522 Proceedings of Royal Society of Edinburgh. [sess. 
On a Simple Way of Obtaining the Half-Shade Field 
in Polarimeters. By James Robert Milne, B.Sc., 
Carnegie Research Fellow. 
(Road July 16, 1906. MS. received October 5, 1906.) 
Summary. 
The half-shade effect in polarimeters is usually obtained, either 
by the well-known method of Laurent, or else by the more recent 
method of Lippich.* In the former a quartz plate is employed to 
give the necessary rotation to one-half of the beam of polarised 
light propagated through the instrument ; in the latter, a Xicol 
prism additional to the polariser serves the same end. 
It occurred to the author that the required effect might be 
obtained very simply by merely interposing a glass plate in the 
beam of light, so that half the beam traversed it, in an oblique 
direction. It follows at once, from Fresnel’s laws of the intensity 
of refracted light, that this will produce a slight rotation of the 
vibration-direction in the traversing half of the beam. 
In practice the method is found to give very good results.! 
Theory of the Method. 
Let a parallel beam of plane polarised light proceeding in the 
direction 0 Z (fig. 1) meet the glass plate 0 Q R V as shown. Let 
0 P represent the light vibration both in direction and amplitude ; 
and let the angle Q 0 Y be the angle of polarisation for glass. 
On resolving 0 P along 0 X and 0 Y, the latter component will 
be transmitted through the glass with undiminished amplitude, 
but the former will have its amplitude 0 S reduced to (say) 0 S'. 
* For a description of the latter, see, for instance, Landolt’s “ Das optische 
Drehungsvermogen. ” 
t The author afterwards learned that the same principle of rotation by 
selective reflection had already been applied to the polarimeter, although in 
a different manner, by Professor Poynting. See A Method of Making a Half- 
Shadow Field in a Polarimeter by two Inclined Glass Plates, by J. H. 
Poynting, Sc.D., F.R.S. ; B. A. Report , p. 662, 1899 ; also Catalogue of the 
Optical Convention, p. 224, 1905. 
