analysis of both Lorentz and Abraham seems to be equally consistent with Kaufmann's results on the deflexion of Becquerel rays, Lorentz conforms Abraham's theory to his own, by shrinking the undeformable spherical electrons of the latter into flattened ellipsoids in the line of drift; while Abraham himself shows that these will be unstable unless the greatest axis is in this direction. The latter writer shows[1] that work must be done against the electrical forces to produce this deformation, so that the total energy in any acceleration is greater than that furnished by the outside forces.
Hence there must be inner forces as well which determine the form of the electron. Thus the hypothesis of Lorentz is incomplete without defining the law of forces further. Hence we must either abandon the contraction hypothesis or modify it. 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.
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.
It becomes then a serious question, whether to seek still for decisive results with experiments involving the higher order tests, on the one hand, or direct entrainment tests on the other, in order to settle the question.
The recent repetition by Morley and Miller[2] of the original Michelson-Morley interference experiment, with a sensibility one hundred times the calculated effect, leaves perhaps no question as to the absence of any such second order optical effect. Lorentz's analysis requires a negative result, likewise, if the rays pass through a transparent substance instead of a vacuum: and it seems desirable therefore that this point should be tested for water, say.
The interferometer method might also be used to test for double refraction if the light were polarized so as to make the electric displacements perpendicular to the plane of the interfering rays, i. e. respectively parallel and perpendicular to the
