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 second postulate of relativity (our postulate R). A remark in this direction has already been made by Tolman. An indication of the results of this character obtained in the present paper is given below in the description of the contents of part II. The principal value of such a matter, from the point of view of physical science, consists in the fact that it affords alternative methods for the experimental proof or disproof of the theory of relativity and that it emphasizes in an effective way the essential difficulties and limitations of such experimental verification in general.

It is the writer's purpose to treat further in a future paper the matter of the logical equivalents of the postulates. In this forthcoming work it is the intention to introduce the general laws of conservation of energy, mass, momentum and electricity, to deduce certain joint consequences of these laws and the principle of relativity, and to determine which of the theorems so obtained may replace the relativity postulates (or one of them) without destroying the equivalence of the resulting totality of doctrine.

Part I. of the present paper is devoted to a general statement and preliminary analysis of the postulates of relativity. In § 1 I give the fundamental homogeneity postulates of space and time which underlie all physical theory. In § 2 the first characteristic postulate of relativity is given, while § 3 contains a statement of the second postulate. It is shown that a part of this postulate (in the form in which the postulate is usually stated) is a consequence of the other part and of the first postulate, together with the fundamental homogeneity postulates.

Writers on relativity have usually stated only these two postulates. But as a matter of fact every one has made further assumptions; in some cases it appears to have been done unconsciously. To the present writer it seems desirable that these assumptions should be brought into the light as postulates. Accordingly, in § 4, 1 give those additional postulates which I shall use. One familiar with the theory will see that these assumptions are different from those usually employed (without explicit statement as postulates), as by Einstein for instance. The choice has been made in the interest of simplicity in postulates and in proofs. The writer believes that this innovation in the statement of the postulates is important. It leads to new and simpler proofs than those ordinarily employed; and this, it is hoped, will in large measure remove the feeling of vagueness which many persons experience in approaching the theory of relativity for the first time.