1890 - 91 .] Mr E. Sang on NicoVs Polarising Eye-Piece. 
329 
cos PO u 
a cos (/x — v) + Jy 2 — a 2 sin (/ x — v ) 
ay 
The object is to find a value of v which would give 
POU + POz* = 2(/x-A) , 
which would be accomplished by resolving the equation 
sin POU 4- sin PO u 
tan ( /t cos POU + cos POi« ’ 
but the labour attending the exhibition and direct resolution of this 
equation would be enormous, I have, therefore, preferred the method 
of approximation. 
In making this approximation we derive a guide from the last 
term of the numerator of cosPOU ; which becomes imaginary when 
a 2 
e 2 cos v 2 is less than the known quantity — 2 (/3 2 - y 2 ). This limit, 
which gives (V) = 57° . . 55', corresponds to the intersection of the 
ellipse with a circle described with the radius OR. 
I, therefore, assumed three values of v, or rather of /x — v, and com- 
puted thence the corresponding values of POU, POw, and of the 
error J(POU + POw) - (/x - A), as under 
/x - v v POU PO u Error 
85° 53°. . 45'. . 46" 80°. . 04'. . 56" 40°. . OP. . 32" - 14°. . 57'. . 46" 
90 48 . . 45 . . 46 83 . . 00. . 21 50 . . 35 . . 13 - 8 . . 13 . . 13 
95 43.. 45.. 46 86 . . 48 . . 08 60 . . 03 . . 04 - 1 . . 35 . . 24 
where the extent of field (POU - PO^) is observed to decrease, the 
greatest possible extent of field being obtained when v has the 
limiting value : but then this convenience of a large field is counter- 
acted by having it unsymmetrically placed in reference to the line 
of sight ; as well as by the necessity of using a very long rhomb 
which would give another limit to the extent of view. 
Computing, by the ordinary method, from these three results, 
that value of v which may give no error, we find v = 42° . . 33' . . 00"; 
but this is only an approximation. Computing from it the value of 
the error, we find 
POU = 87°. . 52'. . 39"; PO^= 62°. . 14'. . 39", 
