482 Prof. 0. W. Richardson on the Theory of 



scheme of relations may be framed whereby 



<j>(y) = hv 



universally, at all temperatures. The deduction will depend 

 on assumptions (1), (2), and (4) but not on the first part of 

 assumption (3). 



The Amount of Decomposition. 



The function e¥(y) is of great interest. The experiments- 

 on photoelectric action show that it may be very complicated,, 

 and the simple solutions of the equations which I have so far- 

 been able to consider exhibit only a rough correspondence 

 with the experimental results*. It is, however, important 

 to know whether they are affected by the considerations 

 about the specific heat of electricity which I have previously 

 made use of. 



eF(v) is a function of v as well as v. Let us denote it by 

 FOo, v). Then from (4) and (5), 



?_. /»» hv d 



*4\ ~hT -F(v ,v)^=AT% 



C'Jpq e UT— 1 



rr w 



dT 



w = N. . (16)* 



This equation may be varied by giving to w a small incre- 

 ment 7) (independent of T) and a corresponding increment f 

 to j/ , the other quantities being unchanged. This variation 

 is admissible* because it can be realized physically by making 

 use of a layer of attracting matter or an electrical double 

 layer. Hence 



J*o+£ 



Jw* 



<?RT_ i 



■F(v +f,v)rfv: 





"o e kt — 1 



Neglecting squares and higher powers of the small quantities: 

 f, 7), and remembering that F(v , v) = when v = v , this 



Equation (17) is solved by 



|=7 i ,a n dF(v ,")= C ^ S! '(l-^-^)x(v-v )'' . (18) 



where p is any positive number. This solution includes the 



Compton and Richardson (loc. cit.). 



