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 the points F, F′, are also known à priori, so that the directions FI, F′I may be constructed; whereupon we may remark, that in many cases the extraordinarily refracted pencil F′I does not lie in the plane of emergence NIO.

Such is the process devised by Malus; if we admit it, we may admit also all his observations, and consider them as data to be satisfied, but I will shortly indicate a more simple method, which would allow us to repeat these same measurements with equal facility and accuracy.

Among all the positions that may be given to the crystal, resting always on the same face, there is one which deserves particularly to be remarked, because the extraordinary refraction takes place, like the ordinary, in the plane of emergence. To find this position, it is necessary to conceive a vertical plane to pass through the side BC of the triangle, to place the eye in this plane, and slowly turn the crystal round on its base, till the two images of BC coincide; then, as the ordinary image is always in the plane of emergence, the extraordinary must in that case be in it likewise. The particular plane for which this takes place is called the principal section of the rhomboid. If the crystal used in the experiment be of the primitive form, for the carbonate of lime, the bases of the rhomboid will be perfect rhombs, and the principal section will be that containing the shorter diagonals of the upper and lower faces. This section of the rhomboid will be a parallelogram ABA′B′, (Fig. 214.) in which AB, A′B′ are the diagonals just mentioned, and AB′, A′B edges of the rhomboid. The line AA′ is called the axis of the crystal; it is equally inclined to all the faces, forming with them angles of 45° 23′ 25″. It is to this line that all the phænomena of double refraction are referred.

Let us examine at first the manner of this refraction in the principal section. All its general phænomena are exhibited in Fig. 215, in which SI represents an incident ray, IO the ordinary refracted ray, IE the extraordinary: IN is the normal. When the incidence is perpendicular, the ordinary ray is confounded with the normal, and passes through the crystal without deviation; but the extraordinary is refracted at the point of incidence, and is more or less deflected towards the lesser solid angle B′. A similar effect