764 Bending oj Electric Wdiies round a Large Sphere-. 



of orientation 6 on the surface was, by (99), 



A = F(^)-t(27rsin^/3-^-W^ . . (188) 



where ka is z as usual. 



The amplitude at distance r and orientation 6 is ac- 

 cordingly 



a f{^y^(^y^co^ a ?i . . (189) 

 where by (183) and (186) 



R B= ^r(i)/3V. 



Finally* therefore^ the amplitude in the shadow becomes 

 T (sin 0)^1-^ * •">, (190) 



where £=-696, and o- = 2*3"tt*//8 */r(£). 



Thus the magnetic force at a great distance is inversely 

 proportional to r, as it should be. 



The numerical value of o- is 3'21. 



The mode of derivation of this formula is still valid for 

 points near the axis of the shadow, where = tt, and we con- 

 clude that the effect on the axis is absolutely zero^ as it would 

 be if the sphere were absent. This result has an analogy with 

 the usual geometrical theory of Poisson's disk, on which 

 plane waves impinge. In the axis of the shadow thrown by 

 the disk, there is an effect of the same order as though the 

 disk were absent. ^The theoretical description of this pheno- 

 menon was one of the earliest successes of the wave theory 

 of light. A description of the phenomenon on the strict 

 basis of the electromagnetic theory has not been given. 



When plane waves fall on a large conducting sphere, the 

 results of an Unpublished investigation by the writer indicate 

 brightness on the axis of the shadow^ which should be capable 

 of experimental detection at a sufficient distance. This 

 experiment has been performed by Lord Rayleigh *, who 

 found a bright spot on the axis, at a sufficient distance, 

 which could be clearly seen with a magnifying lens. 



Accordingly, there is an essential difference between the 

 cases of incident plane waves> and of a Hertzian oscillator 

 placed close to the sphere > in so far as the axis of the shadow 

 is concerned, but in each case the effect has the same 

 character as though the sphere were absent; 



* Vide Ptde. itov. Sdc. 19()4. p. 40. 



