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



We shall indicate the various cells by the coordinates of 

 their centres referred to O as origin and axes parallel to the 

 sides of the cube. Thus, of the cubes outside the hollow, 

 the nearest to the origin will be those whose centres have for 



coordinates the 24 permutations formed by (±1, ±1, +3) ^ , 



the next by (±1, +3, +3), and so on, the integers which 

 *occur being all odd integers. 



The cells of the type (1, 1, 3) furnish - -0038 x 24 e 2 jd. 



(1, 3, 3) , 



, + -0014x24 e 2 /d. 



(1,1,5) „ -■0018x24e 2 /tf. 



(3, 3, 3 , 



+ '0012x8 e°-ld. 



(1, 3, 5) , 



- -00006 X 48 e 2 /d. 



(3, 3, 5) , 



+ -0002x24e 2 /^ 



(1, 1, 7) , 



- -00026 X 24 e 2 /d. 



(3, 5, 5) , : 



- -00012 x 24 e 2 /d. 



(3,1,7) „ - -00020 X 24 e 2 /d. 



(3, 3, 7) , 



, - -00004 X 24 e 2 /d. 



Adding these to the preceding we find that ^ee'/r for the 



electron is 



e 2 

 -3-65^. 

 a 



This will be the same as the value of 2 ee'jr for the positive 

 atom, for the arrangement of atoms and electrons may be 

 represented either as a system of cubes with electrons at the 

 corners and atoms at the centre, or a series with electrons at 

 the centre and atoms at the corner; hence, if there are N 

 atoms and N electrons per unit volume, the potential energy 

 ^ 2 ee'/r due to the forces varying inversely as the square of 

 the distance will be 



-3*65 — -. 

 d 



Now consider the part of the energy due to the forces 

 varying inversely as the cube of the distance, and suppose 

 that the supplementary forces between the atoms also varies 

 according to this law. The potential energy due to forces 

 varying inversely as the cub 3 will for two charges ee' vary 

 as 1/r 2 , where r is the distance between the charges; hence 

 when we take the summation for all the charges per unit 

 volume we shall get for the potential energy of unit volume 

 .an expression of the form 



,~Be 2 



