92 Wheeler — Expert mental Investigation on the Reflection 



Expanding the radical and retaining no terms higher than 

 the second in ,* and substituting 



* = -^-5^ («.'-!) cos 2Q (6); 



« = 4 5 ^K i -l)«n2Q; (7) 



we have, on equating the real and imaginary parts of each 

 side, approximately,* 



n = ~(l+8) (8); Q-Q o= _ £ . (9) 



Thus from the observed values of A and 2-^r we can calcu- 

 late, by means of equations (3) and (6) the right-hand side 

 of equation (8). Calling the value so calculated n', we have, 

 n o = 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 contamina- 

 tkm present, their effect may be expressed as a correction term 

 to equation (5) as follows : 



n n S„ 



e'Qo = J . (l-i V K A).f (10) 



V K— n sin 4> 



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

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

 given by 







where X is the wave length of the light employed, L the 

 thickness, and w„ 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 appreciable 

 transition layer, that may be omitted. 



* These approximations are justified by the magnitudes of S and Q as 

 found from experiment. 



f Since the results of tbe experiments I have to report in this paper seem 

 to show that A=0 (for the liquids used, at least), 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 deriva- 

 tion is given in full in the papers of Drude in Wied. Ann. already cited. 



