394 MR- J. C. MAXWELL GARNETT ON 



volume of the medium (except when p, is evidently used to denote the thousandth 



part of a millimetre). Thus JJL = - - 9Ja 3 , and equation (10) becomes 



O 



N 2 - l 

 rf/i 2~-~ 



< 10 '>- 



If the metal spheres be situated in glass of refractive index v instead of in vacua, 

 this equation becomes 



(11).* 



The constants ' and K' of the medium thus depend only on /z, the relative volume 

 of metal, and not on the radii of the individual spheres. It is clear that the spheres 

 may now be supposed to be of quite various radii, provided only that there be many 

 spheres to a wave-length of light in the medium. 



We have given the general result which holds for all values of /x, as we shall 

 require it later. But in the case of metal glasses, by which name we shall describe 

 glasses- in which a metal is present in metallic form, the value of p. varies from about 

 10~ l for a silver glass down to about 10~ (i for a soda glass coloured by radium. The 

 last equation giving the optical constant N' = n' (\ i/c') of the metal glass may be 

 written 



2 - 



. . (12), 



where N is the optical constant of the metal and v the index of refraction of the glass 

 by itself. 



5. Equation (12) may now be written 



2m' 



., , n- (/c 2 1) + v- + 2m 2 /c . _ , / ., ^ 

 = 3 p.v- v , ' v , - 3/xv 3 (a 2t/3). 



n~ (K~ 1) 2v~ + 2un~K 



Thus, equating real and imaginary parts, we find, after some reduction, 



= 



4V 



o = 

 ~ 



" [n?.(K 2 ---1.) .- 



f TVT' 1 ' *' "VT"' 2 T 



I Note added IQth May, 1904. This equation may be written ."-, -, =/i *~- .}. 



L W 2 + 2v 2 N 2 + 2i'' ! J 



