SMOOTH LINUS AND SIMULATING NETWORKS 31 



Equation (20) K = J - t, k ^ \ 



if _J g 2 +fe 2 £ 2 +V(i+fe 4 £ 2 ) 0? 4 +£ 2 ) 



N=- 



2 (g< + £ 2 ) 



(i-g 2 * 2 )£ 



2(g<+£ 2 )M' 



(l — g*k 2 )E 



Equation (21) : K = \/k 2 -i/E; 



M = ^-= y jk 2 +Vk i +l/E 2 , 



iV = - 1 /2E il/ = - VM 2 -k\ 



M -k = ^ ?— , 



8£ 2 (M+fc)71f 2 



ag K=-\ cot" 1 F£. 

 The relation iV = — V Af 2 — & 2 can be written in the form 



-N \M+k' 



which shows that M—k is always smaller than —N, though the two 

 approach equality when E approaches zero. 



The network of curves of K in the AfiV-plane are the equi-& curves 

 consisting of the family of hyperbolas M 2 — N 2 — k 2 , and the equi-.E 

 curves consisting of the family of hyperbolas MN = —1/2E. 



Appendix B 



On the Simple Type of Complete Network (F"ig. 6) 



The network in Fig. 6c consisting of a resistance Ri and capacity 

 C\ in series with each other and having the values expressed by equa- 

 tions (30) and (31) was originally arrived at by working with values of 

 F large or at least fairly large compared with unity; for then, by 

 equation (12), the characteristic impedance K has approximately the 

 value. 



K = k-ik/2F. (1-B) 



