ON COLOURS IN METAL GLASSES, ETC. 241 



Substituting these expressions in equation (I) we obtain 



N /2 -l N A 2 -1 N c a -l 

 N' 2 +2 ~ MA N A 2 +2 +Mc N c 2 +2 ' 



If, now, we suppose that C is a transparent isotropic substance of refractive index v, 

 and that A is a metal, we have, by omitting the suffix A and putting /u, c = 1 ft, 



N /2 -l N 2 -l , .v 2 -! 

 N' 2 +2 /A N 2 +2 +( M V+2' 

 or, 



22 , 



N' 3 +2 

 When fj, is very small this equation becomes 



......... (4). 



These equations give the optical constants of the metalliferous medium in the 

 amorphous state. When the microstructure is granular, these equations (3) and (4) 

 are, as has been already shown,* replaced by 



N' 2 -V = _N 2 -v 2 /r , 



N' 2 +2v 2 I 

 so that when p. is small, 



Comparison of equations (3) and (5) shows that the optical properties of a 

 metalliferous medium, containing a given volume proportion ju, of the metal, vary 

 according as the metal is in small spheres or in a state of molecular subdivision, 

 except when //,= !. Thus when metal is in solution in water or glass the colour of 

 the compound medium will change as crystallisation commences. When, however, 

 v = 1, the equations (3) and (5) both reduce to 



N' 2 -l N 2 -l m 



N /2 +2 ^N 2 +2 ' 



It follows that the optical properties of a metal in a state in which its specific 



* Loc. tit., equations (11) and (12), p. 394. The mathematical treatment of the optical properties of 

 media containing minute metallic ellipsoids, instead of the spheres which give the granular microstructure, 

 is under consideration, but, with the exception of the case wherein the volume proportion, p., of metal is 

 small, it is not yet complete. 



[Note added 1st August, 1905. The investigation of the general case (any value of /*) has now been 

 completed. The results for the case when p. is small, which, when this memoir was communicated to the 

 Royal Society, were given in 12, have therefore been reserved for subsequent publication in a more 

 complete form.] 



VOL. COV. A. 2 I 



