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720 agreement with equation I. Recently, however, Bucherer, by a method of exceptional ingenuity, has made further determinations of the mass of electrons moving with varying velocities, and his results are in remarkable accord with this equation obtained from the principle of relativity.

This very satisfactory corroboration of the fundamental equation of non-Newtonian mechanics must in future be regarded as a very important part of the experimental material which justifies the principle of relativity. By a slight extrapolation we may find with accuracy from the results of Bucherer that limiting velocity at which the mass becomes infinite, in other words, a numerical value of c which in no way depends upon the properties of light. Indeed, merely from the first postulate of relativity and these experiments of Bucherer we may deduce the second postulate and all the further conclusions obtained in this paper. This fact can hardly be emphasized too strongly.

Leaving now the subject of mass, let us consider whether the unit of force depends upon our choice of a point of rest. An observer in a given system allows such a force to act upon unit mass as to give it an acceleration of one $$\frac{\mathrm{cm}}{\mathrm{sec}^{2}}$$, and calls this force the dyne. If now we assume that the system is in motion, with a velocity v, in a direction perpendicular to the line of application of the force, we conclude that the acceleration is really less than unity, since in a moving system the second is longer in the ratio $$\frac{1}{\sqrt{1-\beta^{2}}}$$, and the centimeter in this transverse direction is the same as at rest. On the other hand, the mass is increased owing to the motion of the system by the factor $$\frac{1}{\sqrt{1-\beta^{2}}}$$. Since the time enters to the second power, the product of mass and acceleration is smaller by the ratio $$\frac{\sqrt{1-\beta^{2}}}{1}$$ than it would be if the system were at rest. And we conclude, therefore, that the unit of force, or the dyne, in a direction transverse to the line of motion is smaller in a moving system than in one at rest by this same ratio.

In order now to obtain a value for the force in a longitudinal direction in the moving system, let us consider (Figure 3) a rigid lever abc whose arms are equal and perpendicular, and equal forces applied at a and c, in directions parallel to bc and ba. The system is thus in equilibrium.