ANISOTROPJC CONDUCTORS. 203 



conductivity of the medium along the principal axes, the flow of 

 electricity dM across an element of surface dS will have an analogous 

 expression as a function of potentials. If l n is the strength of the 

 current for unit surface along the perpendicular to the current, we 

 shall have 





or 



av 



r ay "sv av~i 



? /S= -</S i + ^o' + ^a f/ . 

 ~dx ty 1)2 J 



^y ~dz I 



This latter expression is the sum of the projections on the per- 

 pendicular of the currents I, I', I" in the three principal directions, 

 or the projection of the resultant current I . 



If 9 is the angle made by the perpendicular to the element dS 

 with the direction of the current, which makes with the axes angles 

 whose cosines are A, A', A", we have then 



I n = (al + aT + a"I") = (aA + a' A' + a"A")I = I Q COS 0, 

 and 



A A' A" 



216. We may now without difficulty extend the same kind ot 

 reasoning to phenomena of induction in anisotropic dielectrics. 

 Here again are three principal directions of induction, such that the 

 flow of force is perpendicular to the equipotential surfaces, and 

 which we may characterise by the specific inductive capacities /*, // 

 and /A". If (f> is the flow for unit surface, the flow of induction 

 across an element dS is 



f t>V dV <>V~1 



= -^S ;ua + /a' + /t"a" 



~bx ty ~bz J 



If /?, ft' and ft" are the cosines of the angles formed by the 

 electrical force F at the point in question, which is not perpendicular 

 to the equipotential surface, we may write 



</> = (pap + /* 'a' ft' + p "a" ft") F. 



