212 Theory of a Non-Conservative Gas [CH. x 



In discussing the transfer of energy from the ether to the translational 

 energy of a gas, we are dealing with the phenomenon known as the "pressure 

 of radiation." From electrodynamical considerations, it can be shewn that 

 a transfer of this kind will actually occur, and this again is fully in agreement 

 with the results of observation as, for instance, the fact that the air is 

 warmed by sunlight. 



To attempt to represent this mathematically, let us suppose that the 

 aggregate energies in the gas represented by the temperatures T, T I} r 2 ... 

 are respectively ST, s^, s. 2 r 2 .., etc., so that S, s lt s 2 ... are each pro- 

 portional to v. Let us suppose that the wave energies in the ether of 

 frequencies equal to those of the vibrations T I} T 2 ... are E lt E 2 .... Let us 

 suppose further that the ether-energy E l increases the value of TI at a rate 

 ^ 1 E 1 and the value of T at a rate X 1 E 1 , the quantities a , X 1 being of course 

 independent of v. Then, if we neglect all the energy in the ether except that 

 of definite trains of waves, we shall have equations of the forms 



.(504), 

 etc. 



O/TT "I 



toQ _i_ o /? _i_ \ _i_ ( ~^r T? _i_ y T^ _i_ ^ ^ ^o %\ 



for the changes of material energy, and for the changes of the energy of the 

 ether, equations of the forms 



= 2**^ - s^E, - 8X& , etc ................ (506). 



vt 



From these equations we obtain at once 



...) = ............ (507), 



i 

 ot 



expressing that the total energy remains unaltered. 



255. There is now possible an absolutely steady state, the mathematical 

 expression of which is obtained by equating to zero the right-hand side of 

 every equation from (504) to (506). These equations, however, are not 

 independent, in virtue of equation (507). We may therefore omit one 

 equation, let us say (505). We are left with equations of the types 



(508), 



the remaining equations being obtained by replacing the suffix 1 by 2, 3 ... 

 Solving the pair of equations (508), we obtain 



E* Q 



(509), 



