PROCEEDINGS OP SECTION A. 39 



does not become zero every surge as when a = b, its minimum value 

 being 



which = 0, as it ought, when a = b. 



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



iZjff^fl-^sin^^sin^'^^) 



and ^K,E^ x 4 ^ sin^ ^ sin^ ''•^ t, 



showing that the energy which surges into, and out of, each circuit is 

 equal to 



iKiE^ X ^ sin2 xl^ = 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 desired result can be very approxi- 

 mately 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 

 adjustment of the circuits. 



As examples, three cases will be briefly considered. Many ^ch 

 cases will present themselves or arise in practice. 



(a) Let us investigate the conditions for obtaining the greatest 

 maximum amplitude of V2, the P.D. of the secondary condenser, for 

 a given initial value, E, of Fj. 



By equations (I) § 5 the max. amp. is equal to 



c Li 



M 



For this to be a maximum, if — be given, h/c must be a maximum. 



^1 



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

 the ratios 



M : Ly : ij ^.re given. 



