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 T—(Ô — Ô') X f ^
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 a0 — o!0 in order to get a finite width of fringes. This width is of the order of i mm, so that (8 —S' = o) we have the order of magnitude
, X 5‘io_s „
&o 7 = -Z7=2. 5-IO 4.
2 A y 2*io 1
In the actual experiment, we have in addition to a0— af0 the rotation Aa:
a—cl' — cio — aé+Aa ,
= _ X_ Ô-Ô'
^ 2t cio — a0+Aa The order of magnitude is
Aa= - cos 2# = (22-- cos 2# = io“8 cos 2#
W \3 • io10/
Therefore an expansion is permissible:
\ / Ô-Ô' Ô-Ô' A
( / ( f\2
27T \cto a0 (a0— a0J2
X 5-5' A Aa
yo=-— -—-41
27T a0 — a0\ a0 — 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-4 of the first term, that is, quite outside the possibility of observation under the conditions of Michelson, Morley, and Miller’s experiment.
CONFERENCE ON MICHELSON-MORLEY EXPERIMENT 385
It is interesting that in the ideal case
= X ô-ô'= X hß2 cos 2Ô__ \h
27r Aa 27T ß2 COS 2# 27T *
That is, we have a constant position, independent of the orientation of the instrument. If Michelson had devised the experiment so as to have no fringes, but light in a certain position of the ideally adjusted interferometer, expecting to have darkness in another position, because of the phase difference, the experiment would not have proved anything.
Dr. Kennedy’s arrangement occupies an intermediate position. He takes fringes of considerably greater width. The width necessary to produce an appreciable error is about 250 cm, however, and it is quite certain that his fringes were not as wide as that. Professor Hedrick’s theory is, however, very interesting and important in connection with Kennedy’s experiment.
VI. PROFESSOR PAUL S. EPSTEIN (CALIFORNIA INSTITUTE
OF technology)
I cannot report to you today on anything of my own. What I intended was a short review of some recent experiments which relate to Mr. Miller’s experiment, and which have been performed mainly outside of Pasadena.
I shall give you a brief account of three experiments, carried out by Tomaschek in Germany, by Chase in Pasadena, and by Piccard in Brussels.
In one of his experiments Tomaschek used the following arrangement. In the immediate neighborhood of a charged condenser I (Fig. 17) was suspended a magnetic needle II. The experiment was intended to check an old idea of Röntgen’s which was as follows: The charged condenser, being in motion, represents a system of two parallel currents moving in opposite directions. These currents produce a magnetic field which should exert a force on the magnetic needle. In case the condenser is in motion relative to the ether, a deflection of the magnetic needle should be found. In reality this device cannot provide a crucial test for a decision between the old and the new theory. An exact analysis shows that both theories lead