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 modes of action, which has occasioned their distinction, by him, into crystals of attractive and repulsive double refraction; these denominations, which express at once the phænomena, are useful in innumerable cases, to indicate how the extraordinary ray is disposed with respect to the other, since it is only necessary afterwards to know the direction of the axis at the point where the refraction and separation of the rays take place. The progressive and increasing separation of the rays, as their direction deviates more and more from the axis in each of these classes of crystals, may also be conveniently expressed by saying, that the phænomena take place as if there emanated from the axis a force attractive in the one class, and repulsive in the other; which does not, however, imply a belief that such forces do actually exist, or are immediately exerted.

There are, however, other crystals in great number, in which the double refraction disappears in two distinct directions, forming an angle more or less considerable, so that rays are singly refracted along those two lines, but are separated more and more widely as their incident direction deviates from them, crystals of this kind have been called crystals with two axes. In those which have hitherto been examined, it has been found that one of the refractions is always of the ordinary kind, as if the substance was not crystallized, whilst the other follows a law analogous to that of the crystals with one axis, but more complex, which will be afterwards explained. There are here, as in the simpler case, two classes distinguished by attractive and repulsive double refraction. No crystals have as yet been discovered, possessing more than two directions of single refraction, except indeed those in which it is single in all directions, which is the case with those of which the primitive form is either a cube, or a regular octohedron.

The general circumstances which characterise the phænomenon of double refraction, being thus recognised, its effects must be exactly measured in each class of crystals, in order to try and discover the laws of it. In order to this, there is no better plan to be