730 Sir J. J. Thomson on the Application of the 



to be replaced by a uniform distribution o£ negative elec- 

 tricity of the same density as that due to the electrons, and 

 calculated the effect of these by integration. I find, using 

 arithmetic to calculate all the terms for which p 2 -f q 2 + r 2 > 30, 

 that 



Z e x P 6 2 q €/ D pqr = — 0^3 • 



The value of A, i. e. 



2c e 2 ( 1 \ 2 



^ X \{(2p + iy + (2q + iy + (2r±lf}) ' 



will depend upon the range over which we can use the 

 expression 



for the force between a positive charge and an electron. 

 It is certain that this expression cannot represent the force 

 at distances which are considerable multiples of the atomic 

 radii. We shall suppose that the expression holds for the 

 atoms which are the nearest, next nearest, and next next 

 nearest atoms to an electron, and that for the more distant 

 atoms the force is represented by the inverse square law. 

 The coordinates of the atoms which are the nearest neigh- 

 bours to the electron are the permutations of (+d, 

 ±d, ±d) of the next nearest neighbours of { + d, +d, ±3d) 

 of the next next nearest neighbours ( + d, +3d, +3<i) ; 

 the value of A for this collection of atoms I find to be 

 given by 



A-^; • (4> 



hence, in order that A + 2 e/ e 2 q e/ B pqr should be positive 

 and the equilibrium stable, 



•384ce 2 5'2* s 

 must be positive, i. e. 



d± Sd' 



3 > 1-69. 



d 



The shortest distance between an atom and an electron 

 is V'6d or 1*724 d, hence the size of the cell for the equi- 

 librium to be stable must be such that the distance between 



