CONFERENCE ON MICHELSON-MORLEY EXPERIMENT 383 V. PROFESSOR PAUL S. EPSTEIN (CALIFORNIA INSTITUTE OF technology) The result of Professor Hedrick’s analysis is that the two beams of light acquire a difference of phase d—8 and a difference in direction Aa = ß Fig. 16 in which terms of the fourth order are neglected. Let us now choose the plane in which we observe the fringes as x = o of a cartesian system (Fig. 16). We can then represent the two waves by the formulae (s = light-vector) I 27r I s = A cos — (x cos a+y sin a+c/)+5 , s' = A cos The illumination of the screen is then (x = o, sin a = a) (s-\-s We have maxima, where the argument of the cosine is a multiple of 7r. The position of the central fringe is therefore given by | 3&4 PAUL S. EPSTEIN The distance between two maxima, or the width of the fringes, is given by the equation Ay(a— a^+S — ô' = t , A or
A y =--—r-t---. (2) a—a 27r Let us first consider the interferometer at rest. We cannot take the ideal adjustment, because then we should have no fringes. Formula (2) shows that we must have a finite difference a , X 5‘io &o 7 2 A y 2*io In the actual experiment, we have in addition to a a—cl' — cio — aé+Aa ,
^ 2t cio — a Aa= - cos 2# = ( W \3 • io Therefore an expansion is permissible: \ / Ô-Ô' Ô-Ô' ( / ( f\2 27T \cto a X 5-5' A Aa yo=-— -—-41 27T a The first term represents the shift due to the difference of phase; the second term is due to the rotation. We see that it is 0.4-io |