488 



THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1954 



I, II, III shown in Fig. 11.2. It may be verified that for large negative 

 values of nii the boundary lines in Fig. 11.2 are given approximately by 



mr = dz 2"'7r''p\mi\''\ (11.4) 



There was a period, while these curves were being worked out, during 

 which it appeared that the regions I, II, III told the entire story. How- 

 ever, when small \'alues of 7n were studied it was found that region I 

 splits up into the two sub-regions, la and lb, such that the boundary 

 between them is given by 



Imf/(^i) -Khe-'n] ^ 0. (11.5) 



Vl 



'iu. 



to//5 W, Wl 



m -o.oobp^ 

 U/p 



Fig. 11.3 — • Paths of steepest descent for \m\ = 0.005 (P-, z = i^'^p. Away from 

 t = ii all paths look much like Fig. 11.3(a). 



