364 



Mr. Mesh Nad Sal) 



the 



velocity components {i\. r 2 , v 3 )] upon another electron A 

 [charge e, coordinates of centre (&•, y, z, I), velocities 



(wi, w 2 , «s)j- 



The components of the pouderomotive force upon a point 

 (#', y' , z\ V) of the electron A are given by the four com- 

 ponents of the matrix 



Po 



w x 



10 2 



w t 



w 4 





9 



a#' 



B 



B 

 B*' 



B 

 B/ 





a/ 



a/ 



a 3 



a/ 



e'w' 











where a' = pj- , 



R'«a:(#-a) 1 +(y-ft) i + ^-c) f + (Z-X) > 



and 



[w/, 10 2 ' 5 W> 3 ', '"V] = x /( 1 _ v 2) l V U V 2, V 2i i] 



The total force is obtained by integrating each of these 

 four expressions over the whole volume of the electron A. 

 The X-component of force 



where 



eh' — \/(l — u 2 ) m dt, 



an 



w l = 



dX' dX 



for all points of the electron move with the same velocity, 

 and </>' = -,57 [wiWi ' + w> 2 20 2 ' + w 3 iv s ' + w 4 w 4 ' ] . 



The total force 



d£2 being the contents of the normal section of the cylinder 

 ( x -^ + (y-y o y + (z-z V- + (l-l o y 



+ [(je'-tfoM + 0/'-yo)?«2 + O'-ZoVs + (I' -lo)w i \~ = ') s - 



. . . (13) 



