Reflexion of Light at certain Metal-Liquid Surfaces. 229 



determine p 2 from the resulting simple equation, we get the 

 confirmed and corrected value p 2 = "9241. Restoring the 

 omitted factors, we have finally as the result of the second 

 approximation 



96 #x-9241 



P ~ -p(l+rt* ' (13) 



in which yu, = *225. 



The value thus obtained is not so low, and therefore not so 

 good, as that derived by Ritz from the series of ^-functions. 

 One of the advantages of the latter is that, being normal 

 functions for the simple bar, they allow T to be expressed as 

 a sum of squares of the generalized coordinates q x &c. As a 

 consequence, p 2 appears only in the diagonal terms of the 

 system of equations analogous to (11). 



From (11) we find further 



? 2 /?i= --0852, 



so that for the approximate form of io corresponding to the 

 gravest pitch we may take 



w = xy-'0852xy(x 2 +y 2 ), .... (14) 



in which the side of the square is supposed equal to 2. 



XX Y. An Experimental Investigation on the Reflexion of 

 Light at certain Metal-Liquid Surfaces. By Lynde P. 

 Wheeler, Assistant Professor of Physics, Sheffield Scientific 

 School of Yale University *. 



Introduction. 



"TT7HEN light is incident on a transparent substance at an 

 ▼ T angle whose tangent has the numerical value of the 

 index of refraction of the material, theory, as embodied in 

 the Fresnel equations, demands that the reflected light should 

 be plane polarized in the plane of incidence. Experience 

 teaches, however, that for but a very few substances, solid or 

 liquid, is this true. Most substances show at this angle an 

 elliptic polarization of small ellipticity. The ellipticity 

 (detined as the ratio of the amplitudes of the components of 

 the vibration parallel and perpendicular to the plane of 

 incidence) is found to be sometimes positive and sometimes 

 negative. (Positive ellipticity corresponds to a counter- 

 clockwise description of the ellipse when viewed from the 

 side of the incident light.) 



* Communicated b\ the Author. 



