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



expenditure of energy, and i£ the velocity curve is approxi- 

 mately v 3 = V 3 (l — #/R), then it follows directly that the 

 ionization is approximately inversely proportional to the 

 velocity ; and no further significance need be attached to 

 this relation. 



Part II.— Scattering. 



The mechanism which accounts for absorption must also 

 be capable of accounting for scattering. The problem of 

 scattering is the more complicated of the two, as it deals 

 not with a mean effect, but with the mean departure from 

 such an effect, and in this way is analogous to the problem 

 of straggling rather than to that of absorption. In conse- 

 quence of this difference, difficulties enter which prevent 

 the complete solution, and we must be satisfied with an 

 approximation. 



§ 5. The Formulas for the Scattering. 



The difficulty of the scattering lies in the fact that when 

 an electron lies very close to the path of the particle it 

 exerts a much greater effect than the average, and this effect 

 is not counterbalanced by the absence of an electron in 

 succeeding encounters. In the case of the absorption, any 

 effect of such an electron does not alter the mean, but only 

 tells on the amount of straggling. To consider the scat- 

 tering it is thus convenient to divide the effect of the atom 

 into two parts. The first is due to the regular average 

 distribution of electrons together with the effect of the 

 central charge. The combined effect of these is a deflexion 

 in a plane through the centre. The second is due to the 

 chance occurrence of electrons very near the path of 

 the a. particle. This deflexion wili be in an arbitrary 

 direction. 



(i.) The deflexion by a single electron is from (2) equal 



t 2k- — — z. The component of this expression in a 



plane through the centre of the atom is to be summed for 

 all the electrons. In this summation the electrons very near 

 the path of the particle will contribute equal amounts in all 

 directions, so that there is no need to exclude them on the 

 ground that they are to be counted later. The summation 

 of all the electrons, and the averaging for all positions of the 

 a particle, gives, as in the case of the absorption, a quadruple 



