Page:Popular Science Monthly Volume 83.djvu/617

Rh of his law, the following being his expression: "Cylindrische Leiter von einerlei Art und verschiedenen Durchmcsser haben denselben Leitungswerth, wenn sich ihre Langen wie ihre querschitte verhalten," which may be rendered: "Conductors of the same material have the same resistance if they all have the same ratio of length to cross-section." Now while this condensed statement is equivalent to the more elaborate statement contained in the book of 1827, this fact might easily be overlooked by a casual reader. It is also to be remembered that in the earlier stages of the discussion of Ohm's law part I. received general acceptance, while part II. was by no means universally agreed upon.

5. Lastly the fact that he wrote his book from a theoretical and not an experimental point of view invited the judgment passed upon it that his conclusions were "a web of naked fancies" without "the semblance of support from even the most superficial observation of facts."

From a modern point of view it may well be questioned whether the two propositions constituting Ohm's law could ever have been arrived at by any other than an experimental route. Weight is given to this conclusion by the following: (1) Our present knowledge of certain deviations from Ohm's law are accounted for only by the present corpuscular theory of electricity. Now Ohm, so far as he developed his ideas theoretically, did so on the basis of heat flow and the theory of heat was not corpuscular. While such ideas may not be opposed to the corpuscular conception, we can not expect an inadequate conception at the basis of a theory to lead, by a process of deduction, to correct predictions. The same partial conception may, however, prove of great value in an inductive process which is checked at every step by experiment. (2) In the formulation of a theory so essentially simple as is Ohm's law, one must look for a background of clear ideas, and we can admit of but one source of data for this purpose—namely, experiment. The absence of clear ideas of such terms as current flow, resistance and electromotive-force, at the time of, and their presence after Ohm's work is direct evidence of an experimental source of information. Thus the mathematical theory of electrostatics was based on Coulomb's law experimentally established, and a similar experimental basis was necessary for Ohm's law.

The discussion of the origin of Ohm's law may then be summarized as follows: Dr. Ohm carried along his experimental or inductive work simultaneously with the theoretical or deductive work; first the one then the other was to the front, until finally in 1826 he was able, from his experimental data, to announce the true law. In 1827 he ill-advisedly advanced his hypotheses as the origin of his theory without making it sufficiently clear that they were based on experiment. As an example of deductive reasoning the law means little, while as an