CRYSTALLOGRAPHY. 9 
equally inclined severally to the adjoining faces, Only edges that are 
formed by the meeting of two simular planes can be truncated or bev- 
elled. The angle between the truncating plane and the plane adjoining 
it on either side always equals 9)” plus half the interfacial angle ove) 
the truncated edge. When a rectangular edge, or one of 90°, is trun. 
cated, this angle is accordingly 135° (=90°+ 45°); when an edge of 70°, 
it is 125° (=90° + 35°); when an edge of 140°, it is 160° (=90° +70°). 
7. Zone.—A zone of planes includes a series of planes having the 
edges between them, that is, their mutual intersections, all parallel. 
Thus is: Fig. 14, on page 6, O at top of figure, 22, 7+, O in front, and 
two planes below, and others on the back of the crystal are in one zone, 
a vertical zone. Again, in the same figure, O at top, 42, 33, 22, 42, 72, 42, 
22, 33, and the continuation of this series below and over the back of 
the crystal lie in another vertical zone. And so in other cases, in 
other directions. All planes in the same zone may be viewed as on the 
circumference of the same circle. The planes of crystals are generally 
all comprised in a few zones, and the study of the mathematics of 
crystals is largely the study of zones of planes. 
Azes.—Imaginary lines in crystals intersecting one another at their 
centres. Axes are assumed in order to describe the positions of the 
planes of crystals. Ineach system of crystallization there is one verti- 
cal axis, and in all but hexagonal forms there are two lateral axes. 
Diametral sections. —The sections of crystals in which lie any two of 
the axes. In forms having two lateral axes, there are two vertical 
diametral sections and one basal. 
Diametral prisms.—Prisms whose sides are parallel to the diametral 
sections. 
Measurement of Angles. 
The angles of crystals are measured by means of instruments called 
goniometers. These instruments are of two kinds, one the common 
gonwmeter, the other, the reflecting goniometer. 
The common goniometer depends for its use on the very simple prin- 
ciple that when two straight lines cross one an- 
other, as A H, C D, in the annexed figure, the parts = D 
will diverge equally on opposite sides of the point 
of intersection (O); that is in mathematical lan- De 
guage, the angle A O D is equal to the angle COE, 
and A OC is equalto DO HE. 
A common form of the instrument is represented in the figure on 
page 10. 
The two arms @ 0, cd, move on a pivot at 0, and their divergence, 
or the angle they make with one another. is read off on the graduated 
are attached. In using it, press up between the edges @ o and ¢€ a, 
the edge of the crystal whose angle is to be measured, and con- 
tinue thus opening the arms until these edges lie evenly against the 
faces that include the required angle. To insure accuracy in this 
resvect, hold the instrument and crystal between the eye and the light, 
and observe that no Jight passes between the arm and the applied faces 
oi the crystal. The arms may then be secured in position by tighten- 
ing the screw at 0; the angle will then be measured by the distance on 
the are from £ to the /ft or outer edge of the arm c d, this edge being in 
_ the line of 0, the centre of motion. As the instrument stands in the 
