[Vol. LXIII, No. 1635
the smallest quantity which can be measured by the present interferometer. It is for this reason that it is concluded that the velocity of the motion of the solar system is at least two hundred kilometers per second and it may be much greater. The fact that the observed effect is dependent upon sidereal time and is independent of diurnal and seasonal changes of temperature and other terrestrial causes shows that it is a cosmical phenomenon.
The previous observations made at Mount Wilson, while not sufficiently extended to determine curves of the kind just indicated, should, nevertheless, be consistent with these observations. In Fig. 7 the results of the observations for April 15, 1921, are compared with the curves calculated from the observations of 1925, showing a very good agreement.
The complete study of the ether-drift experiments of 1925, at Mount Wilson, leads to the conclusion that there is a systematic displacement of the interference fringes of the interferometer corresponding to a constant relative motion of the earth and the ether at this observatory of ten kilometers per second ; and that the variations in the direction and magnitude of the indicated motion are exactly such as would be produced by a constant motion of the solar system in space, with a velocity of two hundred kilometers, or more, per second, towards an apex in the constellation Draco, near the pole of the elliptic, which has a right ascension of 262° and a declination of + 65°. In order to account for these effects as the result of an ether drift, it seems necessary to assume that, in effect, the earth drags the ether so that the ap
parent relative motion at the point of observation is reduced from two hundred, or more, to ten kilometers per second, and further that this drag also displaces the apparent azimuth of the motion about 45° to the west of north.
It is evident that the present experiments are no more consistent with the old theories of a stagnant ether than were those of Michelson and Morley of 1887, and of Morley and Miller of 1905; the present work is in no way a contradiction of the earlier results, but is rather a confirmation and extension of them. That a set of six characteristic curves obtained from observations which are wholly independent of each other, and which were made at times of year with extreme differences of weather conditions, so consistently fit curves depending upon the assumed motion, as shown in Figs. 5 and 6, leads irresistibly to the conclusion that the observed effects are related to the presumed cause. One is compelled therefore to consider whether there can be a possible readjustment of the theories of the ether that will account for the reduced velocity and other experimental results.
The values of the quantities defining the absolute motion of the solar system as obtained from these ether-drift observations are in general agreement with the results obtained by other methods. The recent study of proper motions of stars by Ralph Wilson, of the Dudley Observatory, and of the radial motions of the stars by Campbell and Moore, of the Lick Observatory, give the apex of the sun's way in the constellation Hercules with a right ascension of 270° and a declination of about +30°, with a velocity of about nineteen kilometers per second. Dr. G. Stromberg, of the Mount Wilson Observatory, from a study of globular clusters and spiral nebulae, finds evidence of a motion of the solar system towards a point having a right ascension of 307° and a declination of +56°, with a velocity of three hundred kilometers per second. Lundmark, studying the spiral nebulae, finds evidence of a motion having a velocity of four hundred kilometers per second. The various determinations of the motion of the solar system are all in the same general direction and lie within a circle having a radius of 20°. Our assumed velocity of two hundred kilometers per second is simply a lower limit; it might equally well be three hundred or four hundred kilometers per second. The first assumption therefore seems to offer no difficulty. The location of the apex in the constellation Draco, at right ascension 262° and declination + 65°, is within 6° of the pole of the ecliptic, that is, the indicated motion of the solar system is almost perpendicular to the plane of the ecliptic. The sun's axis of rotation points to within 12° of this apex. One can not help wondering whether there may be some dynamic significance in these facts.
Apkil 30, 1926]
The assumption that there is a drag of the ether by the earth involves a considerable readjustment of the theories of the ether, inasmuch as it requires a modification of the accepted explanation of aberration. In commenting on the preliminary report of this work presented to the National Academy of Sciences in April, 1925, Dr. L. Silberstein said: “From the point of view of an ether theory, this set of results, as well as all others previously discovered, are easily explicable by'means of the Stokes ether concept, as modified by Planck and Lorentz, and discussed by the writer (Silberstein) in the Philosophical Magazine,”6
The theory of Stokes may be described by means of the following sentences selected from Sir Joseph Larmor^ treatise on “Aether and Matter,” pages 10, 13, 35 and 36:
As Sir George Stokes was not disposed to admit that the aether could pass freely through the interstices of material bodies in the manner required by Fresnel ’s views, and as any other theory of its motion which could be consistent with the fact of astronomical aberration required irrotationai flow, an explanation of the limitation to that flow had, he considered, to be found. This chain of argument, that motion of bodies disturbs the aether, that aberration requires the disturbance to be differen-. tially irrotationai, that this can only be explained by the - dispersion of incipient rotational disturbance by transverse waves, and further that radiation itself involves transverse undulation, he regards as mutually consistent and self supporting, and therefore, as forming distinct evidence in favor of this view of the constitution of the aether. . . . The question then arises how far this explanation will extend to the case in which the aether is entrained by the matter that is moving through it. Attention has already been drawn to Sir George Stokes’s considerations which would make the luminiferous property itself prevent the initiation of any rotational motion in the aether. It is in fact not difficult to prove that the energy of strain of a rigid incompressible medium of the type of ordinary matter may be expressed as a volume integral involving only the differential rotation, together with surface integrals extended over boundaries; and it follows that any local beginnings of rotational motion in an aether of elastic-solid type would be immediately carried off and distributed by transverse waves, so that if the rigidity is great enough no trace of rotational motion ef the medium in bulk can ever accumulate.
There are systematic differences in the so-called constant of aberration and in standard star places as determined at different observatories, which might be explained on the hypothesis of a variation in ether drift due to differences in the local coefficient of drag. The drag at any given station may depend more or less upon altitude, local contour and the distribution of large masses of land such as mountain ranges. The
6 February, 1920, Vol. 39, page 161.
ether-drift experiments have never been made at sea-level, nor, in fact, at any place except Mount Wilson, with sufficient completeness to give accurate measures of the effects. The evidence now indicates that the drift at Mount Wilson does not differ greatly in magnitude from that at Cleveland and that at sea-level it would probably have about the same value.
The reduction of the indicated velocity of two hundred or more kilometers per second to the observed value of ten kilometers per second may be explained on the theory of the Lorentz-FitzGerald contraction without assuming a drag of the ether. This contraction may or may not depend upon the physical properties of the solid, and it may or may not be exactly proportional to the square of the relative velocities of the earth and the ether. A very slight departure of the contraction from the amount calculated by Lorentz would account for the observed effect. A reexamination of the Morley-Miller experiments of 1902-1904 on the Lorentz-FitzGerald effect is now being made, with the indication that the interpretation may be modified when taken in connection with the large velocity of the solar system indicated by the observations of 1925.
It need hardly be said that the determination of the absolute motion of the solar system from such interferometer observations is one of considerable complexity. I am under obligation to Professor J. J. Nassau, of the Department of Mathematics and Astronomy of Case School of Applied Science, and to Dr. G. Stromberg, of the staff of the Mount Wilson Observatory, who have given very great assistance in the analysis and in the mathematical solutions of various parts of the problem.
Note.—Since this paper was prepared, a very complete series of observations involving 2,000 turns of the interferometer has been made at Mount Wilson, corresponding to the epoch February 8, 1926. The general indications are that the latest observations are entirely consistent with the report here made, though it is possible that there will be slight modifications in the numerical results when all observations are combined. A definitive numerical calculation will require several months of continuous work and is now in progress.
Dayton C. Miller
Case School of Applied Science
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