( 251 ) 



area perpendicular lo tlie A^-axis, would according to classical mecha- 

 nics be : 



According- to onr considerations tiie (juestion would be a bttie less 

 simple. We shall have to conceive IT to be sc|)ai'ated into three 

 parts: IFi moving- along with the rod with the velocity i\ W^ 

 moving with the velocity ii).^ in the -{- A and IK, moving with the 

 velocity iï>., in the — A-direction. We are inclined to su|)pose that 

 \l\ -j- IF, ^^i" '*6 ^'^c elastic energy which is a consequence of the 

 compression, and that \i\, and iiv, are the velocities with which a 

 j^ertnrbation propagates in the moving rod according to a stationary 

 observer. If we put t> = 0, we get ir.^ =: lUj and the assumption, which 

 I introduce here is, that also in this case the elastic energy is not 

 in ]-est, but that we cannot ascertain its motion because two equal 

 currents of energy move in opposite directions. If we again inqiart the 

 velocity i-» , both currents will be changed, but in a diiferent degree, 

 in consequence of which a current of energy in a definite direction 

 can be ascertained. These considerations are conlirmed by the fact 

 that the energy transported by the tension through the moving rod 

 cannot move with a velocity, r. So it cannot be transformed into rest 

 togedier with the rod. 



For our jMirpose however it is not necessary to determine the 

 values of If^^, W^, ii\, , and \i\. We certaiidy may |mt: 



©,= IFi.-]^ It>.^— ir,av, (3) 



The force exerted by the rod on a body against which its end 



B rests, may not simply be put equal to /x, . For we must take 



into account that the rod contains two quantities of momentum : a 



1 

 quantitv with a density ^^ IF,u\^ moving with the relative velocity \l\, — i^ 



1 



towards the end />, and a (puintiiy with a density - [l'',a>, movijig 



with a relative velocity m\ -j- ^ away from it. The force exerted on 

 the end of the rod is therefore : 



1 1 



1) It is obvious tlial in principle txx has llic closest analoiry lo what is ordina- 

 rily called clastic tension. Tiie quantity txj; however cannot be measured and in 

 so far T.,:i, which represents the force as il is mcasureil, is a more important 

 quantity. An easy calculation shows that fn is the same quantity as the (juantity 

 tzz of Lauk. The tensor / is symmetrical, whereas t {t in the notation of Lauk) 

 is an asymmetrical tensor. 



