( 245 ) 



(ho liiw action = I'cuc'lion and llie law ol' (lie imilbrin motion of (he 

 centre of iner(ia. Coniparinj;- these assnniptions wi(h (iiose of the 

 older theory of electi'ons, where the total mass was a variable 

 (jnantity, it appears that we hv no means deviate farlhei- from classical 

 niechaiiics, hut rathei- that we i-eturn to it. 



§ 3. Let us now consider a special case: a hodv is set in motion 

 bv a force -^t. We will assume 



1 ^ 



(2) 



Without making use of the theory of relativity we tind therefore 

 the well-known ex|n'ession derived l)y Lorkntz ^) in iiis ingenious 

 })aper in which he di-ew^ n}) that theory. Perhaps we may be astonished 

 to tind this relation without introdncing the Lorkntz contraction, 

 \vliereas Lorkntz derived it for bodies which do luidergo this con- 

 traction. In order to explain this fact we observe tliat the above 

 dednction is always ap|)licable, if the force ^v represents the only 

 change of the energy of the body. And this is the case, l-"^ if (he 

 shape of the body is invariable, 2'"Mf the body undergoes (he Lorkntz 

 con(rac(ion according (o the theory of relativity. For according to 

 this theory the contracted form is the form of e(iuilil)rinm for 

 the moving body. A virtnal change of form, therefore, does not 

 require any w^ork, and if a body is accelerated quasistationarily, no 

 work is exjiejided for the change of form. For an electrically charged 

 body e. g. the negative work done by the electrical forces when the 

 body contracts will be compensated by positive work of other foi-ces 

 (which we will call elastic forces). 



1) H. A. LoRKKïz. These proceedings VI, p. 809, Anno l'J04. 



