we divide the cube of their mean distance apart by the square of their time of revolution, we shall get a quotient which will not indeed be 1, but which will be a number expressing the combined mass of the two bodies. If one body is so small that we leave its mass out of consideration, then the quotient will express the mass of the larger body. If the latter has several minute satellites moving around it, the quotients will be equal, as in the case of the Sun, and will express the mass of this central body. If, as in the case we have supposed, we take the year as a unit of time and the distance of the earth from the Sun as a unit of length, the quotient will express the mass of the central body in terms of the mass of the Sun. It is thus that the masses of the planets are determined from the periodic times and distances of their satellites,
Fig. 1.
and the masses of binary systems from their mean distance apart and their periods. To express the general law by a formula we put
Then we shall have:
Another conclusion we draw is that if we know the time of revolution and the radius of the orbit of a binary system, we can determine what the time of revolution would be if the radius of the orbit had some standard length, say unity.
We cannot determine the dimensions of a binary system unless we know its parallax. But there is a remarkable law which, so far as I know, was first announced by Pickering, by virtue of which we can determine a certain relation between the surface brilliancy and the density of a binary system without knowing its parallax.
Let us suppose a number of bodies of the same constitution and temperature as the Sun—models of the latter we may say—differing from it only in size. To fix the ideas, we shall suppose two such bodies, one having twice the diameter of the other. Being of the same brilliancy, we suppose them to emit the same amount of light per unit of
