48 CRYSTALLOGRAPHY. 
2. Lettering of Crystals.—The prism of fig. 5 is lettered 7-2, be- 
cause it is parallel to the vertical axis, and has the ratio of 1: 2 between 
two lateral axes. This is shown in the annexed figure, which repre- 
sents the hexagonal outline of the prism 
t-2 circumscribing that of the prism J, 
The plane 7-2 is produced to meet axis 
w, which it does when @ is extended to 
twice its ee whence the ratio for 
the axes a, @, 
The numbers 1. 2, on the double hexa- 
gonal pyramids in fig. 1 indicate the 
relative lengths of the vertical axis 
of the two pyramids, they having the 
same 1:1 ratio of the lateral axes; and 
so in figs. 2, 5, and others. 
The lettering on the pyramids of the other series in fig. 3, 1-2, 2-2, 
4-2, indicates. by the second figure, that the planes are in the same 
vertical zone with the prismatic plane 7-2, and by the first figure the rel- 
ative lengths of the vertical axes. 
In the twelve-sided prisms such ratios as 1-2, 2-4, 7-2 occur. The 
fraction in any case expresses the ratio of the lateral axes for the par- 
ticular planes. The double twelve-sided pyramids have the ratios 3-3 
(fig. 2), 4-3, and others. Both in these forms and the twelve-sided 
prisms, the second figure in the lettering, expressing the ratio of the 
lateral axes, has necessarily a value between 1 and 2. 

3. Hemihedral Forms.—Fig. 13 rep eee: : ee of a 
tite in which there are two sets of planes, 0 (=3-3) and o’ (=4 
which are hemihedral, only half of 
the full number of éach o existing - 
instead of all. This kind of hemi- 
hedrism consists in the suppression 
of an alternate half of the planes 
in each pyramid of the double 
twelve-sided pyramid (fig. 10), and 
in the suppressed planes of the 
upper pyramid being here directly 
over those suppressed in the lower 
pyramid. If the student will shade 
over half the planes alternately of 
the two pyramids, putting the APATITE. 
shaded planes above directly over 
those below, he will understand the nature of the hemihedrism. 
Jn some henuhedral forms the suppressed planes of the upper 
pyramid alternate with those of the lower; but this kind 
occurs only in the rhombohedral section of the hexagonal 
system. 
4, Cleavage,—Cleavage is usually basal, or parallel to a six 
a- 
4-4) 
=) 

