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The value of the constant must be unity, because we know already that, for w = 0,1 = 1.
We are therefore led to suppose that the influence of a translation on the dimensions (of the separate electrons and of a ■ponderable body as a zohole) is confined to those that have the direction of the motion, these becoming k times smaller than they are in the state of rest. If this hypothesis is added to those we have already made, we may be sure that two states, the one in the moving system, the other in the same system while at rest, corresponding as stated above, may both be possible. Moreover, this correspondence is not limited to the electric moments of the particles. In corresponding points that are situated either in the aether between the particles, or in that surrounding the ponderable' bodies, we shall find at corresponding times the same vector &' and, as is easily showp, the same lector I/. We may sum up by saying: If, in the system without translation, there is a state of motion in which, at a definite place, the components of p, b and f) are certain functions of the time, then the same system after it has been put in motion (and thereby deformed) can be the seat of a state of motion in which, at the corresponding place, the components of p', &' and V are the same functions of the local time.
There is one point which requires further consideration. The values of the masses m, and m, having been deduced from the theory of quasi-stationary motion, the question arises, whether we are justified in reckoning with them in the case of the rapid vibrations of light. Now it is found on closer examination that the motion of an electron may be treated as quasi-stationary if it changes very little during the time a light-wave takes to travel over a distance equal to the diameter. This condition is fulfilled in optical phenomena, because the diameter of an electron is extremely small in comparison with the wave-length.
$ 11. It is easily seen that the proposed theory can account for a large number of facts.
Let us take in the first place the case of a system without translation, in some parts of which we have continually p = 0, t> = 0, () = 0. Then, in the corresponding state for the moving system, we shall have in corresponding parts (or, as we may say, in the same parts of the deformed system) p' = 0, b' = 0, l/=0. These equations implying *> = 0, b = 0, () = 0, as is seen by (26) and (6), it appears
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that those parts which are dark while the system is at rest, will remain so after it has been put m motion. It will therefore be impossible to detect an influence of the Earth’s motion on any optical experiment, made with a terrestrial source of light, in which the geometrical distribution of light and darkness is observed. Many experiments on interference and diffraction belong to this class.
In the second place, if in two points of a system, rays of light of the same state of polarization are propagated in the same direction, the ratio between the amplitudes in these points may be shown not to be altered by a translation. The latter remark applies to those experiments in which the intensities in adjacent parts of the field of view are compared.
The above conclusions confirm the results I have formerly obtained by a similar train of reasoning, in which however the terms of the second order were neglected. They also contain an explanation of Michelson’s negative result, more general and of somewhat different form than the one previously given, and they show why Rayleigh and Brace could find no signs of double refraction produced by the motion of the Earth.
As to the experiments of Trodton and Noble, their negative result becomes at once clear, if we admit the hypotheses of § 8. It may be inferred from these and from our last assumption (§10) that the only effect of the translation must have been a contraction of the whole system of electrons and other particles constituting the charged condenser and the beam and thread of the torsion-balance. Such a contraction does not give rise to a sensible change of direction.
It need hardly be said that the present theory is put forward with all due reserve. Though it seems to me that it can account for all well established facts, it leads to some consequences that cannot as yet be put to the test of experiment. One of these is that the result of MrcHELSON’s experiment must remain negative, if the interfering rays of light are made to travel through some ponderable transparent body.
Our assumption about the contraction of the electrons cannot in itself be pronounced to be either plausible or inadmissible. What we know about the nature of electrons is very little and the only means of pushing our way farther will be to test such hypotheses as 1 have here made. Of course, there will be difficulties, e.g. as soon as we come to consider the rotation of electrons. Perhaps we shall have to suppose that in those phenomena in which, if there is no translation, spherical electrons rotate about a diameter, the points of the electrons in the moving system will describe elliptic paths,