interesting case in which the facet is parallel to the two directions of single refraction, the second shadow-edge moves across the one which is invariable in position. In intermediate positions of the facet both shadow-edges move, and give therefore critical values. Of the intermediate pair, _i.e._ the lower maximum and the higher minimum, one corresponds to the mean principal refractive index, and the other depends upon the relation of the facet to the optical symmetry. If it is desired to distinguish between them, observations must be made on a second facet; but for discriminative purposes such exactitude is unnecessary, since the least and the greatest refractive indices are all that are required. The character of the refraction of gem-stones is given in Table V at the end of the book. CHAPTER VII ABSORPTION EFFECTS: COLOUR, DICHROISM, ETC. When white light passes through a cut stone, colour effects result which arise from a variety of causes. The most obvious is the fundamental colour of the stone, which is due to its selective absorption of the light passing through it, and would characterize it before it was cut. Intermingled with the colour in a transparent stone is the dispersive effect known as ‘fire,’ which has already been discussed (p. 20). In many instances the want of homogeneity is responsible for some peculiar effects such as opalescence, chatoyancy, and asterism. These phenomena will now be considered in fuller detail. COLOUR All substances absorb light to some extent. If the action is slight and affects equally the whole of the visible spectrum, the stone appears white or colourless. Usually some portion is more strongly absorbed than the rest, and the stone seems to be coloured. What is the precise tint depends not only upon the portions transmitted through the stone, but also upon their relative intensities. The eye, unlike the ear, has not the power of analysis and it cannot of itself determine how a composite colour has been made up. Indeed, so far as it is concerned, any colour may be exactly matched by compounding in certain proportions three simple primary colours—red, yellow, and violet. Alexandrite, a variety of chrysoberyl, is a curious and instructive case. The balance in the spectrum of light transmitted through it is such that, whereas in daylight such stones appear green, in artificial light, especially in gas-light, they are a pronounced raspberry-red (Plate XXVII, Figs. 11, 13). The phenomenon is intensified by the strong dichroism characteristic of this species.