444 Prof. Thomson on the Dynamical Theory of Heat. 



electrical circuits are completed. Hence if V denote the elec- 

 trical potential at [x, y, z) due to these accumulations^ the com- 

 ponents of the reactional electromotive force are 

 _dY _dY _dY 

 dx' dy' dz'' 



and the components of the efficient electromotive force in the 

 solid are therefore 





dY dV 



dy' dz' 



where E^ F, G are given by the following equations, derived from 

 (34) by substituting for u, v, w their values -y-, -j-, -j-, in terms 

 of the notation now introduced : — 



ax dy 



dz 



-r= 



dt 



dt , dt ,, 



-^=->' + i^"+i^J 



(45). 



dx ^ dy^ dz 

 dt I dt fj dt 

 ' dx dy^ dz 



176. The body, being crystalline, probably possesses different 

 electrical conductivities in different directions, and the relation 

 between current and electromotive force cannot, without hypo- 

 thesis, be expressed with less than nine coefficients. These, 

 which we shall call the coefficients of electric conductivity, we 

 shall denote by k, X, &c. ; and we have the following equations, 

 expressing by means of them the components of the intensity of 

 electric current in terms of the efficient electromotive force at 

 any point of the solid : — 



These equations (45) and (46), with 



dx dy d^ \ }> 



which expresses that as much electricity flows out of any portion 

 of the solid as into it, in any time, (in all seven equations,) are 

 sufficient to determine the seven functions E, F, G, V, h, i,j, 



