80 Mr. Megh Nad Saha on the 



The theorem is proved by substituting, in equations (1), 

 the values of p w u /o w 2 , PqW^ poW^ obtained from the 

 fundamental equation 



lor/=47r/o (w 1 , w 2 , w 3 , w 4 ) 



and effecting the necessary transformations with the aid of 

 the second fundamental equation 



lor/*=0. 



In the present case, the field is due to a single moving 

 charge. The quantities [X z , K y . . .] can be easily calcu- 

 lated from the Potential four-vector a, for the six-vector /is 

 equivalent to curl a. 



In a paper * communicated some time ago to the Philo- 

 sophical Magazine, I have shown that the Potential four- 

 vector a at an external space-time point (V, y\ z', V) due to 

 the motion of a charge e occupying the point (#, y, z y I) is 



equivalent to ^ , where 



, ., P , (dx dy dz dl\ 



«, = velo 01 ty four-vector = ^, %1 Jg , ^, 



and R is the perpendicular distance from the external point 

 on the line of motion of the electron. We have 



W= (*_*;)!+ (y-y') f + (*~s') 2 + {l-l'Y 



+ [( x ~x')w l +{y-y')w,+ {z-z')w 3 + (l—r)w i ]\ 



We have now 



da 2 _ Bai _ d /gw 2 \ d_/^i\ 



/l2 ~ a#' v ~ a* 7 V R / 9/ V R j 



where 



" 1= ^(s)' a2= ^'(l)' "» = S?(b)' " 4= p(b)- 



* It seems to have escaped the notice of investigators on this particular 

 subject that the Potential four-vector in the form given by me is im- 

 plicitly contained in a statement of Minkowski's (" Raum und Zeit," § 5). 

 The passage came to my notice only recently when I was making a 

 critical study of Minkowski's works. 



