PIERCE. — THEORY OF COUPLED CIRCUITS. 317 



of square of current in Circuit IV plotted against wave-length adjust- 

 ment of Circuit IV, and are obtained by setting Circuit III at its best 

 value and leaving it at that value during the tuning. The appropri- 

 ate best-value settings of the wave length of Circuit III are indicated 

 by the positions of the two lines marked " 7^4 = .01" at the lower 

 margin of the figure. The short-wave adjustment of Ag (at Ag/A. =.877) 

 is required for the short-wave resonance curve (with its maximum at 

 A^/X = .877), and the long- wave adjustment of Ag (at Ag/A = l.li)6) is 

 required for the long- wave resonance curve (with maximum at 

 A4/A = 1.196). It is seen that in this particular case, with 7/3 = 7/4 = .01, 

 the resonant adjustment of Circuit III and that of Circuit IV have the 

 same wave-length A3 = A4 ; and because of the smalluess of the damp- 

 ing factors rj3 and 7;^, the two curves are sharp. 



Case I (continued). Assuming again t= .30, 773= .01, hut with 

 ■q^ = .1. — Suppose now that we give to Circuit IV a higher resistance 

 so that 7/4 = .1. This may be done by using a higher resistance 

 detector in Circuit IV. This will cnt down the maximum value of the 

 current in Circuit IV, but will leave the square of the current times 

 the resistance (namely, Y-Ha) the same as before, so that the curve in 

 terms of V^Ili will have the same maximum amplitude for 7/4 = .1 as 

 for 7^4 = .01. Complete computations from equations (44) and (41) 

 show that the curve will have the form and position given in 

 Figure 8 and marked "7/4 = .!." The corresponding appropriate 

 adjustment of Circuit III is given by the line marked 'S;^ = .1 " of the 

 lower margin. The curve going out to the right, also marked 

 " ,;4 = .1 " in Figure 8, is a part of another possible resonance curve in 

 this case. This second resonance curve culminates beyond the limit 

 of the figure with its maximum at \/\ = 4.18, and requires the adjust- 

 ment of Ag/A at l.(t'). 



The results of the computations in this case show in an interesting 

 manner the necessity of tuning both circuits to get resonance, and 

 show how markedly the adjustment of Circuit IV may be aff'ected by 

 the adjustment of Circuit 111 ; since with the constants here assumed, 

 the change of Circuit III from Ag/A = .96 to Ag/A = 1.05 necessitates 

 the shifting of A4/A from .716 to 4.18. The resonance in the former 

 case is sharp, and that in the latter case is very dull. 



Case I {continued). Assuming again t = .30, 773 = .01, vhilerjiis 

 made = 1. We obtain the resonance curve marked 7;^ = 1.0 (Figure 8) 

 with appropriate adjustment of A3/A4 at .986. In this case the second 

 resonance value in the region of long waves is imaginary. 



Case I (continued), r = .30, 7/3 = .01, while 7/4 = 9. — This is the 

 special case requiring the use of equation (47) and gives the curve 



