not yet sufficiently established to be made the basis of calculation for determining their real diameters, magnitudes, &c.; and we have therefore omitted them in the subsequent tables. The real diameters of the planets, in English miles, The comparative diameters of these bodies, when that of the earth is taken for unity, are about, The magnitudes of these celestial bodies (that is their cubic contents) vary as the cubes of their diameters; and hence their comparative magnitudes are exhibited in the following table, in which that of the earth is taken for unity. Hence, if each of these numbers were multiplied by the number of cubic miles in the content of the earth, the products would be the real magnitudes of the other bodies in the same terms; but here the numbers would be too great to afford the mind any clear idea of the bodies they were designed to represent. A much better notion would be formed of their relative size, by supposing a number of globes to be made, that representing the earth being one inch in diameter; then the diameters of those which represent the other bodies would be as in the following table; viz. that which represented pro To ascertain the masses and densities of the heavenly bodies, which are situated at such inmense distances from us, appears at first to involve difficulties too great for the human mind to overcome; but even these difficulties have, in a great measure, vanished before the power of the Newtonian philosophy. The mass or quantity of matter in any body is as the duct of its magnitude and density; or, if that body be a globe, as the cube of its diameter and density; hence, since the diameters are already ascertained, all that is necessary for the solution of this problem is to ascertain the densities of the several bodies. This astronomers accomplish by the united means of observation and computation, by which they ascertain the perturbations that each planet produces in the motions of the other planets, or in those of its own satellites. For this purpose, the most eminent astronomers have formed equations with unknown coefficients, having a given ratio to the masses; and hence, when the values of these coefficients have been determined by observation, those of the masses become known. When a planet has satellities, the effects which the primary produces in the revolutions of these become the subject of investigation for ascertaining the mass of the primary. In this case M. Delambre has given the following formula: m= 3 (@). ; in which m is the mass of the planet in parts of the mass of the Sun, T the time of one sidereal revolution of the planet, a its mean distance from the Sun, t the revolution of the satellite, and a' its mean distance from the planet. Here the difficulty is to ascertain, with sufficient accuracy, the distance of the satellite from the planet about which it revolves, in order to have the ratio which enters into mass with the required α α correctness. Neither the masses nor the densities, however, have yet been determined with that precision which it is desirable to attain ; nor are those of the new planets yet known. The following masses have been determined by M. Laplace, and are regarded as the most accurate, that of the Sun being taken for unity : As these fractions are so small, they will convey much clearer conceptions to the mind when the. masses of the various bodies are compared with that of the earth; and with this view we shall present them. They will then be, The densities of bodies are to each other as their masses divided by their magnitudes; and hence, as the planets are nearly spherical bodies, which are as the cubes of their radii, their densities are as their masses directly and the cubes of their radii inversely. In this manner the following densities have been found, that of the Sun being assumed as unity; viz. If the density of the earth be taken for unity, the comparative density of the other bodies will then be as follows; viz. In order to furnish a still more familiar idea of this quality of the heavenly bodies, it will be necessary to compare it with that of some other body relative to which our conceptions are more clear and definite. For this purpose, water has been selected as the most convenient. Dr. Hutton, at the request of the Royal Society, calculated the mean density of the earth from observations on the pendulum made at the mountain Schehallien by Dr. Maskelyne, and found it to be to that of the hill as 9 to 5. Professor Playfair, from numerous observations, also determined the specific gravity of the hill to be between 2.7 and 2.8 times that of water; and, therefore, if the mean of these, 2.75, be taken, we shall have the mean density of the earth, supposing it equal to that of the hill, compar 9 ed with that of water; for x 2 = 5 to 1; that is, the mean density of the earth is 5 times as great as that of water. Hence the densities of the other bodies, when compared with that of water, will be, Mercury 12.9135 6'4030 \5.0000 |