h . . (i) 



78 Mr. Megh Nad Saha on the 



The rate at which work is done is given by the equation 



ft=fxv 1 +f 1/ v 2 +f 2 v 3 



=p[Xv 1 -{-Yv 2 + Zv 3 ], 



In accordance with the ideas of the Principle of Relativity 

 we can write the components of the force-four- vector in the 

 form 



fx = pO [ +Jl2 W 2 + Ws/lS + W±fu] 



fy = Po L/*2i™i + W3/23 + ^4/24] 



fz = Po[ W lfsi + ^2/32 + w if**\ 



fi—Po[^ifu + ^2/42+^3/43 ] _ 



these equations are obtained by writing * 



/ 2 s,/3i,/i2 for L, M, N, 



/l4,/24,/34 f01' -i(X,Y,Z), 



w 1} w 2 , w 3 , w± for — r===[v l /c, v 2 /c, v s /c, t], 

 v 1 — v^c z 



p for p\/l — v 2 lc 2 . 



For finding out the total force on the electron, we have to 

 integrate the above expressions for the force-four-vector over 

 the whole volume of the electron. Supposing that the com- 

 ponents of the electric and magnetic force do not vary 

 throughout the volume of the electron, the force-components 

 are obtained by writing simply (e) the invariant charge 

 instead of (p ) in equations (1). 



The calculation of the Effective force is a matter of some 

 difficulty. The question is : "If an electron moves with a 

 variable velocity, what are the terms corresponding to the 



quantities (m-r^i m 772> m 'li) m P ar ticle dynamics? 



Einstein solves the difficulty by saying that instead of the 

 observer's time dt we have to introduce here the proper time 



* The notation used throughout the paper is that of Minkowski, vide 

 Math. Ann. vol. lxviii. p. 472 et seq. § 12, where this particular theorem 

 occurs in an abbreviated form. 



