251, 252] ELECTROMAGNETIC WAVES. 527 



The experiments of Hertz* confirmed the above results, the 

 boundary of the conductor being more nearly a node for the electric 

 than for the magnetic force. If the amplitude of the reflected 

 waves approaches that of the direct ones, the two systems will 

 interfere and produce a set of standing waves, with nodes at regular 

 distances from the conductor. This field was explored by Hertz 

 by means of a resonator, composed of a circle of wire with its ends 

 terminating in two small balls near together, constituting a con- 

 denser. This system has a certain period of its own, and what has 

 been said in 240 applies to it. It was tuned to the period of 

 the waves, and being placed anywhere in the field would have 

 currents induced in it by the harmonic electromotive forces of 

 the field. 



Thus where the force is a maximum sparks appear between the 

 balls of the resonator, disappearing at the nodes. For the further 

 theory of the resonator the reader is referred to Poincare, Les 

 Oscillations Electriques, J. J. Thomson, Recent Researches in Elec- 

 tricity and Magnetism, and Drude, Physik des Aethers, 



252. Spherical Oscillator. We have hitherto considered 

 waves in insulators, without considering how they are produced. 

 In the experiments of Hertz the waves were produced by disturb- 

 ing the charges in a peculiar dumb-bell-shaped conductor, and 

 allowing oscillations to set in, which were propagated outward 

 through the air. A satisfactory theory of the oscillations in Hertz's 

 oscillator has not been given. We may state the general problem : 

 given a charge disposed in any manner not in equilibrium upon a 

 conductor of any form, find the nature of the oscillations that 

 ensue while the conductor is settling down to its state of equi- 

 librium, together with the fields to which they give rise. This 

 problem is a very complicated one, and has been solved for very 

 few cases. We shall consider the case of a conducting sphere, 

 the charge upon which is that induced by placing the sphere in a 

 steady uniform electric field. The field is supposed suddenly 

 destroyed, and the charge then oscillates until equilibrium is 

 attained. 



We shall suppose e = /A = 1. 



* "Ueber elektrodynamische Wellen im Luftraume und deren Reflexion." Wied. 

 Ann. 34, p. 609, 1888. 



