THE HISTORY OF OHM'S LAW 613 



of his law, the following heing his expression : " Cylindrische Leiter von 

 einerlei Art und verschiedenen Durchmcsser haben denselben Leitungs- 

 werth, 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 over- 

 looked 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. Xow 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. AYhile 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, experi- 

 ment. 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 infor- 

 mation. 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 Olim'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 exam- 



