Mr Haidinger on the Series (^X^rystallisation qf Apatite. 151 
in these combinations contiguous to both the apices, only the 
right, or only the left faces of the scalene six-sided pyramids 
can be observed. The inclination of u to if/ is=rl50° 40.5', that 
of 6 to M— 157° ; this inclination being equal to the sum of 
one-half of the angle at the lateral edge of (P -f n)”^, and 90° 
As to the twelve-sided prisms, it is evident, from the horizon- 
tal edges of combination between u 8.nd c, that the latter is the 
limit of that very same series of which the former is a member. 
Since it does not appear with the full number of its faces, but 
only with those which, considered from one extremity of the 
crystal, appears on the left, from the other on the right of the 
faces of E., its representative sign v/ill be 
1 (P + ^)L 
For the want of appropriate edges of combination, I have 
been obliged to resort to immediate measurement for ascertain- 
ing the position of the faces, marked y, and the law, by which 
the form produced by these faces depends upon the fundamen- 
tal rhombohedron R. The prism in question is the limit of 
that series of six-sided pyramids, whose derivative exponent is 
the number The sign of these faces as they appear in the 
combination, to the right of R on the one side, and to its left 
on the other, will therefore be ~ * 
i 
The angles of the transverse . section of the two twelve-sided 
prisms are the folio v/ing : 
Angle y, contiguous to the 
faces of 2(R), or of R -f- oo (e). 
Angle z, contiguous to the ter- 
minal edges of 2 (R), or to the 
faces of P -f CD (M). 
(F -1- o) )5 
158° 12' 48" 
14r 47' 12" 
(p+«r 
141° 47' 12" 
158° 12' 48" 
The lateral edge z Fig. 16., is obtained by the formula, 
( (3m2-.l)a2 — 9\ 
(3 9^2 + 1) aQ -1-9 I 
n being the axis of the rhombohedron, and m the exponent or number of derivU" 
Uon upon which the pyramid depends. 
