Another method of finding the sun's horizontal paral lax is shewn in Plate XXXVIII. Fig. 8, where ADB is the earth, V Venus, and RST the sun's eastern limb. To a spectator placed at D, the point I of the sun's limb will be on the meridian, and will be referred to the point M in the heavens. Venus will appear just within the limb at S; but to a spectator at B, she will appear in the heavens at N, while the point 1 of the sun's limb will ap pear at an The horizontal parallax of Venus CVB, or its equal NVM, is measured by the arch M1V ; and the sun's horizontal parallax CSB, or its equal MSm, is mea sured by the arch Mm. Now the angle CBV, the hori zontal parallax of Venus, may easily be found by observ ing the difference between the ingress of Venus upon the sun's limb, as seen from B and D, or the time she takes to move from V to v, allowance being made for the difference of meridians BD. But CBV : CSB=SC : VC, and the ratio of SC to VC is known ; and CBV be ing determined, we have the sun's horizontal parallax x VC SC • By comparing the observed difference between the to tal durations of the transit of 1769 at Wardhuys in Lap land, and Otaheite, which was 23' 10", and the calculat ed difference, which was 23' 26".95 upon the supposition that the sun's parallax was 8".S3, Dr IVIaskelyne found the sun's true horizontal parallax to be The angle CSB, Fig 7, being therefore about 8".7, and BC, the radius of the earth, being known, we can easily find, by plain trigonometry, the side CS, or the distance of the earth from the sun. Much interesting informa tion respecting the transits of Venus and Mercury, will be found in the Phil. Trans. passim, and in the Mem. Acad. passim. Sec also Ferguson's Astronomy, vol. ii. Edin. 1810, where the subject of transits is treated very fully and perspicuously. Olinthus Gregory's Astronomy, p. 382. La Lande's Astronomic, § 2000, vol. ii, p. 448. Vince's Astronomy, vol. i.
In the preceding Sections we have not assumed the earth of any particular form, but have considered it mere ly as a solid moving round an axis. The globular form of all the planets in the system, whether primary or se condary, and the spheroidal figure of those which have a rapid rotation upon their axes, affords us strong rea sons to believe that the earth is a solid of a similar form. We are fortunately, however, not left in this case to an alogical reasoning. The roundness of the earth, and the flattening at its poles, are phenomena established by the most irresistible evidence.
A spectator placed on any part of the earth, sees around him a certain limited portion of its surface, which is call ed the visible horizon of that place. The point of the horizon which lies in the same direction with the sun when on the meridian, is called the south ; the opposite point, the north ; the point of the horizon exactly be tween the north and south points, near which the sun rises, is called the east, and the opposite point the west. If the spectator advances 20 or 30 miles from his first position, either to the south, west, north, or east, he will have a new visible horizon, which does not contain one of the objects which were comprehended in the ho rizon of his first position. By advancing still farther, he will have another visible horizon filled with new ob jects, and bounded by a different portion of the earth.
Now this perpetual change in the visible horizon cannot arise from the inequalities on the earth's surface, for even from the top of the highest hill in one of the hori zons we cannot see the objects contained in another: It follows, therefore, that the surface of the earth is convex, and since this change in the visible horizon takes place in every part of the globe that has been visited, we are entitled to conclude that the earth is round.
If the visible horizon is composed wholly or partly of sea, we obtain an occular demonstration of the earth's convexity. When a ship comes in sight, its mast first appears, while the hull and the lower parts of the ves sel are invisible. As the ship approaches, more of the mast and rigging become visible, till the whole of the vessel gets above, as it were, the convexity of the earth.
The globular form of the earth is still more satisfac torily proved by the variation in the meridian altitude, or in the zenith distance of the celestial bodies, as seen from different parts of its surface; and this variation, when accurately observed at two places whose distance is known, enables us to measure with great accuracy the earth's diameter. Thus let E, Plate XXXIX.
1. be the earth, A and B two places lying north and south of each other, or in the same meridian, and S a fixed star or planet. The zenith of the place A will be Z, and SZ, or the angle SEZ, will he the zenith dis tance of the star, 30° for example. The zenith of the place B will be z, and the zenith distance of the star will be Sz, or SEz, for example. The difference between the zenith distances will be Zz, or the angle ZEz=10°; for the radius AE does not subtend a sen sible angle at the star S; but Zz is evidently the same portion of the whole circle ZzXY, as the distance AB is of the whole circumference of the earth ABM, and therefore the distance AB being measured, we have ABx360 Zz : 360=AB : Zz = the circumference of the earth, from which its diameter is easily found, being = ABx360 3.1416 When the distance between the two places AB is measured, and the difference between the zenith distance of a star situated in the same meridian, corres ponding with the distance AB, is ascertained, astrono mers are said to measure a degree of the meridian.
Several degrees of the meridian have been measured in different parts of the earth, and the result of these measurements is, that the earth is about 7912 English miles in diameter; that a degree is longer at the poles than at the equator; and, therefore, that the earth is an oblate spheroid, or a solid generated by the revolution of an ellipse round its lesser axis, the proportion be tween the two axes of the ellipse, or between the polar and equatorial diameters of the earth, being as 300 to 301. The difference, however, in the results which have been obtained, by measuring degrees in various parts of the earth, are sufficiently great to induce La Place to maintain, that the earth is not a solid of revo lution, but that the terrestrial meridian is a curve of double curvature. Professor Playfair with more justice ascribes these irregularities to the unequal density of the materials near the surface of the earth where the degrees have been measured, by means of which the direction of gravity is disturbed.