112 FUNDAMENTAL PRINCIPLES OF MATHEMATICS. 



which iutercepts the conduction of the current might itself be under- 

 going changes in the distribution of the electricity, so that apparently 

 incomplete circuits might in reality be complete. 



Faraday, who would not admit the existence of forces acting at a dis- 

 tance, because it appeared to him unthinkable that an action could take 

 place between two separated bodies without change in the medium 

 lying between, sought to find such a medium intervening between elec- 

 trical or magnetic bodies. He succeeded in showing that in almost all 

 bodies there exists magnetism or diamagnetism, and that in good insu- 

 lators under the action of electric forces, a change may be observed, 

 which he designated as dielectric polarization. If, now, one assumes 

 with Faraday and with Maxwell, who mathematically stated this 

 hypothesis, that in insulators there may be set up electro-dynamic 

 activity by which these become dielectrically polarized, then the poten- 

 tial law follows from the complete theory without modification. 



Partly before, partly during the progress of these important re- 

 searches on the theory of electrodynamics, Helmholtz pursued investi- 

 gations on the laws of the division of electric currents in solid con- 

 ductors and on electric boundary layers, lu these investigations the 

 theorem of the charging of a surface with electricity was extended 

 with regard to electromotive forces for which a certain distribution of 

 electrical potential upon the surface of a conductor may be predicted, 

 which in all other adjacent conductors produces exactly the same cur- 

 rents as the given distribution of electromotive forces within the inte- 

 rior of the conductor. It was further shown that the previous assump- 

 tion that electricity when in a state of equilibrium on one or more bodies 

 leaves the interior of the bodies completely and is distributed in an 

 infinitely thin surface layer, is only correct when we have to do with a 

 single electrical boundary layer on a conductor which touches neigh- 

 boring conductors or insulators without sudden changes in the poten- 

 tial function. In those cases, on the other hand, in which irregularities 

 in the value of the potential function occur on the boundary between 

 different bodies, as when two conductors under the influence of a gal- 

 vanic force working between them touch each other, there is formed 

 along the boundary surface an electrical double layer, whose signifi- 

 cance for the phenomena which occur when liquids flow along a solid 

 wall which they moisten was investigated. 



In the meantime the conceptions of Maxwell, who, as already men- 

 tioned, following Faraday, replaced the notion of action at a distance 

 by the action of the intervening medium, had become of deciding influ- 

 ence on the works of Helmholtz. In an investigation published in 

 1881 with the title "On the forces acting in the interior of bodies sub- 

 jected to magnetic or dielectric polarization," Helmholtz showed that 

 it is possible to determine the mechanical forces which act in the inte- 

 rior of bodies electrically or magnetically polarized without making 

 any hypotheses regarding the inner constitution of the bodies. The 



