Coupled Circuits used hi Wireless Telegraphy. 583 



the amplitude of Y x does not become zero every surge as 

 when a = b, its minimum value being 



Ey^l-i^Wf 



which =0 as it ought when a = b. 



The energies in the two circuits are now (see § 9) 



i^E' (l - 1 J sin^ sin 2 ^=^), 



i^B* x 4 J sinV sin 2 ^=f?i(, 



showing that the energy which surges into and out of each 

 circuit is equal to 



iK 1 E 2 x^ > sin 2 ^=S (say). 



If at the instant when S has all entered the radiating 

 circuit for the first time the primary circuit be broken, then 

 S will have to remain in the radiating circuit, which will now 

 proceed to vibrate with its own natural frequency, and the 

 vibrations will persist until damping and radiation have used 

 up the energy S. 



This is the theory of the quenched spark which can be 

 very strikingly demonstrated by means of the pendulum 

 model. 



In doing so, it is obviously impossible to perform on the 

 first pendulum the action analogous to breaking the primary 

 circuit without disturbing the motion of the remainder of 

 the system. Instead of placing the bob on its platform, the 

 result desired can be very approximately obtained by taking 

 it in the hand so as to slacken its strings. 



11. The "triangle" with its associated equations will be 

 useful as a means for solving many questions dealing with 

 the tuning or adiustment of the circuits. 



As examples, three cases will be briefly considered. Many 

 such cases will present themselves or arise in practice. 



(1) Let us investigate the conditions for obtaining the 

 greatest maximum amplitude of V 2 , the P.D. of the secondary 

 condenser, for a given initial value E of V^. 



By equations 1. § 5 the max. amp. of V 2 is equal to 



c Lj 



