THE HISTORY OF OHM'S LAW 605 



combination of these two results led for the first time without ambiguity 

 to the conclusion that the conducting power varies directly as the sec- 

 tional area and inversely as the length of the conductor, thus consti- 

 tuting a complete statement of part II. of Ohm's law. Becquerel also 

 determined by direct experiment that the total current is the same in 

 every part of a series circuit. This fact, so familiar to-day as to seem 

 all but self-evident, was an important one, for without it Ohm's law 

 would be meaningless. 



Ohm's Experimental Investigations. — George Simon Ohm was born 

 in Erlangen, Germany, on March 16, 1789. After attending the uni- 

 versity of his native town he taught in Gottstadt, Neufchatel and Ham- 

 burg. In 1818 he became the teacher of mathematics and physics at the 

 gymnasium at Cologne, where he remained for nine years. He was a 

 superior instructor and looked forward with the ambition of securing a 

 university appointment. Then, as now, the best, if not the only, path 

 to preferment lay along the line of scientific research and discovery. 

 To this endeavor Ohm brought three prime qualifications. His father, 

 who was a lock-smith, had trained him as a lad in the use of tools ; from 

 his university he gained excellent training in mathematics; in himself 

 he possessed a firm determination to do his best and a strong ambition 

 to succeed. "With scant leisure, few books and only the apparatus he 

 himself devised and for the most part built, he had need of patience and 

 perseverance. Difficult as was his progress, he was able in 1825 to pub- 

 lish three papers dealing with the galvanic circuit. 



I. The first of these, entitled " Yorlaiifige Anzeige des Gesetzes, 

 nach welchem Metalle die Contact-Elektrieitat leiten," occupies eight 

 pages of Schiveigger's Journal fur Chemie und Ehysxk, and describes 

 experiments on the "loss of force" (1. e., loss of potential) due to 

 increasing the length of the wire in a simple circuit. In modern 

 language it is the study of the effect on the terminal potential differ- 

 ence of varying the external resistance of the , 

 circuit. The results of these experiments jj 

 were expressed by Ohm by the following 

 empirical formula, 



V = m.\og (I + x/a). (3) 



|-4W- 



k V— - 



^WHVMV-^ 



J 



1 



In this equation V is the loss of terminal 

 potential difference, due to the insertion of 

 an external resistance of length x, a is a con- 

 stant depending on the length of the connect- £^ 

 ing wires, and m a coefficient depending (sup- 

 posedly) upon the electromotive-force of the 

 circuit, the cross-section of the wire and the constant a. The scheme of 

 the experiment is shown in Fig. 2. 



Fig. 2 



