548 Dr. W. F. G. Swann on the Pulse 



thou oh we must admit that this law cannot hold right up to 

 the point at which the electron gets free, we must imagine 

 our actual atom replaced by a kind of hypothetical atom in 

 which the law does hold. We shall assume a case where 

 there is resonance between the light-waves, and the oscilla- 

 tions parallel to the y axis, and our equations of motion 

 become approximately 



y +4.7rhi 2 y=^sin27rnt, . . . . (19) 



leading to •« , . „ 9 Y n e . • * /on\ 



& a: +4:7r 2 u?x=- .ysm2irnt, . . . (20) 



- {^ 2 + 27rV?/ 2 }=i7+,47r 2 j/A 2 ^ . . (21) 



c 



n and /ul being the natural frequencies of the electron parallel 

 to the y and x axes respectively. 



We have already, on p. 544, given reasons for supposing 

 that for the cases in which we are concerned jul is small. 

 In the Appendix (problem 4) we shall consider the case 

 where fx is not absolutely zero, i. e. where the electrons are 

 not entirely free along the x axis, an assumption which leads 

 to a theory very similar to that given below, in which we 

 take the simpler case where fi is zero. 



The solution of (19) subject to y=y=y = 0, when t = 0, is 



v = -r^- (^sin27T7i*-*cos27m*"l, . (22) 

 J kirmn l m 2irn ) v y 



giving . Y <?, . , /OON 



to & y= — — i sin lirnt (23) 



Unless pis as small as one or two, at the joth maximum (mea- 

 sured in the positive direction only) the value of y is very 

 approximately 



(</),= ( £± ^) £= \~ approximately. 



If co is the minimum energy which the electron must have 

 in order to get away, the first integer p which makes 



1 fl YgeV 



4 ii 2 \ m J 



2co 

 m 



will result in the electron becoming free. If at the (p— l)th 

 maximum the electron has nearly enough energy to escape, 

 it will after the pth maximum get away with practically the 



