1890-91.] Mr E. Sang on Nicol’s Polarising Eye-Piece. 335 
in reality, all positions of the plane OR give the same value, 
22° . . 33', to the angle ROs, so that the position of OR between 
these limits is indeterminable by this condition. 
Another and remarkable condition may, however, he proposed : 
viz., so to place the external surface, that no ray of ordinary light 
entering the eye-piece may pass through it ; while at the same time 
not a single extraordinary ray is intercepted. The construction of 
an eye-piece to satisfy these conditions would seem to give every 
requisite desirable in such an instrument. 
Let AB represent the position of the plate of 
Fig. 3. 
balsam, anywhere intermediate between 57°.. 55' and 102°.. 05' 
from the axis. Make ABD = 22° . . 33 ' ; any ray of ordinary light 
passing in the interior between AB and DB would suffer total 
reflection ; no ray beyond DB would be intercepted. We wish, 
then, that no ordinary ray entering the substance may make with 
the line AB an angle greater than 22° . . 33' : in other words, a ray 
of light BD passing in the interior ought to suffer total reflection at 
the outer surface. The angle ADB, then, ought to have for its 
cosine the ratio a ; whence 
ADB = 52° . . 50'. . 35" 
ABD= 22 ..32.. 59 
BAD = 104 ..38.. 26 
Assuming AC as the limit of the rhomb, and making that 
coincide with the direction of the arete of the primary form, the whole 
instrument is defined. With this eye-piece, as a matter of course, 
there are no separating bands perceived. 
In all of these enquiries the object has been to exclude the 
ordinary and transmit the extraordinary pencil. But the converse 
question may also be proposed. 
At a glance it is seen that no combination similar to that which 
we have been considering can supply the requisite conditious. We 
