Page:Somerville Mechanism of the heavens.djvu/37

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. 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, 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 354936 times greater than that of the earth; whence the great perturbations of the moon and the rapid motion of the perigee and nodes of her orbit. Even Jupiter, the largest of the planets, is 1070.5 times less than the sun. The mass of the moon is determined from four different sources,—from her action on the terrestrial equator, which occasions the rotation 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 titles. The three first quantities, computed from theory, and compared with their observed values, give her mass respectively equal to the $\scriptstyle {\frac {1}{71}}$, $\scriptstyle {\frac {1}{74\cdot 2}}$, and $\scriptstyle {\frac {1}{69\cdot 2}}$ part of that of the earth, which do not differ very much from each other; but, from her action in raising the tides, which furnishes the fourth method, her mass appears to be about the seventy-fifth part of that of the earth, a value that cannot differ much from the truth.

The apparent diameters of the sun, moon, and planets are determined by measurement; therefore their real diameters may be compared with that of the earth; for the real diameter of a planet is to the real diameter of the earth, or 8000 miles, as the apparent diameter of the planet to the apparent diameter of the earth as seen from the planet, that is, to twice the parallax of the planet The mean apparent diameter of the sun is 1920″, and with the solar parallax 8″.65, it will be found that the diameter of the sun is about 888000 miles; therefore, the centre of the sun were to coincide with the centre of the earth, his volume would not only include the orbit of the moon, but would extend nearly as far again, for the moon's