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. 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 ZL tan which gives the position of the equivalent fixed mirror. Similarly, A tan 7 = (1 + ß)h .
| 376 E. R. HEDRICK b) If the direction of motion of the mirror makes an angle with the direction of the rays, then from Figure 12 it is clear that the mirror really advances with a velocity _ v sin 0 V cos 0--=— , h so that the formulae for this case may be obtained from those of the previous case by putting / _ sin 0\ 0(cos e- in place of ß. If the mirror is inclined at an angle of 45 tan a=i — ß(cos 0 —sin 0) , while tan 7=i+jS(cos 0 —sin 0) . 3. APPLICATION TO THE MICHELSON-MORLEY EXPERIMENT In the Michelson-Morley experiment a ray of light from a source S (Fig. 13) meets a half-silvered glass plate, inclined at 45 We assume that the earth and the apparatus are moving through the ether in a direction making an angle 0 with the path of the rays SA. It will be necessary to determine the position of the equivalent fixed mirror at B. For convenience denote ß(cos 0 —sin 0) by £. Then the angle CAB = 2a where tan a = 1 — £. In Figure 14, if BE is the wave front of the ray reflected from A and if the mirror at B advances from BM to B |