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LXIV. On a Deduction of Ohm's Laws, in connexion with 

 the Theory of Electro-statics. By G. Kirchhoff*. 



IN the deduction of his laws of galvanic currents, Ohm set 

 out with certain assumptions regarding electricity which 

 are not in conformity with those it has been necessary to make 

 in order to explain electro-static phenomena; he assumes 

 that the electricity in a conductor is at rest when it is distri- 

 buted throughout the latter in a state of uniform density. 

 Now although it must always appear desirable to determine 

 the laws to which electrical currents are subject, by conside- 

 rations connected with the theory of electro-statics, this be- 

 comes absolutely requisite to enable us to produce a satisfac- 

 tory theory of experiments, in which both electricity in mo- 

 tion and electricity at rest are concerned, — experiments simi- 

 lar to those made by M. Kohlrausch upon the closed circuit 

 with the condenser and electrometer f. My present object is 

 to show how Ohm's formulae may be deduced from the elec- 

 tro-static laws of the mutual repulsion of electrical atoms, when 

 certain assumptions referring to questions in the theory of elec- 

 tro-statics, which have remained perfectly open, are brought 

 to bear. 



When electricity is communicated to a conductor, it will 

 assume a state of equilibrium, when the forces exerted by the 

 free electricity upon an electric atom existing in any part of 

 the interior of a conductor mutually neutralize each other. 

 This occurs when the potential of the total amount of free 

 electricity in relation to a point within the conductor remains 

 constant. Theory shows us that this can only be the case 

 when the free electricity has become arranged in a particular 

 manner upon the surface of the conductor. 



When two conductors of different kinds, as a piece of 

 copper and a piece of zinc, which separately contained no free 

 electricity, are brought into contact with each other, one con- 

 ductor becomes positively, whilst the other becomes negatively 

 electrical. The electricity excited at the point of contact 

 soon assumes a state of equilibrium ; in it the potential of the 

 total amount of free electricity must necessarily remain con- 

 stant with regard to all points of each of the two conductors: 

 hence it follows that free electricity cannot exist within the 

 conductor, and that it must be situated solely upon its surface; 

 one portion of the electricity will remain at the surface of 

 contact of the two conductors, whilst another covers its free 

 surface. 



* From Poggendorff's Annalen, No, 12, 1849. 

 f Poggendorff's Annalen, vol. lxxviii. p. 1. 



