16 ORYSTALLOGRAPIIY. 
another rhombic prism; but, unlike figs. 3 and 4, the prisms are 
inclined backward, and are therefore oblique prisms. The lat- 
eral axes (a, 6) are at right angles to one another and unequal, 
as in the preceding system; but the vertical axis is inclined to 
the plane of the lateral axes. Jt is inclined, however, to only 
one of the lateral axes, 1t being at right angles to the other. 
Hence, of the three angles of axial intersection, two are rec- 
tangular, namely a on 6, and ¢ on 6, while one is oblique, that is 
ce (the vertical axis) on a. . In allusion to this fact, there being 
ouly one oblique angle, this system is called the Monoclinic sys- 
ten, from the Greek for one and inclined. 
Fig. 7 represents an oblique prism with a rhomboidal base 
(like fig. 12). The three axes are unequal and the three axial 
intersections are all oblique. The system is called the Zriclinic 
system, from the Greek for three and inclined. 
Fig. 8 represents a six-sided prism, with the sides equal, and 
the base a regular hexagon. ‘The lateral axes are here three in 
number. They intersect at angles of 60°; and this is so, 
whether these lateral axes be lines joining the centres of oppo- 
site lateral planes, or of opposite lateral edges, as a trial will 
show. The vertical axis is at right angles to the plane of the 
three lateral axes, inasmuch as the prism is erect or right. The 
base of the prism being a regular hexagon, the system is called 
the Hexagonal system. 
The systems of crystallization are therefore : 
I. The Isometric system: the three axes rectangular in in- 
tersections ; equal. 
Il. The Dimetric or TETRAGONAL system: the three axes 
rectangular in intersections; the two lateral axes equal, and 
unequal to the vertical. 
« IIL. The Taiwetric or OrTHORHOMBIC system: the three axes 
rectangular in intersections, and unequal. 
IV. The Monoctirnic system: only one oblique inclination 
out of the three made by the intersecting axes; the three axes 
unequal. 
V. The Tricuinic system : all the three axes obliquely inclined 
to one another, and unequal. 
VI. The HExaGonat system: the vertical axis at right angles 
to the lateral; the lateral three in number, and intersecting at 
angles of 60°. 
‘These six systems of crystallization are based on mathemati- 
cal distinctions, and the recognition of them is of great value 
in the study and description of crystals. Yet these distinctions 
are often of feeble importance, since they sometimes separate 
