July 10, 19091 



SCIENCE 



85 



and its mass is now in', then according to the 

 law stated above, 



vvv = . 



(1) 



\- 



(5) 



From our fundamental law concerning the 

 center of mass, it is obvious that, when the 

 body begins to move, some mass must move in 

 the opposite direction in order to keep the 

 center of mass in its original position. But 

 since nothing is moving in this direction ex- 

 cept the small quantity of radiant energy 

 which was emitted, this radiant energy must 

 itself possess a mass m which is to the mass 

 m' inversely as the distances, at any instant, 

 of m and m' from the original center of mass. 

 These distances are proportional to the two 

 velocities and thus, 



-'"="-. (2) 



m' V 



Combining equations (1) and (2) gives 



(3) 



Therefore a beam of light possesses a mass 

 which is equal to its energy divided by the 

 square of the velocity of light. 



By the conservation law the mass associated 

 with the radiant energy must come from the 

 emitting body, the latter therefore loses mass 

 in proportion to the energy it loses. On the 

 other hand, if the same quantity of energy as 

 was emitted is now returned to the body in 

 some other way. say by thermal conduction, 

 the original internal condition of the body 

 being restored, it will regain its original mass. 

 It is evident, therefore, that when a body gains 

 energy in any way, it simultaneously gains 

 mass according to the simple law 



rfm = 'J^. (4) 



This equation connecting the mass of a 

 body with its content of energy is the basic 

 equation of non-Newtonian mechanics. From 

 this the other theorems follow at once. Thus 

 it is obvious that if a body in motion has more 

 energy than one at rest, it must also have a 

 greater mass. Hence, we are led directly, as 

 shown in my paper, to the equation 



where m is the mass of the body moving with 

 velocity v, and m„ is its mass at rest. 



This is the only equation of non-Newtonian 

 mechanics that has been subjected to a direct 

 experimental test. In my paper attention was 

 called to the general agreement between the 

 demands of equation (5) and the experiments 

 of Kaufmaim on the mass of the rapidly 

 moving ^ particles emitted by radium, but 

 some of the differences between the observed 

 and calculated values seemed to some scien- 

 tists too great to ascribe to experimental error. 

 However, this question is now definitely settled 

 by the recent work of Bucherer,'' who investi- 

 gated the same problem by a more accurate 

 method. His results on the change of mass 

 with the velocity are in striking agreement 

 with our equation. 



Since therefore non-Newtonian mechanics 

 is based solely upon laws which have been 

 universally accepted, and has been further 

 verified directly by this decisive experimental 

 test, the new system seems to be upon a thor- 

 oughly secure experimental foundation. 



It is evident in equation (5) that w ap- 

 proaches infinity when v approaches the 

 velocity of light. Hence a body moving as 

 fast as light would have infinite mass and 

 infinite energy. This is the conclusion which 

 to some scientists has seemed incredible. They 

 suggest that if we had started with an observa- 

 tion on the pressure of sound instead of the 

 pressure of light, we might have been led to 

 the conclusion that the velocity of sound is the 

 maximum possible velocity. Of course, if this 

 idea could be substantiated, it would be a very 

 efficient reductio ad ahsurdum of the method. 

 As a matter of fact, however, if we apply to 

 sound energy the kind of reasoning that we 

 have applied to radiant energy, we are brought 

 neither to an absurdity nor to any result which 

 is not readily predicted from the elementary 

 principles of mechanics. 



It is not that we have decided in advance 



' Berichte Deutsch. physik. Gesell., C, 088 

 (1908). 



