-486 Prof. 0. W. Richardson on the Theory of 



From this 



3>(T) = AT 2 (36) 



where A is a constant, and from (34) 



♦Wsfc, (37; 



for every substance and at all temperatures. Thus the 

 restriction to low temperatures which might have been 

 required for (37) to satisfy (10) is not really necessary. 

 Equation (33) now reduces to 



T v =h(v-v \ (38) 



and, putting v — v = l v, (31) becomes 



.v+(.r) = 2^ir(.v)<h; (39) 



|^+^0) = 2fO) (40) 



or 



x 

 Thus 



ir(v-v )=A 1 (v-v ), .... (41) 



where A x is a constant. The values of <J> and -fr given by 

 (36) and (41) respectively satisfy the relations (25), since 



^'(0)=A ] , <D"(0) = 2A, 



and all the other coefficients vanish. Incidentally, from 

 (32), 



.) 



IC 



= hvo+ £RT (42) 



The results of this investigation may be summarized as 

 follows : — Considering the equation 



I 



t { °' V) M y =2BT<^(T>-^ = 2ART 3/2 ^ T2 > 

 e ET -l 



which contains most of the quantities under discussion. 

 This equation and equations (10), (16), and (17), all^ of 

 which involve independent relationships, are all satisfied 



