Coupled Circuits used in Wireless Telegraphy. 585 



(3) Again, to investigate the tuning so that the max. amp. 

 of the current C 2 in the secondary may be a maximum. 

 From equations I. § 5, 



^ 2 =^? 2 K 2 — E -\ — (Oi sin coit + co 2 sin co 2 t r, 

 whose resultant amplitude is equal to 



p 2 K 2 -E \/ coi -\- co 2 2 — 2g> 1 g) 2 cos [(o 2 —ci)i)t, 



c 



whose greatest value is equal to 



p 2 K 2 -E(&> 1 + a) 2 ) J 







which after a few reductions becomes 



1 sin 2 ty nA-H ^s — c 

 M cos^/r c 



Let one condition under which we find this to be a maximum 

 be that M = constant, then as 



sin 2 yfr 

 cos ty 



increases with ^ within the possible range of the latter, we 

 wall determine when 



v s+ v s — c 



c 



is a maximum for a fixed value of sin i|r, the coupling. 

 Now 



Vs+ V s _, 



c V Sr _ s/ s — c 



and, remembering that 



c 2 =a 2 + b 2 -2ab cos 2-sft, 



we find that \^ s— v s — c is a minimum when 



b = a cos 2 ^, 

 and that its minimum value is 



Va . sin i|r, 

 which gives for the max. max. amp. of C 2 when M and the 

 coupling are given, the value 



tani/r 1 



E, 



