266 



NATURE 



[October 31, 1912 



radio-lelegraphic station on the earth's surface. 

 Would there be any light due to diffraction at the 

 equator or even at 45° latitude of this small sphere? 

 It is essentially the province of the mathematical 

 physicists to give us a solution of the above question, 

 but the answer would, I think, be in the negative. 

 To make the case comparable with that of the longest 

 electric waves used for terrestrial radio-telegraphy, the 

 sphere would have to be only the millimetre in 

 diameter. The answer is then not quite so obvious. 



The first attempt at the problem in the case of 

 radio-telegraphic waves was made by Prof. H. M. 

 Macdonald in 1903 and 1904. 



Last year he published a second paper in the Trans- 

 actions of the Royal Society on the same subject. 

 In this last paper a table is given for waves of two 

 wave lengths, viz., o'2 mile and o'25 mile, showing the 

 ratio of the calculated amplitude of the received oscil- 

 lations at a point at certain distances measured along 

 a great circle of the earth to the amplitude which 

 would exist if the earth were absent. For the two 

 wave lengths, and for a distance of 651 miles, the 

 ratios are respectively o'o6 and o'oy, or, say, 1 : 14. 

 It may be remarked, however, that the wave length 

 now used at Marconi's Clifden station in Ireland is 

 nearly four miles, and that the maximum distance at 

 which signals have been received is 6000, and not 600 

 miles. Hence, before Prof. Macdonald's table can be 

 brought into comparison with the latest practice, his 

 wave lengths must be increased twenty times, and his 

 maximum distance ten times.'' 



In this second paper he refers to the previously pub- 

 lished 1004 paper, in which he showed that the effect 

 at a point on a perfectly conducting sphere due to a 

 Hertzian oscillator near its surface was negligible in 

 comparison with the effect which would have been 

 produced at that point if the sphere were removed, 

 when the point is at some distance from the oscillator, 

 and the radius of the sphere is large compared with 

 the wave length. 



The same problem has also been discussed by Prof. 

 H. Poincar^, whose recent decease we have so greatly 

 to deplore, in a series of interesting lectures and 

 papers.' In his latest memoir on the diffraction of 

 Hertzian waves in the Jahrbuch dcr DrahUoscn Tele- 

 s^raphie for iqio, p. 44:;, Prof. Poincard reaches the 

 conclusion that the amplitude of the oscillations at a 

 point on the earth's surface, which is separated from 

 a transmitting station by an angle <6 measured along 

 a great circle through the stations, is proportional to 



_ * 

 nn exnnnontial function e '" ^ uliere w is some 

 numerical constant anfUiis a complex quantity thereal 

 part of which is prooortional to the frequency. This at 

 any rate agrees with one result of practical experience, 

 viz. that to effect radio-telegraphy over long distances 

 large wave lengths are necessary. Rut it is difficult 

 to extract from his conclusions' means to enable us 

 to predict the exact extent to which diffraction really 

 exists for waves two to four miles in length. 



The problem of the bending of electric' waves round 

 the earth has also been discussed by Dr. 1. W. 

 Nicholson in a series of able and critical papers." 



The conclusion arrived at by him after considering 

 the work of Macdonald and Poincar(5 as the result of 



■" See H. M. Macd. 

 iQor^ ; vol. Ixxii.. A, p. 



a'd. Pn 



Ro 



Sor, London, vol. Ivxi., A, p. 551, 



. . - - -onr|„5ions in th- first paoer were 



"(I n some cniici-m hy ' nrrt Rnyl-igli snd Prof. PoincirS. 



Prof H. M. M-.cdo-'aM, "On the Diffr-iclion of Electric Wave'i 



a Perfectly Renectini; Ob-tacle," Tr.ins. Roy. .Soc. London, 1910, 



'";■ '-'-^'•- A. p. IT-). 



5 See Prof. H. Poincar,;, "LaLnmlere l^;lectr!que," vol. iv.. 1008, p. 3^-^, 

 ^'"''',"}, '^ , '*" CmiMcs rrxdus, Ap-il 23, ,009, and Jahyhuch'da- 

 Ptiihilosfn Trlczral>hie. vol. 'v.. p. n^, 1910. 



". See Dr. J. W. Nicholson, I'lM Mag., iq,o. 61I1 ser., vol. xlx.,pp. 276, 

 435, 516, r.i?. 



xo. 2244, VOL. go] 



his own analysis can best be expressed in his own 

 words (see Phil. Mag., vol. xix., pp. 277-278, 1910). 



He assumes that an oscillator is placed near the 

 surface of the sphere with its a.xis radial, and he 

 says : " On the confines of the geometrical shadow 

 within a cone of small angle cutting off but a small 

 portion of the terrestrial surface near the oscillator 

 true diffraction bands are found, arising from terms 

 now important in which the order and arguments are 

 nearly equal. But within the shadow beyond the 

 extreme generators of the cone, the extinction of the 

 waves is very complete." " The harmonics of a high 

 order are found to be so disposed as to neutralise one 

 another in a remarkable way, and the intensity of the 

 diffracted light at a distance of a few thousand miles 

 round the surface sinks to a minute fraction of its 

 value when the sphere is absent. Thus, it is improb- 

 able that diffraction can explain the effects unassisted 

 by reflection from an ionised layer in the upper atmo- 

 sphere, or by some other cause. 



If this result is confirmed for wave lengths of four 

 miles, or one-thousandth part of the earth's mean 

 radius, then it will follow that ordinary diffraction is 

 incapable of explaining long-distance radio-telegraphy, 

 and we must look to some other cause. Before dis- 

 cussing the alternative which has been suggested 

 both by Prof. Poincar^ and Dr. Nicholson, I should 

 like to direct your attention to an explanation of a 

 quite different nature due to Prof. A. Sommerfeld, of 

 Munich. Mathematicians who have dealt with the 

 problem under the assumption of a perfectly conduct- 

 ing earth and a Hertzian oscillator entirely discon- 

 nected from it have assumed conditions which do not 

 hold good in practice. Hence tlie attempt to explain 

 long-distance radio-telegraphy by the aid of diffraction 

 may be a quite unnecessary effort. The actual earth 

 has a crust composed of materials which chiefly owe 

 their conductivity to water. When free from water 

 these materials composing the igneous and sedimen- 

 tary rocks (apart from metallic veins and oxides and 

 sulphides of heavy metals), such as granite, gneiss, 

 quartz, slate, chalk, and sandstone are very fairly 

 good insulators. Although sea water is a conductor, it 

 lias a dielectric constant (K = So) very far from in- 

 finite. Moreover, at no very great depth in the crust 

 the temperature is sufficiently high to exclude the 

 presence of liquid water, and therefore of any con- 

 duction due to it. 



The numerical values which have been given for the 

 materials composing the earth's crust are only very 

 approximate. Experimentalists have mostly measured 

 the resistance and dielectric constant of dry samples 

 with continuous or direct currents. They have omitted 

 to take account of the fact that non-metallic materials, 

 such as quartz, felspar, mica, slate, &c., incref,se in 

 conductivity witli rise of temperature and also have a 

 conductivity for alternating currents quite difTerent 

 from that for direct currents. 



In the majority of cases these rocky materials are 

 very good insulators. Thus dry granite has a di- 

 electric constant about 7 to 8 and a specific resistance 

 which may be as high as one thousand megohms per 

 centimetre cube, and dry slate has a dielectric constant 

 of about 12 and specific resistance of about 500 meg- 

 ohms per centimetre cube.' 



of. 



il.itikonstanle un-t T eitfiihiakeit der Cestelne," hy 

 AiinitUn dcr Phys!k, vol. xxxvi., p. 125. roii, for a 

 lents of the dielectric constants and conductivity of 



t-arth's crust material 



It has been shown r.'cently in a paper hy the present writer, assisted by 

 Mr. Dylse. that the alternatinc current conductivitv of insulators is a 

 Tunction of the freiiuency, and not b" any means identical with the direct 

 cirrent co-du.-ivitv, see Tourn. Inst. Elect. Eng., 1012, "On the power 

 factor and condnrtivitv of dieleclrirs for alternatinc elertric currents." In 

 the case of such substances as marble, slate, and prohahlv others, the con- 

 ductivity appears to increase with the frequency up to a certain point and 

 then diminish a^ain. 



