420 M. I. Pv/pin — Electrical Oscillations of 



Art. LI. — On Electrical Oscillations of Zoic Frequency 

 and their Resonance; by M. I. Putin, Ph.D., Columbia 

 College. 



[Continued from page 334.] 



Part II. Theoretical Discussion with special reference 

 to the Theory of Rise of Potential by Resonance. 



I. Introduction, 



A very faithful mechanical picture of the periodically vary- 

 ing flow in an electrical circuit possessing localized* capacity 

 and self-induction is obtained by considering the motion of a 

 torsional pendulum, that is a heavy bar, say of cylindrical form, 

 suspended on a stiff elastic wire. The moment of inertia of 

 the bar and the elasticity of the suspension wire correspond to 

 the coefficient of self-induction and the capacity of the circuit. 

 The frictional resistance of the air corresponds to ohmic re- 

 sistance, internal friction in the bar and the elastic suspension 

 correspond to magnetic and dielectric hysteresis ; angular dis- 

 placement of the torsional pendulum corresponds to the elec- 

 trical charge of the condenser, and therefore torsional reaction 

 of the suspension to difference of potential between the con- 

 denser plates. Angular velocity in the one case stands for the 

 current in the other, kinetic energy for electrokinetic energy, 

 potential energy of the torsional forces stands for the electro- 

 static energy of the condenser charge. 



In slow mechanical vibrations the decrement of the kinetic 

 energy is chiefly due to external and internal frictional resist- 

 ances. But as the frequency of the vibration increases other 

 losses causing this decrement become more prominent ; so the 

 losses due to radiation in form of sound waves. Similarly in 

 electrical oscillations of very high frequency ; the decrement 

 of the electrokinetic energy due to radiation in form of electro- 

 magnetic waves becomes considerably larger than that due to 

 dissipation in consequence of ohmic resistance, magnetic and 

 dielectric hysteresis. The analogy, therefore, supplied by 

 mechanical vibrations is by no means a poor guide in the study 

 of even very rapid electrical oscillations. For slow vibrations 

 the analogy is very striking and instructive. To return to the 

 torsional pendulum : — 



Let I = moment of inertia of the bar, 



8 = angle of displacement at any moment. 



* The term localized is employed to distinguish the circuits considered in this 

 paper from those electrical circuits in which self-induction and capacity are more 

 or less uniformly distributed over the whole circuit, as, for instance, in the case 

 of a Herzian Resonator. 



