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Rh measurements, since the standards of length must shrink in the same ratio as the bodies to be measured. It would be quite misleading, however, to leave the impression that this hypothesis depends for its credibility altogether upon the fact that it enables us to evade a serious difficulty and that it cannot be disproved by ordinary means. The electrical forces between charged bodies (electrons) are modified by motion through the ether; and they are modified in precisely such a way that if a given system of charges were in equilibrium under these forces in a certain configuration when at rest, it would when in motion be in equilibrium in a configuration obtained from the first by the application of the Lorentz-FitzGerald shrinkage. Now it is a fundamental theorem in electrostatics, that a charged system cannot be in equilibrium under the electrical forces alone; in the case of a collocation of electrons or atoms in equilibrium, the electrical forces must be balanced by other forces. If these inter-electronic forces are ethereal in origin and subject to the same laws as electro-magnetic forces, then the Lorentz-FitzGerald contraction would be expected à priori; and from this point of view the absence of the second order effects is evidence for the ethereal nature of inter-atomic and inter-molecular forces. Forces of this character would suffice to account for the changed dimensions of moving bodies even if the electrons themselves were left unaltered by the motion. But, as Lorentz has pointed out, we must also bring in dynamical considerations which show that for complete absence of second-order effects the electrons themselves must suffer the same contraction. The experiments of Lord Rayleigh and of Brace have shown that there is no double refraction due to the convection of transparent bodies by the earth. This implies that the periods of vibration of the electrons in the line of motion and perpendicular to it must be equal; and in order that this may be so, the longitudinal and the transverse masses of the electron must be altered by the motion in the same manner as the forces in these directions. An electron which does not change its shape (such as the rigid spherical electron of Abraham) will not have this property; nor will an electron which alters its form in any other manner than that described above for material bodies (such as the constant-volume electron of Bucherer). The electron proposed by Lorentz obviates these difficulties. If we assume that it is, when at rest, a sphere of radius, $$\scriptstyle{a}$$, it must when in motion with velocity $$\scriptstyle{v}$$, become an ellipsoid of revolution with its shorter axis in the direction of the motion and equal to $$\scriptstyle{a\sqrt{1-\frac{v^{2}}{\text{V}^{2}}}}$$, the