COMPARISON WITH THERMAL PHENOMENA. 103 



The equation 



/xAV + 47173= 



gives 



W 



= - f 



J 



From Green's formula, and the remark already made (107), this 

 expression reduces to 



We have then, for the energy of unit volume, 



121. COMPARISON WITH THERMAL PHENOMENA. Let us re- 

 sume the comparison of the problem of electrical equilibrium 

 with that of the propagation of heat. We have seen that between 

 two identical level surfaces, if the coefficient of conductivity is 

 equal to unity, the flow of heat in the first is numerically equal 

 to the flow of force in the second ; if the coefficient of conductivity 

 is k, the flow of heat is k times the flow of electrical force. 



Let us now consider two correlative systems, one electrical and 

 the other thermal, each formed of two media separated by the same 

 surface S, and such that the equipotential surfaces of the one, coin- 

 cide with the isothermal surfaces of the other If k- and 2 are the 

 coefficients of conductivity of the two media, the flow of heat across 

 an element d$ at the bounding surface, in the first medium, is 



and in the second 



As thermal equilibrium is supposed to have been attained, these 

 two flows are equal, and we have 



