Crystallogensis. — Hensbldt. 303 
much talked about and sought after by muddle-headed phy- 
sicists. 
Many a student of Natural History, who has hitherto fought 
shy of crystallography on account of the mathematical ele- 
ment which is so prominently associated with it, would be 
startled to observe that behind its grim and uninviting exter- 
ior a world of fascination and splendor is concealed, and that 
in the wealth of its unsolved problems it affords a greater 
richer and fuller field for research than any of the old and 
Avell-beaten paths of animal and vegetable morphology. 
If we consider crystals of every possible shape or dimen- 
sion in reference to the essential factors by which the distinc- 
tive character of each is determined, viz. their axes of symme- 
try, we are struck by a curious fact. If we afterwards consid- 
er the same crystals in reference to their optical jiroperties — 
so far as the latter can be ascertained by sufficient transpar- 
ency — the same curious fact is again forced upon our attention 
and our astonishment is by no means lessened when we find 
it persistently manifested, no matter in what direction we ex- 
tend our comparison of general physical relations, such as 
thermotic, sound and heat-conducting properties, etc. This 
fact consists in the singular recurrence of the numbers 1, 2 
and 3. 
A crystal may be defined as an aggregate of particles, accum- 
ulated and symmetrically disposed in reference to certain lines 
or "axes" in obedience to laws which, as yet, are very imper- 
fectly understood. The fundamental number of these axis is 
three, though for the sake of convenience we assume four in 
one of our crystallographic systems. 
Now when we come to examine these lines of symmetry a 
little closer, we observe that only one system, viz. the isome- 
tric, is characterized by perfect axial uniformity ; the three axes 
are of equal length so that either may be regarded as the prin- 
cipal one. In two systems, however, only two of the axis are 
equal and in jthe remaining three all the axes are unequal. 
The numbers 1, 2 and 3 are thus manifested in the following : 
Axial clamfication . 
One system with 3 equal axes. (Isometric.) 
Two systems with 2 equal axes. (Tetragonal and Hexagonal.) 
Three systems with 3 unequal axes. (Orthorhombic, Mon- 
oclinic and Triclinic.) 
