MINERALOGY. 53 
of the faces, and consequently to determine the system. Certain 
instruments are, however, necessary, accurately to determine the precise 
angle made by two plane faces with each other. 
The oldest and simplest instrument is the common goniometer 
( pl. 32, fig. 8). It is of easy use, and very convenient, when we do not 
require an angle with any very great accuracy. To determine an 
interfacial angle, one face must be applied to an, with the edge of 
inclination opposite to the centre of the diameter. The arm, e’d, is then to 
be brought around until its edge rests on the other face: the crystal is thus 
accurately inclosed between two radii of the semicircular scale. The angle 
indicated on the point of the scale, crossed by the prolonged movable 
radius or arm, indicates the angle of inclination desired, provided that the 
edge, ab, coincide accurately with the single diameter of the semicircle. 
This diameter is jointed at 0, to admit of measuring angles which are partially 
imbedded. When the application of the two radii is completed, the joint, 
m, is to be tightened, and the whole brought back, until ab again coincides 
with the diameter. The inclination of the planes not intersecting each 
other in an edge, may also be measured by turning the movable arm until 
the two edges of the instrument are parallel to, or coincide with the plane 
faces in question. 
Much more accurate measurements may be obtained by the use of 
Wollaston’s reflecting goniometer (pl. 32, fig. 10), an instrument recently 
very much improved. Here, ab is a disk turning on an axis, e/, carrying a 
circle graduated to degrees on its periphery. Rotation takes place in such 
a manner that the disks, fg, ht, and ab, all turn at the same time with the 
horizontal cylindrical body forming their axis; in this axis another axis, 
el, may itself be turned by means of the button, cd; k is a clamp-screw, by 
means of which the entire system, fg, 12, ab, may be fixed by tightening 
hi; at the same time that this is done, the inner axis, el, may still be 
turned independently of the button cd, and any required position thus be 
given to the arm /p. This arm carries the jointed continuation, pm, 
turning on p. At m the crystal to be measured is fixed, and so adjusted, that 
the edge in which the two planes (whose inclination is to be ascertained) 
intersect shall be parallel to the axis el. The circle, ab, is now fixed by 
means of the screw &, and the axis el, turned by means of the button cd, so 
that the image of some distant object, as the horizontal bar of an opposite 
window, may be seen in one of the planes of the crystal. The spot from 
which the image is seen in the face of the crystal is marked by drawing a 
black line on paper, and so placing this paper as that its line may be seen as 
a continuation of the reflected line of the window-bar in the crystal. If we 
were to suppose a thin metal plate, polished on both sides, to be fixed at n, 
instead of the crystal, after obtaining the image of the window-bar in one 
of the faces, as just described, we should have to rotate it just 180° to see 
the same image in the other face. The case is similar in respect to our 
two crystal faces. If two of these be parallel, like the faces of our plate, 
the angle thus obtained will be 180°. Any other inclination will be 
obtained in a similar manner. The operation must be commenced by 
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