Relations of Dielectric and Magnetic Polarization. 167 

 the introduction of surface integrals. We have therefore 



= - (V(V, p$s)dv+ I dv ]((Ss, V')^ ^ E )- 

 J J Jo 



Now 



1 E ((8 5 , V')D, dE)=- (D, (&, V)E) + (SsV) I E (ME), 

 Jo Jo 



so that on integrating the first integral by parts, we get 

 SW= j^[/9(^V)0~(D(^V)E) + (^V) j (ME)]. 



(ME), 



in its leading terms, which are 



The vector coefficient of 8s with sign changed is now taken 

 to determine the linear components of the mechanical forcive 

 on the dielectric medium ; its «r-component for example is 



-,l* + ( D * E )-sT 



This expression is far more complex than that given by 

 Maxwell's theory, and it leads to a stress whose specification 

 differs from that of Maxwell 

 now of the type 



T,., = E,.D,-P(ME). 

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These general formulae were first given by Colin for the 

 particular case of isotropic magnetic media for which a 

 general law of induction is valid ; they are here seen to be 

 in no way limited by these assumptions. In the most 

 general case, however, their form alone suggests an obvious 

 difficulty. The type of forces which are represented in them 

 are much more general than is the case in all known 

 mechanical systems, in so far as the force on any element of 

 the medium is a function not only of the conditions in that 

 element at the instant when it is under examination, but 

 also of the whole of its past history. In any ordinary 

 physical theory the existence of such forces is entirely 

 excluded as it would, for instance, result in a force on an 

 unpolarized element of matter formed by the combination of 

 two opposite but. equal polarized elements with different past 

 histories. 



We need not, however, dwell upon the difficulties of this 

 kind inherent in the present form of the theory, as it will 

 soon be seen that the deduction given is entirelv fallacious. 



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