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 manner as those commonly referred to in this Treatise, because the figure of the instrument in question is not one of revolution, though something of the same general appearance.

$AB$, $BC$, $CD$, $DE$, $EF$ represent plane surfaces, which refract the rays falling on them and produce several images $q$, $q′$, $q″$, $q_{′}$, $q_{″}$ …. thus to appearance $multiplying$ the object $Q$, whence the name.

152. The purpose of this instrument, is to measure the inclination of two planes of a chrystal, by bringing them successively into the same position, which is known by their reflecting the light from a given object in the same direction, and observing on the graduated rim of the instrument, the number of degrees through which the chrystal has been turned.

153. The principle of this instrument is, that when a ray or pencil of rays is reflected successively by two plane mirrors, inclined to each other, the angle between the first and last directions of the light, is double the inclination of the mirrors. The manner in which this is applied is as follows, $ABC$ (Fig. 159) is an instrument in form of a sector of a circle; $AD$ a moveable radius, carrying a mirror at the centre $A$. This is placed in such a position, that a pencil of light from $S$, may be reflected at $A$, and again at $E$, where there is a mirror fixed on the limb of the instrument, so that it may pass along the axis of the tube $F$, which is directed to some determined object, or to the horizon. This is managed in practice, by having the glass at $E$ silvered on the part next to the instrument, and the other part transparent, so that the one object may be seen through the plain glass, and the reflexion of the other in the mirror.

When the two mirrors are parallel, of course the first and last rays are parallel, and the image of a distant object appears just where the object itself does. The position of the moveable radius, with regard to the arc or limb of the instrument, is marked in that particular case; and when this radius is moved so as to bring the image of another object to touch the former, their angular distance is found, from its being twice the angle of the mirror, that is, twice