1905 - 6 .] Obtaining the Half -Shade Field in Polarimeters. 525 
between the edge B and the lower half of the beam, because the 
rays which enter AD are, on account of their refraction, more 
inclined upwards than the surface A B. 
The rays which strike the surface A B, whether internally or 
externally, are reflected by it harmlessly aside out of the way, as 
may easily be shown. 
At C, where the first multiple reflection emerges from the glass, 
a change of intensity occurs, the two portions of the surface, B C 
and C E, appearing of different brightness to the eye. This makes 
it necessary to screen off all the surface beyond C, and to use the 
portion B C only. The explanation of the change of intensity lies 
in the fact that beyond C the light emerges elliptically polarised, 
being a combination of rectilinear vibrations rotated to different ex- 
tents, due to the direct and to the retransmitted rays respectively. 
Now it might be supposed that the necessity for limiting the 
field could be avoided by using an exceedingly thin plate of glass 
so that C would sensibly coincide with B. This would mean, how- 
ever, that the light proceeding from each point of the surface 
would be polarised in a slightly elliptical manner (which is attested 
in practice by the fact that it is impossible with any position of 
the analyser to obtain complete extinction over the rotated half 
of the field). Now it may be shown from the mathematical theory 
of the polarimeter, that in such circumstances the sensitiveness of 
the instrument must be somewhat impaired. It can be shown, how- 
ever, that the ellipticity is very slight, and in practice the author 
has found that very good results may be obtained by this method ; 
and that with nothing more elaborate in the way of apparatus 
than a microscope cover-glass cemented to a piece of cork, fixed 
slantwise behind the polariser. 
For the better plan of the thick plate there is necessary a piece 
of plain parallel glass, optically unstrained, and having one edge 
ground off at the proper angle, and subsequently polished. A 
piece of plate glass can be selected which is sufficiently good to 
fulfil all requirements. The thickness of the plate is determined 
by the desired area of the field — it can easily be proved that in 
fig. 2 the connection between the dimensions of B C and D E is, 
2 
BC = -DE. The plate is to be securely mounted behind the 
/X 
