# Page:CarmichealMass.djvu/1

ON THE THEORY OF RELATIVITY: MASS, FORCE AND ENERGY.

By R. D. Carmichael.

## Introduction.

In a previous paper[1] I have given an analysis of the characteristic postulates on which the theory of relativity depends and have developed in a general way some of the fundamental conclusions of this theory. The plan of treatment adopted makes it possible to arrive at these results by arguments which are not complicated in form; and the notions which enter into them are of simpler character than those usually to be found in memoirs on this subject.

It seems desirable that the general theory should be further worked out along the same lines, even though this should require in part a repetition of some things already in the memoirs. Accordingly, in the present paper I develop the fundamental properties[2] of mass, force and energy, using as a basis the theorems of my previous paper. In the derivation of these results the theory of electricity is not employed. Consequently the conclusions are of wider applicability than when they are proved by means of electrical theory; in particular, they may be applied to the derivation of results in the theory of electricity itself.

In § 1, after giving some definitions, I state the laws of conservation of momentum and energy and electricity and the principle of least action in the form in which I shall have occasion to use them. The law of conservation of electricity is employed in this paper only in the applications of the results concerning mass and energy.

In § 2 the question of the dependence of mass on velocity is treated. First the transverse mass of a moving body is determined by the elegant method of Lewis and Tolman. The relation between transverse mass and longitudinal mass is found by the method of Bumstead, and thus the longitudinal mass of a moving body is obtained.

In § 3 dimensional equations are employed to derive the relations of acceleration and force in two systems of reference.

In § 4 from considerations concerning the mass of a moving body two essential equivalents of postulate R are determined, each of which

1. Physical Review, Vol. 35 (1912), pp. 153-176.
2. Several applications of the principal conclusions are also given.