4. _The Foucault Prism_ (_Comptes Rendus_, 1857, xlv., 238).--This construction differs from all those hitherto mentioned, in that a film of air is employed between the two cut surfaces as the totally reflecting medium instead of a layer of cement. The two halves of the prism are kept in position, without touching each other, by means of the mounting. The length of the prism is in this way much reduced, and amounts to only 1.528 times its breadth. The end surfaces are cleavage planes, and the sectional cut makes with them an angle of 59 deg.. The field, however, includes not more than about 8 deg., so that this prism can be used only in the case of nearly parallel rays; and in addition to this the pictures which may be seen through it are to some extent veiled and indistinct, owing to repeated internal reflection. 5. _The Hartnack Prism_ (_Ann. de Ch. et de Physique_, ser. iv., vii., 181).--This form of prism was devised in 1866 by MM. Hartnack and Prazmowiski; the original memoir is a valuable one; a translation of it, with some additions, has lately been published (_Journ. of the R. Microscopical Soc._, June, 1883, 428). It is considered by Dr. Feussner to be the most perfect prism capable of being prepared from calc-spar. The ends of the prism are perpendicular to its length; the section carried through it is in a plane perpendicular to the principal axis of the crystal. The cementing medium is linseed oil, the index of refraction of which is 1.485. This form of prism is certainly not so well known in this country as it deserves to be; a very excellent one, supplied to the present writer by Dr. Steeg is of rectangular form throughout, the terminal surfaces are 19 x 15 mm., and the length 41 mm. The lateral shifting of the field is scarcely perceptible, the prism is perfectly colorless and transparent, and its performance is far superior to that of the ordinary Nicol. The field of view afforded by this construction depends upon the cementing substance used, and also upon the inclination of the sectional cut in regard to the end of the prism; it may vary from 20 deg. to 41 deg.. If the utmost extent of field is not required, the prism may be shortened by lessening the angle of the section, at the expense, however, of interfering with the symmetrical disposition of the field. 6. _The Glan Prism_ (Carl's "Repertorium," xvi., 570, and xvii., 195).--This is a modification of the Foucault, and in a similar manner includes a film of air between the sectional surfaces. The end surfaces and also the cut carried through the prism are parallel to the principal axis of the calc-spar. The ends are normal to the length, and the field includes about 8 deg.. This prism is very short, and may indeed be even shorter than it is broad. It is subject to the same defect as that mentioned in the case of the Foucault, although perhaps not quite to the same extent. II.--THE NEW POLARIZING PRISM.