Electron Theory of Chemistry to Solids. 735 



where /is a positive quantity, since these supplementary 

 forces are always in the opposite direction to the corre- 

 sponding inverse square one. Hence the potential energy 

 of a system containing N atoms will be expressed in the 

 form, 



-M 5 ?-!)- 



But, neglecting temperature effects, for the equilibrium to 

 be stable d must have such a value that the quantity inside 

 the bracket is a maximum, i. e. 



-*#♦¥- m 



or a~ t^tv, 



e 2 

 so that the potential energy of the system = — 1*825 -tN. 



01 



Now let us find an expression for the work required to 

 compress the solid so that d is changed from d to d — Ad; 

 if the potential energy of the N atoms is denoted by u, the 

 work required to compress them will be 



uAd + ±'u(Ad) 2 + , 



where u is the first and u the second differential of u with 

 respect to d. But u = and u is equal to 



-M"?-Jf) ' 



Ne- 

 = 3-65^ by (7). 



Hence the work required to compress the cells is 



N<? 2 

 J3-"65.-y.(Arf)*5 



if Y denotes the volume occupied by these cells 



Ad _ 1 AY 

 d ~6 Y ; 



„ , 13*65N* 2 /AY\ 2 

 hence the work = ~ — ^ -5- ! -y- I ; 



