OHM'S THEORY. 187 



k being the coefficient of conductivity for heat ; the sign - signifies 

 that the flow of heat is in the direction in which the temperatures 

 decrease. The expression for the flow is the same across an element 

 dS' of any given surface S', isothermal or not ; it is proportional to 



the partial differential , of the temperature in reference to the per- 

 pendicular ri to the surface S', and we have 



200. OHM'S THEORY. Ohm transferred Fourier's method of 

 reasoning to the study of the propagation of electricity. He assumes 

 that all points of a conductor in equilibrium are in the same elec- 

 trical condition, at the same tension. When there is no equilibrium, 

 interchanges of electricity take place ; the tension at every point is 

 generally a function of the time and of the co-ordinates but if any 

 extraneous cause maintains a constant difference between the ten- 

 sions of the different parts of the conductor, a stationary condition 

 is established in the system, after a shorter or longer time, in which 

 the tension at each point becomes independent of the time. 



Ohm assumes, further, that between two molecules whose tensions 

 are U and U', an exchange of electricity is produced in unit time, 

 proportional to the difference of tensions and to a function of the 

 distance, such that the adjacent molecules have a preponderating 

 influence. 



This hypothesis is identical with that of Fourier (70). Without 

 its being necessary to repeat the reasoning, it follows that the 

 exchanges of electricity take place at right angles to the surfaces 

 of equal tension, or to the surfaces of electrical level relative to this 

 new property. The flow of electricity */Q, which traverses an element 

 </S, of an equipotential surface in unit time, is proportional to the 

 differential of the tension in respect of the perpendicular to this 

 surface, and is expressed by 



the coefficient c depending on the nature of the medium, and may 

 be called the coefficient of electrical conductivity. The differential 



-- is the electromotive force at the point in question. It will be 



an 

 seen that through an element ^S', of any given surface, there is a flow 



