Page:Popular Science Monthly Volume 83.djvu/605

Rh In any given circuit, in a steady state, the current I will he directly proportional to the electromotive-force E, and the constant obtained by dividing the latter by the former is termed the resistance of the circuit.

II

The resistance of a homogeneous conductor of uniform cross-section is inversely proportional to its area of cross-section and directly proportional to its length. The constant $$\rho$$ entering into the equation is termed the specific resistance of the conductor, since it is the value of $$R$$ when $$l$$ and $$A$$ are unity. The first proposition states that whatever else the resistance may depend upon, it does not depend upon the current. The 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 considerations 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 would vary inversely as the circumference of the conductor rather than as the cross-section. The true circumstances of current 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 speaking 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 long one. Even when one omits those who studied the applicability of the law to