170 Lord Kelvin on Ether and 



approximately constant for nearly as long a time as twenty- 

 five million years. It would, in fact, have many chances of 

 being much greater than 108 kilometres per second, and 

 many chances also of being considerably less. 



§ 15. Without attempting to solve the problem of finding the 

 motions and velocities of the thousand million bodies, we can 

 see that if they had been given at rest * twenty-five million 

 years ago distributed uniformly or non-uniform ly through 

 our sphere (5) of 3*09 . 10 ,G kilometres radius, a very large 

 proportion of them would now have velocities not less than 

 twenty or thirty kilometres per second, while many would 

 have velocities less than that ; and certainly some would have 

 velocities greater than 108 kilometres per second; or if 

 thousands of millions of years ago they had been given at 

 rest, at distances from one another very great in comparison 

 with r (5), so distributed that they should temporarily now 

 be equably spaced throughout a spherical surface of radius r 

 (5), their mean velocity (reckoned as the square root of the 

 mean of the squares of their actual velocities), would now be 

 50*4 kilometres per second f . This is not very unlike what 

 we know of the stars visible to us. Thus it is quite possible, 

 perhaps probable,, that there may be as much matter as a 

 thousand million suns within the distance corresponding to 

 parallax one one-thousandth of a second (3'09 . 10 16 kilometres) . 

 But it seems perfectly certain that there cannot be within 

 this distance as much matter as ten thousand million suns ; 

 because if there were, we should find much greater velocities 



* " The potential energy of gravitation may be in reality the ultimate 

 " created antecedent of all the motion, heat, and light at present in the 

 " universe." See ' Mechanical Antecedents of Motion, Heat, and Light.' 

 Art. LXIX. of my ' Collected Math. & Phys. Papers,' vol. ii. 



"J' To prove this, remark that the exhaustion of gravitational energy 



1 f + oc f + 0D f +0 ° 

 C^ = o- I 1 I ~R 2 dxdydz, Thomson and Tait's Natural 



cn: 



Philosophy, Part II. § 549) when a vast number, N, of equal masses come 

 from rest at infinite distances from one another to an equably spaced 

 distribution through a sphere of radius r is easily found to be 3/10 Fr, 

 where F denotes the resultant force of the attraction of all of them on a 

 material point, of mass equal to the sum of their masses, placed at the 

 spherical surface. Now this exhaustion of gravitational energy is spent 

 wholly in the generation of kinetic energy ; and therefore we have 



2 Iwm; 2 = A Fr, and by (7) F=P37 . 10" 13 2?n ; whence 



^ = !l-37.10- 13 .;- 

 2m 5 



which, for the case of equal masses, gives, with (5) for the value of r, 

 2 ^ 2 = V<! 1'37 . 10- 13 . 3-09 . 10 16 ) = 50-4 kilometres per second. 



V 



