Electron Theory of Chemistry to Solids, 729 



Then if M is the mass of an atom, 



72 



where 



E = A + X F^ -t- Se^ e 2 « e s * (B^ + F^), 



and 



r pqr — ~*T~Tr \ r /' 



'par i par Ml P n,r \ 'par J 



where r. pqr is the distance between the atom ]), q, r and the 

 atom whose displacement is a> . 



As the muss of an atom is very large compared with that 

 of an electron, an approximate solution for the motion of the 

 electrons will be got by supposing that the atoms are not 

 displaced; putting co equal to zero in equation (2) we get 



m S° MA+26/6/6/B,,,), ... (3) 



or, if p varies as s ipi , 



7np 2 = A + ^€ 1 Pe 2 U s r B pqr : 



this equation gives the frequency for all the types of vibra- 

 tion got by giving different values to e 1? e 2 , e 3 . For the 

 stability of the equilbrium all these frequencies must be 

 real, i. e. 



A + Sefe^B^, 



must be positive for all possible values of e u e 2 , e 3 . The 

 most likely vertical displacement to produce instability is 

 when the displacement of each electron is equal and opposite 

 to that of its nearest neighbours in a horizontal plane, while 

 all electrons in the same vertical line have the same displace- 

 ment. This is represented by putting e x = — 1, e 2 — — 1, 

 € 3 =1, and then 



_ J^(-W 1 *! \ 



I,,have calculated the right-hand side by the method I have 

 employed all through, i. e. by calculating the terms corre- 

 sponding to the smaller values of p, q, r by arithmetic, while 

 for the larger values of p, q, r I have supposed the electrons 



