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This paper deals with four topics: The first subject is Abraham's sphericalelectron, Lorentz's contracted electron and B\"ucherer's electron. The secondtopic is Einstein's 1905 relativity theory of the motion of an electron.Einstein obtained expressions for the longitudinal and transverse masses of theelectron using the principle of relativity and that of the constancy of thevelocity of light. The third topic is Einstein's reply to Ehrenfest's query.Einstein's above solution appeared to Ehrenfest very similar to Lorentz's one:a deformed electron. Einstein commented on Ehrenfest's paper and characterizedhis work as a theory of principle and reasoned that beyond kinematics, the 1905heuristic relativity principle could offer new connections betweennon-kinematical concepts. The final topic is Kaufmann's experiments. Kaufmannconcluded that his measuring procedures were not compatible with the hypothesisposited by Lorentz and Einstein. However, unlike Ehrenfest, he gave the firstclear account of the basic theoretical difference between Lorentz's andEinstein's views. Finally, B\"ucherer conducted experiments that confirmedLorentz's and Einstein's models; Max Born analyzed the problem of a rigid bodyand showed the existence of a limited class of rigid motions, and concluded,"The main result was a confirmation of Lorentz's formula".

Variation of Mass with Velocity: "Kugeltheorie" or "Relativtheorie"