SMOOTH LINES AND SIMULATING NETWORKS 23 



readily compared by means of the following equations (38) derived 

 from (32), . . . (37): 



C 4 + G ] C * C < \R 



C 2 +C, D C 2 " C 3 Mr 



-< 



(38) 



Fig. 10 represents the two limiting forms of the excess-simulators 

 in Fig. 7, corresponding to the limiting values and 1 of the para- 

 meter D occurring in the design-equations (32), . . . (37). For 

 D = the limiting form is that in Fig. 10a, and will be recognized as 



c 4 =c=c 



(a). — 1|-^> 2 



DO 



(b) 

 D=1 ^ 



,A C 2 C 1 



^5~^3"^^1 



Fjt. 10— The Two Limiting Forms of the Excess-Simulators in Fig. 7, Corresponding 

 to the Limits and 1 of the Parameter D 



the simple excess-simulator already shown in Fig. 6b consisting of a 

 mere capacity C\ having the value expressed by (31); while for D = 1 

 the limiting form is that in Fig. 10b, and is thus of the same form as 

 one mentioned below, under the heading Modifications for Very Low 

 Frequencies, as being capable of furnishing approximate simulation 

 extending down to zero frequency. The departure-curves for these 

 two limiting forms (£> = and D = l) are included in Fig. 8, as already 

 mentioned; and from them it is seen that the form in Fig. 10b (Z) = l) 

 possesses much higher simulative precision than the form in Fig. 10a 

 (D = 0) — as would be expected. 



Four Precise Types of Complete Networks, and Their Limiting Forms 



Figs. 11a and lib represent the two potentially equivalent com- 

 plete networks that can be constructed from the basic resistance 

 Ri of Fig. 5a, and the excess-simulators in Figs. 7a and 7b respectively; 

 and hence having for their elements approximately the values ex- 

 pressed by equations (30), (32), . . . (37). 



