584 Prof. T. R. Lyle on Mechanical Analogy to the 



For this to be a maximum, if M/L : be given, b/c must be 

 a maximum. 



Let the coupling be given also, so that the conditions now 

 are that the ratios 



M : L x : L 2 are given. 



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 b is a 

 right angle. Hence, in this case, when the max. amp. of 

 V 2 is a maximum, 



a = b cos 2-*/r ; 

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



2 COSi|r V 1j 2 



which as Lj/L 2 is given obviously increases as yjr, and hence 

 as the coupling becomes closer. 



Hence, if T 1 and T 2 be the natural period of the circuits, 



s/a s/b 



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

 the law 



T^TjVcos^, 



after making the coupling as close as is desirable. 



(2) 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 



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



Aab . o , 

 — — snr yfr 



must be a maximum. 

 But 



4ab . „ , 4:(s — a)(s — b) - /a—b\ 2 

 _ rS1 „^= A__^ =1- ^— ) , 



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

 periods of the two circuits are equal. 



