166 Mohs’ Systeni of Crystallography 
4S. Some Applications. Division of Combinations. — The first 
application of the doctrines now explained respecting crystallisa- 
tion, is shewn in the easy and accurate division of combinations. 
Fig. 4. Plate VIII. represents a combination of two rhom- 
boids. The parallelism of their edges of combination shews, 
that they form two immediately adjacent members of the same 
series. Hence, if we know the dimensions of the one, we shall 
also know those of the other, and the magnitude of the edges of 
combination likewise. Fig. 13. PI. VIII. is a combination of two 
rhomboids and two scalene six-sided pyramids. As the rhom- 
boids produce parallel edges of combination with each other, they 
must form two consecutive terms of the same series the more 
acute. And since the faces of the pyramids in like manner pro- 
duce parallel edges of combination with each other, those pyramids 
must also form two consecutive terms of the preceding se- 
ries (35). Again the edges of combination between y*and a?, Fig. 
13. Pi. VIII. are parallel to the edges of the rhomboid f; and 
the edges of combination between P and r, to the edges of the 
rhomboid P. The former pyramid, consequently, depends on 
the rhomboid f the latter on the rhomboid P (32). If, there- 
fore, we can discover that r is a secondary, or a- a primary py- 
ramid, which, after some acquaintance with these forms has 
been gained, may be decided by the eye itself ; and if we know 
the dimensions of one rhomboid, P for example ; from these da- 
ta we are enabled to find every dimension of the whole com- 
bination. Fig. 1. PI. VIII. represents a combination of nine 
simple forms. The edges between g and t are parallel to those 
between t and P, to the oblique diagonals of g^ and also to 
the axis-edges of P. Let Pr=?"; then is r— 1. The 
edges between P and f are parallel to each other, to the axis- 
edges of f and to the diagonals of P. Whence f is = r -f- 1* 
The edges between f and m stand in a similar relation ; conse- 
quently m is r + 2. But farther, the edges between m, a 
and h are parallel ; consequently h is = r -f- 3. Flence the 
rhomboids included in this combination form five consecutive 
terms of one series. Moreover, the edges between w and f be- 
ing pai'allel to the axis-edges of ^ a? is a scalene six-sided pyra- 
mid depending onj^ that is, on r -1- 1 ; and the edges between 
X and a being parallel to those between x and f and therefore 
