PIERCE. — THEORY OF COUPLED CIRCUITS. 305 



ing to different values of ( — ) . In examining the table and the 

 figure it should be remembered that 



(27) 





in which w and X are respectively the angular velocity and the wave 

 length of the incident waves ; A3 and A4 are the wave lengths corres- 

 ponding to the natural period of Circuits III and IV respectively when 

 standing alona. The abscissas of the curves of Figure 5 are values of 



( — V, or (— ) , which equals LsCsuy^; the ordinates are values of 



( -^ ) ^, or ( — ) , which equals L^Ctuy^. For fixed values of Z3, Z4, 



and oi the abscissas and ordinates are, therefore, proportional to C3 and 

 Ci respectively. 



V. The General Resonance Relation {continued). Special Case 



Where rj^ = 0. 



An examination of equation (25) shows that when 773^ = the curve 



of ( ;-^ j vs. ( ^ j for resonance is an equilateral hyperbola, with 



/A \^ 1 



horizontal asymptote at f -^ j = ^, and vertical asymptote at 



( r^ J = 2- This curve with its asymptotes is also plotted in 



Figure 5. In the part of the curves plotted in Figure 5, even when 773^ 

 is not equal to zero the curve does not appreciably depart from the 

 equilateral hyperbola provided 773^ < .001. The corresponding curve 

 in Ci vs. Cz for rj^^ = 0, or ^^^ < .001, has its asymptotes at 



^3 = 7-. 27T — 2 ^^^ ^i — T\ 277 — 2"' and the equation giving 



the resonance relation of C^ to C^ in this case, obtained by a transfor- 

 mation of equation (25), is 



(28) \Gz-^^_ ^,^ Z30.V \ * ~ (1 - O U^'J " (1 - O •^Xa^o)"- 



VOL. XLVI. — 20 



