They are both greatest in the horizon, and vanish at the zenith. The moon is depressed by parallax near twice as much as it is elevated by refraction; but the sun is depressed by parallax only about so as much as it is elevated by refraction. Refraction is the same, whether the light come from the sun, moon, or any other heavenly body; bęing generally about 33' in the horizon.

147. Parallax or diurnal parallax is to be understood as above explained. But there is an annual parallax; by which is meant, the difference in the apparent place of a heavenly body, as seen from the earth in opposite points of its orbit. As the mean distance of the earth from the sun is 93 millions of miles, it is obvious that the earth, in one part of its orbit, as at s, is (2 x93) 186 millions of miles further eastward, than when in the opposite part, as at ig. Hence we might suppose, that if a particular star is exactly in the north when the earth is in one part of its orbit, it would deviate somewhat from the north, when the earth comes to the opposite point. (For the earth's axis is always parallel with itself.) But the pole star (and indeed all stars) have no annual parallax, that can be discovered ; owing to their inconceivable distance. The nicest instruments, which the most ingenious artists have been able to construct, fail entirely to indicate to us any deviation arising from this cause of any star from its true place. But these instruments would indicate such deviation, were not the stars more than 200,000 times further off than we are from the sun. (18,600,000 millions of miles.) The probability is, that the nearest stars are at a much greater distance.

The following Numbers of this section cannot be fully understood without a knowledge of plane Trigonometry. They may therefore be omitted by those who are ignorant of that branch of mathematics.

148. The distance of the moon was long since ascertained with the utmost accuracy by means of her parallax. There are several methods of obtaining this parallax, and of applying it. The following is one of the most sure and simple. Let us suppose that two observers are at the points A and B in the same meridian; and let the distance between them, that is, their difference

B

of latitude, be previously

M known. When the moon M passes the meridian of these observers, let each, with a good instrument,take her zenith distance; that is, the arc ZM and z M. In the triangle AOB, the sides OA and B are each equal to the semidiameter of the earth, which is known; and the angle AOB is measured by the arc AB, which is the difference of latitude between the observers, and is also known (by the supposition.) These three things therefore being known, we can readily calculate the length of the side AB, and the magnitude of the angles OAB and OBA.

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,