380 Mr. 0. Heaviside on Electromagnetic Waves, and the 



a current from somewhere else, so he suggested two conducting 

 spheres to be connected with the poles of an alternating dynamo. 

 The idea seems to be here that electricity would be forced out 

 of one sphere and into the other to and fro with great rapidity, 

 and that between the spheres there might be condensational 

 waves. 



But in this case, according to the Faraday law of induction, 

 the result would be the setting up of alternatingelectromagnetic 

 disturbances in the dielectric, exposing the bounding surfaces 

 of the two spheres to rapidly alternating magnetizing and 

 electrizing force, causing waves, approximately spherical 

 at least, to be transmitted into the spheres, in the diffusion 

 manner, greatly attenuating as they progressed inward. 



Perhaps, however, there can be condensational waves if we 

 admit that a certain quite hypothetical something called elec- 

 tricity is compressible, instead of being incompressible, as it 

 must be if we in Maxwell's scheme make the unnecessary 

 assumption that an electric current is the motion through 

 space of the something. In fact, Prof. J. J. Thomson has 

 calculated* the speed of condensational waves supposed to 

 arise by allowing the electric current to have convergence. 

 But a careful examination of his equations will show that the 

 condensational waves there investigated do not exist, i. e. the 

 function determining them has the value zerof. 



16. To construct a perfectly general spherical wave we may 

 proceed thus. The characteristic equation of H, the magnetic 

 force, in a homogeneous medium free from impressed force is, 

 by (2) and (3), 



V 2 H = (47r^p + /^> 2 )H (93) 



Now, let r be the vector distance from the origin, and Q any 

 scalar function satisfying this equation. Let 



H=curl(rQ) (94) 



Then this derived vector will satisfy (93), and have no con- 

 vergence, and have no radial component, or will be arranged 

 in spherical sheets. From it derive the other electromagnetic 

 quantities. Change H to E to obtain spherical sheets of 

 electric force. 



This method leads to the spherical sheets depending upon 

 any kind of spherical harmonic. They are, however, too 

 general to be really useful except as mathematical exercises. 

 For the examination of the manner of origin and propagation 



* B. A. Report on Electrical Theories. 



t I ought to qualify this by adding tli.it the investigation seems very 

 obscure, so that although I cannot make the system work, yet others may. 



