720 PROCEEDINGS OF THE AMERICAN ACADEMY. 



agreement with equation I. Recently, however, Bucherer, 12 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 prin- 

 ciple 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 prin- 

 ciple of relativity. By a slight extrapolation we may find with accur- 

 acy 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 — s, and calls this force the dyne. If now we 



sec J 



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 , and the centimeter in this trans- 



V1-/3 2 



verse 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 . 



VI — p 



Since the time enters to the second power, the product of mass and 



acceleration is smaller by the ratio — — 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 direc- 

 tion 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 be and ba. The system is thus in 

 equilibrium. 



12 Bucherer, loc. cit. 



