Page:Aether and Matter, 1900.djvu/219

 done in a representation of their magnetism, and thus the phase-change makes no difference for the present purpose. The case is however different when there are electric currents flowing in the system, for that involves the transfer of some electrons into entirely new positions, it may be at a finite distance: these wandering electrons or ions interfere with the exact statement of the correlation, and they interfere to a like extent with any conclusions that may be drawn from it, as to change of form of solid bodies carrying currents arising from their motion with the Earth through the aether.

How far then is the correlation between the fixed material system and the moving system modified by electric conduction? In the theorem the position of each electron in the material medium in motion, at time t, corresponds with that which it would occupy in the medium at rest at time $$t-vx/c^2$$. When the material medium is a solid dielectric mass, the mean position of the electron is the same at all times, and as we have seen this element of time does not enter into the comparison at all: but when the medium is conducting, the electric currents in it involve migration of electrons through it, and we must consider how far the correspondence is thereby prejudiced. Only two views of the nature of conduction, in this connexion, are open. The current in metals may possibly (but not likely) be carried by very few electrons, in which case they will migrate with sensible speed; but the smallness of their number, compared with the total number of combined electrons, prevents their changes of position from sensibly affecting the molecular structure of the medium: we know in fact that the mechanical structure of a conductor is not sensibly affected when it carries a current. On the other hand a considerable proportion of the electrons may take part in carrying the current; in which case their velocity of migration is excessively minute, as for instance follows from the phenomena of migration in electrolysis; and the discrepancy of position of those electrons, in the application of the correlation theorem, involving the factor $$v/c^2$$ as well as this velocity, is negligible to an order higher than the second, just as was the discrepancy of phase in the individual molecular