150 Mr Haidinger on the Series (f Crystallisation of Apatite, 
Hence IA= J a^ and the axis of the pyraxnid, 
is — § a. The exponent m is therefore and the original sign 
for the pyramid == (P)!, which, on account of the peculiar cha- 
racter of the combinations, still must undergo a farther modifi- 
cation. 
The pyramid h is determined by the parallelism of the edges 
of combination between s and 5, and between h and M. In 
Fig. SO., as in the preceding, ABKC is one of the faces of R, 
but A'EB, A'BD, and A'DC, are three faces of P-}-l,.and 
not of P, because in this consists the difference between the two 
cases. The axis of the derived pyramid is equal to 2 I A 4 * | 
AG. In order to find lA, we have 
lA: AN=r:IA-h AG: GK, 
and, a being the axis of K, 
lA : J = lA 4- I : 1 . 
Hence lA iz § and the axis of the pyramid :=z I a. The 
original sign of the pyramid becomes therefore (P)^. 
The signs (P) 3 ' and (F)^, although they in general denote 
the direction of the faces, yet do not suffice for expressing that 
mode in which they are contained in the combinations of the 
species. According to the method of Professor Mohs, i the sign 
of a dirhombohedron in general is S (R 4 n), that of ^ is 2 (R) ; 
in a like manner the dipyramids are in general designated by 
2 ((p+ n)«^). Supposing, in the developed combination, all the 
faces of the pyramids to appear, these signs would become, 
2 ((P)^) and S ((P)?). But there are only the alternating 
faces to be observed in the combinations, and the way to denote 
the pyramids, including the situation of their faces to the right 
or the left of the faces of R, will therefore be : 
I g((p)b 
r t 
, and 
1 Q f (pxs) 
- — as referring to the figures. The addition of the 
r 
letters r (right), and 1 (left), is required for distinguishing the 
combinations occurring in apatite, from those which are to be 
met with in quartz, where, in different individuals, we have to 
express by ~ (Fig, S.) and (pig. 4 ,)^ that 
