426 M. 1. Pupin — Electrical Oscillations of 



The resonant flow consists in a conversion of electrokinetic 

 into electrostatic energy, and vice versa, during each semi- 

 oscillation, accompanied by a loss due to ohmic resistance 

 which is the only work which the e. m. f. does. The ampli- 

 tudes of the electrokinetic and electrostatic energies must 

 therefore be equal to each other, hence 



4 l/§-Y= i p o 3 c 



where P = amplitude of the potential difference in the con- 

 denser. 



The last relation gives, remembering that owing to resonance 

 p'LG = 1, 



_ _E_ _ ])L _ Indu ctance 

 °">CR~ R Resistance A K ' 



If L and p are large and R small the rise in potential can he 

 made as large as we please, or rather as large as the condenser 

 will stand. 



The analogy between this rise of potential due to resonance 

 and the torsional reaction of the suspension in the resonant 

 swinging of the torsion pendulum mentioned above is striking. 

 In both cases the reaction is produced by an accumulative 

 effect of the impressed force. 



A rough experiment only, bearing on this point and which 

 can be easily repeated in a few minutes in every electrical 

 laboratory, will be briefly described here. 



Two large choking coils and a Marshall condenser were con- 

 nected in series with the secondary of a transformer. The core 

 of the smaller of the two choking coils consisted of a removable 

 bundle of soft iron wire. The condenser terminals were con- 

 nected to a Thomson Electrostatic Yoltmeter. The frequency 

 of the impressed e. m. f. was about 100 periods per second. 

 The capacity of the condenser was adjusted until the removal 

 of the plug was accompanied by bright snapping sparks, which 

 was a signal that resonance was near. Then the removable iron 

 core of the smaller choking coil was moved up and down grad- 

 ually until the Yoltmeter gave the largest deflection. A rise 

 from 60 volts (generated in the secondary and indicated by a 

 Cardew Yoltmeter) to about 900 volts in the condenser was 

 easily obtained. When the impressed e. m. f. was raised to 80 

 the condenser indicated about 1200 volts, which showed that 

 the rise in the condenser was proportional to the impressed e. m. 

 f., as the theory requires.* The rise of potential is practically 



*I feel that it is only just to mention here that Mr. Marshall's ordinary con- 

 densers stood these voltages very well indeed, considering that they are guaran- 

 teed to stand a 1000 volts as their upper limit. 



