174 



Physical Properties 



[CH. vii 



As regards the degrees of freedom represented by the spectral lines, we 

 shall find that equation (420) is satisfied very approximately by taking 



= 0, a = 7 (422). 



That is to say, the vibrations set up by collisions are no longer balanced by 

 the transfer of energy back from these degrees of freedom to the translational 

 energy, but by radiation into the ether. 



Mechanical Illustration. 



206. A simple analogy will probably elucidate the meaning of these 

 solutions better than pages of discussion. Suppose that we have two vessels 

 A, B filled with gas and connected by a passage C. Suppose the vessels and 



Fio. 12. 



passage to be bounded by non-conducting walls, then the whole gas forms 

 a conservative dynamical system, and in its steady or normal state, the mean 

 energy of the molecules in A is equal to the mean energy of the molecules 

 in B in other words the temperatures in A, B are equal, being equalised by 

 conduction through the passage C. The temperature in A is analogous to 

 the mean energy of one of the momentoids of translation, say ^mti*, the 

 temperature in B is analogous to the mean energy of a momfiCLtoid repre- 

 sented by one of the spectral lines, say |a< 2 in equation (417). 



/ The equivalence of these two temperatures is the analogue of the 

 /solution /3 = 7 (equation (421)) in the case in which there is no dissipation 

 of energy. 



To represent the dissipation of energy, let us suppose that one of the 

 walls bb' of the vessel B is made a conductor of heat, the further face being 

 kept at a zero temperature. The loss of heat which occurs by conduction 

 through the wall bb' is now analogous to the loss of energy to which the 

 momentoids represented by the spectral lines are subjected on account of 

 the radiation into the ether. The analogy of the steady state represented by 

 equation (422) is a state in which the gas in the chamber B is almost 

 entirely devoid of heat, so that the loss of energy by conduction through bb' 

 is very small, and in which this loss is just counterbalanced by the supply 

 of heat which reaches the gas in B through the passage G. It is clear 



