Relations of Dielectric and Magnetic Polarization. 169- 

 same surface integral : thus finally we get 



5W = $dv[p(8sV)<l>- (D, (^V)E)] 



as the expression for the variation of the energy in the 

 specified portion of the medium followed in its motion. As 

 the result now applies for any arbitrary surface /, the inte- 

 grand represents quite properly the distribution of the 

 variational energy throughout the material dielectric ; the 

 coefficient of 8s in it therefore gives properly the linear 

 constituent of the forcive on the element ; its x component 

 per unit volume is 



-£♦( 



Dg)= /9 K + (DV)E ; 



provided a potential of force exists. This type of forcive is,, 

 however, quite an impossible one, as it points to the existence 

 of a bodily forcive of amount 



s rad (i E2 ) 



on the elements of free aether, which could not therefore be- 

 in equilibrium. 



The final form of this result deduced by an elaboration of 

 Larmor's argument can be verified by a simple direct 

 calculation if it is noticed that it is in reality the variation 

 of W with respect to the electrical potential, when the 

 variation of this is brought about by a virtual displacement 

 of the matter, that is really required ; for it is the work of 

 the mechanical forces balancing the electrical attractions 

 that is to be determined; and if the elastic conditions of the 

 dielectric medium specified completely by the vector D 

 remain unaltered in any displacement, we may be sure that 

 ail the work done is used up as purely electrical energy of 

 configuration, none of it having then been absorbed by the 

 medium into its store of internal energy of effectively non- 

 electric nature. In fact, if we perform the variation in this 

 way with D. and consequently also p, constant we get 



SW=Jrfw[p(8*V)*-(D(fi*V)E)], 



exactly as above. 



This simple mode of treatment also emphasises what it is 

 that really determines the internal electrical coordinates of 

 the medium. Helmholtz asserts that they, or at least the 

 conditions in them, are determined by the potential distri- 

 bution, and for the simple case examined by himself and 



J' 

 ■Ml. 



