/>/e/r/.V{;-/'o/.VY i.Mri-.i>.i\ct-. or TH-o-Afi-..sii cikciiis ut) 



Iran paranicUT k. In ^;^•lu•ral. tlicrefnre. live nf thi- elements m.i\ 

 l>e speritie<l. or h\e relations among the elements; whereupon th«- 

 equations ran l)e sol\ed. Thus it is to \>e exfierterl that a strven- 

 cli-ment network will realize, in general, any sperihed drivinp-poini 

 im|H'(lance. 



This (nflh<Kl of solution is best illustrated \)\ considering a par- 

 ticular rase. Take, for example, the deri\ation of the formulas for 

 Network 1 of Fig. 1, as Ki\en l)y Table I. This is the special case of 

 the general network of Fig. 7 obtained by making L\ = Ri = C\'^ = Mu 

 = .l/is = 0. Substituting these values, together with the notation of 

 Table I. e(|uaiions (7) (lo) become 



DiD3=a,k-, 

 R„ + R, = b.k-. 

 R2Di-R:,D2=l\k\ 



LiR3-LJii-{Ri-R2)Mij=rik\ 



Kliminating /?;, R3. D-i. and D3 from the second, third, lifih, sixth, 

 and seventh of these equations, the value of k is found to be equal to 

 db U i T\. Knowing the \alue of k, the equations may then be soKed 

 for the se\en elements, obtaining the results given in Table I. The 

 two sign choices for k in this example correspond to the possibility of 

 interchanging branches 2 and 3 in the network. The values gi\en in 

 Table I are computed for k taken with the negative sign. 



In the general solution, the parameter d is obtained from the 

 quadratic equation (21). The explicit solution of this equation is 



, 2a^bl--\-a•bi* + 2a(jbr—aibxb^ — 2a^b\b3 — albib^±2^ ,., ,, 



d = b^^^AbJ. ■ ^-^^^ 



where 



A- = 04-61* +a„a,6o*+ay-'6.i' — «.i«46i'62— (2<ija4—a.V')6i'6,i — a 1016165' 

 — aoa.i6;'6j — (2afla. — a i'}bib,' — OoU 16263' 

 +a2a46r6;2 + (a2' + 2anrt4 — 2aIa3)6I'6.^-+ao0262■•'63'' 

 +(3flla^— a:Ki3)6i'6:6i— f4onrti— rti(Jj)6i62'63 

 + (3flofl3-aias)6i6!6j'. (35) 



=-ao'(ai»6, + a,6.4-6,)(a5=6i + a56, + 63) 



(a,«6, + a,6. + 6,)(a4'6, +0462 + 63). (36) 



= ao»6,«(ai-^s)(ai-^i)(«s-/Ji)(«-.-/5.i) 



(aj-/3j)(aj-^j)(a4-/32)(a4-^3). (37) 



