We see from equation _b_ (p. 18), connecting the angle of total-reflection with the refractive indices of the adjacent media, that, if the denser medium be constant, the indices of all less dense media may be easily determined from a measurement of the corresponding critical angle. In all refractometers the constant medium is a glass with a high refractive index. Some instruments have rotatory parts, by means of which this angle is actually measured. Such instruments give very good results, but suffer from the disadvantages of being neither portable nor convenient to handle, and of not giving a result without some computation. [Illustration: FIG. 16.—Refractometer (actual size).] For use in the identification of cut stones, a refractometer with a fixed scale, such as that (Fig. 16) devised by the author, is far more convenient. In order to facilitate the observations, a totally reflecting prism has been inserted between the two lenses of the eyepiece. The eyepiece may be adjusted to suit the individual eyesight; but for observers with exceptionally long sight an adapter is provided, which permits the eyepiece being drawn out to the requisite extent. The refractometer must be held in the manner illustrated in Fig. 17, so that the light from a window or other source of illumination enters the instrument by the lenticular opening underneath. Good, even illumination of the field may also very simply be secured by reflecting light into the instrument from a sheet of white paper laid on a table. On looking down the eyepiece we see a scale (Fig. 18), the eyepiece being, if necessary, focused until the divisions of the scale are clearly and distinctly seen. Suppose, for experiment, we smear a little vaseline or similar fatty substance on the plane surface of the dense glass, which just projects beyond the level of the brass plate embracing it. The field of view is now no longer uniformly illuminated, but is divided into two parts (Fig. 19): a dark portion above, which terminates in a curved edge, apparently green in colour, and a bright portion underneath, which is composed of totally reflected light. If we tilt the instrument downwards so that light enters the instrument from above through the vaseline we find that the portions of the field are reversed, the dark portion being underneath and terminated by a red edge. It is possible so to arrange the illumination that the two portions are evenly lighted, and the common edge becomes almost invisible. It is therefore essential for obtaining satisfactory results that the plate and the dense glass be shielded from the light by the disengaged hand. The shadow-edge is curved, and is, indeed, an arc of a circle, because spherical surfaces are used in the optical arrangements of the refractometer; by the substitution of cylindrical surfaces it becomes straight, but sufficient advantage is not secured thereby to compensate for the greatly increased complexity of the construction.