666 



BELL SYSTEM lECHMCAL JOURSAL 



pools art- all real and equal in pairs the domain is bounded by a circle 

 E, tangent to the vertical axis and pa.«6inR ihrongh the two double 

 r<X)ts, E\ and £3. and by the reflection of this circle in the real axis. 

 Thus the domain has cusps at the double roots. I'or two pairs of 



1 !>;. 4 -Domain of the poles of the driving-point impedance of a two-mesh circuit 



with two pairs of complex roots, showing the portions of the domain realizable bv 



each network listed in Talile III. 



equal roots, whether rc.il or coniplcv. liu' <iislanci' On is the geo- 

 metrical mean \alue of all four roots. 



Another kind of special case is shown b\ I'ig. 'M\. the case of two 

 pairs of roots with equal angles. The first and third roots are on 

 a line with the origin, so that the second and fourth roots, being 

 their conjugates, are also (m a line with the origin. Fig. M shows 

 the boundary curves {A . . . E) for five sets of roots {Ai, A^ . . . Eu £3) 

 satisfying these conditions and with the same absolute values of the 

 roots in each set, so that the roots lie on two circles about the origin. 



