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



Thus if m be the mass of an electron 



72 



m ~oW ~ ^ V ^° ~~ P n '^ ^ vqr ~~ ^ ^° _ Wpq ^ ^ pqr ' ' ^ 



Since the electrons and the atoms are so distributed that 

 if one of these has coordinates p, q, r, there are others whose 

 coordinates are g, p, r, p,r,g, r, p, q, r,q,p, q,r,p, and 

 since for such a group of six 



t( 1 ^ Wo 



\{p 2 + q 2 + r 2 f 2 (p 2 + q 2 + r 2 )»i 2 ) " ' 



s / 1_ 4r 2 \ 2 



\{p 2 + g 2 + r*f (p 2 + q 2 + r 2 )*) ~ .( p * + 2 » + r»)*' 



Zl5pqr — U, AKjpq r — 2, 2 2 g2 X JS X 



2 ^ C 



(p'+q' + r 2 ) 2 * d* X d 

 Thus equation (1) may be written, 



m -,.„■ = A po ^ /^r -t>p ?r -r 2< ft)^ \jpq r . 



dt 



where . _ 2c e 2 ^ 



d d z ^(p 2 +q 2 + r 2 ) 2 ' 



where p, q, r must all be odd. 



If the disturbance is represented by 



2?T 27T 2-7T 

 p = COS — - X . COS —y . COS — ?, 

 A,j A 2 A3 



we may put 



p P , q ,r = e 1 p e 2 ( t€- i p , 



where e 1? e 2 , e 3 are the roots, real and imaginary, of the 

 equations 



Al A2 Ao 



-2d 1 -2d -1 c 2~d 1 



€1 — 1, 6 2 — 1, €^ — ±, 



and the equation for p Q becomes, 



m^ = - Po (A + X e? e 2 * ef B pqr ) + €><£(& e 2 « e{ C pqr ). (2) 



To find the equation of motion of the atoms we must make 

 some assumption as to the repulsion between two positive 

 charges at a distance r ; we shall suppose that this is 

 expressed by 



