SECTION VIII. Masses of Planets that have no Satellites determined from their Perturbations—Masses of the others obtained from the Motions of their Satellites—Masses of the Sun, the Earth, of Jupiter and of the Jovial System—Mass of the Moon—Real Diameters of Planets, how obtained—Size of Sun, Densities of the Heavenly Bodies—Formation of Astronomical Tables—Requisite Data and Means of obtaining them. THE masses of such planets as have no satellites are known by comparing the inequalities they produce in the motions of the earth and of each other, determined theoretically, with the same inequalities given by observation; for the disturbing cause must necessarily be proportional to the effect it produces. The masses of the satellites themselves may also be compared with that of the sun by their perturbations. Thus, it is found, from the comparison of a vast number of observations with La Place’s theory of Jupiter’s satellites, that the mass of the sun is no less than 65,000,000 times greater than the least of these moons. But, as the quantities of matter in any two primary planets are directly as the cubes of the mean distances at which their satellites revolve, and inversely as the squares of their periodic times (N. 135), the mass of the sun and of any planets which have satellites may be compared with the mass of the earth. In this manner it is computed that the mass of the sun is 354,936 times that of the earth; whence the great perturbations of the moon, and the rapid motion of the perigee and nodes of her orbit (N. 136). Even Jupiter, the largest of the planets, has been found by Professor Airy to be 1047·871 times less than the sun; and, indeed, the mass of the whole Jovial system is not more than the 1054·4th part of that of the sun. So that the mass of the satellites bears a very small proportion to that of their primary. The mass of the moon is determined from several sources—from her action on the terrestrial equator, which occasions the nutation in the axis of rotation; from her horizontal parallax; from an inequality she produces in the sun’s longitude; and from her action on the tides. The three first quantities, computed from theory and compared with their observed values, give her mass respectively equal to the 1/71, 1/74·2, and 1/69·2, part of that of the earth, which do not differ much from each other. Dr. Brinkley has found it to be 1/80 from the constant of lunar nutation: but, from the moon’s action in raising the tides, her mass appears to be about the 1/75 part of that of the earth—a value that cannot differ much from the truth.