662 REPORT—1899. 
respectively. And if from these coefficients indices be calculated for a temperature 
of 59° F, (equals 15 C. nearly) we have the following :— 
Quartz prism 30°. Calcite prism 30°, Calcite prism 60°. 
1:5441896 see 1-6582423 ces 1:6582624 
For Quartz at 15°C. Rudberg and Mascart give... 1:54418 
a » Sarasin gives act) .» 1°54419 
For Calcite 5 a A ats ses §61:65839 
¥ on fi s 2nd prism 1°65825 
The above indices are uncorrected for air. 
5, A Workshop Form of Resistance Balance. Jy Professor 
J. A. Furmine, 72S. 
6. A Method of Making a Half-shadow Field in a Polarimeter by two 
inclined Glass Plates. By J. H. Poynrine, Sc.D., PRS. 
When a beam of light polarised in a plane neither parallel nor perpendicular to 
the plane of incidence falls on a plate of glass with parallel sides, Fresnel’s formula 
shows that it emerges still plane polarised, but with the plane of polarisation 
rotated away from the plane of incidence. Regarding the incident beam as resolved 
into two polarised respectively in and perpendicular to the plane of incidence, the 
former suffers most loss by reflection at the two faces, so that in emergence it bears 
a less proportion to the latter, and the resultant plane is therefore turned round 
from the plane of incidence. 
To make use of this rotation to obtain a half-shadow field—z.e. a field divided ~ 
into two halves in which the planes of polarisation are slightly inclined to each 
other—two glass plates are bevelled each at one edge and fitted with the bevels 
together to forma V. This V is fixed in a frame and put in the usual position of 
the half wave plate, with the sharp edge down the middle of the field and turned 
towards the polariser. The frame can be rotated about a horizontal axis—the 
‘ tilt-axis’—through the middle of the edge and perpendicular to the axis of the 
instrument. 
Let us suppose the plane of polarisation of the light incident on the V plates 
to be vertical. If the edge of the V is also vertical, the light passes through 
the two plates unchanged in plane, and the two halves will suffer extinction at the 
same time when the analyser is crossed. But ifthe V is turned through any angle 
about the tilt-axis the planes of polarisation of the two halves on emergence 
from the V are rotated each slightly from the vertical in opposite directions by 
equal amounts, and now when the analyser is crossed the two halves have equal 
brightness, and extinction occurs for the two in different positions of the analyser. 
The V therefore serves to give a half-shadow field. ‘The sensitiveness ot the 
instrument can be increased or diminished by lessening or increasing the tilt of 
the V. 
In general, when light comes through a parallel plate, that which comes straight 
through is mixed with that which has suffered two or more internal’ reflections, 
and if the incident beam is polarised the components of the emergent ‘beam have 
suffered different rotations. But looking towards the VY from the concayve—2.e. 
the analyser-side—it can easily be shown that there is a strip on each side of the 
junction of the plates in which the light has no admixture of internally reflected 
beams, and is therefore in each strip all in one plane of polarisation, The thicker 
the plates the wider are these strips, and they must. be so thick that the strips 
wholly fill the aperture of a diaphragm placed just in front of the V.— 
Like all other half-shadow instruments, this instrument gives the best results 
with monochromatic light, but the same V of course serves equally well for any 
single wave length. 
a 
