the bottom of the model; the four epochal positions are marked by the arrows at the bottom. This part of the model corresponds to the orbital circle on the chart, Fig. 28, and to the model of the orbit with the four globes, Fig. 24.
Probable error
A study of the numerical results as plotted in Fig. 26 shows that the probable error of the observed velocity, which has a magnitude of from ten to eleven kilometers per second, is
±0.33 kilometer per second, while the probable error in the determination of the azimuth is ±2.5°. The probable error in the right ascensions and declinations of the polar chart, Fig. 28, is ±0.5°.
Full-Period Effect
Throughout these experiments, while the attention has been given to the second-order, half-period effect, there has been present a full-period, first-order effect of comparable magnitude. The theory of the ether-drift experiment as usually given is exact but it is also abstract, being based upon simplified conditions of the apparatus which never exist in the actual experiment. What actually happens to the interference fringes depends not only upon the ether-drift effect but also upon the geometrical arrangement of the mirrors. The simple theory assumes that the mirrors at the ends of the two arms of the interferometer are perpendicular to the rays of light; this would produce fringes of infinite width, the whole field of view being uniformly illuminated, a critical condition never desired nor used in practice. In order to produce a series of straight fringes, suitable for the measurement of displacements, as shown in Fig. 7, it is necessary that one of the end mirrors be rotated about a vertical axis through a very small angle so that the two virtual interfering planes intersect. The width of the fringes and the number of fringes in the field of view are directly dependent upon this inclination of the end mirror. The angle of incidence of the light on the mirror, as used in these experiments, differs from 0° by about ±4″. The late Professor W. M. Hicks of University College, Sheffield, has given an elaborate
discussion of the theory,15 using methods which are not only rigorous but also general, applying to any adjustment whatever of the optical parts of the apparatus. In the theory of Hicks it is shown that when the periodic variation in the relative phases of the two beams of light in the interferometer takes place with the mirrors adjusted as in actual practice, there is introduced an additional effect which is periodic in a full turn of the instrument. The amplitude of this full-period effect, which varies inversely as the width of the fringes being used at the time of observation, is about equal to the amplitude of the ether-drift effect when there are eight fringes in the field of view; with the adjustment usually secured for six fringes in the field of view, the full-period effect is smaller than the half-period effect, as shown in Fig. 21.
The full-period effect, which has usually been overlooked, is present in all of the observations, including the original observations of Michelson and Morley. Hicks called attention to the latter fact and calculated its magnitude. Unfortunately, in none of the observations heretofore made have there been quantitative measurements of the width of the fringes which determines the angle of inclination of the mirror and it is not possible to use the full-period effect for a solution of the problem of ether-drift. However, the approximate number of fringes visible in the field of view has frequently been recorded. A comparison of the width of fringes thus indicated with the magnitude of the full-period effect shows a direct
Fig. 30. The full-period effect; the relation of amplitude to width of fringes.
16 W. M. Hicks, Phil. Mag. [6] 3, 9, 256, 555 (1902); Nature 65, 343 (1902); E. W. Morley and D. C. Miller, Phil. Mag. [6] 9, 669 (1905).
linear relation as required by the theory of Hicks; this relation is shown in Fig. 30.
The Entrained Ether Hypothesis
In order to account for the results here presented, it seems necessary to accept the reality of a modified Lorentz-FitzGerald contraction, or to postulate a viscous or dragged ether. In commenting upon 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, is 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.”16 The theory of Stokes may be described by means of the following sentences selected from Sir Joseph Larmor’s 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 irrotational 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 differently irrotational, 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.
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 ether-drift experiments have never been
16 L. Silberstein, Phil. Mag. [6] 39, 161 (1920).
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. Sir Oliver Lodge in his autobiography says: “I still cling to the idea that the FitzGerald contraction is a reality which must be taken into consideration in any physical contemplation of the universe.”17
One is compelled, therefore, to consider whether there are possible readjustments of the theories of the ether that will account for the reduction in the observed velocities of absolute motion and for the displaced azimuths. The difficulties presented by these anomalies are certainly not greater than those existing in many other fields of experimental research.
Other Recent Ether-Drift Experiments
Since the announcement of the evidence of absolute motion of the solar system made at Kansas City in 1925, several other experimenters have performed ether-drift experiments with interferometers of various designs and under various conditions, leading to results which are generally considered to be at variance with the conclusions of this paper. Brief reference to these experiments will be made but without extended analysis.
Dr. Roy J. Kennedy, at Pasadena, used an interferometer with an optical device of original design, giving great sensitivity.18 The length of
17 O. J. Lodge, Past Years, 206 (1932).
18 R. J. Kennedy, Proc. Nat. Acad. Sci. 12, 621 (1926); Astrophys. J. 68, 367 (1928).
