40 PROCEEDINGS OF SECTION A. 



When the coupling is known the angle included between a and b 

 is fixed, and it is easy to show that in the triangle the ratio b/c will be 

 a maximum when the angle opposite 6 is a right angle. Hence in this 

 case when the max. amp. of V^ is a maximum 



a = b cos 2 \p, 



and the max. max. value of V.2 is easily shown to be equal to 



_1_ . /5 

 2 cos\L ^ L.2.' ^' 



Ti = 7=> ^2 



which, as L^/L^ is given, obviously increases as i// increases and hence 

 as the coupling becomes closer 



Hence if T^ and T% be the natiiral periods of the circuits as 



27r 27r 



\/a \/b' 



the tuning, or rather mistuning, should be done in accordance with the 

 law 



■^2 = ^1 V COS 2 -^ 



after making the coupling as close as is desirable. 



(6) Again to find the tuning so that the energy that surges into the 

 radiator circuit may be a maximum. 



In § 10 we have shown that the maximum energy in the secondary 



is equal to 



, iab 



iK-^E^. -^ sin2 J/, 



and for this to be a maximum, if Ki and E are given 



-^ sin2 ;// 



must be a maximum. 

 But 



iab 4(s - a){s - 6) /a - b\^ 



-^ snr -ib = 



= ^ - c-^y 



which is a maximum when a = b, that is, when the natural periods of 

 the two circuits are equal. 



(c) Again, to investigate the tuning so that the maximum amplitude 

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



From Eqns. (I) § 5,' 



" C 



whose resultant amplitude is equal to 



P2K2 ~ E Jut^i + W^2 - ^ <*>! ^2. cos (W2 ~ f^i) ^ 



c 



