['265 ] 



XXXIII. Electric Oscillations in Straight Wires and Sole- 

 noids. By J. S. Townsend, M.A., Wykeham Professor of 

 Physics, Oxford, and J. H. 'Morrell, M.A., Oxford *. 



1. 7T1HE improved methods of generating continuous 



JL oscillations by means of valves provide simple 

 means of investigating an harmonic series of oscillations and 

 free oscillations in circuits with distributed capacity and 

 inductance, such as solenoids and parallel wires. 



The points of resonance and the frequencies of the oscilla- 

 tions may be thus obtained to a higher degree of accuracy 

 than was possible in the earlier determinations, where the 

 resonance effects were obtained with waves emamating from 

 a spark oscillator. 



in some cases the frequencies of a series of free oscillations 

 are almost exactly simple multiples of the lowest frequency 

 of the series, and, as in the mechanical analogy of the vibra- 

 tions of strings, the oscillation of the lowest frequency is 

 generally called the fundamental oscillation and the others 

 the harmonics. This relation does not hold in general, and 

 it is more convenient to denote a free oscillation which may 

 exist independently of other oscillations as a normal mode of 

 oscillation in all systems having distributed inductance and 

 capacity, 



2. When the oscillations are maintained by connecting a 

 circuit consisting of an inductance and a condenser to a valve 

 or an arc, the period of the principal or fundamental oscilla- 

 tion is determined by the product of the self-induction and 

 capacity of the circuit. This oscillation is accompanied by a 

 series of oscillations of smaller amplitude which are true 

 harmonics of the fundamental oscillation, the frequencies of 

 the series being exactly proportional to the numbers 1, 2, 3, 

 etc. The harmonics in these cases are not free oscillations 

 which can exist independently, and are not connected with 

 normal modes of oscillation. 



A simple case of a similar phenomenon in mechanical 

 vibrations is that of a tuning-fork or spring, maintained in 

 continuous vibration by means of an interrupted circuit. 

 Thus, when a fork of low frequency is used to interrupt the 

 current that maintains it in vibration, the interrupted current 

 may be represented by a Fourier Scries of periodic currents 

 with frequencies which are multiples of the frequency of the 

 fundamental note of the fork. In this case sharp resonance 



* Communicated by the Authors. 



Phil. Mag. S. 6. Vol. 42. No. 248. Aug. 1921. T 



