26 g ME. J. C. MAXWELL GARNETT 



It has been shown that the optical properties of a metal, so diffused in vacuo (v = 1) 

 that p. has some definite value, are the same whether the microstructure be amorphous 

 (molecularly sub-divided) or consist of small spheres, these optical properties being 

 in either case deducible from equation (7), p. 241.* If then, in accordance with the 

 notation adopted in the former communication (pp. 403 et seq.), the accents' hitherto 

 used to denote the optical constants, n and HK, when p. differs from unity, be now 

 omitted, and the values of those constants corresponding to any particular value /*' 

 of p be denoted by a suffix (e.g., HK^^), the values of n and HK are given by 

 equation (17), p. 404, t namely, 



a ; 



where, as in equation (13'), p. 403, t 



- { n'(K'-l)-2}' + 4nV > K(^-l)-2 



By these equations the values of n and UK, determining optical properties of 

 amorphous or " small-sphere " metallic media of any density, may be calculated for 

 light of wave-length X, in terms of the values of n^ =l and of nK IL=l for the same mono- 

 chromatic light. The values of n and of UK for gold and for silver have already been 

 calculated for all values of \L in the case of red light (X = '630) and in that of 

 yellow light (X = '58 9). The results are given in Table IV. of the former com- 

 munication. | But in order to obtain a true conception of the colours of such media, 

 corresponding calculations must be effected for other colours also. 



Now, in the case of silver, the numerical values of all those functions of HK^I and 

 M=1 which have hitherto been calculated for the case of v = 1 those functions, in 

 fact, which relate to molecules or small spheres of silver in vacuo vary continuously 

 from red (X = -630) to blue (X = '450). If, therefore, the values of n and UK 

 corresponding to X = '450 and X = '500 be now calculated for all values of p., the 

 values of n and n/c for other colours may be obtained approximately by interpolation 

 between X = '630 and X = '450. 



The values of n and UK corresponding to X = '450 and X = '500 have therefore 

 been calculated for certain values of /A, by means of equations (18) and (19). The 

 values of ?i/c /1=1 and n^ =l used for the calculations were carefully determined by 

 B. S. MINOB. The results are tabulated below (Table VIII.). 



In the case of gold it is not so easy to apply this method of interpolation. 

 The values of n and HK corresponding both to blue (X = '458) and to green (X = '527) 



* 'Phil. Trans.,' A, 1904, equation (16), p. 403. 



t ' Phil. Trans.,' A, 1904. 



I ' Phil. Trans.,' A, 1904, p. 406. 



Loc. cit. (vide ante, Table II). 



