CHAPTERS ON THE STARS. 131 



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 considera- 

 tion, 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, 



Oc 



A 



c o 



o 



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 



a, the mean distance apart of the two bodies, or the semi-major axis 

 of their relative orbit in terms of the earth's mean distance from the 

 Sun; 



P, their periodic time; 



M, their combined mass in terms of the Sun's mass as unity. 



Then we shall have: 



Another conclusion we draw is that if we know the time of revolu- 

 tion 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 bril- 

 liancy, we suppose them to emit the same amount of light per unit of 



