ON COLOURS IN METAL GLASSES, ETC. 243 



Thus, when light of wave-length X traverses a thickness d of a metalliferous 



n"n" n'n' 



medium, the intensity of the light is reduced in the proportion* e~ M A or e~ M * 

 according as the metal is in true solution or in spherical aggregates. 



Suppose now that two kinds of monochromatic light, of wave-lengths Xj and X 2 , are, 

 by traversing a distance d in an absorbing medium, reduced in intensity by e~ K<d and 

 e -:M res p ec tively. Then the absorbing medium reduces the proportion of the inten- 

 sities of the two kinds of light in the ratio e~ (Kl ~ v>d , which is a function of d. Thus 

 the tint of a coloured medium, viewed by transmitted light, depends on its thickness.! 

 We shall, however, speak of two absorbing media as possessing the same colour when, 

 whatever be the values of X x and X 2 , the ratio KI : K 2 is the same for either medium ; 

 for, if suitable thicknesses of such media be chosen, the light transmitted by them will 

 be of precisely the same tint. 



Since, therefore, it appears from equations (8) and (9) above that the ratio 



is independent of v, it follows that a niolecularly subdivided metal produces the same 

 coloration (by transmitted light) in all non-dispersive transparent isotropic " solvents," 

 irrespective of their refractive indices. \ Thus, neglecting the small dispersion, a 

 borax bead and a glass bead, each containing a metal in solution, will be of the same 

 colour ; but so soon as crystallisation of the metal begins, so that part of the metal is 

 in small spheres, the beads will cease to be of the same colour, since the ratio 



is not independent of v. 



4. Numerical Values of Optical Constants of Metal Glasses, &c. 



Consider any transparent isotropic non-dispersive medium of refractive index v, 

 containing either molecules or small spheres of a metal, the optical constants of 

 which, for light of wave-length X, are n and UK, the particles of metal being so 

 distributed that there are many of them to a wave-length of light. The 

 "absorptions," nV/X and w'V/X, of the compound medium can be easily determined 

 by means of equations (9) and (10), when the values of a, ft, a!, /3', are known for 

 light of wave-length X. These values can be calculated by means of equations (11) 



* Of. 'Phil. Trans.,' A, 1904, p. 395. 



t Thus, for example, a thin sheet of gold ruby glass will appear pink, a considerable amount of blue 

 light being transmitted, whereas a thick sheet of the same glass will appear deep red, almost like a copper 

 ruby. Again, by increasing the depth of a silver stain on glass, we get all gradations in colour from 

 canary yellow through amber to red. 



| This, then, must be the colour of the vapour of the metal provided that the molecules are monatomic, 

 or, at least, do not dissociate when the metal is vapourised. We shall term it the " vapour colour." 



2 I 2 



