90 Wheeler — Experimental Investigation on the Reflection 



while its index should be greater when n' is greater than n„. 

 Such effects might possibly be expected as a result of surface 

 tension. 



There are thus two possible explanations of the observed dis- 

 crepancies. It would seem worth while, therefore, to attempt 

 to eliminate the possibility of gaseous films between the mirror 

 and the liquid. The desirability of doing this has been 

 pointed out by Drude,* but so far as lean ascertain, it has not 

 up to the present time been attempted. Drude has expressed 

 the opinion that there would still remain evidence of a transi- 

 tion layer when such gaseous films have been removed. f But 

 this opinion is supported by no evidence which cannot) be 

 interpreted, as we have seen, in another manner. Hence I 

 have attempted, in the investigation reported in this paper, to 

 see if any residual effect of a transition layer remains, when 

 the possibility of the presence of a gaseous film between the 

 mirror and the liquid is reduced to a minimum. 



Theory. 



The theory of metallic reflection in transparent liquids is 

 not developed in any of the ordinary works of reference, 

 though it is, of course, accessible in the original memoirs. So 

 it may not be out of place to give a brief resume of the theory 

 here. We start with the equation 



1 + \.sxbe lA sin d> sin v 



=—^- = -,\ (1) 



1— tgipe lA cos <j> cos x 



where i/r is the azimuth of the restored polarization (the angle 

 whose tangent gives the ratio of the amplitudes of the two 

 components of the reflected vibration when the incident vibra- 

 tion is polarized in a plane making an angle of 45° with the' 

 plane of incidence; tgyjr is what we have called the "ellip- 

 ticity" in the introduction) ; e is the Naperian base; i = i/^i? 

 <t> and x are the angles of incidence and refraction respectively ; 

 while a is the phase difference between the two components 

 of the reflected vibration. 



In the case of the reflection in a vacuum (or air) we have 

 the relation 



sin <i> T 



^— = a/K, (2) 



sin x 



where K is the dielectric constant of the reflecting medium. 



*Wied. Ann., xxxix, p. 545, 1891. Also, Winklemann, Handbuch der 

 Physik, 2 l ° Aufl., 1906, vol. vi, p. 1308. 



f Winklemann, loc. cit. 



X The derivation of this equation may be found in any standard text on 

 Optics; e. g., those of Drude, Schuster, Wood. 



