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of m/m₀ as a function of β, namely,

(a)	${\frac {m}{m_{0}}}={\frac {3}{4}}{\frac {1}{\beta ^{2}}}\left({\frac {1+\beta ^{2}}{2\beta }}\log {\frac {1+\beta }{1-\beta }}-1\right)$,

(b)	${\frac {m}{m_{0}}}={\frac {1}{\left(1-\beta ^{2}\right)^{1/3}}}$,

(c)	${\frac {m}{m_{0}}}={\frac {1}{\left(1-\beta ^{2}\right)^{1/2}}}$.

The extraordinary significance of the similarity of the first two of these equations and the identity of the third with equation (15), which we have derived from strikingly different principles, needs no emphasis. Kaufmann shows that his results agree better with the first two of these equations than with the third, but to regard this as serious evidence as to the validity of equation (15) would, as Planck has pointed out, be laying too great a stress on the accuracy of the experimental observations.

The agreement of Kaufmann's results with the above equations has led him, and all others who have discussed his results, to the conclusion that all of the mass of an electron is electromagnetic.

Their argument is based on the assumption that ordinary mass, the mass of "ponderable matter," is independent of the velocity, while "electromagnetic mass" varies with the velocity according to one of the above equations. But in this paper we have assumed that all mass is one, and that any bodies, whether charged or not, moving at the velocities of Kaufmann's electrons would show the same values of m/m₀.

There is some hope that the correctness of this view may be decided by an experimental study of the mass of a positive or α particle at different speeds. According to the ordinary view, the mass of such a positive particle as issues from a radioactive source is chiefly that of its "ponderable" matter and only to a very small extent "electromagnetic mass." It would therefore be generally assumed that at the highest velocity of the particle, about one-tenth of the velocity of light, it would have substantially the same mass as at rest. According to our view, on the other hand, the mass of this or any other particle would change with the velocity in the same way as the mass of an electron. From equation (15) we should therefore expect the particle moving with one- tenth of the velocity of light to have a mass two per cent. greater than when at rest. The experimental difficulties in