352 Mr. Megh Nad Saba on the 



electron come out in very elegant forms, enabling us 

 ultimately to- write out the equations of motion of two 

 electrons round each other in a Lagrangian form. When 

 one electron is at rest, the equations lead to Darwin's results 

 (Phil. Mag. 1915). 



3. dotation. 



Tbe notation used in this paper is identical with that used 

 by Minkowski and Sommerfeld in the memoirs just men- 

 tioned, and is to be found in any one of the general treatises 

 on Relativity (Cunningham or Silberstein). However, for 

 the convenience of the reader, it is explained below. 



The unit of time used in this paper is — times the ordinary 



unit(c, velocity of light measured in ordinary O.G.S. units), 

 so that, with this notation, the velocity of light becomes 

 unity. 



We shall, in most cases, use l — \/ — It, so that (#, ?/, z, /) 

 denotes the space-time coordinates of a world-point ( Welt- 

 pun kt). 



The quantities 



(Wi, W 2 , 10 3 , W y ) = y 2 (Ul, U 2 , U 3 , \Z—i), 



where (u l5 u 2 , u 3 ) are the ordinary space components of the 

 velocity of a material point, will denote the space-time com- 

 ponents of the Velocity-four-vector. It should be noticed 



that (n 1? u 2 , u 3 ) =— (#, ^, z), and if by r we denote the 



proper-time (Ei^enzeit) of motion of the material point, we 

 shall have dr = dt^/(l— u 2 ), and 



(w x , w 2 , w z , Wi )= — {w, y, z, I). 



a will denote a four-vector of which the space components 

 are equivalent to the vector-potentials used in Electro- 

 dynamics, the time-component =\/ — 1^, where (j> is the 

 ordinary scalar-potential. This is known as the Potential- 

 fourrvector. 



The operator 





