Scattering of a and ft Particles hy Matter. 677 



deviation of 90° in traversing an aluminium atom. This is 

 of a magnitude to be easily detected experimentally. Since 

 the value of K is very large for an encounter of a ft particle 

 with an atom, the reduction of velocity on this formula is 

 very small. 



Some very interesting cases of the theory arise in con- 

 sider in o- the changes of velocitv and the distribution of 

 scattered particles when the a particle encounters a light 

 atom, for example a hydrogen or helium atom. A discussion 

 of these and similar cases is reserved until the question has 

 been examined experimentally. 



§ 5. Comparison of single and compound scattering. 



Before comparing the results of theory with experiment, it 

 is desirable to consider the relative importance of single and 

 compound scattering in determining the distribution of the 

 scattered particles. Since the atom is supposed to consist of 

 a central charge surrounded by a uniform distribution of the 

 opposite sign through a sphere of radius R, the chance of 

 encounters with the atom involving small deflexions is very 

 great compared with the chance of a single large deflexion. 



This question of compound scattering has been examined 

 by Sir J. J.Thomson in the paper previously discussed (§ 1). 

 In the notation of this paper, the average deflexion (/> : due to 

 the field of the sphere of positive electricity of radius R and 

 quantity N<? was found by him to be 



#.= 



7T N*E 1 



1 4 * mu 2 ' Jbfc' 



The average deflexion c£ 2 due to the N negative corpuscles 

 supposed distributed uniformly throughout the sphere was 

 found to be 



^ 16 <?E 1 /3N 



♦ , -"W iiV "2 



The mean deflexion due to both positive and negative electricity 

 was taken as 



(& 2 +« 1/a . 



In a similar way, it is not difficult to calculate the average 

 deflexion due to the atom with a central charge discussed in 

 this paper. 



Since the radial electric field X at any distance r from the 



