174 Lord Kelvin on Ether and 



sun's mass, moving nearly in the same direction with a 

 velocity of 50 kilometres per second, and to overtake it and 

 pass it as nearly as may be without collision. Its own direction 

 would be nearly reversed and its velocity would be diminished 

 by nearly 100 kilometres per second. By two or three such 

 casualties the greater part of its kinetic energy might be 

 given to much larger bodies previously moving with velocities 

 of less than 100 kilometres per second. By supposing reversed, 

 the motions of this ideal history, we see that 1830 Groom- 

 bridge may have had a velocity of less than 100 kilometres 

 per second at some remote past time, and may have had its 

 present great velocity produced by several cases of near 

 approach to other bodies of much larger mass than its own, 

 previously moving in directions nearly opposite to its own, 

 and with velocities of less than 100 kilometres per second. 

 Still it seems to me quite possible that Newcomb's brilliant 

 suggestion may be true, and that 1830 Groombridge is a 

 ro\ing star which has entered our galaxy, and is destined to 

 travel through it in the course of perhaps two or three million 

 years, and to pass away into space never to return to us. 



§ 18. Many of our supposed thousand million stars, perhaps 

 a great majority of them, may be dark bodies ; but let us 

 suppose for a moment each of them to be bright, and of 

 the same size and brightness as our sun ; and on this supposi- 

 tion and on the further suppositions that they are uniformly 

 scattered through a sphere (5) of radius 3'09 . 10 16 kilometres, 

 and that there are no stars outside this sphere, let us find 

 what the total amount of starlight would be in comparison 

 with sunlight. Let n be the number per unit of volume, of 

 an assemblage of globes of radius a scattered uniformly 

 through a vast space. The number in a shell of radius q 

 and thickness dq will be nArrq 2 dq y and the sum of their 

 apparent areas as seen from the centre will be 



— - n . 4.7rcfdq or n . 4:ir 2 a 2 dq. 

 f 

 Hence by integrating from ^ = to q = r we mid 



n.47rW (8) 



for the sum of their apparent areas. Now if N be the total 

 number in the sphere of radius r we have 



n =N/(^>) (9). 



Hence (8) becomes N . 3tt( - ) ; and if we denote by a the 



