1819.] Hatiy on the Measuring of the Angles of Crystals. 423 
The largest of the crystals sent me by M. Selb (represented 
in fig. 9), exhibits the faces s, /, which I have not observed in any 
of the crystals from England. This induces me to give here a 
complete description of the variety to which this crystal belongs. 
I call it dectsexdecimal. 
But I must premise that, for reasons the explanation of which 
would carry me too far from my subject, I have adopted relatively 
to all the secondary forms which have an octahedron for nucleus 
the method indicated in my Treatise (tom. i. p. 464) for those 
derived from the regular octahedron. It consists in transforming 
the octahedron into a parallelopiped by the addition of two 
tetrahedrons, similar to those obtained by the mechanical division 
on two opposite faces of this octahedron ; and in considering 
the decrements on which the secondary faces depend, as taking 
place on the edges or angles of the parallelopiped by the abstrae- 
tion of one or more ranges of small parallelopipeds of the same 
form. The parallelopiped substituted for the octahedron in the 
present case, represented in fig. 10, results from the application 
of two tetrahedrons on the face P’ (fig. 8) and on its opposite 
face. After this way of viewing the crystal, the sign, represent- 
ing the present variety, is 
P E*(¢ EB’ D’y A 
PS L O 
The decrements producing the faces /, s (fig. 9) are so con- 
nected, that the intersections y, y, of the first with S and P”, are 
exactly parallel. 
The following are the measures of the different angles result- 
ing from my determination : 
Incidence of P on P” 76° 1927 
pe P’ 101 32 
ir P’ 119 51 
P o 41 54 
p” o 129 14 
P s 154 17 
p” s 141 40 
Z P” 156 15 
Z s 166 25 
l o 1385 55 
Before coming to the consequences which flow from all that 
precedes, I must explain the method which I followed to deduce 
from observation the data which enabled me to resolve the 
evens relative to the determination of the crystalline forms. 
e quantities composing the formulas, which represent generally 
the sides of the triangles, which I call measuring, express certain 
lines which we may conceive traced on the surface of the primi- 
tive solids, or drawn in their interior, such as the diagonals of 
