106 PROF. A. E. H. LOVE ON THE TRANSMISSION OF 



that have been obtained are somewhat discordant. In these circumstances it appears 

 to be desirable to undertake a critical survey of the question. 



The various theoretical investigations may be classified as developments of three 

 suggestions: (l) The imperfectly conducting quality, or resistance, of the material, 

 generally sea-water, over which the transmission takes place, may cause the effect 

 observable at a distance to be greater than it would be if the material were perfectly 

 conducting. (2) Owing to the numerical relations connecting the actual wave-lengths 

 used in practice, the size of the earth, and the distances involved, the amount of 

 diffraction, even in the case of perfect conduction, may be greater than would, at first 

 sight, be expected. (3) Transmission through the atmosphere may be notably 

 different from transmission through a homogeneous dielectric. We may refer to these 

 suggestions briefly as the " resistance theory," the " diffraction theory," and the 

 " atmospheric theory." It may be said at once that the atmospheric theory has 

 arisen from the alleged failure of the other two, and that it has not yet been 

 formulated in such a way as to admit of being tested in the same precise analytical 

 fashion as they can. It is still rather speculative and indefinite. In what follows 

 I propose to attend chiefly to the first two suggestions, and to investigate the result 

 that can be obtained by combining them. 



To facilitate reference the following list of some of the principal writings on the 

 subject is prefixed. These will hereafter be cited by the numbers placed before them, 

 thus : " MACDONALD (')." The list does not pretend to be complete : 



O MACDONALD, H. M., ' Proc. Roy. Soc.,' vol. 71 (1903), p. 251. 

 (-) RAYLEKJH, Lord, 'Proc. Roy. Soc.,' vol. 72 (1904), p. 40. 



( 3 ) POINCARK, H., 'Proc. Roy. Soc.,' vol. 72 (1904), p. 42. 



( 4 ) MACDONALD, II. M., 'Proc. Roy. Soc.,' vol. 72 (1904), p. 59. 



( 5 ) ZENNECK, J., ' Ann. d. Phys.' (4te Folge), 13d. 23 (1907), p. 846. 



( 6 ) SOMMERFELD, A., 'Ann. d. Phys.' (4te Folge), Bd. 28 (1909), p. 665. 



('} MACDOXALD, H. M., 'Roy. Soc. Phil. Trans.' (Scr. A.), vol. 210 (1911), p. 113. 



(*) POINCARK, H., 'Rund, Circ. Mat. Palermo,' t, 29 (1910), p. 169. 



( 9 ) NICHOLSON-, J. W., 'Phil. Mag.' (Ser. 6), vol. 19 (1910), p. 516; vol. 20 (1910), p. 157; 



vol. 21 (1911), pp. 62, 281. 



( 10 ) NICHOLSON, J. W., 'Phil. Mag.' (Ser. 6), vol. 19 (1910), p. 757. 

 ( u ) MACDONALD, H. M., 'Proc. Roy. Soc.' (Ser. A), vol. 90 (1914), p. 50. 

 H MARCH, H. W., 'Ann. d. Phys.' (4te Folge), Bd. 37 (1912), p. 29. 



( 13 ) RYBCZYNSKI, W. vox, 'Ann. d. Phys.' (4te Folge), Bd. 41 (1913), p. 191. 



( 14 ) AUSTIN, L. W, 'Bulletin of the Bureau of Standards (Washington),' vol. 7, -No. 3 (1911), 



p. 315. 



( 15 ) HOGAN, J. L., 'Electrician,' August 8, 1913. 



( 16 ) ECCLES, W. H., 'Proc. Roy. Soc.' (Ser. A), vol. 87 (1912), p. 79. 



( 17 ) "Report of a Discussion," 'Brit. Assoc. Rep.,' 1912, p. 401. 



( 18 ) ZENNECK, J., 'Lehrbuch der Drahtlosen Telegraphic,' 2te Aufl. (Stuttgart, 1913). 



2. In order to simplify the problem and render it definite, certain assumptions are 

 usually made. These may be stated as follows: (l) The earth is taken to be a 



