1903.] Electric Waves round a Conducting Obstacle. 25 < 



convenient for purposes of comparison to substitute for Fi in terms of 

 another quantity ; let F 2 denote the electric force clue to the oscillator 

 at a point in its equatorial plane at a distance ciO from the oscillator, 

 which is the same as the arcual distance of the receiver ; then 



F_ _ fleos 2 ^! - sin £0 ) _ 

 f 2 = 2sin £0 = ' 



where F is the amplitude of F, and F 2 the amplitude of F 2 • the ratio 

 of the intensities in the two cases is /j 2 . The following table shows 

 the manner of variation of the amplitudes and the intensity (/j 2 ) near 

 the sphere as increases from 20° to 120° :- — 



d 



1 — sin— 

 2 



Jc 





20° 



-82635 



-80551 



-64885 



25° 



'78356 



-73567 



-54121 



30° 



0-74118 



-69949 



-48929 



35° 



-69929 



-64546 



-41661 



40° 



-65797 



0-59297 



-35162 



45° 



0-61731 



-54070 



-29235 



50° 



0-57738 



-48964 



23975 



55° 



-53825 



-44019 



0-19377 



60° 



0-5 



0-39269 



-15421 



65° 



0*46270 



-34745 



0-12072 



70° 



'42642 



-30473 



-09286 



75° 



0-39127 



-26477 



-07010 



80° 



0-35721 



0-22766 



-05183 



85° 



0-32440 



-19343 



-03741 



90° 



-29289 



0-16266 



-02645 



95° 



-26272 



0-13483 



-01818 



100° 



0-23395 



0-1101L 



0-01212 



105° 



-20664 



-08844 



-00782 



110° 



0-18084 



-06972 



-00486 



115° 



-15660 



-05379 



0- 00289 



120° 



0-13397 



-04050 



-00164 



For example, when = \tt, that is for the case of the earth at a 

 distance of rather more than 3000 miles, the amplitude of the electric 

 force acting on the receiver is more than half the amplitude of the 

 electric force that would be directly due to the oscillator at that 

 distance, and the intensity nearly three-tenths. These results will 

 apply when the two places are separated by good conducting material 

 such as sea water, the effect of the imperfect conduction of such 

 substances being by § 3 negligible. They explain why wireless 

 telegraphy is more effective over the sea or wet soil than over dry 

 soil ; from § 3 it follows that a badly-conducting obstacle diminishes 

 the effect. It is also to be expected from § 2 that the influence of a 



VOL. LXXI. U 



