980 Dr. Gr. Breit on the Effective Capacity of 



IT 



Hence the argument of (1 — t^ 4 )* is ^— ZB01 as long 



as this quantity is less than it and greater than — it (by 

 the definition of the meaning of the square root). Now 

 draw BA tangent to the unit circle at B. The argument 

 of the stroke BA is 



J+ZBOl. 



But this is the argument of dr in (21). Therefore, by (21), 

 the argument of dz is 



~-r ZB01+£-ZB01 + £ = 7r. 

 2 4 4 



This means that as B moves on the unit circle, z moves in 

 a straight line parallel to the axis of reals and in the negative 

 direction. 



Such is the case as long as the argument of (1 — t~ 4 )s is 



-- — ZB01. Consider now the behaviour of arg, (1 — t -4 ). 

 4 



As B moves from 1 to ^/j 9 Q moves from 1 to —1 so that 



IT 



arg. (1 — t -4 ) varies from - to 0. Further, as B moves from 

 V y t° fa Q follows the upper part of the unit circle and 



err 



arg. (1 — t -4 ) varies from to - T . Within this region 

 arg. (1-T- 4 ) is |"-2ZB01 and, therefore, arg. (1-T^)*is 

 I-/B01. 



But as soon as t crosses ;', the principal value of the 

 arg. (1 — t~ 4 ) must again be taken as £, for otherwise 



the real part of the square root will be negative. Hence, 

 from j on, arg. (1 — t -4 )* must be taken as 



4 

 As before, arg. dr is 



'zBOl-Q. 



J+ZB01 



and, therefore, by (21) 



01+- — f/"RM -' 



9) • 2 



arg.^=|+ZB01 + |'-(zB01-^) 



