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§ 1. Fundamental Definitions and Postulates
§ 2. Dependence of Mass on Velocity
§ 3. On the Dimensions of Units
§ 4. Equivalents of the Postulates
§ 5. The Bucherer Experiment
§ 6. Another Means for the Experimental Verification of the Theory of Relativity
§ 7. Mass and Energy
§ 8. Remarks on the Principle of Least Action
§ 9. Speculative Considerations

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 furnishes a possible means for the experimental proof or disproof of the theory of relativity. The researches of Bucherer have been thought to afford the requisite experimental confirmation in the first case; this matter is treated in § 5. In § 6 suggestions are given for a new crucial experiment for testing the theory of relativity, this being associated with the second essential equivalent of R in § 4. The writer desires to call especial attention to this proposed experiment.

In § 7 the intimate relation of the mass and the total energy of a body is pointed out and two theoretical means are suggested for determining the velocity of light indirectly, that is, without direct measurement of this velocity. These experiments, if they could be performed with sufficient accuracy, would afford an interesting and striking confirmation of the theory of relativity, provided of course that they turn out according to the predictions of this theory.

A few remarks on the principle of least action are found in § 8, and § 9 is given to some speculative considerations which are intended as brief suggestions of means by which one may represent to himself the conclusions of relativity as natural parts of a consistent view of physical phenomena.
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