1. The Nicol Prism (Edin.  New Phil.  Journal, 1828, vi., 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 facility of manufacture, the end surfaces are cleavage planes, and the oblique cut, instead of being perpendicular, makes with these an angle of about 84 deg..  By this alteration the prism becomes shorter, and is now only 2.83 times its breadth; but if Canada balsam is still used as the cement, the field will occupy a very unsymmetrical position in regard to the long axis.  If balsam of copaiba is made use of, the index of refraction of which is 1.50, a symmetrical field of about 24 deg. will be obtained.  A prism of this kind has also been designed by Prof.  B. Hasert of Eisenach (Pogg.  Ann., cxiii., 189), but its performance appears to be inferior to the above.