Properties of the single conductor: New fundamental relations

The properties of a unit length of single, straight conductor, far removed from all other circuits, are investigated to endeavor to find whether such a unit is a basic, fundamental one, on which deductions and a method of mathematical treatment could be based, as was advocated by. Ampere, to supplement (not to replace) the Maxwell system based on a complete circuit, and to test the correctness of some of the postulates now in common use, based on the latter system. By several new, simple, and direct proofs based only on a few well-established and accepted relations, chiefly the internal stresses in a conductor, but excluding infinities, self-inductances, induction, and any postulates, a constant is deduced for the energy stored by a current in such a unit length, which seems to be one of the most fundamental, basic constants in electrodynamics, from which many useful deductions can be made, some of which are given. This energy of the flowing current corresponds to the m v
²
/2 energy of moving masses. Some of the results differ from those which have been in use; explanations are offered of the cause of these differences, and it is shown how the results may be brought into agreement, involving some changes in our previous conceptions. It is shown that with flux lines a distinction ought to be made which is analogous to that which distinguishes the wattless ampere from the one in phase, or between a true resistance and an impedance; it is shown why what might be called wattless flux, ought to be recognized. It is shown that self-inductance is used in two senses which may sometimes lead to different results, and that a distinction should therefore be made between them somewhat analogous to that between resistance and impedance or reactance. This it is believed would clear up the ambiguity now existing in that term. It is believed that some of these results could not have been obtained from the Maxwell complete circuit system, which rather leads one away from them.