combination of those two results led for the first time without ambiguity to the conclusion that the conducting power varies directly as the sectional area and inversely as the length of the conductor, thus constituting 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 university of his native town he taught in Gottstadt, Neufchatel and Hamburg. 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 publish three papers dealing with the galvanic circuit.
I. The first of these, entitled "Vorlaüfige Anzeige des Gesetzes, nach welchem Metalle die Contact-Elektricität leiten," occupies eight pages of Schweigger's Journal für Chemie und Physik, and describes experiments on the "loss of force" (i. 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 difference
Fig. 2. of varying the external resistance of the circuit. The results of these experiments were expressed by Ohm by the following empirical formula,
.(3)
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 constant depending on the length of the connecting wires, and m a coefficient depending (supposedly) 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.
