Page:TolmanNon2.djvu/1

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XXXIII. Non-Newtonian Mechanics, The Mass of a Moving Body.

By Richard C. Tolman, Ph. D., Assistant Professor of Physical Chemistry at the University of Cincinnati^[1].

AN acceptance of the Einstein theory of relativity necessitates a revision of the Newtonian system of mechanics. In making such a revision it is desirable to retain as many as possible of the simpler principles of Newtonian mechanics. Some of the consequences have already been presented^[2] of a system of mechanics which retains the conservation laws of mass, energy, and momentum, and defines force as the rate of increase of momentum; but to agree with the theory of relativity introduces an idea foreign to Newtonian mechanics by considering that both the mass and velocity of a body are variable.

From the theory of relativity, Einstein has calculated both the transverse and the longitudinal accelerations experienced by a charged body moving in an electromagnetic field. On the basis of these accelerations, it has been usual to place the "transverse mass" of a body moving with the velocity $u$ as equal to $m_{0}/{\sqrt {1-u^{2}/c^{2}}}$, and its "longitudinal" mass as equal to $m_{0}/\left(1-u^{2}/c^{2}\right)^{\frac {3}{2}}$, where $m_{0}$ is the mass of the body at rest and $c$ is the velocity of light. If, however, mass is a quantity to which a conservation law applies, the mass of a body cannot well be different in different directions; and

1. Communicated by the Author. Contribution from the Chemical Laboratory of the University of Cincinnati.
2. Lewis, Phil. Mag. xvi. p. 705 (1908). Lewis & Tolman, Phil. Mag. xviii. p. 510 (1909), Online. Tolman, Phil. Mag. xxi. p. 296 (1911); xxii. p. 458 (1911).