Electric Waves round a Large Sphere. 537 



Thus in the transition, the value of n given by 



n + ±/z = x - sin 0/(1 — 2c cos + c 2 ) 1 * 



must make z — n — \ of higher order than z%. 



In the case of electric waves and the earth, or of visible 

 light and a sphere of an inch diameter, z is about 10 6 , and 

 one order higher than zi is sufficiently represented by 

 10 3 or zk. 



Now 





z — n — f 



1 -sin 0/(1— 2c cos + e 2 )* 



leading to c = cos 6 ±2z~i sin (65) 



This defines the exterior of a double cone whose axis is along 

 the oscillator, and whose semi- vertical angle is the complement 

 of tan -1 2z~K For the numerical case in question, this angle 

 is about two degrees. 



Deep 



Shado, 



Thus the transitional region does not extend more than 

 about two degrees on either side of its axial plane through 

 the oscillator. 



It will be shown in a subsequent communication that this 

 region consists of a series of true diffraction bands determined 

 by the maxima and minima of an Airy's integral, and that 

 behind it, there is a very dense shadow. 



Trinity College, Cambridge. 



