510 THE ELECTROMAGNETIC FIELD. [PT. III. CH. XIII. 



we have for the electric and magnetic energies and the dissipativity, 

 or heat generated per unit of time, 



(F> T = (m + Mm + 



H = II '(Xu + Yv + Zw] dr. 



246. Eolotropic Media. The equations (C), (D) and (E) 

 have been established on the supposition that the medium is 

 isotropic, that is that it has the same properties in all directions 

 at any point. In some bodies, such as certain natural crystals, this 

 is not true. The assumption next in order of simplicity to that 

 made in Chapter IX is to assume that the energy per unit volume 

 is a homogeneous quadratic function of the components of the field 



^ [eaXf + e^F 2 + 6 33 ^ 2 + e n YZ + e 3l ZX + e la Z7}, 



the six coefficients being properties of the medium. If we then 

 apply the reasoning of 180, we find that our results are the 

 same as before, providing that we define the inductions by the 

 equations 



= e n X -f e 12 F + e u Z 9 8 = /A U 



3 = S1 X + e 32 F+ e 33 ^, 91 



where rs =e sr : p rs = p sr . 



The inductions thus defined have all the properties that we have 

 hitherto predicated with regard to them. It has been pointed out 

 by Pupin* that these are not the only possible generalizations of 

 the equations (C) and (D). 



Media which are not isotropic are called eolotropic. A body 

 may also be eolotropic with respect to conduction, in which case 



* Pupin. "Studies in the Electro-magnetic Theory." American Journal of 

 Science, Vol. L., p. 326, 1895. 



