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



It will be seen at once that the values of F are of the 

 right order of magnitude. F should tend to a value 18 

 for chlorine, and 10 for sodium, as sin 6 approaches zero, 

 assuming the atoms in the crystal to be ionized. The 

 greatest value of Fci is 11'67, and of F Na is 6*90, when 

 sin (9 = 0-10. 



17. It now remains to take various models of the atom 

 and see hew the form of the function F calculated for these 

 models agrees with that actually observed. 



It is not intended here to lay much stress on the agree- 

 ment between the calculated and observed forms of F for all 

 values of 6. The object of the comparison is to demonstrate 

 that any probable arrangement of electrons gives a close 

 agreement between theory and experiment at small glancing- 

 angles_, and therefore to prove that the formula for the 

 intensity of reflexion is very probably the true one. 



The first atom model is one in which the electrons are 

 supposed to be distributed uniformly throughout a sphere 

 whose radius is 1*02 x 10 ~ s cm. in the case of chlorine, 

 0*67 x 10" 8 cm. in the case of sodium. 



In the second model the electrons are supposed to be 

 arranged in a series of spherical shells. It is also assumed 

 that, in considering the average effect of the atom, we may 

 take the effect of the electrons in each shell to be equivalent 

 to a uniform distribution of diffracting particles over the 

 whole surface of the shell. The radii of these shells and 

 the number of electrons in each are as follows : — 





No. of 







No. of 





Chlorine. 



electrons. 



Radius. 



Sodium. 



electrons. 



Eadius 



1st shell . 



2 



012 



1st shell 



o 



0-40 



2nd shell .. 



8 



0-41 



2nd shell 



8 



0-67 



3rd shell .. 



8 



1-02 









The diameters of the outer shells are those calculated by 

 one of the authors * from crystal data. 



In the third model the electrons are supposed to be 

 arranged on shells of the same diameters as in the second 

 model, but to be in oscillation about their mean positions 

 along a line joining them to the centre of the atom with a 

 total amplitude equal to their distance from the centre. 

 This extreme case has been chosen to illustrate the effect 

 of such an oscillation of the electrons on the form of the 

 curve. 



* W. L. Bragg, Phil. Mag. xl. p. 169, August 1920. 



