CONFERENCE ON MICHELSON-MORLEY EXPERIMENT 345
Miller, who again obtained a negative result. Miller then continued alone, and seems now to get some positive effect. This effect, however, has nothing to do with the orbital motion of the earth. It seems to be due to a velocity of the solar system relative to stellar space, which may be much greater than the orbital velocity.
The observations of Mr. Miller have stimulated new interest in the problem. An excellent piece of work has already been done by Mr. Kennedy, whose report you will hear. I intend myself to go over the experiments again, but several months may pass before I shall be able to give my results, which, I hope, will shed more light on the subject.
n. PROFESSOR H. A. LORENTZ (LEIDEN, HOLLAND)
The motion of the earth through a hypothetical ether (talking in historical terms) might have an effect on different phenomena. The first relevant phenomenon found experimentally was the aberration of fight. It was discussed on the basis of the emission theory and also on the wave theory in the form Fresnel had given it. From Fresnel’s point of view we may argue as follows: We draw our diagrams in a system of co-ordinates which is fixed to the earth. In this system all ponderable matter is at rest. But the ether may move through it. Say the velocity of the ether is w. If the ether does not move, then the velocity of light through matter would be u = c//j, (/x = index of refraction ; c = velocity of light). Now let an elementary wave be formed around P. This after the time dt will be a sphere of radius udt. The center 0 of this wave will, however, not coincide with P, being displaced over a distance kwdt, where i—k is FresnePs coefficient 1 —1 /m2 = P- Thus k = i/p2. PQ is a ray of light. (We denote by v the velocity of the rays of light.)
We have then from Figure 4, in which PQ = vdt, PO = kwdt, and OQ = udt, the relation
PQ:PO:OQ = v:kw:u. p 0
Thus
U2 = V2-\-k2W^—2kv COS Û (1) IG’ 4
The derivation of this formula is based on Huyghens’ principle and FresnePs entrainment. Huyghens’ principle can be used in any
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case. One has simply to follow the elementary waves and to construct the successive wave fronts. As to the coefficient of entrain-ment, I mention that Fresnel found it at first on a mechanical basis from his elastic theory of light. This was a very remarkable performance at that time.
If we neglect terms in w2 we find
v = u-\-kw COS # ,
II kw Q
- =---- COS V .
■ V u u2
The course of a ray of light between given points is determined by the condition (Fermat’s principle)
or
-/( f-
cos â ds ) . (2)
u
Suppose now
* f = const.,
u*
that is, k is inversely proportional to /x2. For fi=i, there is necessarily k = i. Thus it follows that
*=-a.
p
The second term in (2) becomes then
— I w cos û ds c2
Now let the motion of the ether in our diagram be irrotational, so that w depends on a velocity potential <p,
w = grad <p .
Then the integral
jw cos û ds
for a path between two given points P and Pf becomes
rd* /jc