Page:BraceNegative1905.djvu/2

72 indicate a complete correspondence, to all orders, of the molecular phases in the moving and in the fixed systems.

On the other hand, Lorentz has shown in his analysis for "electromagnetic phenomena in a system moving with any velocity smaller than that of light that, with the aid of the contraction-hypothesis, many electrical and optical effects will be independent of the motion of the system for all orders. This assumption of a shrinkage, although bold and thus far entirely hypothetical, is not impossible, and is the only suggestion yet made which is capable of reconciling the negative results of second and third order experiments with a quiescent æther. Poincaré has raised objection to the electromagnetic theory for moving bodies, that each time new facts are brought to light a new hypothesis has to be introduced. This criticism seems to have been fairly met by Lorentz in his latest treatment of the subject. The deductions, however, from his theory make it untenable without further development. 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, 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.

On the other hand, Abraham finds, neglecting fourth and higher order quantities, the ratio of the transverse to the longitudinal mass of the moving electrons to be

$$1+\frac{2}{5}\left(\frac{v}{V}\right)^{2}:1+\frac{6}{5}\left(\frac{v}{V}\right)^{2}=1-\frac{4}{5}\left(\frac{v}{V}\right)^{2}$$,

while Lorentz requires the ratio to be

$$\left(1+\left(\frac{v}{V}\right)^{2}\right)^{-\frac{1}{2}}:\left(1-\left(\frac{v}{V}\right)^{2}\right)^{-\frac{3}{2}}=1-\left(\frac{v}{V}\right)^{2}$$,

for perfect compensation: thus leaving a double refraction of the order $$\frac{1}{5}\left(\frac{v}{V}\right)^{2}$$ to be accounted for, which would have been detected several thousand times over in my experiment. The