COLOURS IN METAL GLASSES AND IN METALLIC FILMS. 393 



neighbouring doublets, be the force causing the polarisation f (t), then we have 

 proved (2) that 



f /A __ ~3 N 1 ,,/ 



' N* + 2 



Now by means of the analysis given by H. A. LORKNTZ (' Wied. Ann.,' 9, 1879, 

 p. 641) and by LARMOR ('Phil. Trans.,' A, 1897, p. 238), and which has been fully 

 verified in LORENTZ'S own paper and by others, it can be proved that (see 7 below) 



provided the medium under consideration extends throughout a space of dimensions 

 which in no direction are of an order of magnitude so small as a wave-length of lifht. 



o o o 



This provision is satisfied except in the case of very thin films. When dealing with 

 such films in a later portion ( 7) of this paper we shall return to the consideration of 

 this point. 



From equation (9) we obtain 



so that 



N- - 



CLERK MAXAVELL'S equations written with Hertzian units for this medium, now, 

 therefore, are 



^ = c curl II and - ? , H = - c curl E, 

 at dt 



where 



e '=(E 



_. . 



We have therefore proved that a medium consisting of small metal spheres 

 distributed in vacuo, many to a wave-length of light, is optically equivalent toji 

 medium of refractive index n' and absorption K' given by N' = n'(l -- IK') = v/e', 

 where 



-^ 



We shall throughout use the symbol /* to denote the volume of metal per unit 

 VOL. com. A. 3 E 



