828 
SECOND REPORT- 1832 . 
popular notice as Haiiy’s establishment of the fixity of forms 
and the laws of their derivation, the subject has undergone a 
complete change since his time ; and a principle of classification 
of forms has been introduced, so scientific and yet so simple, 
that it is irresistibly superseding the older Haiiyian arrange¬ 
ments, and the more so, as it is strikingly confirmed by the op¬ 
tical properties of crystals. I speak of the division of forms into 
systems of crystallization; namely, the tesseral; the tetragonal, 
or square pyramidal, or pyramidal of Mohs ; the rhombic, or ob¬ 
long pyramidal, or prismatic of Mohs ; the rhombohedral of 
Mohs, or hexagonal of Naumann ; and the monoklinohedral, di- 
klinohedral, and triklinohedral of the last-named writer. Some 
notion may perhaps be formed of the nature of these distinc¬ 
tions from the following representation. 
If we conceive a square steeple with all the four sides of the 
walls and roof exactly alike, so that every slope and face which 
occurs on one side, occurs similarly on the other three ; we have 
before us a form belonging to the square pyramidal system. 
If instead of this we imagine a house of which the two ends 
are like each other, and the two sides also precisely like each 
other, but different from the former, this will belong to the 
oblong prismatic or rhombic system. 
If again we conceive a triangular pillar, as an ancient tripod, 
its three sides being similarly cut and ornamented; this will 
belong to the rhombohedral system *. In fact, its three faces 
may be terminated by slopes which may meet and form an apex 
resembling in all respects the apex of a rhombohedron. And 
if each of its three faces be formed into an edge by planes 
sloping to the right and left, the form may be thus converted 
into a six-sided pillar with no loss of its regularity. 
If we conceive the form of the house of which we spoke as 
representing the prismatic system to be made less regular by 
sloping its end walls in the direction of one end ; we have the 
monoklinohedral system; and if the side walls slope also, we 
may have thus the diklinohedral and triklinohedral forms. 
The tesseral or tessular system includes the forms which 
are derived from the regular solids of geometry, the cube, the 
octahedron,the dodecahedron. 
This distinction of different kinds of forms, is one founded 
on the most general relation of their parts, and regulated by the 
degree and kind of their symmetry. The claim of priority in 
introducing this classification of forms has been a subject of 
controversy between Prof. Mohs and Prof. Weiss. However 
this question may be decided, the merit of this valuable sim- 
* The rhombohedral and rhombic systems are quite distinct. A rhombic 
prism has its base a rhomb;—a rhombohedron has all its sides equal rhombs. 
