Electric Waves round a Large Sphere. 517 



this ratio is very large. This problem has been attacked by 

 more than one investigator, but no quite satisfactory solution 

 has been obtained. Lorenz*, in a discussion of the problem 

 of the incidence of light on a transparent sphere, indicated 

 a mode of obtaining a first approximation to the solution. 

 But his method is not sufficient for the treatment of many 

 important problems, including that of the bending of electric 

 waves round the earth. This special problem has given rise 

 to some discussion. Macdonaldt deduced, for a source 

 situated on the surface of a perfectly conducting sphere, an 

 effect at a great orientation from the source, of the same 

 magnitude as though the sphere were absent. But Lord 

 Rayleigh J pointed out that this result was not in accord with 

 optical experience, for the ratio of diameter to wave-length 

 is about the same in Marconi's experiments as for visible 

 light incident on an opaque sphere of an inch diameter. 

 Even for a highly polished spherical obstacle, the light does 

 not sensibly creep into the dark space in this case. Lord 

 ftayleigh further suggested that the important terms of the 

 harmonic series would probably have an order nearly equal 

 to kc, where 2irjk and c are respectively the wave-length of 

 the vibration, and the radius of the sphere. Taking account 

 of this flaw, which was also independently pointed out by 

 Poincare §, and employing some results from Lorenz's paper, 

 Macdonald subsequently || investigated the effect close to the 

 surface of the conductor, and found that the first order effect 

 was zero at a finite angular distance from the oscillator, in 

 harmony with experimental fact. But the problem still 

 remains whose object is to determine the actual amount of 

 diffraction taking place. A recent investigation by M. 

 Poincare IF has been the subject of previous notes**. 



The corresponding acoustic problem has been investigated 

 by Lord Rayleighff when kc is as large as 10, but, as he 

 suggests, although this case clearly indicates the formation 

 of the sound shadow, it probably throws little light upon 

 what happens when kc is really large. 



The object of this communication is to indicate a method 

 capable of finding the solution of all problems of this class 

 for which an harmonic series can be obtained, and to examine 



* CEnvres Scientifigues, i. p. 405. 

 + Proc. Roy. Soc. 1903, lxxii. 

 X Proc. Roy. Soc. 1904, lxxiii. 

 § Ibid. |j Ibid. 



•f[ Comptes JRendus, April 29, 1909, and other dates. Rendiconti del 

 Circ. Mat. di Palermo, Marzo-Aprile 1910. 

 ** Phil. Mag. Feb. and March 1910. 

 ft Phil. Trans. 1903. 



