io2 HERMANN VON HELMHOLTZ 



the law of electromotive surfaces, which states that if electro- 

 motive forces existing anywhere within a conductor produce 

 certain currents in an attached conductor, it must be possible 

 to devise a distribution of electromotive forces on the surface 

 of the first conductor which would produce the same currents. 

 He arrives at the distribution on the surface by assuming 

 the conductor to be insulated and determining the electrical 

 potential at any point of its surface due to the currents excited 

 by the internal forces ; the required surface electromotive force 

 (taken from within outwards) is then equal to this difference 

 of electrical potential. He terms the surface, thus conceived 

 as electromotive, the positive effective surface ; and from these 

 two theorems (deduced by strict mathematics) derives a series 

 of important conclusions. These again yield the theorem that 

 the potentials within the attached conductor are equal to the 

 sum of the potentials existing in it antecedently, and of those 

 produced by the positive effective surface. It is obvious that 

 different modes of distribution of e. m. f. at the surface of 

 a conductor (if they are to give the same derived currents as 

 the internal electromotive forces) can only vary by a difference 

 of potential that is constant for all points of the surface ; and 

 from equally simple considerations (based entirely on Ohm's 

 Law) results the general and important theorem, that when 

 any two points on the surface of an extended conductor con- 

 taining constant forces are connected with a given system of 

 linear conductors, it is always possible to substitute for it 

 a linear conductor of definite e. m. f. and resistance, which 

 will give rise to precisely the same current in all linear con- 

 ductors connected with it, as the material conductor. He 

 introduces the conception of electrical double layers, which 

 assumes that at opposite sides of a surface and at infinitesimal 

 distances from it, there will be exactly the same quantity of 

 positive electricity on the one side as there is of negative on 

 the other. By this device he transforms the Poisson-Gauss 

 equation for non-equilibrium states on which Kirchhoff founded 

 his equation for equilibrium so that the potential shall not (as 

 in that equation) be uniform, and the force components on 

 either side of the surface non-uniform, but conversely, with 

 uniformity of force the difference of potential function shall 

 be a quantity that is different from zero, which he terms the 



