270 MR. J. C. MAXWELL GARNETT 



have been calculated ; but the values of nK^ =l and n^i used for the purpose are 

 those given by HAGEN and RUBENS,* and are not by any means so accurate as 

 those which MINOR has determined for silver.! The results are included in Table VII. 



We return to the consideration of the transmission and reflection of light by a 

 metallic film. We confine our present attention to films the microstructure of which 

 is either amorphous or consists of small spheres of metal ; the films in question are 

 thus optically isotropic. Suppose that, as explained in the preceding section, the 

 optical constants of the film are n and K when its specific gravity is p. times that of 

 the metal of which it is composed. 



When light of wave-length \ in vacua is directly incident on such a film, ot 

 thickness d, let R ft and T denote the ratios of the intensities of the reflected and of 

 the transmitted light to that of the incident beam. Adopting the analysis already 

 given in the previous paper, p. 409, we suppose the film to be bounded by z = and 

 z = d, and that 



Incident wave is 



E = 0, exp {ij> (tz/<-)}, ; H = -exp {ip (t-zjc}, 0, 0. 

 Reflected wave is 



E = 0, B exp { ip (I + z/c)} , ; H = B exp { ip (t + z/c) } , 0, 0. 

 Wave in film, i.e., hot ween z = and z = d, is 



E = 0, A' exp {q> (/-c/V)} t-B' exp { lp (t + z/V)}, 0, 



H = -c/V[A' exp {tjp(-*/V)}-F exp {q>(f + z/V)}], 0, 0. 



Transmitted wave is 



E = 0, Cexp{ip(*-z/c)},0; H= -(! exp [q, ((-z/c)}, 0, 0, 

 where c/V = H (1 IK). 



We shall suppose:]: that Trdn K /\> 1, so that we shall be correct within 2 per cent. 

 when we neglect B' in comparison with A'. The boundary conditions at 2 = 0, 

 namely the continuity of the components of E and H which are parallel to the 

 interface, then give 



1 + B = A'; (l-B) = e/V. A' = (!-) A'. 

 Eliminating A' we obtain, by taking the squares of moduli, 



* Loc. cit. 



t Cj. above, 4. 



| Of. 'Phil. Trans.,' A, 1904, p. 409. 



