A General Theory of Systems of Electric and Magnetic Units

A system of electric and magnetic units may be shown to be characterized by five parameters, namely: a numeric, n, which gives the ratio between the density of electric displacement used in that system and the so-called theoretical density; a numeric, p, which gives the corresponding ratio for magnetic flux densities; a physical conversion factor, k, which converts a given volume of current into the corresponding magnetomotive force; the absolute permittivity, κ; and the absolute permeability, μ. On the basis of these five parameters, the principal fundamental equations of electricity, magnetism, and electromagnetic waves are written in what the author calls the general system of units, without assigning definite values to these parameters. He also shows that the five parameters must satisfy the equation vk = √np/κ√, where v is the velocity of propagation of electromagnetic waves in that particular medium to which κ and μ refer; otherwise the five parameters may be chosen arbitrarily. By giving these parameters specific values, seven different systems of units are derived, namely, the electrostatic, the electromagnetic, the practical, the Gauss system, the Heaviside-Lorentz system, one which the author calls the compromise system, and the ampere-ohm system introduced by him some twenty years ago. The characteristics, the advantages, and the disadvantages of each system are briefly discussed, and it is shown how to deduce a new system of units from the general system, to conform to certain desired specifications.