46 MINERALOGY. 
amount of roughness, of unctuosity or softness, and of polish. Some give 
out a peculiar sound when struck, or afford a peculiar taste, or smell, of 
which others again may be destitute. The determination of their hardness 
is of great value in distinguishing minerals, for which purpose we may 
employ the ingenious method of Mohs, of rubbing fragments of two different 
species together, and examining which of the two scratches the other. 
The different degrees of hardness may thus be represented by a scale 
beginning with the softest ; and any mineral in the scale will be scratched 
by those below, but not above it. The hardness of any mineral may then 
be subjected to comparison with that of the standard. This scale of 
hardness, as introduced by Mohs, is as follows : 
Talc; common laminated green variety. 
Unerystallized gypsum. 
. Foliated mica. 
Transparent calcareous spar. i 
Crystallized fluor spar. 
Apatite. 
54. Scapolite-crystalline. 
wo wo = 
Nie ° x 
er ore Ge 
6. Feldspar-white, cleavable variety. 
7. Transparent quartz. 
8. ‘Transparent topaz. 
9. Corundum (sapphire). 
10. Diamond. 
Thus, a mineral which abrades feldspar, but not topaz, is said to have a 
hardness of seven, equivalent to that of transparent quartz, &c. The 
external shape of minerals is also of great interest and importance. This, 
indeed, in many cases is objective, being determined by that of other bodies ; 
sometimes by the gravity of the mass itself; but in most instances there is 
another subjective form, independent of extraneous influences, and peculiar 
to the particular species of mineral. Direct observation first of all teaches. 
us that the natural form of every mineral is a solid, bounded by plane 
surfaces. A still closer examination enables us to ascertain that the true 
external shape of a mineral is that of a closed figure, bounded by sharp 
edges and angles, the points and lines of intersection of the planes just 
mentioned. Bodies thus inclosed are called crystals. In view of the appa- 
rently infinite variety of crystalline forms, we might at first be induced to 
suppose that the precise outline of any body is capable of being infinitely 
and indefinitely varied ; observation, however, shows this not to be the case, 
nature here exhibiting a remarkable simplicity, and a most admirable law. 
As mineralogy deals with solid bodies, that method for their determination 
were most desirable which mathematics shows to be the simplest. A body 
has height, thickness, and breadth; thus, three dimensions. Clearly to 
illustrate and compare these three forms of extension, let us suppose the 
height to be indicated by a vertical line, which shall in future be called the 
principal axis. Let other lines be passed through this principal axis, at 
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