Dr. Brewster on the laws of polarisation, &c. 241 
by means of the law, for any crystal in which the rings round 
the resultant axes can be seen at. one view, and project them 
upon paper, after they are reduced to different thicknesses, 
corresponding to the oblique transit of the rays through 
the parallel plate, we shall have a representation of the rings 
actually observed, expressing in the most accurate manner 
all the inversions of the tints, and exhibiting the points of 
contrary flexure, and the innumerable varieties of form 
which the curves assume. 
In order to determine the tints of sulphate of lime at great 
obliquities, M. Biot placed the laminae in a tube shut up at 
both ends by plates of glass ; and by means of a metallic 
rod he was able to fix them at any angle with the axis 
of the tube. He then filled the tube with water, or oil of 
turpentine, and observed the tints at inclinations as high as 
seventy-eight degrees, two minutes. In this way he 'con- 
structed a formula which represented these observations, and 
by means of this formula he computed the following table, in 
which I have reduced his numbers, in order to represent the 
tints at equal thicknesses, by dividing them by the secants of 
the angles of refraction. 
Table of the tints of sulphate of lime in different azimuths 
reduced from M. Bior’s experiments. 
Angle of 
refraction 
Angular 
dist. from 
the axis. 
Azimuth 
of o° 
Azimuth 
of 22° 30 / 
Azimuth 
of 45 * 
Azimuth 
of 67° 30' 
Azimuth 
of 90° 
o° 
90° 
1. 0000 
1 .0000 
1. 0000 
l .0000 
1. 0000 
10 
80 
0.9768 
0.9787 
0.9838 
0.9905 
0.9944 
20 
70 
0.9105 
0.9164 
0.9352 
0.9615; 
0.9756 
3 ° 
60 
0.8101 
0.8213 
o.86og 
0.9117 
0.9434 
40 
5 ° 
0.6885 
07047 
0.7664 
0 8523 
0.9002 
5 ° 
40 
0.5559 
0.5751 
0.6607 
0.7794 
0.8482 
60 
30 
0.4241 
0.4409 
0.5483 
0.6982 , 
0.7938 
70 
20 
0.3027 
0.3043 
0.4121 
0.5949 
Q -7337 
80 
to 
0.2077 
0.1599 
0.2501 
0.4060 
0.6184 
90 
0 
MDCCCXVIII. I i 
