II A. Bumstead — Lorentz-Fitz Gerald Hypothesis. 495 



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 impres- 

 sion 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 modi- 

 fied 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 theo- 

 rem in electrostatics, that a charged system cannot be in equili- 

 brium under the electrical forces alone ; in the case of a collo- 

 cation 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 contrac- 

 tion would be expected d 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 consider- 

 ations which show that for complete absence of second-order 

 effects the electrons themselves must suffer the same contrac- 

 tion, The experiments of Lord Rayleighf and of Brace:); have 

 shown that there is no double refraction due to the con- 

 vection 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 elec- 

 tron 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-vol- 

 ume electron of Bucherer). The electron proposed by Lorentz 

 obviates these difficulties. If we assume that it is, when at rest, 

 a sphere of radius, a, it must when in motion with velocity v, 

 become an ellipsoid of revolution with its shorter axis in the 



direction of the motion and equal to a y i __ _?L , the dimen- 



* Ions, Electrons, Corpuscuies. vol. i, p. 477. 



f Phil. Mag., vol. iv, p. 678, 1902. % Phil. Mag., vol. vii, p. 317, 1904. 



