the relation which we have just derived, requires that the observer will also obtain the time 1/c even if he is in motion towards or away from the source.
Let us suppose that the observer B is moving towards the light with the velocity v, the velocity with which light is passing his system is v+c, the time taken for it to travel over a centimeter length is 1/(v+c). Since, however, the centimeters which B marks off are shorter than "stationary" ones in the ratio , and the seconds which he uses are longer in the inverse ratio, the time required in his units would be (1-β²)·1/(v+c), and further since the rearmost clock is set ahead by the amount v/c², we finally conclude that B will obtain the time (1-β²)·1/(v+c)+v/c² which reduces to 1/c. We thus conclude that the velocity of light appears the same whatever the motion of the observer, or by the first postulate of relativity whatever the relative motion of the source of light and the observer, and have obtained a proof of the second postulate of relativity with the help of the Bucherer experiment.
In this connection, it must be again pointed out that the Kaufmann-Bucherer experiment may not really indicate an increase in the mass of an electron in motion. It is, at first sight, equally possible that the forces acting on an electron in rapid motion through electrostatic or magnetic fields are not as large as those calculated on the basis of Maxwell's fifth equation, since its application to high velocities certainly lacks experimental justification. The balance of all the evidence which has been presented, however, is in favor of the second postulate of relativity.
Summary.
In this paper it is shown that the extraordinary conclusions of the theory of relativity are forced on it by the second postulate of relativity. This postulate is obtained by combining the first postulate of relativity with the principle that the velocity of light is independent of the velocity of the source. The alternative hypothesis that the velocity of light and the velocity of its source are additive would lead to none of the complications of the theory of relativity. Two methods are presented for deciding between the two hypotheses.
