THE HISTORY OF OHM'S LAW 609 



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 interpre- 

 tation 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 : 



X=Jc.w.a/l, (6) 



where X is the current strength, Tc the specific conductivity of the wire, 

 w the cross-section, a the electromotive-force of the source of current 

 and I the length of the conductor. A second equation brings out for the 

 first time the conception of "reduced length" or resistance. This 

 equation is 



X = a/L, (7) 



where L is the length of a hypothetical wire of unit conductivity and 

 unit cross-section and takes the place of the terms Tc-w/l 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 Galva- 

 nische 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 multi- 

 tude 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 con- 

 tents 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; (&) mode of dispersion of electricity into the atmos- 

 phere; (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 par- 

 ticle 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 



