Relations of Dielectric and Magnetic Polarization. 165 



The remaining gpart of the total electric energy of the 

 polarizations, viz. 



-C(EdP), 



'0 



represents the energy supplied from the total store of internal 

 energy of other than electric type in the medium during the 

 process of setting up the polarization. This expression with 

 sign changed thus represents the increase in the energy of 

 non-electric nature in the dielectric medium consequent upon 

 the induction of its polarized condition. 



3. In the theory of von Helmholtz the whole argument is 

 placed on a different footing. No distinction is now drawn 

 between the fundamental constituents, aether and polarizable 

 matter, of the dielectric field, which is regarded as consisting 

 of a single uniform medium capable of transmitting the 

 electric actions in the same manner as an ordinary elastic 

 solid transmits mechanical forces ; the electric force at any 

 point of the field is the straining force and the total electric 

 displacement in Maxwell's sense represents the strain 

 produced. The displacement D is subject to the usual 

 characteristic equation of the theory, viz. 



div D = p, 



and the electric force exciting the displacement is derived 

 from a potential. 



The first step in the formulation of the theory is to express 

 the energy per unit volume in terms of the field vectors and 

 the potential in such a form that the variation of the integral 

 which represents the energy for the whole volume leads on 

 integration by parts to the characteristic equation for the 

 displacement as one of the conditions of internal equilibrium ; 

 the integral is then asserted to be in its normal form, which 

 means that it represents the actual distribution of the energy 

 of the medium as well as its total amount. Its variation 

 with sign changed, owing to change of material configuration, 

 should then give the extraneous fo reive that must be applied 

 in order to maintain mechanical equilibrium ; the variation 

 with respect to the electrical configuration being null, so 

 that electric equilibrium is provided for by the characteristic 

 equation already satisfied. The variation without change of 

 sign should thus give the mechanical forcive of electric 

 origin that acts on the medium. 



The organized energy in the medium is known to be 



where 



W=r^f D (E^D), 

 divD = p and E = — grad<£, 



