52 MINERALOGY. 
different rhombohedrons, derived from the fundamental rhombohedrons. 
Figs. 77 and 78 represent the natural situation of two rhombohedrons. 
3. InTERNAL STRUCTURE OF CRYSTALS. 
What we have said in the preceding section has reference to the external 
form only, whatever might have béen the relation in this respect between 
the different figures. A close investigation, however, discloses the fact, 
that they sustain remarkable relations in respect to their internal structure. 
Many crystals, on being broken, naturally separate into definite forms, as 
caleareous spar into rhombohedrons, and galena into cubes. Nearly all 
crystals may be split, by means of a sharp knife and a hammer, into certain 
other forms of the same system. Thus fluor spar may, by cleavage, he 
converted from a cube into a regular octahedron. We may, in many cases, 
therefore, suppose a crystal to be a mass built up of those elementary forms 
into which they split. Hauy, the founder of the science of crystallography, 
assumed an elementary form for each system, and supposed all forms 
belonging to a system as composed of aggregations of such simple forms. 
It would rather seem, however, that each crystal is composed of very small 
crystals of the same form; that a cube must be composed of smaller cubes ; 
and that an octahedron is not composed of regularly decreasing layers of 
small cubes, as according to figs. 92 and 93, given by Hauy, but consists 
of a mass of very small octahedrons. Besides these peculiarities, there are 
crystalline formations of interest, which appear to consist of a series of 
layers, regularly applied to an originally minute crystal. On making a 
section of such a crystal, we may see a series of concentric outlines 
inclosing the central nucleus, these different outlines indicating so many 
different layers, being often of different colors. This feature is often seen 
in six-sided prisms of calcareous spar, and in quartz (figs. 88 and 89). 
Besides the fact that a large crystal may be produced by a regular 
ageregation of smaller ones, several distinct crystals may unite or grow 
together, and produce a definite form. Combinations consisting of two 
individuals are called twin-crystals. Groups of a similar character, 
consisting of many individuals, are frequently found. Substances which 
crystallize in right rhombic prisms, sometimes exhibit a stellated grouping 
( fig. 79). 
4, MrasurEMENT OF THE. ANGLES or CrysTALS, AND THE NeEcrEssary 
APPARATUS. 
In section two it has been shown that the positions of the surfaces 
inclosing a crystal depend on the axes. Hence it follows, that as these 
axes occupy a definite angular relation to each other, the faces of the 
crystal must mutually exhibit the same relation. In consequence of this 
dependence we are enabled to tell the inclination of the axes, knowing that 
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