Theory of Photoelectric Action. 571 



indicate that eF(v, 0) is practically independent of 0, so that 

 we should expect eF(v, 0) to be a function of v only. We 

 shall assume that we can put 



w = w + |R# 



where w is independent of .0. As yet, this equation has 

 only been justified as a convenient approximation. For 

 the present we shall also assume that « = 1, i. e. that there 

 is no reflexion of the incident electrons. This assumption has 

 probably more serious physical consequences than any of the 

 others when the results come to be applied to the behaviour 

 of real matter. Under these circumstances equation (2) 

 reduces to 



_ ^ . 



N = A0 2 * Ry (3) 



For the radiation formula we shall assume 



E(,^)=5^-^ (4) 



It can be shown that the replacement of Planck's formula 

 by (4) only introduces inaccuracies in the final results which 



_^ 

 are proportional to ^ . This is a very small proper 



fraction. The integral equation to be solved is now reduced 

 to 



_ hv _ w 



^(y)ltvh~^dv = A l 2 e M , . . . (5) 



I 







4 1 — 9^- ^' 

 £7T 



This is satisfied by 







eF(v) = 





when < hv < ic 



and j*. ■ AJt 



(1 



— j^j when w <hv<<x> 



(5 a) 



A 

 This is of the general form, —~ x a universal function of 



j— 3 which was previously specified ; it is not, however, the 



same analytic function of v throughout the range from to oo . 



