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On the Theory of Aberration and the Principle of Relativity.

By H. C. Plummer, M.A.

I. In a former paper (vol. lxix. p. 496) the theory of aberration has been discussed from the standpoint of ordinary optical theory. This suffices for the conclusion that beyond the astronomical effects as commonly understood no first-order optical effects can be put in evidence, and that, in the absence of greater experimental refinement, it is impossible for the observer to detect his own absolute motion in the ether. With this position the astronomer must be content. If we have reason to be dissatisfied with the results of the efforts hitherto made to determine the constant of aberration, we have little ground for taking into account the second-order effects. But on the other hand an optical experiment has been performed which cannot be reconciled with the ordinary theory, and we have been forced to admit that the theory, if not actually erroneous, can be no more than an approximation to the truth. Meanwhile the electronic theory of matter has been developed, and has embraced in its synthesis an explanation of this difficulty. The result is that the Principle of Relativity, with its far-reaching implications, has obtained a cardinal position in modern science. It is possible that there are some astronomers who are not familiar with the literature of the subject, and to whom an elementary account of the new ideas in physics may be of interest. Accordingly the subject will be approached from the purely optical side, and an attempt will be made to present the theory, which is a product of the last decade and is due chiefly to Professor Lorentz,^[1] in the simplest possible way.

2. According to the principle of relativity, it is impossible to find experimental evidence of the absolute motion through the ether. Let us consider the bearing of this on a very simple experiment. Let AB and AC (fig. 1) be actual lengths l' and l at right angles to one another, and let mirrors be placed at B and C perpendicular to AB, AC, so that rays of light from A will be reflected back to A. Now suppose that the whole apparatus is carried through the ether with the velocity v in the direction AB, the velocity of light being U. The time from A to B and back again will be

$t_{1}=l'/(U-v)+l'/(U+v)=2l'U/\left(U^{2}-v^{2}\right).$

But the time by the path AC'A' in the ether will be

$t_{2}=2AC'/U=2l/{\sqrt {U^{2}-v^{2}}}$

Hence if $t_{1}=t_{2}$,

$l'=l{\sqrt {1-v^{2}/U^{2}}}$

1. The fundamental hypothesis concerning the contraction of matter in motion is due to Fitzgerald; the first mention of his suggestion occurs in an abstract of a paper by Sir O. Lodge (Nature, 1892, June 16). This reference I owe to Professor Whittaker.