202 CLAUSIUS ON THE WORK PERFORMED 



particular point of the conductor*. Against this view, how- 

 ever, KirchhofFt justly urged that it is in direct contradiction to 

 a known electro-statical theorem ; for according to Ohm^s view, 

 the electricity in a conductor would remain at rest if it were dis- 

 tributed equally throughout the whole volume of the conductor, 

 whereas it is sufficiently well known that the free electricity 

 of a body — which of course can alone here enter into consider- 

 ation, as it alone exercises any force — is, in a condition of rest, 

 distributed only over the surface of the body. 



This objection might, perhaps, create some mistrust as to the 

 general admissibility of Ohm's law ; nevertheless, Kirchhoft' 

 himself has proved that the law can be made to harmonize very 

 well with the fundamental laws of electro-statics, and has like- 

 wise shown what meaning must be attached to the function V 

 in order that this may be the case. 



As already stated, -p^^ represents the component of the ac- 

 celerating force at any particular point, in the direction of the 

 normal N ; and similarly, the components of the same force 

 in the directions of the three coordinate axes will be represented 



by -T-, ~j—, -T-. This denotes that the force is caused by 



attractions and repulsions proceeding from fixed points, both of 

 which are dependent, as far as their intensity is concerned, 

 solely on the distance, and not on the position of the acting 

 point, the law of this dependence remaining for the present 

 arbitrary. This, however, can be inferred from other grounds, 

 namely, in our case it is evident that such attractions and re- 

 pulsions can only be exercised by the electricity itself, and its 

 attractions and repulsions are subject to the law of the inverse 

 square of the distance. Hence it follows that the function V is 

 to be considered simply as the potential function of the whole 

 free electricity J. 



♦ Die galvanische Kette, mathematisch bearbeitet von Dr. G. S. Ohm, 

 p. 95, and Scientific Memoirs, 1st Series, vol. ii. p. 401. 



t Pogg. Ann. vol. Ixxviii. p. 506 ; and Phil. Mag. S. 3. vol. xxxvii. p. 463. 



X 1 have chosen the letter V to represent this function instead of the letter 

 U, which Ohm and Kirchhoff have employed, because in my former memoir 

 this letter was used for this function ; and to make the agreement with my 

 former memoir more complete, I have also changed its sign. 



