﻿916 Mr. C. G. Darwin : A Theory of the 



(ii.) Sir J. J. Thomson * has shown how to deal with the 

 irregular deflexions due to electrons lying very close to the 

 path of the a ray. The present is a modification of his 

 method to suit the hypotheses of this paper. Suppose that 

 any electron in a cylinder of radius I round the path is to be 

 counted as very near it. The mean deflexion of such an 

 electron is 



When v is large the second term is negligible, and unless 

 this. is so progress is prevented, since I will not disappear 

 from the equation and it is impossible to know what is the 

 right value to take for I. To estimate the whole effect of all 

 the electrons in the cylinder w T e must multiply this expression 

 by the square root of their number. For volume distribution 

 their number is 



and the mean of the square root of this for all values of P is 



Z4 /3 



3 



Thus the whole deflexion due to these electrons is 



The corresponding expression for surface distribution is 

 . ,„ U\ ,-4 /I 



These deflexions are in arbitrary directions and must be 

 compounded with those of (i.). The results are i/r b -ijr 2 the 

 mean deflexion of the whole atom. 



^=s{(t^)Miviwy /2 



= ^ r . r r v /„ 1+ 2-77; (10) 



* Sir J. J. Thomson. Proc. Camb. Phil. Soc. xv. pt. 5 (1910). 



