PIERCE. — THEORY OF COUPLED CIRCUITS. 313 



where M'ui^ > Ihl'u and let us suppose that V has, in general, not 

 its optimum value, but a value k times its optimum value ; that is, 



(38) V=k\\ 



oph 



in which k is a variable parameter, which may Tdo positive, negative, 

 whole, or fractional. 



Equation (IG) then becomes 



'opt' 



V{k ■ Uopt Voj,t-M'i^'-R^K,f+ {R^Uovt+Jis ■ k ■ Kpt y- 



Replacing Ugpt and Vopt by their values (equations (21) and (22)) 

 we have after simplification 



(40) Y,u. = ^ 



""^ V{k - 1 y ( jy V - R,A\) + 4 R^R, 



Now dividing the square of equation (40) by the square of equation 

 (23) we have 



^^^^opt) y_ 1 



^^^^ \Yma.maJ - {k-lY ( MW ^ ^^^ 



\R: 



.Ri J 



4 V 773774 / 



This equation gives the current in terms of the parameter k provided 

 "T^ > VsVi- Let us now obtain the wave lengths in terms of the same 

 parameter. The values of V and Vopt from equations (15) and (22) 

 substituted in (38) give 



(42) L,a>~~ = ±k |/|i (J/ V - R,R,). 



Dividing (42) by X4W gives 



(43) l-(^^y=±k l/|-^(3/V-i?3i?4) 



= ± kv, i/— - 1. 



