The compensating eye-pieces of these makers are constructed on the same principle as those of Zeiss’s for the correction of errors of colour in the marginal portion of the field, and consequently are in every way as effective as those of Continental manufacture. Figs. 106, 107, and 108 show in dotted outline the form and position of the several lenses combined in these eye-pieces. _Projection Eye-pieces_ are chiefly used in micro-photography, and for screen demonstrations. The cap of this eye-piece is provided with a spiral adjustment for focussing, the diaphragm being placed in front of the eye-lens, an essential arrangement for obtaining an accurate focus. The ring seen below the cap, Fig. 108, is graduated so that the rotation for distance of screen may be carefully recorded. [Illustration: Fig. 107.--The Compensating Eye-piece.] [Illustration: Fig. 108.--Projection Eye-piece.] Schmidt’s goniometer positive eye-piece, for measuring the angles of crystals, is so arranged as to be easily rotated within a large and accurately graduated circle. In the focus of the eye-piece a single cobweb is drawn across, and to the upper part is attached a vernier. The crystals being placed in the field of the microscope, care being taken that they lie _perfectly flat_, the vernier is brought to zero, and then the whole apparatus turned until the line is parallel with one face of the crystal; the frame-work bearing the cobweb, with the vernier, is now rotated until the cobweb becomes parallel with the next face of the crystal, and the number of degrees which it has traversed may then be accurately read off. _Goniometer._--If a higher degree of precision is required, then, the double-refracting goniometer invented by the late Dr. Leeson must be substituted. With this goniometer (Fig. 109) the angles of crystals, whether microscopic or otherwise, can be measured. It has removed the earlier difficulties incident to similar instruments formerly in use. Among other advantages, it is capable of measuring opaque and even imperfect crystals, beside microscopic crystals and those in the interior of other transparent media. It is equally applicable to the largest crystals, and will measure angles without removing the crystal from a specimen, provided only the whole is placed on a suitable adjusting stage. The value of the goniometer depends on the application of a doubly refracting prism, either of Iceland spar or of quartz, cut of such a thickness as will partially separate the two images of the angle it is proposed to measure. Dr. Leeson strongly insisted on the importance of the microscope in the examination of the planes of crystals subjected to measurement, as obliquity in many cases arises from not only conchoidal fractures, but also from imperfect laminæ elevating one portion of a plane, and yet allowing a very tolerable reflection when measured by the double refracting goniometer. [Illustration: Fig. 109.--Leeson’s Goniometer.]