ON COLOURS IN METAL GLASSES, ETC. 239 



The microstructures to be assumed are suggested by the preceding remarks cm 

 crystallisation. Calculations will be made for three types of microstructure, namely, 



(1) amorphous that in which the metal molecules are distributed at random ; 



(2) granular that in which the metal molecules are arranged in spherical groups ; 



(3) spicular* that in which these small spheres are replaced by oblate spheroids. 

 It will subsequently appear that when the surrounding non-absorbing medium is of 

 refractive index unity, an amorphous and a granular microstructure produce the same 

 colours. 



In order to calculate the optical constants the refractive index and the coefficient 

 of absorption which correspond to any given microstructure, it is necessary to know 

 the values of the constants for some standard amorphous state of the metal. Now 

 BEILBY t has shown that the process of polishing a metal surface causes the surface 

 layer to " flow " as a liquid, and thus the polished surface is that of the metal in the 

 amorphous state. It follows that the optical constants which we are to use as 

 data for our calculations should, so far as possible, be those which have been 

 determined by means of reflection from the polished surface of the metal in its 

 normal state according to DRUDE'SJ method, rather than those obtained by means of 

 the light transmitted through thin prisms of the metal, after the method adopted by 

 KUNDT. 



2. Expressions for Optical Constants of Media containing Metal in Amorphous or 



Granular Forms. 



The optical properties of a homogeneous isotropic medium are determined when 

 the values of the refractive index n and the absorption coefficient x, which correspond 

 to light of every frequency, are known. We proceed to obtain the values of n and HK 

 for a substance composed of molecules of metal embedded in an isotropic non-absorbing 

 medium, the microstructure being amorphous. 



Consider then a medium consisting of one substance A, in solution in another C, so 

 that the molecules of each substance are distributed at random. Let the number of 

 molecules present per unit volume in the standard amorphous forms of A and C be 

 respectively 9tf A and 9R C , and let the number of molecules present per unit volume of 

 the composite medium be MA^A an d /AC^C respectively. We shall assume /A A and p. c to 

 be constant throughout the medium ; or, more precisely, we assume that a length ?, 

 very small compared with a wave-length of light, can be found such that, for all 

 values of r greater than r , the number of molecules of A contained by a spherical 

 surface situated wholly within the medium having a radius r and its centre being 



* The calculations for a spicular microstructure are reserved for subsequent publication, see note p. 241. 

 t Loc. cit., Lord KAYLEIGH (Royal Institution Lecture on Polish, March, 1901) also holds the view that 

 the process of polishing is a molecular one. 

 J 'Ann. der Phys.,' XXXIX. (1889). 



