1 88 PROPAGATION OF ELECTRICITY. 



of electricity which is proportional to the electromotive force along 



the normal to this surface, or to the differential coefficient ^-7. 



on 



On Ohm's theory, as well as on that of Fourier, it is assumed 

 that the direction of the flow is constantly parallel to the direction 

 of the force which acts upon it, and is therefore independent of its 

 previous condition. This hypothesis is incompatible with the notion 

 of inertia, and therefore with the materiality of that which constitutes 

 the flow. 



Ohm regarded tension as a particular condition in virtue of which 

 electricity tends to escape, and, when the tensions in any medium are 

 variable, electricity flows from points at a high towards points at a 

 lower tension. We see at once the analogies of this function with the 

 potential, for the tension is also constant in a conductor in equi- 

 librium. In some of his memoirs Ohm appeared to establish too 

 close a relation between electrical density and tension ; but he also 

 points out that the tension at a point, even in the variable state, 

 could be determined by connecting it with an insulated electroscope, 

 and the quantity, which is thus measured, is nothing else than the 

 potential. 



201. KIRCHHOFF'S HYPOTHESIS. To express Ohm's theory with 

 our present views respecting electricity, we must assume with Kirchhoff 

 that tension and potential are two identical functions. 



It follows from this hypothesis that, in a system of conductors 

 connected together, but not in electrical equilibrium, the flow of 

 electricity at each point is proportional to the differential of the 

 potential in reference to the normal to the equipotential surface, or, 

 in other words, is proportional to the electrical force exerted at this 

 point that is to say, to the resultant of the actions of all the masses 

 of the system in their condition for the time being. 



Or, more simply, the flow of electricity is parallel and proportional 

 to the flow of force. 



202, SUPERPOSITION OF PERMANENT STATES. In another form 

 it may be said that the hypothesis amounts to the assumption that 

 the superposition of two states of electrical equilibrium is itself a 

 new state of equilibrium, in which the flow across an element of 

 surface is equal to the sum of the flows relative to the two original 

 states. 



For consider two states in which the flows across an element of 

 surface dS are AdS and A'dS ; the perpendicular components of the 



c)V c)V 



force on this element are - ^S and ~-^-dS. By superposing 



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