Electron Theory of Chemistry to Solids. 741 



The equations of motion are 



m dt 2 = a (Ps~Pv~Prt^ 



d 2 P? i \ o 



m dt 2 = a ( pz ~P l > "W 



m 



%->(*¥-»>*»• 



mp'—fa, 



— a, a 



— a, 



mp 2 — /3 2 , a 



a 

 2' 



g, mp~ — a-/3 s 



if Pi? p2, Pz are proportional to e*** ; p is given by the- 

 equation 



0. 



Putting mp 2 -=xe l ld z and y — c\d, we find when E=4tf that 



# 3 -^ 2 (15%- 6-44) + «r(290-l%-12ri6?/ 2 - 133) 



-?/(474?/- 252/ -204) = 0. 



For stability the values of x given by this equation must 

 be real and positive ; for this to be so, the constant term 

 and the coefficient of x 2 in the cubic must be negative and 

 the coefficient of x positive. This will be the case if y 

 is between *71 and 1*17. The shortest distance between the 

 atom and an electron isc?; hence for equilibrium the distance 

 must be between l*4c and *85c. 



If the atoms are different, as in a binary compound AB, 

 we may have an atom with one charge inside one cell and an 

 atom with another charge inside another. It is easy to see, 

 however, that if the atoms are arranged according to the 



scheme below — 







B A B A 





A B . A B 





B A B A, 



the expressions we have obtained will hold provided the sum 

 of the positive charges on the atoms A and B is equal to 8, 

 which is the relation when the compound obeys the ordinary 

 valency conditions. 



Specific Inductive Capacity. 



If the external electric force F parallel to z acts on the 

 medium, the displacements p u p 2 , pz relative to the positive 



