Page:Lorentz Simplified1899.djvu/16

 are in S0. If therefore the required agreement is to exist with regard to the vibrations parallel to OX, the ratio of the masses of the ions in S and S0 should be $$\tfrac{k^{3}}{\varepsilon}$$; on the contrary we find for this ratio $$\tfrac{k}{\varepsilon}$$, if we consider in the same way the forces and the accelerations in the directions of OY and OZ.

Since k is different from unity, these values cannot both be 1; consequently, states of motion, related to each other in the way we have indicated, will only be possible, if in the transformation of S0 into S the masses of the ions change; even, this must take place in such a way that the same ion will have different masses for vibrations parallel and perpendicular to the velocity of translation.

Such a hypothesis seems very startling at first sight. Nevertheless we need not wholly reject it. Indeed, as is well known, the effective mass of an ion depends on what goes on in the aether; it may therefore very well be altered by a translation and even to different degrees for vibrations of different directions.

If the hypothesis might be taken for granted, 's experiment should always give a negative result, whatever transparent media wore placed on the path of the rays of light, and even if one of these went through air, and the other, say through glass. This is seen by remarking that the correspondence between the two motions we have examined is such that, if in S0 we had a certain distribution of light and dark (interference-bands) we should have in S a similar distribution, which might be got from that in S0 by the dilatations (6), provided however that in S the time of vibration be $$k\varepsilon$$ times as great as in S0. The necessity of this last difference follows from (9). Now the number $$k\varepsilon$$ would be the same in all positions we can give to the apparatus; therefore, if we continue to use the same sort of light, while rotating the instruments, the interference-bands will never leave the parts of the ponderable system, e. g. the lines of a micrometer, with which they coincided at first.

We shall conclude by remarking that the alteration of the molecular forces that has been spoken of in this § would be one of the second order, so that we have not come into contradiction with what has been said in § 7.