﻿Absorption and Scattering of the a Rays. 917 



For high velocities the scattering should thus vary in- 

 versely as the square. The measurements of Geiger * on 

 the dependence of scattering n velocity are not very 

 accurate, but the inverse cube gave the best agreement. 

 As this was determined with some quite low velocities, (10) 

 and (11) may be regarded as reasonably satisfactory from 

 this point of view. 



The quantities ^r 1? yfr 2 are mean angles of deflexion. 

 Geiger measured the most probable angle. Assuming (as 

 has already been tacitly done) an error law of distribution, 

 the latter is obtained by multiplying y[r by \^2/tt. 



It is convenient to consider both y[r 1 and -\jr 2 together by 

 writing them 



JcXnV 2 



where 



Vi = 2 v/^i + 2'77 and *> 2 = ^?i 2 + l'4:±. 



For a thin foil the whole scattering is obtained by multi- 

 plying -yjr by the square root of the number of atoms 

 encountered. In a foil of thickness Ax this number is 

 ]S T 7rc7 2 Ajt' and the most probable angle of scattering is 



x = ~ thi 1 ^ \/2NA.y (12) 



Experiments on scattering at high velocities should thus be 

 able to determine n without a. 



Geiger performed experiments with both small and great 

 thicknesses of gold, but for other metals he only had thick 

 foils, and for such the change of velocity during transit has 

 to be taken into account. Geiger f has shown how this 

 explains the shape of the curve connecting scattering with 

 thickness of the scattering foil. I follow his method, but 

 use my own formula? as the result is rather simple. When 

 the variation of velocity is taken into account the most 

 probable angle of scattering is 



X 



Now 



AXTrnVV^N.S^y* 



SN7r<j 2 A.r/^= \ dv/pv\ 

 where V and v are the incident and emergent velocities 



* II. Geiger, Proc. Roy. Soc. A. vol. lxxxiii. p. 492 (1910). 

 f II. Geiger, Proc. Roy. Soc. A. vol. lxxxvi. p. 286 (1912). 



