said to close Ohm's experimental work in so far as it relates to the establishment of the law under discussion.
Ohm's Theoretical Work.—Turning to the mathematical interpretation which Dr. Ohm gave to the mass of experimental material already considered, we will first examine the paper of 1826 cited above under V. At the beginning of this paper is found the following expression of Ohm's law:
where is the current strength, the specific conductivity of the wire, the cross-section, the electromotive-force of the source of current and the length of the conductor. A second equation brings out for the first time the conception of "reduced length" or resistance. This equation is
where is the length of a hypothetical wire of unit conductivity and unit cross-section and takes the place of the terms in equation (6). Equations (6) and (7) constitute Ohm's formal expression of the law.
In 1827 Dr. Ohm secured leave of absence from the gymnasium in Cologne, and proceeded to Berlin for the purpose of bringing out a book which should contain the theoretical conclusions which he had elaborated from his experiments. This book is entitled "Die Galvanische Kette, mathematisch bearbeitet," "The Mathematical Theory of the Galvanic Circuit." This book is the best known of his works. It contains a comprehensive theory of galvanic electricity, deduced from simple hypotheses and developed mathematically so as to cover a multitude of practical cases. The book may be divided into two parts, of which the first contains an introductory statement of principles on which the theory is based, together with applications to simple problems. Part two involves the use of differential equations and constitutes a more general development of the theory. The absence of a table of contents would seem to indicate haste in getting the book issued. An examination of the text gives the following partial outline of its contents:
Part One: 1. Discussion of the three fundamental hypotheses lying at the basis of his general theory and dealing with (a) the distribution of electricity in any element of a body; (b) mode of dispersion of electricity into the atmosphere; (c) law accounting for the generation of contact electricity. Of these three only the first is directly concerned with Ohm's law. Of it he says: "I have started from the supposition that the communication of electricity from one particle takes place directly to the one next to it. The magnitude of the transition between two adjacent particles under otherwise exactly similar circumstances, I have assumed as being proportional to the difference of potential between them."
In this passage it will be seen that Ohm proposed to follow, in the consideration of the flow of electricity, the lines laid down by Fourier
