Photoelectric and Photochemical Action. 483 



one previously discussed *, viz : — 



|=/ t ,andF(,„,v)=^- t (v-v ) . . . (19) 



as the particular case p — 1 restricted in validity to small 

 values of T. 



Now consider the equation (16), which we may write 



hu hvn 



e - kt Mv = *(!>- fir , . (20) 



_f v 3 F(v ,v) 



-J„ o l_,-VKT 



when 



<S>(T) = AT 5 , 



KT 



+ J RT2 



rfT 



(21) 



This may be regarded as defining <£(T). Equation (18) 

 suggests putting 



1 hv 



F(V , v) = -j (1 - e ~ kt ty(„ - „ ), 



(22) 



where >Jr is an undetermined function of v — v only and does 

 not involve T. It follows from (18) that ifr can include 

 every function of the argument which is regular between 

 v = v and v = vo and still be a solution of (17). By changing 

 h(v—v ) 



the variable to z== 



KT 



I = RT^ ktI ty[-r-z\e *-dz, 

 and by successive integration by parts 



RT{^(0) + ^ T ^(0) + (^)V"(0)+ . • • 



+ (x)V(0)+...}=*(T). • (23) 



Since, by hypothesis ^r(v — y ) does not depend on T, 

 •^r(O), ^r'(O) . . . ip(0) . . . &c. are all independent of T. 

 If the solution we are seeking exists, equation (23) must 

 be true for all real positive values of T. The solution there- 

 fore will only exist if <E>(T) can be expanded as a series of 

 positive integral powers of T. By Maclaurin's theorem, if 

 such an expansion is possible, 



T- 



T« 



3>(T)=<S>(0) + T<I>'(0) + ^$"(0)+ . . . + — } ^ n (0)+. . . (24) 



* Phil. Mag-, vol. xxiv. p. 570 (1912). 



