If a relatively fixed source and receiver move through the ether with velocity u, such that u/v=α the aberration constant; then the time of any to and fro journey S M, inclined at angle θ to the direction of the drift, is increased, above what it would be if there were no drift, in the ratio
√(1 − α² sin² θ) / 1 − α²
This follows from merely geometrical considerations.
Hence if a ray is split, and half sent so that θ=0 while the other half is sent so that θ=90 (as in Fig. [10]), the one will lag behind the other by a distance ½α² times the distance travelled; which, though very small, may be a perceptible fraction of a wave-length, and therefore may cause a perceptible shift of the bands.
But when the experiment is properly performed, no such shift is observed.
The experiment thus seems to prove that there is no motion through the ether at all, that there is no etherial drift past the earth, that the ether immediately in contact with the earth is stagnant—or that the earth to that extent carries all neighbouring ether with it.
If we wish to evade this conclusion, there is no easy way of doing so. For it depends on no doubtful properties of transparent substances, but on the straightforward fundamental principle underlying all such simple facts as that—It takes longer to row a certain distance and back, up and down stream, than it does to row the same distance in still water; or that it takes longer to run up and down a hill, than to run the same distance laid out flat; or that it costs more to buy a certain number of oranges at three a penny and an equal number at two a penny than it does to buy the whole lot at five for twopence.
Hence, although there may be some way of getting round Mr. Michelson's experiment, there is no obvious way; and if the true conclusion be not that the ether near the earth is stagnant, it must lead to some other important and unknown fact.
That fact has now come clearly to light. It was first suggested by the late Professor G.F. FitzGerald, of Trinity College Dublin, while sitting in my study at Liverpool and discussing the matter with me. The suggestion bore the impress of truth from the first. It independently occurred also to Professor H.A. Lorentz, of Leiden, into whose theory it completely fits, and who has brilliantly worked it into his system. It may be explained briefly thus:—
Electric charges in motion constitute an electric current. Similar charges repel each other, but currents in the same direction attract. Consequently two similar charges moving in parallel lines will repel each other less than if stationary,—less also than if moving one after the other in the same line. Likewise two opposite charges, a fixed distance apart, attract each other less when moving side by side, than when chasing each other. The modification of the static force, thus caused, depends on the squared ratio of their joint speed to the velocity of light.
Atoms of matter are charged; and cohesion is a residual electric attraction (see end of Appendix [1]). So when a block of matter is moving through the ether of space its cohesive forces across the line of motion are diminished, and consequently in that direction it expands, by an amount proportioned to the square of aberration magnitude.
A light journey, to and fro, across the path of a relatively moving medium is slightly quicker than the same journey, to and fro, along (see p. [64]). But if the journeys are planned or set out on a block of matter, they do not remain quite the same when it is conveyed through space: the journey across the direction of motion becomes longer than the other journey, as we have just seen. And the extra distance compensates or neutralises the extra speed; so that light takes the same time for both.