( 252 ) 



Therefore we (iiid for llie energy whicli passes tlie slatioiuiry plane : 



We will iiilrodiice in (his equation the (pianlity />j., which ib 

 equal to : 



C' 



We eiisiiy tind : 



Taking- e(piation (3) into accotmt and putting - = ,i' we lind : 



0" 



Z,{l^-ii') = {W+p,,)i^ (4) 



It is imporlant lo remark diat this eipiation, dcdneed hei-e widioul 

 making use ot ihe theory of relalixity, can also l»e derived (Vom the 

 equations (102; of Laue ^) : 



^J = 



l-^-^ 



c- 

 \V— 



1 — ^' 



C' 



If namely we imagine tiie rod to rest relative to Ihe aceentualed 

 system, then ^',,= 0. We find then equation (4) by eliminaling 

 j)',.r and 11 '. 



In the same way we can discuss the case that the rod lies paral- 

 lel to the }^-axis and that a force in the -\- X direction is applied 

 iji the middle of the rod. In the ends of the rod two equal forces 

 act in the A'-direction, which together exactly balance the force in 

 the middle. This system moves with a velocity i> in the A-direc(ion. 

 For this case both ways of calculating yield 



So we see that it is i»ossible to derive several conclusions from 

 the law of the uniform motion of the centre of inertia which usually 

 are derived from the theory of relativity. In priiiciple the two ways 

 of deducing them are equally justitied. In both we start from laws 

 which ai-e pr()\ed lo hold good for some regions of observations and 



^) M. Laue. Das Pielulivilülspriuzip p. 87. 



