PIERCE. — TUEORY OF COUPLED CIRCUITS. 307 



In like manner equation (;>()j becomes 



(3-2) i-f-v =±,y^-i. 



\<^ Join VaVi 



Replacing the ratio of angular velocities by the reciprocal ratio of 

 wave lengths, in accordance with equations (27), we may transform 

 equations (31) and (32) into the following equations: 



(33) f^^" 



1 ± vs f — - 1 

 and 



(34) 





It should be borne in mind that in order to get properly correspond- 

 ing resonant values of A3 and \, one must use either the plus sign in 

 both of the equations or else the minus sign in both the equations. If 

 one employs the plus sign in one of the equations and the minus sign 

 in the other equation, the values of A3 and A^ so obtained are not ap- 

 propriate simultaneous adjustments for best resonance. This is seen 

 by an examination of equation (19). 



By an examination of the discussion on p. 302 it will be seen that 

 the optimum condition in the form of equations (33) and (34) can be 

 attained only provided 



(35) — > 1. 



In order to facilitate the computation of A3 and A4 for various values 

 of T, 713, 'q^ and A, equations (33) and (34) may be put in the form 



(36) (^\ = 1. , where <^3 = ^3 /-^ - 1, 



and 



(37) [\\ = — i=, where <t>. = v^ f — - 1. 

 X-^ /opt VI ± 04 ' VsVi 



The following table (Table II) gives the values of ( t^ ) for various 



V-^ /opt 



values of cf>s. 



