27G Dr. J. W. Nicholson on the Bending of 



5. W. Jaeger and St. Lindeck. Zeitschr. f. Instrumentenk.,. 



xxi. p. 33 and p. G5, 1901. 



6. H. C. Bijl. Zeitschr. f. physik. Chemie, xli. p. G41, 1902. 



7. W. Jaeger. Zeitschr. f. physik. Chemie, xlii. p. 632, 1903. 



8. Puschin. Zeitschr. f. anorg. Chem., xxxvi. p. 201, 1903. 



9. H. von Steinwehr. Zeitschr. f. Instrumentenk., xxy. p. 205, 



1905. 



10. F. E. Smith. Report Elec. Stands. Committee: B. A. Beport, 



1905. 



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3908. 



12. F. E. Smith. Phil. Trans. Boy. Soc, ccvii. p. 393, 1908. 



13. H. Tinsley. The Electrician, lxi. p. 821, June 12, 1908. 



14. F. A. Wolff. Bull. Bureau of Standards, vol. v. no. 2, p. 309, 



1908. 



15. P. Janet and B. Jottast. Bull de la Societe internationale des 



Electriciens. Aug.-Sept. 1908. 



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p. 359, 1909. 



XXY. On the Bending of Electric Waves round the Earth. 

 Bij J. VY. Nicholson, M.A., D.Sc* 



A CONSIDERABLE amount of discussion has taken place 

 in recent years concerning the extent to which the 

 results of experiments in wireless telegraphy can be ex- 

 plained by the diffraction round the surface of the earth, of 

 the waves sent out by an oscillator. No satisfactory con- 

 clusion has as yet been reached. About eighteen months 

 ago, in the course of some investigations on diffraction of 

 electric waves, the writer completed an estimate of the 

 intensity, to be expected from theory, caused by an oscillator 

 placed on the surface. This investigation has not 3-et been 

 published, but as a treatment of the same problem by 

 M. Poincare, which contains a flaw in the mathematical 

 work rendering the results erroneous even in their order of 

 magnitude, has recently been given f, it seems desirable to 

 state at once the results which follow when this flaw is avoided. 

 The method adopted by M. Poincare is in the first place to 

 express the force round the surface of the earth, regarded as 

 a sphere of perfect conductivity, in the form of an integral of 

 Fredholm's type. This is subsequently reduced to a series, 

 proceeding in zonal harmonics, the coefficient of a typical 

 harmonic of order n being a complicated function of the two 

 kinds of Bessel function of order ?n = w-fj, and of their 

 derivates. If X be the wave-length of the vibration, a the 



* Communicated by the Author. 



t Comptes Rendn?, Stance de March 2£th. 1909, and other notes. 



