Langevin’s derivation of the relativistic expressions for energy

Langevin showed that the relativistic expression for the kinetic energy, as well as the inertia of energy, could be derived entirely from the principle of conservation of energy, in addition to the two usual postulates of special relativity. Unfortunately, this beautiful derivation, given in a lecture and not published by the author, passed almost unnoticed. The object of this paper is to popularize it in a modernized presentation. Langevin’s approach is compared with the well-known one starting from the relativistic law of linear momentum conservation, following an idea of Lewis and Tolman.