366 Mr. Megh Nad Saha on the 



Neglecting terms of higher order than the first, we have 



I (In view of the fact that the radius of the electron is 

 extremely small, the second term must be infinitesimal of a 

 higher order compared with the first.) 

 Therefore as a first approximation, 



ee' 



<3> = t5" (lOilCi + IV 2 W»' + W3W3 

 d.v dr\'dw l / 



k (14) 



Y= B^ d /B<£>\ 

 Z __B3>_ d /d<£\ 



. (^ dr \lfrio s / 

 L=^— - — /^-) 



dropping the subscripts (#, y, z, Z), now denoting the co- 

 ordinates of the centre. 



We shall now reduce the Lagrangian function to three- 

 dimensions. We have 



10. Laws of Electrodynamical Action. 



reduce the Lagrangian functtc 

 i have 



ee' {w x Wi 4- w 2 w 2 ' -hw 3 w^' 4- w 4 w 4 ') 

 \( x - a y + (y-by i + {z-c)* + (l-\y+[{x-a)w{ + ...Y}l 



Putting (x-a) 2 { (y-hf+ (z-c) 2 + (Z-\) 2 = just as we 

 did in the interpretation of the potential-four-vector, we have 



^ ^'(u^x + u^+ng^ — 1) 

 r(l-v r v/(l— u 2 ) 



with the same interpretation for r and v r as before. 



Excepting for the factor [(1 — v r )y/(l — u 2 )] in the 

 denominator, the form for P is identical with that assumed 

 by Clausius for explaining the laws of electrodynamic action. 

 The occurrence of these terms need not cause us any con- 

 fusion; following in the wake of Clausius, we can easily 

 prove that this formula leads to the laws of electrodynamical 

 action just as well as any one of the formulae mentioned in 

 the introduction. We have to take terms up to the second 



