234 Proceedings of Royal Society of Edinburgh. [sess. 
motionless as in an absolutely cold solid, or they may have the 
thermal motions of the molecules of a solid, liquid, or gas at any 
temperature not so high but that the thermal velocities are every- 
where small in comparison with the velocity of light. The effective 
inertia of the ether per unit volume of the assemblage will be 
exceedingly nearly the same as if the atoms were all absolutely 
fixed, and will therefore, by § 15, be equal to 
l+N^s 3 -634 (15), 
6 
where N denotes the number of atoms per cubic centimetre of the 
assemblage, one centimetre being now our unit of length. Hence, 
if we denote by V the velocity of light in undisturbed ether, its 
velocity through the space occupied by the supposed assemblage of 
atoms will be 
V/( ln-N^s 3 ^) 4 ..... (16). 
§ 17. Tor example, let us take N = 4 x 10 20 *; and, as I find 
suits the cases of oxygen and argon, s=T42xlO~ 8 , which 
gives s 3 = *60 x 10 -3 . The assemblage thus defined would, 
if condensed one-thousandfold, have *6 of its whole volume 
occupied by the atoms and *4 by undisturbed ether; which is 
somewhat denser than the cubic arrangement of globes 
(space unoccupied = 1 - ^ = *47 64), and less dense than the 
7 r 
densest possible arrangement (space unoccupied = 1 - — = = 
•2595). Taking now N ^s 3 = *60 x 10~ 3 in (16), we find for 
the refractive index of our assemblage 1 '0001 9, which is somewhat 
smaller than the refractive index of oxygen (1 *000273). By taking 
* I am forced to take this very large number instead of Maxwell’s 
19xl0 18 , as I have found it otherwise impossible to reconcile the known 
viscosities and the known condensations of hydrogen, oxygen, and 
1 v v 
nitrogen with Maxwell’s theoretical formula D~ ’3989|y 
where v is the Newtonian velocity of sound in the particular gas, and D is 
its diffusivity, that is, its viscosity divided by its density. It must be 
remembered that Avogadro’s law makes N the same for all gases. 
