But as in the case of the wire micrometer we must know the value of the screw, so in the case of the heliometer we must know how much arc is moved over by a certain motion of one half of the object-glass. [Illustration: FIG. 108.—Double images seen through Iceland spar. ] [Illustration: FIG. 109.—Diagram showing the path of the ordinary and extraordinary rays in a crystal of Iceland spar, producing two images apparently at E and O. ] THE DOUBLE-IMAGE MICROMETER. Now there is another kind of double-image micrometer which merits attention. In this case the double image is derived from a different physical fact altogether, namely, double refraction. Those who have looked through a crystal of Iceland spar, Fig. 108, have seen two images of everything looked at when the crystal is held in certain positions, but the surfaces of the crystal can be cut in a certain plane such that when looked through, the images are single. For the micrometer therefore we have doubly refracting prisms, cut in such a way as to vary the distance of the images. Generally speaking, whenever a ray of light falls on a crystal of Iceland spar or other double refracting substance, it is divided up into two portions, one of which is refracted more than the other. If we trace the rays proceeding from a point S, Fig. 109, we find one portion of the light reaching the eye is more refracted at the surfaces than the other, and consequently one appears to come from E and the other from O, so that if we insert such a crystal in the path of rays from any object, that object appears doubled. There is, however, a certain direction in the crystal, along which, if the light travel, it is not divided into two rays, and this direction is that of the optic axis of the crystal, A A, Fig. 110; if therefore two prisms of this spar are made so that in one the light shall travel parallel to the axis, and in the other at right angles to it, and if these be fastened together so that their outer sides are parallel, as shown in Fig. 111, light will pass through the first one without being split up, since it passes parallel to the axis, but on reaching the second one it is divided into two rays, one of which proceeds on in the original course, since the two prisms counteract each other for this ray, while the other ray diverges from the first one, and gives a second image of the object in front of the telescope, as shown in Fig. _b_. The separation of the image depends on the distance of the prisms from the eyepiece, so that we can pass the rays from a star or planet through one of these compound crystals and measure the position of the crystal and so the separation of the stars, and then we shall have the means of doing the same that we did by dividing our object-glass, and in a less expensive way, for to take a large object-glass of eight or ten inches in diameter and cut it in two is a brutal operation, and has generally been repented of when it has