718 PROCEEDINGS OF THE AMERICAN ACADEMY. 



distortion of the body in consequence of a real motion through a sta- 

 tionary ether, and his theory has aroused considerable discussion as to 

 the nature of the forces which would be necessary to produce such a 

 deformation. The point of view first advanced by Einstein, which we 

 have here adopted, is radically different. Absolute motion has no sig- 

 nificance. Imagine an electron and a number of observers moving in 

 different directions with respect to it. To each observer, naively con- 

 sidering himself to be at rest, the electron will appear shortened in a 

 different direction and by a different amount ; but the physical con- 

 dition of the electron obviously does not depend upon the state of 

 mind of the observers. 



Although these changes in the units of space and time appear in a 

 certain sense psychological, we adopt them rather than abandon com- 

 pletely the fundamental conceptions of space, time, and velocity, upon 

 which the science of physics now rests. At present there appears no 

 other alternative. 



Non-Newtonian Mechanics. 



Having obtained these relations for the units of space and time, we 

 may turn to some of the other important quantities used in mechanics. 



Let us again consider two systems, a and b, in relative motion with 

 the velocity v. An experimenter A on the first system constructs a 

 ball of some rigid elastic material, with a volume of one cubic centi- 

 meter, and sets it in motion, with a velocity of one centimeter per 

 second, towards the system b (in a direction perpendicular to the line 

 of relative motion of the two systems). On the other system, an ex- 

 perimenter B constructs of the same material a similar ball with a 

 volume of one cubic centimeter in his units, and imparts to it, also in 

 his units, a velocity of one centimeter per second towards a. The ex- 

 periment is so planned that the balls will collide and rebound over 

 their original paths. Since the two systems are entirely symmetrical, it 

 is evident by the principle of relativity, that the (algebraic) change in 

 velocity of the first ball, as measured by A, is the same as the change 

 in velocity of the other ball, as measured by B. This being the case, 

 the observer A, considering himself at rest, concludes that the real 

 change in velocity of the ball b is different from that of his own, 

 for he remembers that while the unit of length is the same in this 

 transverse direction in both systems, the unit of time is longer in 

 the moving system. 



Velocity is measured in centimeters per second, and since the second 

 is longer in the moving system, while the centimeter in the direction 



