Light at certain Metal-Liquid Surfaces. 237 



have the result n = n' ; or, the index of refraction of the 

 liquid calculated by refraction methods should be the same 

 as that deduced from the change of phase and the ellipticity 

 produced by the metal. 



If there are transition layers or films of surface contami- 

 nation present, their effect may be expressed as a correction 

 term to equation (5) as follows : 

 o 



* {Qo =-7ir^r^r (!-*' ^KA) . . . (10)* 

 V K— no sm " <t> 



If we assume that there is but the one transition layer, that 

 between the liquid and the gas film, the value of A will be 



where A. is the wave-length of the light employed, L the 

 thickness, and n 1 the index of the layer. Of course a similar 

 correction term to equation (4) can be written down, but 

 under the assumption that a metal in air possesses no appre- 

 ciable transition layer, that mny be omitted. 



Proceeding now as before, we obtain the equation 



W o§^ q - Qo) =v l-'^w-iy^a+i.VKA). 



Substituting in the correction term the approximate value of 

 VK from (4), 



we have, on expanding and making the substitutions (6) 

 and (7), 



»o=^(l + 8 + ASsinQ); . . . (12) 



o 



Q-Q =-e + AScosQ . . . . (13) 



If we set as before, /i' = S/S (1 + 8), equation (12) can be 

 written 



tt'=7? (l-ASsinQ), (14) 



since both S and AS sin Q are small quantities* 



* Since the results of the experiments I have to report in this paper 

 seem to show that A = for the liquids used, it seems scarcely worth 

 while in this place to devote the very considerable amount of space 

 which would be required, to the derivation of equations (10) and (11). 

 The derivation is given in full in the papers of Drude in Wied. Ann. 

 already cited. 



