302 PROCEEDINGS OF THE AMERICAN ACADEMY. 



Equation (23) gives the max max current in Circuit IV provided 

 equations (21) and (22) express the optimum resonance relation. 

 Instead of (21) an alternative possible solution of equation (20„) is 



Uo,t = 0. 

 Under this condition, according to equation (19) 



Vopt — 0, also. 

 This would give by equation (20) 



EMuy 



(_2d a) ( ^ max maxjo — 



i/V + BsRi 



The question arises under what conditions ( Ymax max)o of equation 

 (23 a) is greater than Y^axviax of equation (23). The answer is seen 

 to be that 



\^maxmax)o ^ ■'^ max max 



when 



that is, when 



Squaring, 



E3Ioy E 



RzRi 



Mo. + ^ < 2 VR^Ri. 



May 



3Po.' + 2 RsR, + %f|- < 4 R^R„ 



RIR^ 

 M' 



I.e., 



MW-2R,R, + ^,<0. 



Extracting square root, 



lUOi 



(23 b) ]\PJ-R,R,<0. 



In this case, the conditions (21) and (22) would give imaginary value 

 of Uope and F^pj. 



Whence we conclude, that we are to use equations (21), (22) and 

 (23) as solutions of the resonance problems, whenever 31W>R^Rs. 

 In other cases the alternative values 



f^opt ^^^ '-'> 'opt "^ "i anCl \J- maxmaxJo ~~ nn 2 i tj d 



HI (X) + sislii 



are to be used. 



