and on some improved forms of Rhombs. 455 
surface of the Canada balsam nearly parallel to ba would pass 
into it, and @ fortiori at smaller angles of incidence. If the 
angle abf equals 90° nearly, as in the older form of Nicol’s 
rhomb, and the ordinary ray ko makes the critical angle of inci- 
dence at o equal to 68° 23/, and the extraordinary ray an angle 
about 6°40! less than that, this latter will be transmitted, whilst the 
ordinary ray is reflected ; and this will continue whilst the angle 
of incidence of the extraordinary ray increases from 68° 23! — 6°40! 
=61° 43! to the critical angle of the extraordinary ray. If !' 
be this critical angle, we have 
sin? 7! = ee es 
fp?(1 — e? cos? 0)’ 
and 
8=45° 20!— (90° —2") =i" — 44° 40), 
which give 
i! = 82° 43! nearly ; 
then 82° 43’—61° 43'’=21° 0! within the erystal. r 
If the refraction were ordinary refraction, multiplying this by 
1:5, we should have the corresponding angle in air 31° 30’; but 
the true angle of the incident pencil would require to be calcu- 
lated from the properties of the extraordinary rays, since these 
furnish the transmitted beam which is plane-polarized. The 
angle 31° 30! is more than the visible angle of the polarized beam 
in the old form of Nicol’s rhomb, and also of the dumpy rhombs 
now much used; but the Canada balsam employed for cement 
may be more dense than the average taken in the computations. 
The pair of large dumpy rhombs which I have had for many 
years in common use, as well as a rhomb of the old form, furnish 
a beam of polarized light of only about 27° for green light, and 
larger for blue, but less than this for red light. 
From the above discussion it is clear that the separation of the 
polarized rays is effected by the first prism a) f, and the second 
part of the rhomb aby has only to transmit the extraordinary 
ray after it has passed through the film of Canada balsam. I 
therefore propose that the second prism shall be of glass, which 
is much easier to work than cale-spar, and the best quality of 
cale-spar has sometimes been very scarce. 
In my descriptive and experimental treatise on Physical Optics, 
p- 81, I have described another form of rhomb which I had tried 
many years ago, with air in place of Canada balsam between the 
prisms, and those of much smaller angles than Nicol’s rhomb, so 
that a much broader beam of polarized light could be obtained. 
I now propose that the prism nearest the eye shall be of glass, 
and the rhomb will then be like M. Biot’s double-image rhomb, 
only with air between the two prisms instead of Canada balsam, 
