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THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 



Now, from Fig. 2 we see also that 



Now 



so 



f«sin((?/2) = rsin(7r/2 - 0/2) = r cos{d/2) 

 tan (0/2) = r/fm 



= 27r - $ 



tan (tt - (<E>/2)) = r/fr, 

 tan (#/2) = - r/rm 



(9) 



For circular motion with, an angular velocity {e/m)B and a circum- 

 ferential speed V = vn = ?;r2, the radius of motion rm is 



(10) 



Fig. 3 — The ratio L2/L: of the electrode spacings shown in Fig. 1 should satisfy equa- 

 tion (6). When this is so, the angle f>, measured in radians, is a function of the voltage 

 ratio Fi/F2 , and this function is shown above. 



From (1), (3), (9) and (10) we obtain 



(e/m)BL2 



tan ($/2) = 



y^^^^ 



(1 + Vv,/v,) 



(1 - Vv^/v,) 



From (7) and (8) we see that this may be written 



4 



ta„(*/2)=-(*/2)(j-Z^7==) 

 Fi/Fj = (1 + 4(*/2)/tan(*/2))' 



(11) 



We note that $ must lie in the third or fourth quadrant. In Fig. 3, ^ is 

 plotted vs. F1/F2. 



