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



atoms of: the three types of electrons are given by the equations 

 "(to— P*)—0iPi = — Fe, 



a(P3—Pi)—PaP2 =— Fe, 



2 (Pi + P2 — 2/> 3 ) — ftps = - F*. 



The solution of these equations is 



p 1 = Fs(ft + 2a)G8 2 -a)/A, 

 p 8 = F*(ft + 2a)(ft--a)/A i 



P3 = F,(/3 1 A~|)(A + A)/A, 



wnere 



A = 



01, 



a, 



A, 



2' 



"~ 2' 



— a, 



-a, 



A 



The electrical moment of each cell due to these dis- 

 placements is 



(pi + p2 + %p3)e. 



The number of cells per unit volume is l/8d 3 . Hence the 

 electrical moment per unit volume is 



(pi+p 2 4-2^)^3, 



and if K is the specific inductive capacity this is equal to 



K-l 



. F. 



Substituting the values for p 1? p 2 , ps, we find 



K-l_ 1 (263% -105/ -109 ) 

 4tt " 8y (47%-252j/' 2 -204) ' 



where y = c/d and must be between *71 and 1*17. 



Substituting the permissible values of y, we find that the 

 specific inductive capacity of solids possessing this structure 

 would be greater than four ; so that it is only substances 

 with a high refractive index which can have their electrons 

 arranged in this way. 



