( 254) 



transformation of ^r is determined. The considerations of Late, 

 therefore, are only jnstified if he can show tiiat it is possible to 

 attribnte to the different kinds of energy a velocity whose value is 

 such -that the ti-ansformation of o and iv yields for ^oa\ ihe same 

 formula as he postulates for the transformation of »3. Considerations 

 of the same kind apply to the quantities p_,, and TT. 



Postscript. Perhaps 1 have not always been consistent in the use 

 of the words force and tension. I have thought for a moment ihat 

 we could do without these notions altogether, and that we could 

 account for every change in the momentum in a volume-element by 

 means of the transport of momentum through its sui-faces. But then 

 we are checked by some difticulties. The nomenclature most accurate 

 in principle is of course to use the word force only for that change 

 of momentum for which we cannot account by a transport of 

 •momentum. But it seems to be impossible to perform tiie separation 

 between the effect of forces and of transport in an iniambigiious 

 way. In § 5 eg. I called t,, the force exerted on tlie rod. This is 

 accurate if the (piantities of energy IF^ and If', are partially reflected 

 at the ends of the rod. if they, however, j)ass the ends and flow 

 into the othei' body, tj-,- would represent the force and Txx—^.rr \voidd 

 represent a quantity of momentum which is imparted to the rod by 

 means of transport. It seems to be inq)0ssible to find good reasons 

 for a choice between those two conceptions. It is after all immaterial 

 to nhich of these quantities we will apply the name of force. 



In the same way we may ask whether we will define the force 

 by the equation 



rfo dm 



■^ = m — + -— 



dt dt 



or by 



K = rn — . 

 di 



The force adds energy and so also mass to the I)ody, and the 

 value which we ascribed to the force will depend on the momentum 

 which this new mass had, before it was added to the body. If we 



think that it was then stationarv, we shall undoubtedlv call tn, — 



* • dt 



dnt 

 the force exerted on the "old mass" and t> — that exerted on the 



dt 



"new mass". But if this new mass had a velocity iv before it was 

 absorbed b\ the Isody, we shall ascribe another \alue to the force 

 properl}' speaking, but say that the momentum of the body is also 



