640 Mr. J. H. Jeans on the 



<k pulses." The energy of these waves will be either partially 

 or entirely absorbed by the other molecules of the gas, either 

 by forcing vibrations in them, or by affecting their velocities 

 of translation or rotation ; and in this way we have a second 

 path for the transfer of energy. If this absorption is com- 

 plete, the total mean energy E + F will remain constant 

 throughout, and a steady state will be possible. If the ab- 

 sorption is only partial, a steady state will only be possible if 

 we suppose energy introduced into the gas by some external 

 •agency, of amount sufficient to compensate that which is lost 

 by the radiation of waves. 



If the law of distribution of E and F among the molecules 

 of the gas is known, it will be possible to calculate the two 

 transfers caused respectively by collisions and electromagnetic 

 waves. The rate at which F increases owing to collisions 

 will be some function of E and F, which will for the present 

 be denoted by $(E, F) ; the rate at which F increases owing 

 to radiation and absorption may similarly be taken to be 

 n|r(E, F). We therefore have, for the total change in F, 



^=*(E,F)+*(E,F) (1) 



There must be at least one steady state; let the corre- 

 sponding root of 



<£(E>F)+>|r(E, F)=0 ..... (2) 

 be 



' F=/(E) (3) 



When the reaction with the sether is of zero amount, 

 equation (3) will reduce to the expression of the Maxwell- 

 Boltzmann law ; but a very small reaction may, as was 

 pointed out in the paper previously referred to, suffice to 

 alter entirely the form of this equation. The value of y is 

 now given by 



6?E 3 , 



d(E + F) *V ij ' 



or 



2 

 7 = 1+ 3(1 + /'(E7)' ' ' * ' * W 



where /'(E) stands for df(E)/d'E. 



This value of y is not restricted to being one of the series 

 given by the formula 1+2/ra, and is, moreover, capable of 

 variation with the temperature. 



§ 3. The right-hand member of equation (1) contains as a 



