COLOURS IN METAL GLASSES AND IN METALLIC FILMS. 395 



We have now to see whether by means of these equations (13), and of the values 

 of n and K for various metals, we shall be able to predict the colour of a glass which 

 contains a number of small metal spheres, whose linear dimensions and distances 

 apart are small compared with a wave-length of visible light.- 



In the annexed table the refractive index of the glasses has been taken to be 

 i/= 1-56. 



The values of n~ (* 2 1) and of n~K for the metal are those given by DRUDE 

 ('Physikalische Zeitschrift,' January, 1900), for yellow light (X = '0000589 centim.), 

 and for red light (X. = '0000630 eeutim.). For the potassium-sodium amalgam, 

 however, blue and yellow light were used instead of yellow and red. 



Now let us suppose that /A, the quantity of metal per unit volume, is very small 

 If, then, a and {$ represent the numbers in the penultimate and last columns of 

 Table I. respectively, we have 



/.I / f r-i\ i o '- 1 f o n o 



n" (1 K ~) = V~ + dfJiVOt., 'II ~K 6/jLV-p. 



Hence 



Hence, neglecting higher powers of p, 



.......... (14). 



Now, suppose that light of wave-length X in racno travels through this composite 

 medium, whose constants are n' and K. The light in vacuo being given by 



X = Aexp {2wi(l/T-z/\)}, 

 in this medium it is given by 



so 



that n'' measures the absorption. In fact, the intensity of the light sinks to 

 e-.-s ( _i nearly) of its original value in traversing a distance 



d= - - - = X ( 15 ) 



2nn'K r Qirfjiv/B 



of the medium. 



We have now to apply the formulae to the observations, in order to test the 

 validity of our analysis as regards the actual phenomena. SIEDENTOPF and ZSIGMONDY 

 give ('Ann. der Physik,' January, 1903, pp. 33, 34) a table of various gold gLsses 

 examined by them. This table is reproduced in Table II. 



3 E 2 



