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regardless of the nature of the process which the energy change accompanies.^[1]

Since therefore when a body loses a given quantity of energy it always loses a definite quantity of mass, we might assume that if it should lose all its energy it would lose all its mass, or, in other words, that the mass of a body is a direct measure of its total energy, according to the equation,

$m={\frac {\mathrm {E} }{\mathrm {V} ^{2}}}$.

(8)

We should then regard mass and energy as different names and different measures of the same quantity, and say that one gram equals $9\times 10^{20}$ ergs in the same sense that we say one metre equals 39.37... inches.

Plausible as this view seems, it rests upon an additional hypothesis besides the fundamental postulate which we have chosen. We shall use therefore, not equation (8) but equation (7) as the basis of the following work.

It is to be noted that equation (8) has also been obtained by Einstein (loc. cit.), who derived it from the general equations of the electromagnetic theory, with the aid of the so-called principle of relativity. That a different method of investigation thus leads to the same simple equation we have here deduced, speaks decidedly for the truth of our fundamental postulate.^[2]

Comstock (loc. cit.) from electromagnetic theory alone has also concluded that mass is proportional to energy, but his equation is

$m={\frac {4}{3}}{\frac {\mathrm {E} }{\mathrm {V} ^{2}}}$.

To investigate for the cases studied by Comstock the cause or the justification for this appearance in the equation of the factor 4/3 would lead too far into electromagnetic theory, from which in the present paper I wish to hold entirely aloof.

Before proceeding to develop fully the consequences of equation (7) it may be well to point out an apparent

1. I was first led to an investigation of the relation of mass to energy by the work of Landolt, on the change of weight in chemical reactions. But it is obvious from equation (7) that although there always will be a loss of mass in a reaction which is accompanied by the evolution of energy, this loss in the case of any ordinary reaction will be far too small to measure. In fact Landolt has very recently shown (Ber. Berlin. Akad. 1908, p. 354) that when all possible precautions are taken there is no measurable change of weight in the reactions which he studied.
2. Einstein, however, obtains (8) as an approximate formula, while we obtain both (7) and (8) as perfectly exact equations.