68 Banding of Electric Waves round a Large Sphere. 



of quantitative measurements of! the effect at the receiver for 

 different distances from the sending apparatus, But when 

 such measurements are available, it will be possible to decide 

 at once what proportion of the observed effect is due to 

 diffraction round the surface. That diffraction may be a 

 very important factor for small orientations is not con- 

 tradicted by the above figures, although the investigation by 

 Sommerfeld* of the effect of conduction through the earth 

 must be borne in mind. 



But the smallness of the numbers corresponding to larger 

 orientations shows very clearly that, as already pointed out, 

 diffraction must be a relatively insignificant agency in the 

 success of experiments such as those of Marconi. For 

 example, the ratio of the energy falling in unit time on a 

 receiver at a distance of 2000 miles, to that falling oil the 

 same receiver at a distance of 70 miles, if diffraction alone 

 were the agency, would be of order 10~ 12 . It is improb ible 

 that any receiver could be sensitive enough to record so 

 small an effect, and we are compelled to seek an explanation 

 of the experiments elsewhere. Two alternatives have been 

 proposed. The first is that of Sommerfeld, who, by taking 

 an infinite plane to represent the surface of the earth for 

 convenience of mathematical analysis, concludes that the 

 finite conductivity of the earth may be sufficient to account 

 for experimental success. But the simplification thus intro- 

 duced into the analysis may render the results, at the same 

 time, inapplicable to large orientations, and for these great 

 distances a more rigorous investigation is desirable. Un- 

 fortunately the method used by Sommerfeld does not appear 

 to be applicable to the case of an obstacle with a spherical 

 boundary. The other alternative is the hypothesis that 

 upper layers of the terrestrial atmosphere may, by being- 

 rendered conducting, reflect back to the earth the radiation 

 which they receive from the sending apparatus. This 

 seems to furnish a hopeful line of attack on the problem, 

 and the view is supported by several known experi- 

 mental results, in particular by the difference experienced 

 in signalling- bv night and by dav. But no investigation 

 of the matter from a theoretical standpoint has yet been 

 published. 



The next section of the paper is concerned with the deter- 

 mination of a higher approximation to the effect in the region 

 previously called the " region of brightness." 



* Ann. der Phjs. 1909, March 1G. 



