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



displacement p 3 tending to increase pi is 

 -a(p 1 —p 3 ). 

 The total force tending to increase p l is thus 



a{pz—p2) ; 

 the force tending to increase p 2 is 



<*>(p2—pi) > 

 and that tending* to increase p z is 



4^-p). 



The force due to the positive charges tending to diminish p t 

 if E is the positive charge of the atom is /3\pi when 



R - F (— - ' -A <L j JL c \ 

 Pl ~ \21 d^l21 d 4 + 361 dtp 



where the effect of the force varying inversely as the cube 

 of the distance is supposed to be confined to the nearest, 

 next nearest, and nexf next nearest atoms. 



The effect of the force varying inversely as the square of 

 the distance exerted by the positive atoms is proportional to 



t ( 1 ^ x 



Up 2 + f it r 2 f 12 (p 2 + q 2 + r 2 ) b ' 2 J 



for all odd values of p, q, r, and therefore vanishes. 



The force tending to diminish p 2 due to the positive atoms- 

 is /9 2 /o 2 , where 





The effect of the force varying inversely as the square of 

 the distance is 



Ee^/ 1 3r 2 



d 6 



x (. x ^ "I 



*\(p 2 + q 2 + r 2 ) s > 2 (p 2 + ^ + r 2 )W 



for all odd values of r and even values of p and q. The sum? 

 under these conditions is — 3'77. 



The force due to the positive charge tending to diminish 

 p 3 is /3 3/ 9 3 , where 



