MECHANICAL EQUIVALENT OF AN ELECTRIC CURRENT. 201 



of the above empirical law is established. The way, however, 

 by which Thomson arrived at this proposition, as well as the 

 form which he has given to it, are very different from mine. 

 He proceeds from the laws of electro-magnetic induction, and 

 makes use of the law of Ohm, while 1 make use of the latter 

 only in the form which Kirchhoff has given to it. His attention 

 is further exclusively confined to a lineal conductor, while my 

 results are independent of the form of the conductor, and hence 

 comprehend the lineal ones as a special case. This reason alone 

 would have been a sufficient inducement to me to publish my 

 inquiry, although his has preceded it; but I have a further in- 

 ducement in the fact, that the principle established in the follow- 

 ing pages derives additional interest from its great similarity with 

 that already proved in the case of machine electricity*. 



The law of Ohm, so far as it refers to the process within a 

 homogeneous conductor, may be expressed quite generally in 

 the following manner. Let dw be any element of surface within 

 the conductor, N the normal upon it, and idw the quantity of 

 electricity which passes through it during the unit of time, 

 where i is to be regarded as positive or negative, according as 

 the electricity, in reference to the normal N, passes from the 

 negative to the positive side of the element, or in a direction 

 contrary to this ; we have then the equation 



*=^^' W 



where k represents the conductibihty of the body, and V is a 

 function which, as soon as the stationary condition has com- 

 menced, is dependent solely on the coordinates of space. 



For in every point of the traversed conductor a force must 

 act sufficient to retain the electricity in motion, notwithstanding 

 the resistance continually opposed to it, and the differential co- 



dY 

 efficient -p^ evidently represents the component of this force in 



the direction of the normal. Nevertheless, the physical sig- 

 nification of this function V was formerly far from certain. 

 Ohm called the quantity represented by it, the eleciroscopic 

 force, and defined it as the density of the electricity at any 



* Pogg. Ann. vol. Ixxxvi. p. 345. 

 SCIEN. MEM.— Nat. Phil. Vol. I. Part III. Q 



