JLov) Frequency and their Resonance. 331 



is 256 per second, make the condenser capacity larger and 

 larger until the deepest note in the telephone (in our case 256), 

 comes out strongest. It is easily recognized, for the difference 

 between the sound of the telephone with the upper harmonics 

 strongly represented and the sound without them, is just about 

 the same as between the sound of a clarinet and that of a 

 drum when playing the same note. Having done that, I then 

 move the iron core of the auxiliary condenser until the tele- 

 phone sounds loudest. The circuit is then in resonance with 

 the fundamental harmonic. 



An interesting phenomenon is observed during the first part 

 of the tuning process. While plugging the condenser, so as 

 to bring the capacity nearer and nearer to the point of reson- 

 ance, a certain point is reached, when taking out a condenser 

 plug is followed by a bright, snapping, spark. The spark is a 

 sign that the point of resonance is very near, for resonance pro- 

 duces a difference of potential between the condenser plates 

 which is many times higher than the amplitude of the impressed 

 electromotive force. I proceed to consider this phenomenon 

 a little more fully. 



Case I.— Method of Tuning for the purpose of producing a high 

 rise of potential at the Condenser plates. 



When resonance is established the ratio of the amplitude E 

 of the impressed e. m. f. to the amplitude E, of the difference 

 of potential at the condenser plates is given by 



E ; _ 10 6 



Where C is the capacity of the condenser in micro-farads, 

 R the resistance in ohms and T the period in seconds. 

 On the other hand, 



T=-, VLC 



Hence 



E, 2;tL Inductance 

 E^~~ TR' — Resistance 

 If the priocl T = T io and E = 5 volts, then 

 27TX400XL 



Hence to get the rise in potential as large as possible it is 

 necessary to make the resistance as small, and the coefficient of 

 self-induction as large as mechanical (and financial) considera- 



