the figure of a perfect sphere. This task of measuring portions of the meridian, has been executed in different countries by means of a system of triangles with astonishing accuracy.* The result is, that the length of a degree increases as we proceed from the equator towards the pole, as may be seen from the following table: Length of a degree in miles, Places of observation. Peru, Pennsylvania, Italy, France, England, Sweden, Latitude. 00° 00' 00" 39 12 00 43 01 00 46 12 00 51 29 541 66 20 10 68.732 68.896 68.998 69.054 69.146 69.292 Combining the results of various estimates, the dimensions of the terrestrial spheroid are found to be as follows: = The difference between the greatest and least, is 26.478: of the greatest. This fraction () is denominated the ellipticity of the earth, being the excess of the transverse over the conjugate axis, on the supposition that the section of the earth coinciding with the meridian, is an ellipse; and that such is the case, is proved by the fact that calculations on this hypothesis, of the lengths of arcs of the meridian in different latitudes, agree with the lengths obtained by actual measurement. 139. Thirdly, the figure of the earth is shown to be spheroidal, by observations with the pendulum. The use of the pendulum in determining the figure of the earth, is founded upon the principle that the number of vibrations performed by the same pendulum, when acted on by different forces, varies as the square root of the forces.† Hence, by carrying a pendulum to different parts of the earth, and counting the number of vibrations it performs in a given time, we obtain the relative forces of gravity at those places, and this leads to a knowledge of the relative distance of each place from the center of the earth, and finally, to the ratio between the equatorial and the polar diameters. * See Day's Trigonometry. + Mechanics, Art. 183. 140. Fourthly, that the earth is of a spheroidal figure, is inferred from the motions of the moon. These are found to be affected by the excess of matter about the equatorial regions, producing certain irregularities in the lunar motions, the amount of which becomes a measure of the excess itself, and hence affords the means of determining the earth's ellipticity. This calculation has been made by the most profound mathematicians, and the figure deduced from this source corresponds very nearly to that derived from the several other independent methods. We thus have the shape of the earth established upon the most satisfactory evidence, and are furnished with a starting point from which to determine various measurements among the heavenly bodies. G-G Fig. 25. I 141. The density of the earth compared with water, that is, its specific gravity, is 5.* The density was first estimated by Dr. Hutton, from observations made by Dr. Maskelyne, Astronomer Royal, on Schehallien, a mountain of Scotland, in the year 1774. Thus, let M (Fig. 25,) represent the mountain, D, B, two stations on opposite sides of the mountain, and I a star; and let IE and IG be the zenith distances as determined by the differences of latitudes of the two stations. But the apparent zenith distances as determined by the plumb line are IE' and IG'. The deviation towards the mountain on each side exceeded 7"+ The attraction of the mountain being observed on both sides of it, and B its mass being computed from a number of sections taken in all directions, these data, when compared with the known attraction and magnitude of the earth, led to a knowledge of its mean density. According to Dr. Hutton, this is to that of water as 9 to 2; * Bailly, Ast. Tables, p. 21. t Robison's Phys. Ast, but later and more accurate estimates have made the specific gravity of the earth as stated above. But this density is nearly double the average density of the materials that compose the exterior crust of the earth, showing a great increase of density towards the center. The density of the earth is an important element, as we shall find that it helps us to a knowledge of the density of each of the other members of the solar system. 69 PART II.-OF THE SOLAR SYSTEM. 142. HAVING Considered the Earth, in its astronomical relations, and the Doctrine of the Sphere, we proceed now to a survey of the Solar System, and shall treat successively of the Sun, Moon, Planets, and Comets. CHAPTER I. OF THE SUN-SOLAR SPOTS-ZODIACAL LIGHT. 143. THE figure which the sun presents to us is that of a perfect circle, whereas most of the planets exhibit a disk more or less elliptical, indicating that the true shape of the body is an oblate spheroid. So great, however, is the distance of the sun, that a line 400 miles long would subtend an angle of only 1" at the eye, and would therefore be the least space that could be measured. Hence, were the difference between two conjugate diameters of the sun any quantity less than this, we could not determine by actual measurement that it existed at all. Still we learn from theoretical considerations, founded upon the known effects of centrifugal force, arising from the sun's revolution on his axis, that his figure is not a perfect sphere, but is slightly spheroidal.* 144. The distance of the sun from the earth, is nearly 95,000,000 miles. For, its horizontal parallax being 8."6, (Art. 86,) and the semi-diameter of the earth 3956 miles, Sin. 8."6 3956:: Rad. 95,000,000 nearly. In order to form some faint conception at least of this vast distance, let us reflect that a railway car, moving at the rate of 20 miles per hour, would require more than 500 years to reach the sun. * See Mecanique Celeste, III, 165. Delambre, t. I, p. 483. 145. The apparent diameter of the sun may be found either by the Sextant, (Art. 129,) by an instrument called the Heliometer, specially designed for measuring its angular breadth, or by the time it occupies in crossing the meridian. If, for example, it occupied 4m, its angular diameter would be 1°. It in fact occupies a little more than 2m, and hence its apparent diameter is a little more than half a degree, (32′ 3′′). Having the distance and angular diameter, we can easily find its linear diameter. Let E (Fig. 26,) be the earth, S the sun, ES a line drawn to the center of the disk, and EC a line drawn touching the disk at C. Join SC; then Rad. ES (95,000,000):: sin. 16′ 1."5 : 442840 semi-diameter, and 885680=diam = eter. And 885680 112 nearly; that is, it would require one hundred and twelve bodies. like the earth, if laid side by side, to reach across the diameter of the sun; and a ship sailing at the rate of ten knots an hour, would require more than ten years to sail across the solar disk. Since spheres are to each other as the cubes of their diameters, Fig. 26. E 13: 1123::1: 1,400,000 nearly; that is, the sun is about 1,400,000 times as large as the earth. The distance of the moon from the earth being 237,000 miles, were the center of the sun made to coincide with the center of the earth, the sun would extend every way from the earth more than twice as far as the moon. 146. In density, the sun is only one fourth that of the earth, being but a little heavier than water (Art. 141); and since the quantity of matter, or mass of a body, is proportioned to its magnitude and density, hence, 1,400,000 ×=350,000, that is, the quantity of matter in the sun is three hundred and fifty thousand (or, more accurately, 354,936) times as great as in the earth. Now the weight of bodies (which is a measure of the force of gravity) varies directly as the quantity of matter, and inversely as the square of the distance. A body, therefore, would weigh 350,000 times as much on the surface of the sun as on the earth, if the |
