Each of these conceptions has something in its favor, and each has something against it, but they should all be regarded merely as con venient mathematical fictions for the present— fictions that are worth considering because they may serve to suggest further researches when their consequences are investigated. The • ex periments of Kaufmann (to which reference will presently be made) appear to be incompat ible with Lorentz's conception of the corpuscle, while the theory of relativity suggests that those of Abraham and of Bucherer and Lange vin are untenable.
The general theory of electricity, as applied to static charges moving rapidly through space, brings us face to face with an exceedingly in teresting topic in connection with the negative corpuscle,—namely, that its apparent mass is doubtless in some measure of electrical origin, and that it is within the bounds of possi bility that it is wholly electrical. Sir J. J. Thomson pointed out, as long ago as 1881, that a moving body (for example, a sphere) pos sesses a somewhat greater apparent inertia, or mass, when it is electrically charged than it does when it is not charged. (Recent Researches in Electricity and Magnetism,' p. 21.) This is due to the fact that the charged body has Fara day °tubes of force" radiating from it, and these tubes are supposed to carry a certain amount of ether along with them and to encounter a sort of hydrodynamic resistance from the sur rounding ether. This resistance is not analo gous to friction, however. It does not neces sarily entail any dissipation of energy, but has the general effect (when considered mathemat ically) of increasing the apparent mass of the charged body. Thomson showed, for example, that a sphere having a radius of r centimeters, and bearing an electric charge of e absolute electromagnetic units, has an apparent mass 2 es equal to (m — 3 • —) grammes, if it is station ary or moving with a speed that is small in comparison with the speed of light; m being its mass, in grammes, when the electric charge is absent.
\Vhen a charged sphere is caused to move with greater and greater speed, the Faraday tubes of force shift their positions in relation to it, and Heaviside showed (in 1889) that as the speed increases, each tube, whatever its original direction, will be displaced more and more toward a plane passing through the cen tre of the sphere perpendicularly to the line of motion. In other words, if we call the diameter
that coincides with the direction of motion of the sphere its •polar axis,* the tubes of force that radiate from the sphere will crowd closer and closer toward the equatorial plane, the faster the sphere moves. Moreover, the shift ing of each tube (according to Heaviside's analysis) will take place in such a way that the original distance of every point in the tube from the equatorial plane will be reduced by the motion in the proportion of V Ve—ve to V, where v is the speed of the sphere, and V is the speed of light. (It is to be observed, in particular, that the tubes approach the equa torial plane in the same way, whether they lie in front of it or behind it, as the sphere moves through space).
Now the effect of the ether upon a Faraday tube is very different when the tube is moving endwise than when the tube is moving side wise (or perpendicularly to its own length) ; and in consequence of this fact, the part of the apparent mass that is due to the electrification increases when the speed of the sphere becomes great enough for the equatorial crowding of the tubes of force to become significant. It is not possible to deal with this phase of the sub ject more than superficially in the present arti cle, but it should be specially noted that mathe matical analysis has shown (1) that owing to the existence of the Faraday tubes of force that stretch out into the ether from an electrified body, that body, whether its charge be positive or negative and whether it be stationary or in .motion, has an apparent mass greater than the mass it has when the charge is absent ; (2) that owing to the crowding of the Faraday tubes toward the equatorial region when the speed of the body increases, the apparent mass of the body increases as the speed increases; (3) that at any ordinary speed this increase in apparent mass is insignificant and does not have to be reckoned with; but (4) that it becomes sig nificant as soon as the body attains a speed equal to a few tenths of the speed of light, and (5) the apparent mass increases with extreme rapidity as the speed approaches closely to the speed of light, and (6) it would become infinite if that speed were fully attained.