251-254] Calculation of Subsidiary Temperatures 211 



In the normal state -^, ^- 2 ... vanish in comparison with T I( r 2 ... so that 



from equations (500) and (501) 



2eTi= 0j = v<f)i(T) etc (502). 



d> f rr ^ 

 Or, writing / x (T 7 ) for -^r 



(503). 

 etc. 



These equations give the subsidiary temperatures as functions of the 

 principal temperature and the molecular-density of the gas. 



An illustration of these equations has already been obtained in 

 equation (469). 



253. There is, however, a second standpoint from which we may attack 

 the problem of obtaining equations for the subsidiary temperatures. Up to 

 the present we have taken full account of the dissipation of energy which is 

 caused by radiation into the ether, but we have not followed this energy any 

 further after it has once been transmitted to the ether. If we are dealing 

 with a thin layer of gas isolated in space, this procedure will probably give 

 an adequate representation of the facts of the case. The energy is merely 

 radiated away from the gas, and since there is no way by which it can 

 return, its existence need not further trouble us. 



254. Suppose, on the other hand, that the gas is enclosed in an ideal 

 vessel, of which the walls are perfect reflectors, and are therefore absolutely 

 incapable either of transmitting or absorbing energy. The total energy 

 inside this vessel must remain constant, so that the energy radiated out 

 by the gas accumulates in the ether. It is now necessary to consider the 

 possibility of a retransference of energy from the ether to the matter. 



The energy lost to the gas by dissipation from a vibration of frequency p 

 will exist in the ether in the form of trains of waves of frequency p. Such 

 a train of waves falling upon a second molecule will be represented by a 

 force-function, simply-harmonic as regards the time and of frequency^?, acting 

 upon the coordinates of the molecule. From the analysis of the last 

 chapter (p. 201) it is clear that this train of waves will "force" vibrations 

 in the molecule of frequency p, if such vibrations are possible, but will have 

 only an infinitesimal effect upon vibrations of other frequencies. Thus the 

 only perceptible transfer of energy from the ether to the vibratory energy of 

 the gas will be a transfer of energy represented by waves of one definite 

 period to vibrations of the same period. This, of course, is fully in agree- 

 ment with the results of spectroscopy, as shewn by absorption bands in 

 the spectrum. 



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