ELECTRICAL EQUILIBRIUM. 



tend to raise the temperature of the colder ones. Fourier assumes, 

 moreover, what is only true for a particular thermometric scale, that 

 the interchanges of heat only depend on differences of temperature, 

 and not on their absolute values. 



The flow of heat which traverses an element dS of an isothermal 

 surface S (Fig. 14) is, by symmetry, perpendicular to this surface, 

 and to all the isothermal surfaces which it meets. The flow of heat 

 ^Q, which passes in unit time from the element dS to the infinitely 

 near element dS', is proportional to the surface dS v to the infinitely 



ds 



Fig. 14. 



small difference of temperature / - /', to a coefficient h which only 

 depends on the nature of the medium ; and, lastly, to a function of 

 the distance of these elements. 

 We may therefore put 



t-t' 



If we consider an intermediate temperature t v the flow of heat 

 from dS to dS' passes first through the element ^S : at the distance 

 e v which gives 



Since the differences of temperature / / x and / /' are, by 

 continuity, proportional to the perpendicular distances, the function 

 < is proportional to the distance only. The flow of heat between 

 two infinitely near corresponding elements, calling dt the variation 

 of temperature measured in the direction of the flow of heat, and dn 



