Page:Aether and Matter, 1900.djvu/220

 orbits. To reach this conclusion, it is by no means necessary to assume that we have any knowledge of the process by which ionisation, or the passing on of electrons from molecule to molecule, occurs in conductive processes.

. In this connexion we can gain some knowledge of the nature and amount of the effect of the Earth's motion on electrolytic conduction. If the convective velocity v is in the direction of the current, and the actions between the ions are, as usual in electrolytic theory, assumed to be wholly electric, and w and w' represent velocities of positive and negative ions, then the position of the positive ion in the electrolyte at rest is given by $$x=wt$$; hence (§ 112) in the electrolyte in motion with the same electric force it is given by $$x=w\left(1-\frac{v}{c^{2}}x\right)$$, so that $$x=\frac{w}{1+vw/c^{2}}t$$; thus the velocity of the positive ion relative to the moving electrolyte is $$w/\left(1+\frac{vw}{c^{2}}\right)$$. The velocity of the negative ion is similarly $$w'/\left(1-\frac{vw'}{c^{2}}\right)$$. The electric current, being determined by the sum of these velocities, is altered as regards these ions in the ratio of $$w+w'-\frac{v}{c^{2}}\left(w^{2}-w'^{2}\right)$$ to $$w+w'$$ approximately; it is thus diminished in the ratio $$1-v(w-w')/c^{2}$$; and the conductivity of the electrolyte is diminished in this ratio, where now $$w-w'$$ represents an average value, the difference of the velocities of drift of positive and negative ions. This change of conductivity is a unilateral one, being reversed when the direction of the current is reversed: it is at most of the second order of small quantities: it vanishes altogether, or rather becomes of two orders higher, when the velocities of the positive and negative ions are the same. It may be remarked incidentally that, as the numbers of positive and negative ions taking part in the current of conduction are the same, the specification of that current with reference to moving matter is just the same as with reference to the stationary aether.