83).--This
(Fig. 1), as is well known, is constructed from a rhombohedron of
Iceland spar, the length of which must be fully three times as great
as the width. The end faces are cut off in such a manner that the
angle of 72 deg. which they originally form with the lateral edge of the
rhombohedron is reduced to 68 deg.. The prism is then cut in two in a
plane perpendicular to the new end surfaces, the section being carried
obliquely from one obtuse corner of the prism to the other, in the
direction of its length. The surfaces of this section, after having
been carefully polished, are cemented together again by means of
Canada balsam. A ray of light, on entering the prism, is separated by
the double refraction of the calc-spar into an ordinary and an
extraordinary ray; the former undergoes total reflection at the layer
of balsam at an incidence which allows the extraordinary ray to be
transmitted; the latter, therefore, passes through unchanged. This
principle of obtaining a single polarized ray by means of total
reflection of the other is common to all the forms of prism now to be
described.

Dr. Feussner gives a mathematical analysis of the paths taken by the
two polarized rays within the Nicol prism, and finds that the emergent
extraordinary ray can include an angular field of 29 deg., but that this
extreme value holds good only for rays incident upon that portion of
the end surface which is near to the obtuse corner, and that from
thence it gradually decreases until the field includes an angle of
only about half the previous amount. He finds, moreover, that,
although of course the ray emerges parallel to its direction of
incidence, yet that the zone of polarized light is shifted to one side
of the central line. Also that the great length of the Nicol--3.28
times its breadth--is not only an inconvenience, but owing to the
large pieces of spar thus required for its construction, prisms of any
but small size become very expensive. To this it may be added that
there is a considerable loss of light by reflection from the first
surface, owing to its inclined position in regard to the long axis of
the prism.

[Illustration: Fig. 4., Fig. 5., and Fig. 6.]

It is with the view of obviating these defects that the modifications
represented in Figs. 2 to 6 have been devised.

2. _The Shortened Nicol Prism_.--This arrangement of the Nicol prism
is constructed by Dr. Steeg and Reuter of Homburg v.d.H. For the sake
of facilit