PROFESSOR AT KONIGSBERG 101 



current, normal to the surface, as that electromotive force 

 applied to ft would produce in a. 



He expects that he will have to leave the proof of this 

 theorem to the future, but at last he overcomes the difficulty, 

 and is able to announce to Ludwig early in March, 1853 : 

 1 1 have meantime discovered and worked out some new 

 theorems on the distribution of galvanic currents in material 

 conductors, by which the theory of currents of animal electricity 

 can be demonstrated with strict accuracy, and by a very 

 simple method, while du Bois-Reymond had to make shift with 

 exceedingly complex approximations. My results of course 

 agree in essentials with those of du Bois.' 



Du Bois-Reymond himself affirmed at a later time that he 

 had been helpless in face of these great difficulties until 

 Helmholtz came to his aid with the conception of electro- 

 motive surfaces, and the theorem of the equal and opposite 

 action of two electromotive surface-elements, by means of 

 which the previously insuperable difficulties became almost 

 elementary. This very interesting and fundamental work on 

 the distribution of electrical currents in material conductors is 

 purely mathematical in character, owing to Helmholtz's method 

 of proving the theorems, which are intelligible enough from the 

 physical point of view. It is essentially connected with the 

 treatise on the Conservation of Energy, since Helmholtz merely 

 substitutes for the expression 'free tension' there employed, 

 the identical concept of Gauss's potential, or Green's potential 

 function. 



In his inquiry he starts from the three equations which 

 Kirchhoff had laid down for dynamic equilibrium in the distri- 

 bution of currents in systems of material conductors, and had 

 shown to be necessary and adequate for the expression of 

 potential as a function of the co-ordinates. He has no diffi- 

 culty in devising a quite general proof of the law of the 

 superposition of electrical currents, which had been already 

 recognized as valid for individual cases. He expresses it very 

 simply by saying, that if in any system of conductors constant 

 electromotive forces are introduced at different points, the 

 electrical potential at any point of the system will be equal 

 to the algebraic sum of the potentials which are due to each of 

 the forces independently of the others. With this he associates 



