and Mineralogy. 155 
Explanation hy example. , Problem of Crystallography 
for a particular case. — Let Fig. 1. PL VIII. represent a crystal- 
lisation of calcareous spar. The form is a compound one, and 
all the faces of the same description belong to the same simple 
form contained in it. The junction of those simple forms is 
symmetrical, because it possesses the highest degree of regulari- 
ty which their nature and position can admit. The symmetry 
in this case is expressed by the parallelism of the several edges 
of combination : and the general problem of crystallogl’aphy is 
here transformed into the special one, (f finding the circum- 
stances under which the edges of combination obtain their paral- 
lelism. 
6. Preparation for the solution. Developement f the com-- 
hinations. — If in any combination the homologous faces (the 
faces agreeing in figure and position,) are ' enlarged till all the 
rest having disappeared, they alone 'bound the wliole solid on 
every side, the simple forms which the combination included, 
will successively appear. By this operation, from the faces g^ 
P, f m^ 6, of Fig. 1., we obtain five rhomboids, (Fig. 3. % 5. 
6. PI. VIII.) ; and from the planes x, y, «, three scalene six- 
sided pyramids^ — pyramids consisting of scalene triangles, (as 
Fig. m PI. VIII.) 
7. Position of the Rhomboids in the Combination. — The 
rhomboids have a particular arrangement in the combination, 
viewed in the distribution presented by this example, the edges 
of any rhomboid, and the oblique diagonals drawn upon the 
faces of the one which follows it, lie in the same vertical plane. 
Such combinations as do not include an uneven number of 
rhomboids, are arranged, so that the edges of one rhomboid 
lie in the same vertical plane with the edges of the next, and 
the diagonals of the one with the diagonals of the next. In 
Fig. 2, 3, 5. 1£. 6. PI. VIII., taken in the order assigned to 
them, (6.) this arrangement is observable. 
8. Combination of two rhomboids. — If the faces of any two 
rhomboids, which stand contiguous in the above mentioned 
order, g and P, for instance, or P andy^ or y’ and m^ or m and 
h of Fig. 1. PI. VIII., are vsimultaneously enlarged, till all the 
other faces disappear, and the faces of this pair include the whole 
solid; a form results, which is a combination f those rhomboids^ 
