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 pursued, than to cut them into plates, or prisms in different directions, relatively to the axes, to observe the extraordinary refractions, under different incidences, and endeavour to comprise them in one general law. This Huyghens has done for Iceland spar. The empiric law inferred by him, has been since verified by Dr. Wollaston, and subsequently by Malus, by means of direct experiments, which have confirmed the exactness of it. M. Biot has made similar experiments with other crystals of both classes, by means of a very simple apparatus, which affords very exact measurements of the deviations of the rays, even in cases where the double refraction is very weak. As observations of this kind are indispensable, as the foundations of all theory, it will be as well to give here a detailed description of the apparatus.

It consists principally of two ivory rulers $$AX, \ AZ,$$ (Fig. 217.) divided into equal parts, and fixed at a right angle. The former, $$AX$$, is placed on a table; the other becomes vertical. A little pillar $$Hh,$$ of which the top and bottom are parallel planes, is moveable along $$AX,$$ and may therefore be placed at any required distance from $$AZ.$$

This disposition is sufficient, when the extraordinary refraction to be observed takes place in the same plane as the ordinary, which we have seen to be the case under particular circumstances. As this is the simplest case, and is all that is necessary to understand the method, I will explain it first.

If the substance to be observed, had a very strong refracting power, it would be sufficient to form a plate of it with parallel surfaces, upon which experiments might be made in the manner about to be described; but this case being of rare occurrence, we will suppose, in general, that the crystal is cut into a prismatic form, to make its refraction more sensible; it is even advisable to give the prism a very large refracting angle, a right angle, for instance, which has the particular advantage of simplifying calculations. As, however, the rays of light cannot pass through both sides of such a prism, of any ordinary solid substance placed in air, being reflected at the second surface, there must be fixed to this surface, represented by $$CD$$ in Fig. 218, another prism, or parallelepiped of glass $$CFED,$$ of which the refracting angle $$D,$$ is nearly equal to the angle $$C$$