224 MR. G. H. LIVENS ON THE 



and include the energies corresponding to these two parts in with the appropriate 

 totals the formulae just obtained are somewhat simpler in form. The total kinetic 

 energy will be now 



(TB a -8ir f (Bdl)-8ir 



oTT J [_ 



or 



where 



and the potential energy is 



-J- f ["E"+8w | (E SP) + 8n i (E JP) 



OTT J 1 J J 



or is 



w 



here 



D'= 



47T 



This, however, leaves out of account the term 



which, representing as it does the energy of local actions and reactions, may be 

 assumed to be inoperative as regards general mechanical processes, and may in 

 consequence be rejected altogether. 



In connexion with the discussions of the expressions for the internal energy of the 

 material media it may be worth while emphasising the significance of the various 

 terms in the expression for the forcive on the polarised material elements derived in 

 the previous paragraph, especially the way in which the various terms arise and their 

 dependence on the term 



Curl [P, M ] 



in the complete current. Further, we may notice how the complete expression for the 

 change of intrinsic energy per unit volume, viz., 



Jo, BJIP) 



I 



is derived, the latter term being due to the above-mentioned term in the current. 



