ELECTRIC WAVES OVEE THE SURFACE OF THE EARTH. 107 



homogeneous conductor, surrounded by homogeneous dielectric, the separating surface 

 being a perfect sphere. (2) The sending apparatus is represented by an ideal 

 Hertzian oscillator, or vibrating electric doublet, situated in the dielectric near to the 

 separating surface, and having its axis directed normally to that surface. (3) The 

 waves emitted by the oscillator are taken to be an infinite train of simple harmonic 

 oscillations of a definite frequency. The problem is to determine, in accordance with 

 these assumptions, the electric and magnetic forces at points in the dielectric, which 

 are near to the separating surface but not near to the oscillator. If this problem 

 were solved satisfactorily we should be in a better position for estimating the degree 

 of success attained by the resistance theory and the diffraction theory ; but it is 

 precisely in regard to this problem that discordant results have been obtained. This 

 unfortunate state of things has arisen partly from the attempt to separate the effects 

 of resistance from those of curvature. With a view to ascertaining the effect of 

 resistance it has been proposed to simplify the problem still further by treating the 

 surface of the earth, in the first instance, as plane, and afterwards attempting to 

 estimate the modification of the results that would be necessary in order to take 

 account of the curvature. When the effect ot curvature is being investigated it is 

 usual to regard the material of the earth, in the first instance, as perfectly conducting, 

 and afterwards to estimate the correction due to resistance. Thus we have a division 

 of the problem into two : the problem of the imperfect conductor with a plane surface, 

 and the problem of the perfect conductor with a spherical surface. It will appear in 

 the sequel that this division of the problem is unnecessary. 



3. Current ideas on the subject have been much influenced by the results of two 

 simple limiting cases of the general problem. In one of these the material is 

 considered as perfectly conducting, the separating surface as plane, and the 

 originating doublet as situated on the surface. In this case the waves in the dielectric 

 are exactly the same as if there were no conductor.* The amplitude is subject to 

 diminution through spherical divergence only, so that at a distance from the 

 originating doublet it is inversely proportional to the distance. 



In the other limiting caset the distance from the originating doublet is supposed to 

 be so great that the waves can be treated as plane, and the separating surface is also 

 taken to be plane. Then, owing to resistance, the planes of the waves are slightly 

 inclined to the plane boundary, energy being continually supplied from the dielectric 

 to maintain the alternating currents in the conductor, and thus the amplitude of the 

 waves in the dielectric is subject to diminution expressed by a factor of the form e~ Al , 

 where x is a co-oi'dinate measured along the plane boundary in the direction of 

 propagation. The constant A depends on the resistance and specific inductive 

 capacity of the conductor, and on the wave-length. For low resistances, such as that 

 of sea- water, and large wave-lengths, such as one or more kilometres, it is nearly 



* Cf. J. A. FLEMING, 'The Principles of Electric Wave Telegraphy,' London, 1906, p. 347. 



t See ZENNECK( 5 ). 



P 2 



