1890-91.] Mr E. Sang on Nicol’s Polarising Eye-Piece. 327 
from which, equations we deduce the value of the tangent of the 
angle LOP, 
tan LOP = - £ cot X S ™ U T m °°^ ^ j > 
a a ~P j'{a 2 sm X. A + (3 A cos A z \ 
from which we obtain the numerical value 
supp. LOP= 41° . , 14' . . 13J" (say 14"); 
whence, by adding the angle LOM, we obtain 
MOQ = 104\.58'..59i" Say 
ADC (fig. 1) = 104 ..59. 
Now, the inclination of the arete to the face of the primitive 
rhomb is 109° . . 08', so that, in forming an eye-piece, the ends must 
be inclined 4° . . 09' less than the natural face is. 
This result is opposed to the instructions given by Mr Nicol in 
his first description of the instrument : he directs that the obliquity 
be increased, whereas we have found that it must be diminished 
4°; and, indeed, on inspection of those eye-pieces which have been 
made agreeably to his instructions, it will be found that the ray bf 
light proceeding in the interior of the crystal parallel to the arete 
suffers refraction at each surface, and that the ray which does not 
suffer refraction passes in a direction intermediate between the line 
of the arete and the diagonal joining the two obtuse corners. 
Having now determined this element of the artificial rhomb, 
there remains for me the solution of another question. It is this : 
To place the plate of balsam so that the extent of field may be 
placed equally on each side of the line of sight. For this, a new 
element enters into the investigation ; the refractive power of the 
balsam. 
Let OK represent the direction of the plate of cement, and 
measure off OK to represent the velocity of light in that medium ; 
the limiting directions of the two pencils will be thus obtained. 
First, for the ordinary ray ; describe a sphere round O with the 
radius a, and from R apply to that sphere the tangent plane Rs, 
meeting the surface OP in the line t ; then from that line apply a 
plane touching the sphere pertaining to the air in the point u, O u 
is the direction of that external ray, of which the ordinary pencil 
