1890-91.] Mr E. Sang on NicoVs Polarising Eye-Piece. 331 
simply on a, /3, y ; after it is determined it will tlien be proper to 
enquire, what position of the ends of the rhomb will give symmetry 
in the placing of the field of view. 
We must, then, determine the position of OR so that the angle 
SOs may be a maximum. Now, it is obvious that the angle ROs 
is constant, having for its cosine the ratio - : and thus we have to 
7 
seek only for that position of OR which gives ROS a minimum or 
a maximum. 
ROS will, in the particular state of matters, be a minimum, 
actually zero, when OR is a semi-diameter of the ellipse, that is, 
when ( v) = 57° . . 55' ; but if ROS be greater than ROs, SOs will 
be the excess ROS - ROs, and we must then seek for ROS a 
maximum, not a minimum. 
The equation of a plane touching the ellipse of S is 
a 2 + /3 2 “ 1 ’ 
and since that plane must pass through R 
a 2 + p 2 ’ 
from which equation, and the equation of the spheroide, we may 
determine x S) y s , the ordinates of the point of contact, 
2 / 3 2 ^r + Vn \J (°?y b + P 2x r “ ° 2 P 2 ) 
X S~ a o 2 02 2 ’ 
a Vr, + ^R 
2 a 2 y R ± x R J{a?yl + fpx\ - a 2 /3 2 ), 
«%+/s%4 
in which, substituting for %, y R their values, we obtain 
a 2 p 2 cos v + sin v J{y 2 (a 2 sin v 2 + P 2 cos v 2 ) - a 2 ft 2 } 
X ^y a 2 sin v 2 + p 2 cos V 2 5 
_ /3 2 a 2 sin v ± cos v J {y 2 (a? sin v 2 + /3 2 cos v 2 ) - a 2 p 2 } 
y a 2 sin v 2 + j3 2 cos v 2 
whence 
jr ) a_fi 2 a 2 sinv±cosv^{y 2 (a 2 sinv 2 + /3 2 cosi/ 2 ) - a 2 P 2 } 
an a 2 j3 2 cos V + si n v ^ { y 2 (a 2 sill V 2 + p 2 cos V 2 ) - a 2 p 2 } * 
