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494 material objects, but when all the apparatus concerned as well as the observer are carried through the ether with the velocity $$\scriptstyle{v}$$. The effects to be expected are of the order of $$\scriptstyle{\left(\frac{v}{\text{V}}\right)^{2}}$$; this is a very small fraction even when $$\scriptstyle{v}$$ is the velocity of the earth in its orbit, but the possible accuracy of certain optical experiments is so great that these effects could certainly be found if they existed without some compensating effect to mask them. As is well known, these effects have never been found; the first conclusively negative results were obtained in the celebrated experiments of Michelson and Morley, and several other optical investigations have also failed to show the expected results. On the electrical side the problem has been attacked by Trouton and Noble, who hung up an electrical condenser by a torsion wire and looked for a torque which, on the theory of a stagnant ether, ought to exist when the condenser is carried along by the earth. Although the sensitiveness of their experimental arrangement was ample for the observation of the expected second order effect, their result was also negative. The most obvious interpretation of these results is that the ether near the earth has the same velocity as the earth; but, as has been stated, it appears to be impossible to reconcile this view with the great mass of optical and electro-dynamic evidence. The only satisfactory way out of this difficulty which has hitherto been suggested is a hypothesis put forward in 1892 by Lorentz, and which had been independently suggested but not published by FitzGerald. According to this hypothesis, when any material body moves relatively to the ether its linear dimensions parallel to the direction of motion are contracted in the ratio of $$\scriptstyle{\sqrt{1-\frac{v^{2}}{\text{V}^{2}}}}$$ to 1, while the dimensions perpendicular to the direction of motion remain unchanged. If this contraction takes place in the interferometer of Michelson and Morley and in the condenser of Trouton and Noble, their negative results are entirely explained on the theory of a stationary ether. As Lorentz points out, this contraction will be very small in any motions of material bodies which we can observe; for example the diameter of the earth in the direction of its orbital path will be diminished by only 6·5$cm$ by its motion. It would moreover be impossible to detect the shrinkage, however great it might be, by ordinary