﻿Absorption and Scattering of the a. Rays. 903 



of absorption much easier than that of transverse scattering, 

 which is really more akin to straggling. In the scattering- 

 there is a considerable effect due to the inequalities and 

 irregularities of distribution of the electrons. In the longi- 

 tudinal motion such irregularities only affect the straggling 

 and produce no change in the mean. The reason for this 

 lies in the fact that here the composition of the effects of 

 successive atoms is by simple addition, while for scattering 

 it is by addition of squares. 



§ 2. The Velocity Curve*. 



If E, M, e, m be the charges and masses of u particle and 

 electron ; if & = m/M and X == (1 + IcfEieJm, and if v be the 

 velocity with which an a particle approaches an electron on 

 a line at distance p from it, then a simple calculation of their 

 orbits shows that after the two have separated the velocity of 

 the a particle is v + Av where 



(v + Av) 2 =v 2 {l + 2kcos2fjL + k 2 )/(l + k) 2 . . (1) 



if tan fi=\/pv 2 . The a particle is deflected through an 

 angle i/r where 



tan i/r = k sin 2fi/(l + k cos 2/ul) (2) 



These formulae are accurate, whatever the values of m and 

 M. But m is the mass of an electron so that k is small and 

 (1) may be rewritten as 



Av=-kv(l-oos2 f ,)=-2kv p ^ I? . . . (3) 



This is the velocity which the a particle loses in passing a 

 single electron. In summing the effects of all the electrons 

 of the atom, we encounter the difficulty that the forces 

 exerted between an electron at one side of an atom and the 

 particle at the other are not greater than the internal forces 

 of the atom. In such a case, however, (3) gives a very small 

 value, so that practically it is only the electrons very near 

 the path of the a ray which contribute sensibly to the 

 reduction of its velocity. It seems that the inclusion of all 

 the electrons in the atom is less objectionable than the fixing 

 of an arbitrary limit beyond which no forces shall be allowed 

 to countf. Let n be the number of electrons in the atom. 



* For a definition of this term see p. 901, note §. 



t I originally worked out the whole theory, supposing that only elec- 

 trons in a cylinder near the path of the particle exerted any force on it. 

 The results are almost identical with the present. 



