i'iKin\u-f(U\i iMi-i n.ixcii oi- ino-\!i.sii i imriis m) 



in ilu- .iu\ili.ir\' di. 1^1.1111 n.irri>w> down in .1 >iii^;lr litir srKinrnl. 

 rin-ii it llu' tiiluT two ri'.il rn(ii> .irr l>rini^;lii i(>y;cilu'r. llif liimrul.ir' 

 ilirvf li.i^ .1 second cusp ,ind tin- (Inni.iin in llu- ,in\ili.ir>' diagram 

 >lirinks in ,1 sin^;K' isnl.ilid pninl. It. now. niic nl llu' pairs of c'(|lial 

 rt-al mots is scp.iralcd inin a pair nt (nnjuvj.iU' inia^inar>- rnnis, the 



Im«. 



il piilc^ c>| lii;, 5, nil l.iri;cr >c.ilc- 



cnrrcspondinK cusp is rniindfd otT away trnin ilic a\is, and ilic pninl 

 in the auxiliary diagram vanishes. Whun the other pair of equal real 

 roots separates into conjugate compie.\ roots, the case illustrated 

 !)>■ Fig. 4 is obtained. As one pair of cf)niplex roots approaches the 

 imaginary axis, the domain narrows imtil, for one pair of roots on the 

 vertical axis, the domain shrinks to a circular arc as illustrated li>' 

 Fig. ."ia. This sort of transformation may Ik- followed through in 

 different ways in order to obtain any desired distribution of the roots. 



The complete domains are unifiue, that is, any one domain is given 

 fiy only one set of roots. 



Kvery domain includes the [loints corresponding to the roots for 

 which the domain is defined. For these points, that is, for a jiole 

 coinciding with a rfK)t. the impedance expression has a common factor 



