and the Partition of Thermal Energy. 687 



That due to the displacement y v 



That due to displacement z 



=4/(9 + 2**. Z^, 



The total energy due to the four molecules 

 =4/(0 + as{£p+/"(0} +*{^ -f'(l) } • 

 The total energy due to the twelve molecules 



= 12/(Z> + 3a 2 { / ^+/' f (/)}+a 2 {^ ) -rw}, 



= 12/(Z)+2a2{^)+/"(0|. 



It may be noted that the variable part of the potential 

 energy is just double of the corresponding portion of the 

 potential energy for the cubical system. It vanishes if the 

 force is propoitiom.l to the inverse square of the distance. 

 This fact seems to give a special significance to the inverse- 

 square law. 



Following the same line of argument we get the following 

 equations : — 



_ " e 



£= 3 ( 1+ -hyVm =5 ' la '\/rS- 



This value of 6 is greater than the corresponding value 

 obtained in the case of the isotropic arrangement by about 

 5 per cent. The value of F is increased and that of a 

 diminished by the same amount. 



June 30, 1921. 



