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LXI. On the Theory of Experiments to detect Aberrations of the Second Degree. By Edward W. Morley, Ph.D., LL.D., Professor in Western Reserve University, and Dayton C. Miller, Ph.D., Professor in Case School of Applied Science, Cleveland, Ohio^[1].

[Plate IX.]

In 1887 Michelson and one of the present writers made an experiment "On the Relative Motion of the Earth and the Luminiferous Æther"^[2]. We found that, if there were any effect, it was not sensibly larger than one-fortieth of the amount expected. To explain this result, FitzGerald and Lorentz suggested that the motion of translation of a solid through the æther produces a contraction in the direction of the drift, with extension transversely, the amount of which is proportional to the square of the ratio of velocities of translation and of light.

Such a contraction can be imagined in two ways. It may be thought to be independent of the physical properties of the solid and governed only by geometric conditions; so that sandstone and pine, if of the same form, should be affected in the same ratio. On the other hand, the contraction may depend upon the physical properties of the solid; so that pine-timber would doubtless suffer a greater compression than sandstone. If the compression annul the expected effect in one apparatus, it may in another apparatus give place to an effect other than zero, perhaps with the contrary sign.

We have now completed an experiment in which two different pine-structures have been used, and in which the optical parts have been so enlarged as to produce an effect 2.3 times as great as the apparatus of 1887. The object was to determine whether there is any difference between the behaviour of sandstone and of pine.

When Michelson and Morley got a null result in 1887, it was thought sufficient to give the theory for merely the maximum and the minimum expected in the four principal azimuths, without mention of the phenomena at intermediate azimuths. The theory also neglected powers higher than the second of the ratio of the velocities. Recently, Dr. Hicks^[3] has published a profound and elaborate discussion of the theory, obtained by methods which are not approximate.

1. Communicated by the Authors. Read at the New York Meeting of the National Academy of Sciences.
2. Am. Jour. Sci. xxxiv. p. 333.
3. Phil. Mag. [6] iii. p. 9 (1902).