principles of Huyghens and Fermat are not independent. The second may be deduced from the first. It is easy to prove that this is true. There is then no question of having two assumptions.
Hedrick: Is this really generally true?
Lorentz: Yes; the relation between Huyghens7 principle and Fermat’s principle is absolutely general. I might repeat more precisely some of the features of the reasoning I gave yesterday.
Suppose P (Fig. 5) to be a luminous point. (The difficulties might of course begin here, if we were obliged to state exactly what we mean by this.) Suppose, further, that rot w = o, which is Fresnel’s idea. Making use of Fresnel’s coefficient and entrainment, we find the influence of a motion of the apparatus on effects of the first order to be the same for each of the paths h and l2.
There is still one point to be considered which I did not mention before. If we take into account effects of the second order, the path of the rays will be changed by the motion of the apparatus, so that we should have to use in one moment I and in the next V. Still I think that for the effects under consideration it does not make any difference which one we take. [Hedrick remarks: “Yes, that is all right.”] It can easily be seen that the difference between I and V produces only an effect of the fourth order. We are thus justified in using the path existing without motion of the ether.
Of course the value of the light-path I must be exact to the second order. For those cases in which we are concerned with the propagation in ether only, this value follows from the expression for v (velocity of light in the moving system) :
i = ? [1--C0S û+% (cos2 #+§ sin2 #)
V C c c
[See expression (3) in Report II.] But the question arises, and this is what I wanted to add, what will be the form of the equation when we deal with light passing through the moving glass plates? In this case w2/c2 would be replaced by k2 uf/c2, where 1 — k = (n2 — i)/n2 is Fresnel’s coefficient. Now this value for k might not be quite rigorous in this connection. The expression wkdt due to the entrainment by matter might be doubted if terms of the second order are to be considered. This indeed might necessitate a change of magnitude for these second-order effects. It is to be remarked, however, that the dis
CONFERENCE ON MICHELSON-MORLEY EXPERIMENT 401
tances through which the light travels in glass in Michelson’s experiment are comparatively so small, and that practically they cannot give rise to any difficulty at all. For all these reasons I think that the theory which I presented is general, and, at tjie same time of exact applicability to the actual instrument. In any case, I intend to study all the recent work such as Mr. Hedrick’s.
Dr. G. Strömberg: It is often said that the sun’s motion “in space” is 20 km/sec. toward the point a = 270°, ô=+30°. This expression is quite inadequate and means that the sun’s motion referred to the brighter stars is of this magnitude and direction. Referred to distant objects, this velocity is much greater. The sun’s velocity relative to the system of globular star clusters is about 300 km/sec. in the direction a = 320°, 5= +65°, and relative to the spiral nebulae it may be even larger, although in about the same direction.
As the bigger reference frame is, presumably, the more fundamental, the higher velocity may also be of more fundamental nature.
And this is just what has been found to be the case. The sun’s motion as referred to different classes of objects in our neighborhood is quite different, and the general rule has been established that the higher the internal velocity dispersion in a group, the larger is the sun’s motion relative to this group. Practically all celestial objects can be arranged in a sequence with increasing velocity dispersion, and moving with different velocity along a certain axis. This sequence terminates with the globular clusters, and a quadratic relationship exists between group motion along a certain axis and the velocity dispersion along the same axis. This phenomenon can, at least formally, be explained as the effect of a velocity restriction in a fundamental reference frame in which the globular star clusters are statistically at rest.
Recent studies of the velocities of giant M stars have completely confirmed this hypothesis. In fact, it has been found possible to represent the velocity distribution along this fundamental axis in a much more satisfactory way by one disposable constant, in addition to this fundamental velocity vector, than by four arbitrary constants, as in the prevalent methods.
In stellar motions we have to introduce a fundamental velocity vector of 300 km/sec. in the direction mentioned in order to secure