488 THE ELECTROMAGNETIC FIELD. [PT. III. CH. XII. 



We have in this case a type of the very important class of 

 phenomena known as electrical oscillations, of which we shall 

 presently give the general theory. The theory here given was 

 published by Lord Kelvin* in 1855 and by Kirchhofff in 1864. 

 The theory was confirmed experimentally in a qualitative manner 

 by FeddersenJ in 1857, by observations on the electric spark 

 arising when a Ley den jar is discharged, and by Helm hoi tz in 

 1869, and Schiller || in 1874, under conditions admitting of quan- 

 titative results. More exact determinations in absolute measure 

 have been made by Lodge and Glazebrook by a method involving 

 the spark, and by the author, by a method similar to that of 

 Helmholtz. 



We have seen that the occurrence of oscillations is due to the 

 presence of both kinetic and potential energy. If there is no 

 kinetic energy, L 0, and we reach the case treated in 207, while 

 if there is no potential energy, we have the case of 237, to which 

 we may pass by putting K = oo . A mechanical model of an 

 oscillation may be obtained from any mechanical system possessing 

 both potential and kinetic energy, such as a pendulum or a heavy 

 body moved by a spriog. The stronger the spring the quicker is 

 the oscillation, so that we may assimilate the reciprocal of the 

 capacity of the condenser to the elasticity of the spring. The 

 self-inductance of the system, on the other hand, is the analogue 

 of the mass, or inertia of the mechanical system. The analogy 

 of the resistance may be obtained by making the system move in 

 a viscous medium, so that the motion is retarded by a force 

 proportional to the velocity. 



240. Periodic Electromotive force. Resonance. If 



into a circuit joined to the plates of a condenser is introduced 

 a harmonically-varying electromotive force, we have for the cur- 

 rent, instead of (4) of the preceding section the equation 



cos cot. 



(i) L -J- + RI + -JJ: lldt = 



* Thomson, " On Transient Electric Currents," Phil Mag. June 1853 ; Math. 

 and Physical Papers, Vol. i. p. 540. 



t Kirchhoff, " Zur Theorie der Entladung einer Leydener Flasche," Pogg. Ann. 

 Bd. 121, 1864 ; Ges. Abh. p. 168. 



I Feddersen, "Beitrage zur Kentniss des elektrischen Funkens," Dissertation, 

 Kiel, 1857; Pogg. Ann. 103, p. 69. 



Helmholtz, "Ueber elektrische Oscillationen," Wissemch. Abh. Bd. i. p. 531. 



|| Schiller, Pogg. Ann. 152, p. 535. 



