242 ME. J. C. MAXWELL GARNETT 



gravity has any known value, are unaltered by a change in the raicrostructure from 

 amorphous to granular.* Or, again, Professor R. W. WOOD'S clouds of sodium 

 vapour, t for which v = I nearly, do not change colour as condensation commences. 



3. Formula? Applicable only when the Volume Proportion of Metal is Small. 



The volume proportion of metal present in all the coloured glasses and colloidal 

 solutions which we shall discuss below is small. We proceed to obtain, from 

 equations (4) and (6) above, expressions for the optical constants of media, such as 

 glass or water, holding in suspension metal in the amorphous and granular states. 



Let N" EE n" (I LK") denote the optical constants of the compound medium when 

 the metal is in the amorphous state in true solution. Then, replacing N' by N" in 

 equation (4), we have 



2 say. 



Equating real and imaginary parts, we find that 



, ^(l-*" 2 )-^ K(K 2 +l)} 2 +ft 2 (* 2 -l)(v 2 -2)-2v 2 



2 --* 



(2 + j/V " K(/c 2 -l)-2} 2 +4nV J 



From (8) we have 



n" 2 ( 1 - K " 2 ) = S + (2 + v 2 ) pa', n"* K " = (2 + v 2 ) /*', 

 so that, neglecting ju, 2 , we obtain 



wV = (2 + !/)/?. ^ n" = v {l + (2 + v 2 )/2v 2 . l j M '} .... (9). 



The corresponding values of W = n'(l iK f ), the optical constants when the 

 metal is in the granular state, have already been obtained.! They are reproduced 

 here for convenience of reference : thus 



n' K ' = 3fjL V /3, w' = v(l+|./4) ....... (10), 



where 



a = 



, , 



* For example, the tables given in the previous paper ('Phil. Trans.,' A, 1904, p. 406), and the curves 

 shown (loc. cit., pp. 411-414), as well as the tables and curves given in 10 of the present communication, 

 represent optical properties of the media as /* diminishes from unity to zero, whether that diminution is 

 associated with the formation of small spheres or whether the metal retains its amorphous state throughout 

 the change in /. 



t Brit. Assoc., Cambridge, 1904. 



t Loc. cit., 5, pp. 394, 395. 



