THE HISTORY OF OHM'S LAW 6oi 



In any given circuit, in a steady state, the current I will he directly 

 proportional to the electromotive-force E, and tlie constant obtained by 

 dividing the latter by the former is termed the resistance of the circuit. 



II. " B = pil/A). (2) 



The resistance of a homogeneous conductor of uniform cross-section 

 is inversely proportional to its area of cross-section and directly pro- 

 portional to its length. The constant p entering into the equation is 

 termed tlie specific resistance of the conductor, since it is the vahie of 

 R when I and A are unity. The first proposition states that whatever 

 else the resistance ma}' depend upon, it does not depend upon the cur- 

 rent. Tlie second proposition shows how circuits of an elementary type 

 have their resistance affected by a change of dimensions. It would be 

 wrong to infer that part two gives any information as to the effect of 

 changing the material, or the physical state of the conductor ; such con- 

 siderations form the subject of the modern study of conduction, but the 

 results form no part of Ohm's law. 



In text-books of physics part I. is generally quoted as Ohm's law, 

 while part II. is discussed under applications of the law. Whether 

 part II. is to be supposed deducible from part I. or is to be regarded as 

 self-evident is not made clear. Of course neither supposition is correct. 

 Part II. must either be taken as the result of experiment, or be justified 

 by some particular hypothesis as to the nature of the electric current. 

 The student of physics taking up the subject of electro-kinetics after 

 that of electro-statics, might, if left to himself, very naturally expect 

 that resistance w^ould vary inversely as the circumference of the con- 

 ductor rather than as the cross-section. The true circumstances of cur- 

 rent distribution are certainly the last which would occur to the student 

 who, for example, conscientiously followed the suggestions in "Watson's 

 " Text-book of Physics," where it is asserted that current flow is a 

 fiction, the only real flow being that of the energized field outside the 

 wire. Whether it is or is not worth while in text-books to exercise more 

 care in the elucidation of Ohm's law, in a historical discussion of the 

 subject ambiguity can only be avoided by a precise statement of both 

 propositions. 



In the present discussion let it be remembered that the terms 

 "resistance" and "potential" had not at the time under discussion 

 been applied to electricity. The idea involved in the first term was 

 introduced by Ohm, previous investigators sjaeaking of "conducting 

 power " or " conductivity " ; while the term " potential " was brought 

 into the subject later by Green, who borrowed it from Laplace. Ohm 

 does not use it, but speaks of " electroscopic force " and " tension." 



Experiments before Ohm. — The list of those who may properly be 

 associated with the historical development of Ohm's law is a lono- one. 

 Even when one omits those who studied the applicability of the law to 



