Non- Newtonian Mechanics. 153 



acting on a body may be best defined as equal to the rate of 

 increase of momentum *, i. e. by the equation 



_ d . da dm 



or Fz= m'x + mx\ 



F y = my +my, 

 F z = m'z + in'z. 



By the substitution of the previous equations presented in 

 this article we obtain: 



vw c 2 — vx J c 2 -vx 



c 2 



*v=-^> w 



1- 



<? 



1 



f;=-*-^f. en) 



-j vx 



~~? 



which are the desired transformation equations of force. 

 These equations, which have here been derived from the 

 principles of non-Newtonian mechanics, are those which 

 were chosen by Planck to agree with electromagnetic con- 

 siderations f» 



Field around a Moving Charge. 



As an application of these transformation equations, we may 

 calculate the force with which a point charge in uniform motion 

 acts on any other point charge, merely assuming Coulomb's 



* See Phil. Mag. xxii. p. 458 (1911). 



t In an article by Lewis and Tolman (loc. cit.) an attempt was made 

 to deduce the transformation equation of force, which was unsuccessful, 

 owing to the authors' assumption that the turning moment around a 

 right-angled lever in uniform irrotational motion should be zero. This 

 error and the interesting fact that in general, if we accept the relativity 

 theory, the actual presence of a turning moment is necessary to produce 

 a pure translatory motion in an elastically stressed body was pointed out 

 by Laue, Verh. d. Deutsch. Phys. Ges. xiii. p. 513 (1911). For the par- 

 ticular case that the body on which the force is acting is stationary with 

 respect to one of the systems, the transformation equations of force were 

 correctly derived by the present author, Phil. Mag. xxi. p. 296 (1911). 



