COLOURS IN METAL GLASSES AND IN METALLIC FILMS. 387 



by an electric field E = ("", 0, 0), is small compared with the wave-length, the 

 electric force due to the sphere is 



E . 3 (K- 



V - e 



By comparing this with HERTZ'S corresponding result 



\ r 



for an oscillating doublet of moment e"*, as given above, it appears from (2) and (3) 

 that the electric and magnetic forces at any point, due to waves emitted by the 

 sphere, must be given by the equations 



E, = V f - (V'n, 0, 0), H, = '-(, f 1 ? , - f " ) . . (4, 5), 



ox c\ ox at oy oil 



where now 



K 1 a :i 

 11 = K + 2 ' r ' eXp ^ ^ ~ r '^' 



Replacing K by N 2 , where N is the quantity defined by equation (1), we conclude 

 that when a metal sphere is excited by a periodic electric force E () , it emits the waves 

 which would be emitted by a Hertzian doublet whicli at time f, was of moment 



equal to 



2 - 3 



N 2 - 1 3 



~ 



The same result can be proved directly by adapting the analysis given by 

 L. LORENZ (' Vidensk. Selsk. Skr.,' Copenhagen, 1890) to the electromagnetic theory. 

 The problem has also been treated by STOKES (' Camb. Trans.,' vol. 9, p. 1, 1849, and 

 ' Papers,' vol. 4, p. 245, p. 262). 



At a great distance from the origin, i.e., when r is great compared with X, 

 equation (4) reduces to [cf. RAYLEIGH, loc. cit., equation (106)] 



7ra- /\>- X1 J x it-\ 



El= * * eXpN;( '" r/C)} ' ' 



If we transform to spherical co-ordinates X, Y, Z in the respective directions of 

 increase of r, 0, <f> (fig. 1) we obtain, at a great distance from the origin, 



l -r/o)} OO.^OM^ 



- 2 

 3 D 2 



