THE MILKY WAY. 257 



personages and the Sun alone counts, so that our 

 molecule is clearly monatomic. And even if we take 

 a double star, it is probable that the action of a foreign 

 star that happened to approach would become suffi- 

 ciently appreciable to deflect the general motion of 

 the system long before it was capable of disturbing 

 the relative orbits of the two components. In a word, 

 the double star would behave like an indivisible atom. 



However this may be, the pressure, and consequently 

 the temperature, at the centre of the gaseous sphere 

 are proportional to the size of the sphere, since the 

 pressure is increased by the weight of all the over- 

 lying strata. We may suppose that we are about at 

 the centre of the Milky Way, and, by observing the 

 actual mean velocity of the stars, we shall know what 

 corresponds to the central temperature of our gaseous 

 sphere and be able to determine its radius. 



We may form an idea of the result by the following 

 considerations. Let us make a simple hypothesis. 

 The Milky Way is spherical, and its masses are dis- 

 tributed homogeneously : it follows that the stars 

 describe ellipses having the same centre. If we sup- 

 pose that the velocity drops to nothing at the surface, 

 we can calculate this velocity at the centre by the 

 equation of vis viva. We thus find that this velocity 

 is proportional to the radius of the sphere and the 

 square root of its density. If the mass of this sphere 

 were that of the Sun, and its radius that of the ter- 

 restrial orbit, this velocity, as is easily seen, would be 

 that of the Earth upon its orbit. But in the case we 

 have supposed, the Sun's mass would have to be 

 distributed throughout a sphere with a radius 1,000,000 

 times as great, this radius being the distance of the 



