force, which is to be regarded as its contribution to the driving-force of any circuit in which it may be placed. This assumption confers a definite meaning on his use of the term "electroscopic force"; the force in question is identical with the electrostatic potential. But Ohm and his contemporaries did not correctly understand the relation of galvanic conceptions to the electrostatic functions of Poisson. The electroscopic force in the open pile was generally identified with the thickness of the electrical stratum at the place tested; while Ohm, recognizing that electric currents are not confined to the surface of the conductors, but penetrate their substance, seems to have thought of the electroscopic force at a place in a circuit as being proportional to the volume-density of electricity there—an idea in which he was confirmed by the relation which, in an analogous case, exists between the temperature of a body and the volume-density of heat supposed to be contained in it.
Denoting, then, by S the current which flows in a wire of conductivity γ, when the difference of the electroscopic forces at the terminals is E, Ohm writes
.
From this formula it is easy to deduce the laws already given by Davy. Thus, if the area of the cross-section of a wire is A, we can by placing a such wires side by side construct a wire of cross-section nA. If the quantity E is the same for each, equal currents will flow in the wires; and therefore the current in the compound wire will be n times that in the single wire; so when the quantity E is unchanged, the current is proportional to the cross-section; that is, the conductivity of a wire is directly proportional to its cross-section, which is one of Davy's laws.
In spite of the confusion which was attached to the idea of electroscopic force, and which was not dispelled for some years, the publication of Ohm's memoir marked a great advance in electrical philosophy. It was now clearly understood that the current flowing in any conductor depends only on the
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