Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/430

the medium initially hotter or colder than the rest. We must remember, however, that since the current is a vector quantity, and since in a circuit the current is in opposite directions at opposite points of the circuit, we must, in calculating any given component of the induction-current, compare the problem with one in which equal quantities of heat and of cold are diffused from neighbouring places, in which case the effect on distant points will be of a smaller order of magnitude.

805.] If the current in the linear circuit is maintained constant, the induction currents, which depend on the initial change of state, will gradually be diffused and die away, leaving the medium in its permanent state, which is analogous to the permanent state of the flow of heat. In this state we have

$\nabla ^{2}F=\nabla ^{2}G=\nabla ^{2}H=0$

(2)

throughout the medium, except at the part occupied by the circuit, in which

$\left.{\begin{aligned}\nabla ^{2}F&=4\pi u,\\\nabla ^{2}G&=4\pi v,\\\nabla ^{2}H&=4\pi w.\end{aligned}}\right\}$

(14)

These equations are sufficient to determine the values of $F,G,H$ throughout the medium. They indicate that there are no currents except in the circuit, and that the magnetic forces are simply those due to the current in the circuit according to the ordinary theory. The rapidity with which this permanent state is established is so great that it could not be measured by our experimental methods, except perhaps in the case of a very large mass of a highly conducting medium such as copper.

NOTE. In a paper published in Poggendorff's Annalen, June 1867, M. Lorenz has deduced from Kirchhoff's equations of electric currents (Pogg. Ann. cii. 1856), by the addition of certain terms which do not affect any experimental result, a new set of equations, indi cating that the distribution of force in the electromagnetic field may be conceived as arising from the mutual action of contiguous elements, and that waves, consisting of transverse electric currents, may be propagated, with a velocity comparable to that of light, in non-conducting media. He therefore regards the disturbance which constitutes light as identical with these electric currents, and he shews that conducting media must be opaque to such radiations.

These conclusions are similar to those of this chapter, though obtained by an entirely different method. The theory given in this chapter was first published in the Phil. Trans, for 1865.