SMOOTH LINES AND SIMULATING NETWORKS 39 



Fig. 2 '•", with a = (since the leakance G is neglected). The F- 

 column was obtained from the /-column by means of the equation 

 F = uL/R — .00222/. Next the values of x and y were read from the 

 curves a = in Fig. 2. Finally M and iV were obtained from M = kx 

 and N = ky, with k=vL/C = 663 ohms (whence M and A 7 ' are in 

 ohms). From the table it will be noted that at / = 200 the excess 

 resistance is about one-third as large as the nominal impedance, and 

 the reactance is about nine-tenths as large as the nominal impedance. 



The columns r, u, —v show the steps in evaluating M and N by 

 means of Fig. 4. After choosing Fi (in Fig. 4) equal to 2 16 , the r- 

 column was obtained from the /-column by means of the equation 

 r =/ t\ = 2irLf l RFi = .OOlllf. Next the values of u and v were read 

 off from the curves Fi = 2 in Fig. 4. Finally the values of M and N 

 were obtained from AI = \Ki\u and N = \Ki\v, with \Ki\ = V i?/a> 1 C = 

 VL/CFi =469-. 



The two last columns (5 , 8) of the table show the percentage pre- 

 cision of certain simulating networks designed in accordance with the 

 first-approximation methods of this paper, and having for their ele- 

 ments the values given in the last paragraph of this Appendix. 



So pertains to the simple 2-element network in Fig. 6c when propor- 

 tioned in accordance with equations (30) and (31). The values of 8 

 were read from the curve D = in Fig. 8. The precision at the lower 

 frequencies could be considerably improved by the addition of a small 

 resistance R n (as already noted in connection with equation (6-B) of 

 Appendix B), but with a corresponding sacrifice in the rest of the 

 range. 



8 pertains to the 4-element networks in Figs. 11a and lib when 

 proportioned in accordance with (30), (32), (33), (34) and (30), (35), 

 (36), (37) respectively; and 5 pertains also to the networks in Figs. 

 lie and lid when these are proportioned, by Appendix D, so as to be 

 equivalent to the network in Fig. 11a. The values of 8 were read 

 from the curve D=0.55 in Fig. 8, this value of D being known from 

 Fig. 9 to be about the best. 



The values of the elements of the networks to which 5o and 8 per- 

 tain will now be set down, each preceded by a reference to the cor- 

 responding diagram and design-formulas: 



Fig. 6c — Formulas (30). (31); Precision 5 . 



#i = 663 ohms, d= l,063xl0" 6 farad. 



16 Or Fig. 1, with 6=0; but Fig. 2 is plotted to a larger scale. 

 16 Fi = \ would be somewhat preferable for reading off values; but the principles 

 are more clearly exhibited by choosing for F\ some other value than unity. 



