218 H. Willy Wien on the Division of Energy in 



unaltered at a different temperature, if the scale of the draw- 

 ing were so changed that the ordinates were decreased in the 

 relation of 1/0 4 and the abscissas increased as 6. The latter is 

 with our value of <f> K only possible if X and 6 occur in ex- 

 ponents only as the product \0. 

 If c denote a constant, then 



fW-± 



e ~~ \6' 



The increase of total energy determines the value of F(\). 

 Indeed the relation must hoi d 



j; 



F(\> «x<7\ = const. 6\ 



F(\) can be found by the method of undetermined coefficients. 

 We imagine F(\) expanded into a series and make X = c/yd, 

 then 



t^x tV c \ 6y 0V 6 n tj 



n , ,n 



yd J c 



c 



Integration of this gives 



jWW jrj>(£).^« i-^j/rv^. 



Therefore . m v 0*" 1 ™ ii 



COnst. 0*= £»«»-— r r (W— 1) . 



c 



All the coefficients are therefore nothing except one of them, 

 the coefficient of 6 n ~ ] = i ; 



therefore n=5. 



Consequently const. 



Accordingly the equation for <f> k is 



. C _£ 



From this follows : — 



d<f> Ce~w/ 



( 8_ 5) 





c 



?("-*?+£)» 



