given, Fig. 24. The details of the lenses, together with their focal lengths in millimetres, are represented half size in Fig. 25. In this instrument the lenses which converge the rays upon the crystal plate can be taken out, and replaced by others giving parallel light; it can then be used as an ordinary polariscope.

An important modification of this instrument has been made by Prof. W. G. Adams, in which the principal objects in view have been :

(1.) To obtain an extensive field of view.

(2.) To afford a means of measuring the rings and the angles between the optic axes of biaxal crystals.

(3) To have a means of immersing the crystal in a liquid in those cases in which the optic axes are too far apart to be seen in air.

These advantages have been obtained by modifying the positions and focal lengths of the lenses usually employed in table polariscopes, so that the rings of a crystal are best seen when there is a space of 14 inch between the two lenses, one on either side of the crystal. Into this space is introduced a central piece, consisting of a circular box with deep planoconvex lenses fixed, one in the bottom and the other in the top of the box, in such a position that their curved surfaces have a common centre of curvature, with their flat faces turned towards one another and enclosing the crystal between them. The box can turn about an axis passing through the common centre of curvature.

The instrument is fully described in the Philosophical Magazine for July 1875; but the following

diagram (Fig. 25A) extracted, by permission, from the paper will explain the general disposition of the parts. The advantages to be obtained by the use of the central piece are :—

(1.) The extension of the field of view. If the angle in air corresponding to the field of view is 74° without the central piece, then the angle will be increased to about 128° when the central piece is introduced, the central piece giving the same angle in glass that is given without it in air. The field of view may be made to include both optic axes of topaz of Brazil.

(2.) When the plane containing the optic axes is at right angles to the axis P Q, either of the optic axes of a biaxal crystal or any ring may be brought into the centre of the field of view where spider-lines cross one another, and the angles between them accurately measured.

Mention has been made above of the effect of the circular polarisation of quartz in the colours produced by a beam of parallel rays of polarised light. It will be worth while to examine the modification which the rings and brushes undergo from the same cause. It has been explained that a ray of plane-polarised light in traversing a crystal of quartz in the direction of its axis is divided into two, the vibrations of which are circular, one right-handed, the other left. If the ray traverses the crystal in a direction perpendicular to the axis, and if the original vibrations are neither parallel nor perpendicular to the axis, it is also divided into two, whereof the vibrations are not circular, but rectilinear. It was suggested

A. Concave mirror.

B. Double-concave lens I inch in diameter.

C. Tourmaline or other polariser.

D. Double-convex crossed lens I inch in diameter, 1 inch focal length.

E. Convexo-plane lens inch in diameter, I inch focal length.

F. Plano-convex lens 1 inch in diameter, 1 inch focal length.

G. Double-convex crossed lens 1 inch in diameter, 1 inch focal length.

H. Double-convex lens 1 inch in diameter, 3 inches focal length.

K L. Nicol's prism and eyepiece.

M and N. Portions of hemispherical lenses with O as the common centre of curvature of their spherical surfaces. Radius of curvature of M is inch, and of N is of an inch, and the distance between the lenses M and N about of an inch.

and Q. The ends of the axis supporting the box fixed so that the axis passes through the point O.

The dotted lines show the path of the light through the instrument.

first by Sir G. Airy, that these circular and rectilinear vibrations are limiting cases of elliptical; and both theory and experiment tend to confirm the suggestion, by showing that if the ray be incident on the crystal in any direction oblique to the axis, it is divided into two, the vibrations of which are similar ellipses having the longer diameter of the one coincident with the shorter of the other, and the motion in the two oppositely directed. The longer diameters of the ellipses coincide with the directions of vibration of the ordinary and extraordinary rays in the case of an ordinary positive crystal; and are consequently directed the one toward the centre of the figure, the other in a direction at right angles to the first.

The exact or even approximate determination of the figures produced is a complicated question, and requires mathematical analysis for its solution, but a general idea of their nature may nevertheless be easily formed. When the polariser and analyser are either parallel or crossed, circular rings are formed, and towards the outer parts of the field traces of the black cross are seen, which grow stronger as we proceed outwards from the centre-that is, towards the parts where the rays are more oblique, and where the polarisation more nearly approaches to rectilinear. But in the centre, and near to it, where the polarisation is circular or nearly so, the effects will resemble those produced by parallel rays, viz. the rays of different colours will emerge plane-polarised in different planes, and will be variously affected by the angle between polariser and analyser. In no position