﻿Absorption and Scattering of the a. Rays. 915 



integral. The mean deflexion from the electrons is 



Only two of the integrations can be performed, and the 

 expression then becomes elliptic and progress would be 

 ditiicult. We shall at once evaluate it on the supposition 

 that aV/A, 2 is large, as the development of (ii.) later is only 

 possible with large velocity. In this case 



^'=2/^(2-3 y 



<r L v \ 8 / 

 In the case of a surface distribution a similar process gives 



The central charge plays a large part in scattering through 

 small angles as well as through large. From (2) the 

 deflexion is t \jr" where 



tan yjr" = 2k'\'Fv 2 /F 2 v 4 (k' + 1) -\ f2 (k' - 1), 

 When k'>l this quantity can take any value positive, 

 negative, or infinite. In experiments on small scattering 

 when a large deflexion occurs, the a particle does not appear 

 on the field of observation. Suppose that a particle which 

 is deflected through an angle greater than 8 is not observed. 

 8 will be of the order of 2° or 3°. This excludes from the 

 mean to be taken values of P less than a certain amount. 

 For larger values of P, f" may replace its tangent. When 

 the mean is taken it appears that when the velocity is high 

 the part dependent on 8 is unimportant and that the mean 

 is given by neglecting the second term of the denominator, 



Thus *"=4^^ T -ii^! 



7 av 1 k' + l av 2 



yfr'^ is away from the centre, yjr' towards it. Hence their 

 combined effect is 



for volume, and 



lit It -17 Wo A. 1 



a.v 2 2 



for surface distribution. Here for the first jtime there enters 

 a^ distinct difference between the effects of the alternative 

 distributions, 



3 02 



