[ 365 ] 



XXXII. On the Propagation of Electromagnetic Waves round 

 the Earth. By Balth. van der Pol, Jun., Bocts. Sc. 

 (Utrecht) *. 



THE theoretical solution of the problem of diffraction 

 round a sphere, surrounded by a perfect insulator, for 

 electric waves emitted from a source close to this sphere and 

 having a wave-length small in comparison with the circum- 

 ference, is of considerable physical importance. For, where 

 a comparison of measurements taken at various points on the 

 earth's surface of the amplitudes of the waves emitted by 

 a transmitting station for Wireless Telegraphy would show 

 that they are not in agreement with the calculated values, it 

 would be obvious that other phenomena than pure diffraction 

 have to be accounted for. That e. g. the electrical conditions 

 of the atmosphere have a pronounced influence on the wave 

 amplitude at big distances is undoubtedly revealed by the 

 fact, that incoming signals from a far distant station are as 

 a rule stronger in night-time than during the day. An 

 annual variation of signal strength in overland transmission 

 has further been found, while very small variations during a 

 solar eclipse are also observed. The measurements of signals 

 received during the dark hours show further appreciable 

 fluctuations, while the daytime measurements are usually 

 more steady. This latter fact suggests that we should con- 

 sider the daytime values of wave-amplitude as " normal " in 

 the sense of probably not being affected by changes in the 

 lower atmosphere which are naturally of a more or less 

 accidental nature. It is the object of this paper to compare 

 these observed normal values with the magnitude to be 

 expected according to the diffraction theory. 



It is, however, obvious that such a comparison cannot be 

 made unless a definite theoretical formula is obtained show- 

 ing the decrease of wave-amplitude with distance in a form 

 admitting numerical interpretation. 



Now expressions for the magnetic force at the surface of a 

 sphere for various orientations from an oscillating dipol w T ere 

 obtained (a.o.) by Nicholson f and Macdonald J, but the 

 numerical values these formulas yield differ to a very great 

 extent. 



An expression for the amplitude of the magnetic force, 

 however, in the form of a rapidly alternating harmonic series 



* Communicated by Prof. Sir J. J. Thomson, O.M., P.R.S. 



t Phil. Mag. (ser. 6) vol. xx. p. 157 (1910) ; vol. xxi. p. 62 (1911). 



\ Proc. Roy. Soc. (ser. A) vol. xc. p. 50 (1914) 



Phil. Mag. S. 6. Vol. 38. No. 225. Sept. 1919. 2 C 



