﻿796 Dr. W. Wilson on the Quantum-Theory 



and further 





and consequently 



Wl T "3j: 



2L 2 =q 2 p 2 





>■ 



(1) 



where 



2L„=^ J 



L 1 = hA 1 q l 2 , L 2 = ±A 2 q 2 2 , &c. 



We assume that the system in one of its steady states has a 

 period — corresponding to q it — corresponding to q 2 , and so 



v l v 2 



on. From the equations (1) we get 



2§L 1 dt=§p i dqi 



and similar equations containing L 2 , L 3 , &c. Our third 

 hypothesis can now be stated as follows : — The discontinuous 

 energy exchanges always occur in such a way that the steady 

 motions satisfy the equations: 



^Pidqi—ph^ 



yp 2 dq 2 = oh I 



(2) 



where p, <r, t, ...are positive integers (including zero) and 

 the integrations are extended over the values ^> s and q s corre- 

 sponding to the period - . The factor h is Planck's universal 



constant. It will be convenient to denote these integrals by 

 Hi, H 2 , . . . respectively. 



We shall now consider the statistical equilibrium of a 

 collection of N similar systems of the type specified above. 

 Let Np<TT... be the number of systems for which R l = ph, 

 H 2 = *h, H s = t/i, and so on ; and N p w ... the number of 

 systems for which Hi = p7*, H 2 =VA, R^r'h.... Let us 

 further write 



Npgr.. . 



N 



(3) 



