﻿658 Sir J. J. Thomson: Further Studies on 



move parallel to any side of the unit cube, the empty cubes 

 and those containing eJectrons occur alternately. 



Assuming this to be the constitution of the metal, we can 

 easily calculate the electrostatic potential energy by the 

 method given in the paper referred to. LetE be the charge 

 on the calcium atom, e the charge on an electron, and 2d 

 the side of the cube taken as the unit. Then the electrostatic 

 potential energy for a single atom is 



V r r j 



where r is the distance of an atom and r that of an electron 

 from an atom under consideration. 



The potential energy of an electron is 



(»?-**)■ 



where r" is the distance of an electron from the one under 

 consideration. 



By the method described in the former paper, I find for 

 the electrostatic potential energy of an atom the expression 



/ 16-23 , 36-85N 



¥ ID{_E.- r - + «..- 7 -J, 



which, since E = 2e, is equal to 



e 2 



The potential energy of a single electron, if it is one at the 

 middle point of a side of the unit cube or at its centre, I 

 find to be 



while if the electron is one of those at the centre of the 

 small cubes, the potential energy is 



, (^ 18-87 35-l\ le\, a , 



i^B.-g ,.- T -j = ^2-65. 



Since the neutral calcium atom consists of one positive 

 nucleus and two electron s, one of each type, the potential 

 energy per normal atom will be 



~(4-4+ 1-325 + -415) = ^6*15. 



