146 Mr Haidinger o/i the Series (^Crystallisation erf Apatite. 
the axis, or a, is expressed by V4.824 a quantity derived 
from measurements with the reflective goniometer. The com- 
bination of 11 with itself in a turned position, or 2 (R), assumes 
the appearance of an isosceles six-sided pyramid (fig. 9.), from 
which, however, it differs by its relative position to other forms 
of the series. Its terminal edges x, x, &c» are = 131° 14' ; the 
lateral z, z, &c. = 111° 20'*)“. In the pyramid P (fig. 10.), de- 
noted in the figure by the letter a?, the value of the kngles is the 
following: x, x, &c. = 142° 20'; z, z, &c. = 80° 25'+. It is 
almost needless to remark,. that the angle produced by two faces 
of P-f-QO (4f) is = 120^^, and that R — CO (P) intersects at right 
angles any one of the faces of P-f oo . 
I shall not endeavour to give here a full desenption of all 
those crystalline varieties of the species, which eitlier have been 
described by several authors, or which I have had myself an 
opportunity of examining; but it may be interesting to retrace 
a« many of them as will suffice for exhibiting a correct and pret- 
ty perfect general view of the series of crystallisation of rhombo- 
hedral fluor-haloide, and of those peculiarities by which it is dis- 
tinguished from the rhombohedral forms of other minerals. 
One of the most simple varieties to be found among the crys- 
tals of rhombohedral fluor-haloide, is the combination of R — oo 
(P) with P-boo (iff) fig. 11., or the regular six-sided prism, ter- 
minated by a plane perpendicular to its axis. It occurs in the 
apatite from Devonshire, from Saxony, and from other places. 
It is the only crystalline form of the asparagus-stone from Salz- 
burg; and it may here be observed, that the distinctive charac- 
terj which some mineralogists have endeavoured to introduce 
between apatite and asparagus-stone, founded upon the presence 
or the want of this face of R-— oo , has no foundation in nature. 
The axis of the rhombohedron being 
2a^—9 
a, the formula for finding the termi- 
4a^ -1-9 
*j- According to the formulae for the dirhombohedron, a being tlte axis of the 
• , , , , , /2a2-}-9\ 
simple rhombohedron -; cos x = = — I 7-— — ;r I ; cos z = — -f ^ l. 
$ According to the formulae for the isosceles six-sided pyramid, a being the 
axis of that rhombohedron, to which the pyramid belongs 1 
'2a2+27' 
/2a2+27\ /4a2_27\ 
2 ~ -p97/ 
