OPTICS. 113 
the line, a window-bar, for instance, be visible by reflection from the 
surface, ab, at a certain readily determined part of the floor; turn the 
crystal about an axis parallel to the edge a, or about this edge itself, until 
the same object is seen in the same place by reflection from the second 
surface, ac; this will be accomplished when the angle, fac, has been 
described, and the surface, ac, is in the same position formerly occupied by 
ab. The angle of rotation, fac, can be measured if the axis of rotation be 
the axis of a graduated altitude circle; subtract this from 180°, we shall 
have the angle required, bac. Figs. 11 and 12 represent a reflecting 
goniometer, the latter of which is a sectional view: ab is the section of the 
graduated circle; 2 that of the part containing the vernier. The disk of 
the circle turns about a graduated axis reaching to ef, turned by means of 
the milled wheel, ef. which carries in addition the disk, cd. For fixing the 
latter disk, as also the circle itself. the pressure screw, /, is employed, and 
for fine adjustments of the circle the screw 0. The axis of the circle itself 
is hollow ; in it, by means of the head, gh, turns another axis, mn, by whose 
rotation is turned the right-angled arm, zqp: to this is fastened a similar 
arm, prs, turning about p. If the circle be fixed by means of the screw, /. 
the axis, mn, can be turned separately ; if / be loosened, then the axis turns 
with the circle. The crystal is fixed to the rod, tu, by a little wax, and the 
whole instrument so adjusted as that the plane of the circle shall be 
perpendicular to that of the window. To measure by means of the 
instrument, adjust the circle to the zero, fix it there by means of the screw, 
7, and arrange the crystal in such a manner that the edge of intersection 
of the two planes whose angle is to be measured, shall fall in the 
prolongation of the axis, mn, until the image of the window-bar appears at 
the given part of the floor. Then loosen the screw, /. and turn again until 
the image of the window-bar is seen at the same part of the floor from the 
second surface. The angular value of this rotation may then be read off. 
For large and heavy crystals the goniometer of Gambey (fig. 18) is 
better suited: it may also be employed in measuring the angle of a prism. 
For this latter purpose the prism is so adjusted that the image of any 
distant object appears in the cross-hairs of the telescope. The prism is then 
turned about its vertical axis until the same image reflected from the 
second surface appears in the cross-hairs, upon which the angle by which 
the prism has been turned is to be read off. 
_ The reflecting Sextant is a very important application of the reflection 
of light: its principle is illustrated by fig. 14. Here A is a small mirror 
whose upper half is not silvered, so that an eye at o can see through the 
uncovered portion of the glass plate. Bis a second mirror, which may be 
turned about an axis perpendicular to the plane of the figure. When the 
mirrors are mutually parallel, the eye at o will see a distant object situated 
in the direction oA, directly through the uncoated half of the mirror, and 
its reflection in the other half, while the ray, eB, coming from the object 
and passing near the mirror, A, is reflected from B to A. and thence to o. 
If the mirror B be turned, an image, visible through the uncovered part 
of the mirror A, will not be seen in the silvered portion, but the image 
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