﻿440 Prof. W. L. Bragg and Messrs. James and Bosanquet : 



The average contribution of the electron in each atom to the 



F factor is therefore —7— , and not unity as it would be 



if the electron were at the centre of the atom. 



If there are n electrons at a distance a from the centre of 

 the atom, their contribution to the F factor would be 



sin 6 , Q . 



n -f < 3 > 



Any arrangement of n electrons at a distance a from the 

 centre of the atom, provided that all orientations of the 

 arrangement were equally probable, would make the same 

 contribution to the F factor. Foe example, eight electrons 

 arranged in a ring about the nucleus would give the same 

 value for F as eight electrons arranged at the corners of a 

 cube, or eight electrons rotating in orbits lying on a sphere 

 of radius a. This illustrates the limitations of our analysis, 

 which cannot distinguish between these cases. We can only 

 expect to get information from our experimental results as 

 to the average distance of the electrons from the atomic 

 centre, and this for the average atom. 



Suppose now that any atom contains a electrons at a 

 distance ?\ from the nucleus, b at a distance r 2 , c at a dis- 

 tance r B . . . n at a distance r n , then the value of F for the 

 average atom would be given by 



F =a !i^ + 6 si ^ + o%i 3 + ... + n ^i". . (4) 

 9i 92 93 9« 



Thus, given the distribution of the electrons on a series of 

 shells or rings, we can calculate the value of F for any value 

 of 6. The problem we have to solve here, however, is the 

 converse of this. We have measured the value of F for a 

 series of values of #, and wish to determine from the results 

 the distribution of the electrons. We have seen above that 

 there is no unique solution of this problem, but we can get 

 some idea of the type of distribution which will fit the 

 experimental curves. 



In order to do this, we suppose the electrons to lie on a 

 series of shells, of definite radii r 1; r 2 , .... and determine 

 the number of electrons a, b, c on the various shells which 

 will give values of F corresponding to those observed 

 experimentally. Suppose, for example, we take six shells 

 uniformly spaced over a distance somewhat greater than 



