It differs essentially from the interference kaleidoscope, Fig. [7], inasmuch as there is now no luminous path B C, and no contour enclosed by the light. Each half-beam goes to and fro on its own path, and these paths, instead of being coincident, are widely separate,—one North and South, for instance, and the other East and West.
Under these conditions the bands are much more tremulous than they were in the arrangement of Fig. [7], and are subject to every kind of disturbance. The apparatus has to be excessively steady, and no fluctuation even of temperature must be permitted in the path of either beam. To secure this, the source, the mirrors, and the observing telescope, were all mounted upon a massive stone slab; and this was floated in a bath of mercury.
The slab could then be slowly turned round, so that sometimes the path A B and sometimes the path A C lay approximately along or athwart the direction of the earth's motion in space.
And inasmuch as the motion along would take a little longer than the motion across, though everything else was accurately the same, some shift of the interference bands might be expected as the slab rotated.
But whereas in all the experiments previously described the effect looked for was a first-order effect, of magnitude one in ten or twenty thousand,—depending, that is to say, on the first power of the ratio of speed of earth to speed of light,—the effect now to be expected depends on the square of that same ratio, and therefore cannot be greater, even in the most favourable circumstances, than 1 part in a hundred million.
It is easy to realise therefore that it is an exceptionally difficult experiment, and that it required both skill and pertinacity to perform it successfully.
That it is an exceptionally difficult experiment will be realised when I say that it would fail in conclusiveness unless one part in 400 millions could be clearly detected.
Mr. Michelson reckons that by his latest arrangement he could see 1 in 4000 millions if it existed (which is equivalent to detecting an error of 1/1000 of an inch in a length of 60 miles); but he saw nothing. Everything behaved precisely as if the ether was stagnant; as if the earth carried with it all the ether in its immediate neighbourhood. And that was his conclusion.
Theory of Michelson Experiment.
The theory of the Michelson experiment can be expressed thus: its optical diagram being the same as is expressed geometrically in Fig. [6].