672 lilll.I. SYSTEM lECHSICAL JOL'KX.IL 



contain suiktAuous clemenis. It is tilso to be expected tt).it oih- 

 additional condition must be satisfied by the roots and i)ok's in order 

 that an impedance may be realized by a six-element iiutwork, and two 

 additional conditions for a fi\e-elenient network. 



Accordingly, a census has lieen made ot all iRtwurks consistint; of 

 not more than sex'en elements, each network (■(iiuainiii.u; at least one 

 re>istani'i', two caiLicitic-s, and two selt-iiuluctances. This census 

 is siiown li\- Table 111. 



l-".arh iwii-nu'sh circuit nieelini; these rc(|iiirenK'nts a> to llie nmnbi-r 

 ol I'knients is rei)resented in symbolical lorni in T.ible 111. The 

 k-tters L. R. and C, printed in the first, second, or third lines of the 

 symbol, indicate the presence of self-inductance, resistance, and 

 capacity in the first, second, or third branches of the circuit, resjiec- 

 lively. The letter .1/ is printed in the two lines of the symbol cor- 

 respondini; to the two branches which are connected by a mutual 

 induct, inci'. Thus I he first circnit in the tabic is represented In' the 

 symbol 



LRCM 

 L CM 

 L 



which indicates self-inductance, resistance, and capacity in the first 

 branch, self-inductance and capacity in the second branch, and self- 

 inductance in the third branch, with mutual inductance between the 

 first two branches. 



Three networks, in general, are obtained Irom e.ich of these circuits 

 b\' openinjj each of the three branches. If twn of these branches are 

 alike, onl\- two dislinct iiclwcirks ,ire niil. lined. If one branch ol 

 a cii-ciiit is a shorl-circuit , there bi'inj; no elcnients ,issi,i.;ned to tjuii 

 br.incli, llu- network obt. lined b\- cipeniiii; one ol tlu' oilier branclu's 

 i> of ilu' typi' shown b\- l-"ig. 7.i: il the short-cinuiled lir.inch i;- opeiU'd, 

 the iH'twork consists sinipK- ol llie i>.ir,ilk'l ('(imliiii.uinii dl ilu' (ilher 

 two branches. 



With circuits represented in this symbolical manner, there is, oppo- 

 site each line of the sNinbol, a reference to the domain of poles indi- 

 cating the ])orti()n of the domain realizable by the network obtained 

 by opening the corresponding branch. Two like branches in a circuit 

 are brackete<l together with a single reference mark, since they each 

 give the same network. The entire domain is indicated 1)\' i."; the 

 boundary curve of tlu' domain b\ I", iliis beiiii.; dixided into se\en 

 segments, I'l, Y«, ■ ■ ■ , 1';; ten critical lines in the domain b\- the 



