48 



CRYSTALLOGRAPHY. 



2. Lettering of Crystals.— The prism of fig. 5 is lettered £-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 

 i-2 circumscribing that of the prism I. 

 The plane i-2 is produced to meet axis 

 «, which it does when a is extended to 

 twice its length ; whence the ratio for 

 the axes a, a', is 1 : 2. 



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, 3, 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 z'-2, arid by the first figure the rel- 

 ative lengths of the vertical axes. 



In the twelve-sided prisms such ratios as a-f, i-%, i-% 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-f 

 (fig. 2), 4-ij, 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. Kemihedral Forms. — Fig. 13 represents a crystal of apa- 

 tite in which there are two sets of planes, o (=3--§) and o' (=4-|) 

 which are hernihedral, only half of 



the full number of each 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 



o*'er those suppressed in the lower 



pyramid. If the student will shade 



over half the plants alternately of 



Ike two pyramids, putting the 



shaded planes above directly over 



those below, he will understand the nature of the hemihedrism. 



In some hernihedral 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 



APATITE. 



