358 Mr. Megh Nad Saha on the 



The coordinates here refer to the coordinates of the point- 

 charges*. 



7. Laiv of Attraction between two Point-charges. 

 We have now 

 Y r r da x £a 2 da 3 da^ 



x= 4y?s; +W2 ^ +w *^ +w ^ ] 



' W* + W ^y +W *Y Z + ^|/} *» 

 i. e., 



' 7\ / 1 \ 



X = po/o '[( M7 i w; i' + ^2^2' + W3W/ + w^O^H w? ) 



for in the expression for a, R is the only term explicitly 

 involving the coordinates (as, y, z, I), (p Q f , w) being indepen- 

 dent of them. 



Now let dr = proper time (Eigenzeit) of motion of A. 



Then dr=dt\/(l-u 2 ), 



and (w u w 2 , w s , w±) = x (a, y, z, I). 



UT 



We have therefore 



d ~d dx ~d dy d dz d dl 

 dr ~dcV ' dr "fty dr ~dz dr "dl ' dr 



~0# 02/ O^ 0^ 



If we now put 

 then, since 



- WiW } ' +W 2 W 2 ' +W S W 3 ' +W4W4 f , Q . 



< ± ) = ^7 popo, . . («) 



Popo'iVi' __d<£ 

 we have 



Similarly for the other components (Y, Z, L). 



* The matriv used for expressing the Ponderomotive Force (X, Y, Z, L) 

 has not been used in the conventional sense (Sommerfeld, Ann. der Physik, 

 vols, xxxii. & xxxiii.), as can be easily observed. 



