292 



NATURE 



[November 7, 1912 



of electric force in crossing the boundary. It is bent 

 away from or towards the normal, and if K, and K, 

 are the dielectric constants and 6^ and 9, the angles 

 the line makes with the normal, then 

 K, cot«, = K, cot«„. 

 The law of refraction of light is 



/*, sin ej=iU, sin 9,. 

 Hence, in the case of light, the velocities of the rays 

 in the two media respectively are proportional to the 

 sines of the angles of incidence and refraction. In 

 the case of the electric force, the velocities are inversely 

 as the square roots of the tangents of the angles of 

 incidence and refraction of the lines of electric force. 



If, then, we consider a Hertzian oscillator which is 

 partly in one medium and partly in another of greater 

 dielectric constant, there will be a distortion at the 

 boundary of the loops of electric force which are 

 thrown off at each oscillation. If the upper medium 

 is air and the lower medium is a material of greater 

 dielectric constant, then corresponding to a normal 

 semi-loop of electric force or air, there will be a 

 completing semi-loop in the other material which is 

 sheared backward, as shown in Fig. i. If in the air 

 at the boundary surface the force is normal to the 

 surface, it will not be normal 

 just below that surface in the 

 medium of greater dielectric 

 constant. It \vill have a longi- 

 tudinal component. As the 

 oscillations take place, these 

 longitudinal components of the 

 force are periodic in space and 

 time, and constitute the sur- 

 face wave which is similar to 

 f"^ I- the electric waves produced on 



wires. 

 If the earth were a perfect conductor, say, a ball 

 of copper at the absolute zero of temperature, these 

 surface waves would be confined merely to the surface 

 skin. In the case of the actual earth, even sea water 

 is a sufficiently poor conductor to allow the penetra- 

 tion of the surface wave to some little depth in it. 

 Although the "numerical distance" is small, it is not 

 so small as to extinguish altogether the surface wave. 

 The objection has been raised (see Dr. Eccles, The 

 Electrician, April 5, 1912, vol. Ixviii., p. 1064) that 

 no experimental proof has been given of the actual 

 existence of Sommerfeld's surface waves. Against 

 this it should be noted that Sommerfeld has carefully 

 explained that the surface waves are not separated 

 sharply from the space waves, and may be regarded 

 merely as a particular distribution of the moving 

 electrostatic field near the common surface of the air 

 and earth and accompanying electric currents in the 

 earth. It is easy to prove that we can have surface 

 electromagnetic waves on a sheet, similar in nature 

 to electromagnetic surface waves on wires, of the 

 existence of which we have abundant experimental 

 proof. An argument in favour of the existence of 

 these surface waves may perhaps be derived from the 

 experience that high antennae do not seem necessary 

 for the reception of signals, even over long distances, 

 thus indicating that there is a concentrated electric 

 and magnetic field near the surface of the earth. 



P. Epstein has delineated from Sommerfeld's 

 equations a portion of the field of electrostatic force 

 round an oscillator placed first over a perfectly con- 

 ducting earth, and, secondly, over an earth of finite 

 conductivity.'" In the first case the loops of lines of 



1** See P. Kpstein, " Kraftliniendiacramme ffir die Aushreitunc der 

 Wellen in der dralitlosen TeVgraphie bei HTiicli^ichtigunp der lioden- 

 bc^chaffenlieit." Jahrhuch der Drahthscn Tch-^aphie, vol. iv., p. 176. 

 1910. Epstein lias, however, only HelineTted the field in the air. He ought 

 to have indicated the nature of t^e fie'd iu^t helow the Mirfare in the sea or 

 earth, as well as to show the refraction of ihe lines of force at the surface. 



i electrostatic force are seen to terminate perpendicularly 



I on the earth, and are divided symmetrically by the 



I surface plane. In the second case they are distorted 



so that the lines at spaced intervals do not terminate 



1 perpendicularly. If, however, they have a component 



parallel to the earth's surface this is equivalent to a 



combination with a true space or Hertzian wave of a 



surface wave, similar to the electric waves on wires, 



which latter can travel along the guiding surface, 



irrespective of curvature of that surface. 



If these conclusions are valid there is nothing to 

 prevent the surface waves going half round the earth. 

 It may, therefore, be quite possible to communicate 

 by radio-telegraphy direct from England to New 

 Zealand. There is one matter which may be of 

 importance. Since the surface waves started from 

 any one point reach an antipodal point by different 

 paths it may be that unless the position of the receiv- 

 ing station is rightly selected, interference will arise 

 between surface waves reaching it by different lengths 

 of path, and hence extinction of signals for some 

 places but not others in the same region. According 

 to this theory, then, we need not endeavour to explain 

 long-distance radio-telegraphy bv diffraction, because 

 true space waves are very little concerned with it. 



We pass on then to consider the next question, viz. 

 the influence of the nature of the surface in radio- 

 telegraphy — why, for instance, it is conducted with 

 certain wave lengths so much more readily over sea 

 than land. 



This matter has been particularly considered by Dr. 

 Zenneck in an interesting paper. Assuming for the 

 sake of simplicity a plane earth and plane electro- 

 magnetic waves, he discusses the effect of the con- 

 ductivity and dielectric constant of the earth's crust 

 on the wave propagation." 



Starting from the same equations as Sommerfeld, 

 he arrives at an expression which enables him to 

 calculate the damping of the waves along the hori- 

 zontal boundarv surface. He shows that this damping 

 is determined by the dielectric constant and conduc- 

 tivitv of the earth's crust. He calculates the distance 

 the plane wave must travel before its amplitude is 

 reduced to i/e of that at the transmitter, and exhibits 

 the results for various values of the dielectric constant 

 and conductivity in the form of curves. Waves 

 1000 ft. in length over a sea surface would travel 

 10, 000 km. before reduction to i/c in amplitude, but 

 over very dry soil only for lo km. or less. The 

 analysis shows that there is a considerable penetration 

 of the wave into dry soil, but into so good a conductor 

 as sea water the penetration is at most a metre or 

 two. Moreover, Zenneck shows that over sea surface 

 the lines of electrostatic force terminate nearly per- 

 pendicularlv to it, but over a dry surface this is not 

 the case. There is then a considerable rotating com- 

 ponent, and the direction of the electric force is repre- 

 sented by the rotating radius vector of a semi-ellipse, 

 the major axis of which slopes forward in the direction 

 in which the wave is travelling. Zenneck's results 

 have been extended by F. Hack, who has shown that 

 underground moisture has the same effect as surface 

 moisture in preventing degradation of amplitude. 



The general result of these investigations, compared 

 with practical experience, is to show that we can by 

 no means consider the earth to be a perfect conductor 

 in the case of radio-telegraohv, but that it has an 

 extremelv influential action in deerading the amplitude 

 of the waves deforming the travelling electrostatfc 

 field, and in creating a tvne of surface wave which 



Wellen lanes ehen-n T 

 graphic." Aim. drr rh 

 translated, with expo. 

 Function of the Earth i 



;ier Hie Fortpflanrune ebener elektrnmagnetische 

 ilerflai-he nnH ihre fieziehung zur drahtlosen Tele- 

 ■sih\ vol. xx-ii., p. ■84'!. igo7 This paper was freely 

 tory no'es bv J. A. Fleming, entitled "The 

 I Radio-telegraphy." .See Engincerhigy June 4 and 



NO. 2245, VOL. go] 



