Dewitt Bristol Brace

“ THE FitzGerald-Lorentz [2] "Contraction" Hypothesis to explain the negative results of the Michelson-Morley [3] experiment of interference between two rays, at right angles and parallel to the earth's motion, has been tested by Rayleigh [4] in his experiments on the double refraction of liquids and of glass. He assumes the contraction to be , and also the excess of the index above unity to be proportional to the density. ”

“ And if indeed it could be proved that the optical effect is null up to the third order, that circumstance would not demolish the theory, but would rather point to some finer adjustment than it provides for; needless to say the attempt would indefinitely transcend existing experimental possibilities." And further, "up to the first order the electron hypothesis, that electricity is atomic, suffices by itself, as Lorentz was first to show." "Up to the second order, the hypothesis that matter is constituted electrically—of electrons—is required in addition." ”

“ While the negative results of the first order experiments involving a study of phase relations between periodic disturbances from the same radiant, optical or electrical, moving with the system, are quite as consistent with a mobile—if we neglect second and higher orders—as with a fixed aether, the explanations of the negative results of second and third order tests are still not in full harmony or free from criticisms, notwithstanding the bold assumption in the premises. ”

“ Hence, we may conclude that to this order of sensibility there is no double refraction in the water due to its motion through the æther. These observations were taken during the latter part of July 1903. It is evident that a rotation of the plane of polarization due to the earth's field of force would not affect this match, as both portions of the field would vary in intensity by the same amount. To make sure of this the trough was rotated through 180° into the meridian so as to reverse the direction: but no effect could be observed. ”

“ Assuming an exponential law for the variation in the velocity of the ether as we recede from the earth, he finds that if the earth carries the ether with it, this influence must extend to a distance comparable with the earth's diameter. ”

“ Supposing the eye could detect a difference in intensity of two per cent, between the two fields (under very favourable conditions this sensibility is one-half of one percent.) , we should need an interval corresponding to one hundred eclipses to detect a change in velocity equal to the aberration constant, since we have to add the effects from each ray. This would mean a distance between the mirrors of 3000 m. for the lower and 750 m. for the higher eclipse frequency referred to, which is much within the distance given above in Newcomb's experiment. ”

“ Against the view of Stokes, Lorentz raises objection to his assumptions concerning the ether motions in the neighborhood of the earth, which he considers inconsistent, a difficulty which he is unable to set aside. Larmor demurs against an appeal to a highly complex medium, such as pitch, for studying the behavior of a simple one like the ether. A time-rate much shorter than the time of relaxation will of course provide approximate rigidity, while a timerate much longer will provide approximate fluidity, but this requires inevitable dissipation. ”

“ A match could be immediately obtained by rotating the compensator 10. By noting the position of the pointer for a match and then shifting the same until such a change could just be detected, a measure of the sensibility of the system could be obtained. This angle was found to be 0°.2 under favourable conditions. At each observation the sensibility was determined. A match was obtained with, say, the trough in the meridian at noon, this was then turned through 90° into the direction of the earth's orbital motion. ”

“ This hypothesis satisfies the phenomena of aberration and the uniformity of the laws of reflection and refraction of a body, whether in motion or at rest, and, as already mentioned, does not affect interference, as Stokes showed, so far as the earth's motion is concerned. That the ether apparently is carried along within moving matter not with its full velocity, but diminished to the extent indicated by Fresnel's coefficient of convection, Fizeau demonstrated in his famous interference experiment with streaming water, repeated later with greater refinement by Michelson and Morley. ”

“ The physical consequences, at least, seem at present to be beyond experimental examination. So far no valid reasons have been brought forward which necessitate the shrinkage hypothesis in the electromagnetic theory. In this connexion, reference should be made to the proof which Hasenöhrl, [6] reasoning from a cyclic process in a moving radiating system, has given, that the second law of thermodynamics is contradicted unless either a second order contraction takes place in the direction of drift or the emission varies with the velocity, which latter he considers impossible. ”

“ If the physical causes, in consequence of which the motion of the ether becomes irrotational, could be adduced, the theory of Stokes would satisfy completely aberration and the negative results of the many and various experimental investigations which have thus far been made and whose validity is unquestioned, whether in refraction, interference, diffraction, rotary polarization, double refraction, induction, electric convection, etc. In an ordinary fluid, tangential forces proportional to the relative velocities destroy the irrotational condition in a steady state of motion. ”

“ If, by means of mirrors, a common source of light were employed, the half-shade principle in the field of view could be used which would be very sensitive in showing any difference in intensity (even if rapidly fluctuating) between the two portions of the field due to any slight difference in the time of propagation of the two rays with and against the æther drift. If we take the conditions in the experiment referred to, [25] namely, an aperture of 2.5 cm. ”

“ The difficulties in formulating a theory which will explain the results of all experiments involving tests to the first order of sensibility only on the assumption of either a quiescent or a convected ether, are much easier met than when second and higher orders have to be taken into consideration. ”

“ A direct shift of the cross-wires gave 13 divisions as the sensibility. Using direct white light and the sensitive strip and compensator 0°.1 rotation of the latter could be detected, thus giving it a sensibility of ×0.1=8 gms., or 12.5 times that of the band under similar conditions of light intensity and adjustment. [6] With greater intensity and more careful adjustment higher sensibility could be obtained by both methods. In fact, Rayleigh, using lime-light and a black band, has been able to detect a weight of 25 gms. on a vertical glass strip 15 mms. ”

“ With each advance in experimental refinement, theory has had to adapt itself by the adoption of new hypotheses. This has now been done up to second order phenomena for a quiescent ether. Thus far, however, no hypothesis has been brought forward to adapt specifically the theory of a quiescent ether to observations which have already been carried up to the third order of the aberration constant. ”

“ Attention should therefore be called to the results in my experiment on the double refraction of water moving through the aether. The sensibility attained was such that the greatest difference in velocity or in index between the two components which could exist, referred to that of water for green light, cm, was less than of the whole. If () [3] be taken as the third order magnitude, this result is then easily within the limit. It was not possible to attain this sensibility with a solid—glass ”

“ Following out the analysis on this supposition, a body, a star for example, will appear displaced toward the direction in which the earth is moving through an angle equal to the ratio of the velocity of the earth to that of light, when moving normal to the star's direction. This rectilinearity of propagation of a ray, which would likely seem to be interfered with in the motion of the ether, is the tacit assumption made in explaining aberration. ”

“ The assumption that the quasi-elastic forces, which maintain the electrons in their positions of equilibrium, experience the same changes as the electrical forces, may possibly be varied, and, together with a modification of the previous hypothesis, be adapted so as to agree with all observations. ”

“ They then reappeared and became narrower with increasing flexure. This compensation increased the sensibility so that a moderate pinch of the prism by the fingers gave a marked shift of the central band which could be observed by means of the two cross-wires already referred to. However, the compensation was not sufficiently satisfactory to obtain good matches with the half-shade. Furthermore, the slightest flexure of the trough or deviation of the beam of sunlight caused the "match" to change in the one case or the band to shift in the other, owing to the narrowness of the beam. ”

“ Polishing machines are now run up to 2000 revolutions per second. Allowing a sensibility of 0°.01, a distance of 15 kilometres would give a variation in velocity of one part in ten thousand.
The objection to the above methods and other similar ones, is the great distance required. If we could increase the eclipse frequency, the distance could be reduced accordingly. This can be attained by the use of electric oscillations in conjunction with suitable optical systems. ”

“ The difficulty in maintaining the conditions for so high a sensibility as was attained, rendered the fictitious effects quite possible. When the greatest care was exercised no change could be detected. Under the most favourable conditions a rotation of the compensator of 0°.2 approximately could be detected. ”

“ If, then, matter is for physical purposes a purely ethereal system, if it is constituted of simple polar singularities or electrons, positive and negative, in the Maxwellian aether, the nuclei of which may be either practically points or else small regions of aether with internal connections of pure constraint, the propositions above stated v for the first order are extended to the second order of with the single addition of the Fitzgerald-Lorentz shrinkage in the scale of space and an equal one in the scale of time, which, being isotropic, is unrecognizable. ”

“ The sensitive strip, compensator, a quarter-wave plate mounted on a vertical circle, and a vertical strip of glass capable of carrying a weight, and, in addition, a micrometer-screw carrying two horizontal cross-wires in front of a horizontal strip of glass held within a clamp so as to produce a flexure, were arranged to be placed in the path of the light. ”

“ While such solutions may seem highly artificial and do violence to our convictions, the consequences of a quiescent ether may, when fully developed and tested, demonstrate its impossibility and command a more extended examination into the structural qualities of an allsufficient medium than the single case of an essentially vesicular medium like jelly brought forward by Stokes and in a different form as a contractile ether by Kelvin. ”

“ With the nicols crossed and the plane of polarization at 45° to the vertical, the circle carrying the quarter-wave plate was adjusted until the light was extinguished and the mean of its positions for a number of settings noted. ”

“ If we suppose these forces to be diminished indefinitely we obtain now a motion totally different from that for the steady state when these forces are assumed to be absent initially; and hence such a motion would be unstable. ”

“ If the two mirrors could be regulated to this degree, we should still have less than one-tenth the fluctuation of our limit, from the two mirrors combined. Hence, so far as speed regulation is concerned, a much higher eclipse frequency, say the forty-million limit, is possible. ”

“ If, on the other hand, we take Wertheim's [10] results for glass, we have approximately for Faraday's flint, 5 x 1011n as Young's Modulus and dynes on a millimetre cube to give a relative retardation of one λ. From above we have
as the relative retardation for 1 mm. ”

“ While the test is now probably within experimental limits with the more highly refined half-shade systems, other modes of experimenting on different optical principles with greater sensibilities have given negative results, thus disproving the existence of a phenomenon which Fizeau's experiment apparently established, and making a repetition of this experiment, which is of doubtful execution, unnecessary. ”

“ Thus Wien [21] proposes to use two synchronized Foucault mirrors or two Fizeau toothed wheels. This plan is of course of long standing, but has been recently revived. The mechanical difficulties in the way do not give much encouragement to hope for success ”