374 E. R. HEDRICK
V. PROFESSOR E. R. HEDRICK (UNIVERSITY OF CALIFORNIA AT LOS ANGELES)
[Because of lack of time Professor Hedrick presented only a summary of the following contribution, prepared by himself and Professor Ingold of the University of Missouri.]
I. INTRODUCTION
The celebrated experiment by Michelson to determine the relative motion of the earth and the luminiferous ether was first made in 1881.1 Objection to the mathematical theory was raised by H. A. Lorentz in 1886,2 and in 1887 the theory was modified by Michelson and Morley to meet this objection.3 It is the theory accompanying the account of their 1887 experiment that is usually given and that is now generally accepted.
Until about 1898 it does not appear that any further serious objections were raised against the theory. From that time on, however, numerous papers4 dealing with the matter have appeared, which, in many instances, contain objections to one feature or another of the theory. The differences of opinion appear to arise mainly from different conceptions regarding the mechanism of interference phenomena.
In view of the wide diversity of opinion on the subject, it has seemed worth while to work out the theory anew, on the basis of some reasonable hypothesis that has been employed in dealing with other phases of interference phenomena.
Some portions of the present investigation appear to be closely related to part of the work of Righi as reported by Stein,5 and
1 American Journal of Science, 22, 120, 1881.
2 Archives Néerlandaises, 31, 2me livre, 1886.
s Philosophical Magazine (5), 24, 449, 1887.
4 We mention the following: Sutherland, ibid. (5), 46, 23, 1898; Hicks, ibid. (6), 3, 9, 1902; Sutherland, Nature, 63, 205, 1900; Luroth, Ber. d. Bayr. Ak. d. W., 7, 1909; Kohl, Annalen der Physick, 28, 259, 1909; Budde, Physikalische Zeitschrift, 12, 979, 1911, and 13, 825, 1912; Righi, Sessions of the Royal Institute of Bologna, 1919 and 1920.
For replies to some of these articles consult the following: Lodge, Philosophical Magazine (5), 46, 1898; Morley and Miller, ibid. (6), 9, 669, 1905; Laue, Annalen d. Physik, 33, 186, 1910, and Physikalische Zeitschrift, 13, 501, 1912; Debye, Beiblätter zu den Annalen der Physik, 34, 1910.
s “Michelson’s Experiment and Its Interpretation according to Righi,” Memorie della Societa Astronomica Italiana, 1, 283, 1920.
CONFERENCE ON MICHELSON-MORLEY EXPERIMENT 375
confirms, by an independent calculation, some of Righi’s results, which is a matter of great importance, since the accuracy of his work has been called in question.1
2. REFLECTION FROM A MOVING MIRROR
We begin by obtaining certain general formulae for the reflection of light from a moving mirror. Two cases are considered: (a) the direction of motion of the mirror coincides with the direction of the rays of light before reflection; (b) the direction of motion of the mirror makes an angle 0 with the direction of the rays of light.
a) Denote the velocity of light by c and the velocity of the
mirror by v. Let h represent the tangent of the angle of inclination of the mirror to the direction of motion.
In Figure 11, AZ represents the front of a wave advancing on the mirror at A. While the mirror moves from AL to A'L', the portion of the wave at Z traverses the distance ZLr. Therefore, denoting the angle A'AL' by a, we have
tan a = J^= (1 —|)Ä= (1 —/3)Ä ,
which gives the position of the equivalent fixed mirror.
Similarly, ArL is the position of the equivalent fixed mirror for a ray coming from the opposite direction CA; and if we denote CA'L by y, we have
tan 7 = (1 + ß)h .
1 See Observatory, 44, 340-341, 1921.