328 Prof. Miller’s Crystallographic Notices. 
It is easily seen that the centre of the stereographic projection 
of a zone-circle is Quenstedt’s projection of the corresponding 
zone-axis, the nearer pole of the primitive being the fixed point 
of Quenstedt’s projection ; and that the straight line through the 
centres of the stereographic projections of two zone-circles, is 
Quenstedt’s projection of the face having its pole in the inter- 
section of the two zone-circles. 
On the Measure of the Dihedral Angles of Crystals. 
Euclid’s definition of a dibedral angle takes no account of the 
difference in the nature of the matter on opposite sides of the 
planes forming the dihedral angle; therefore, though sufficient 
for the purposes of geometry, it must be modified to suit the 
requirements of crystallography. The dihedral angle made by 
two faces of a crystal, considered as planes separating matter of 
one kind from matter of another kind, may be measured in two 
different ways; either by the angle between normals to the faces, 
drawn from any point within the crystal towards the faces; or, 
by the supplement of this angle. The latter measure, which 
was unfortunately adopted by the earlier crystallographers, leads 
to the preposterous conclusion, that if two plane mirrors be 
placed back to back, with their faces perpendicular to a given 
straight line, the angle which the face of one mirror makes with 
itself is 180°, and the angle which the face of one mirror makes 
with that of the other, is 0°, though the mirrors are in the most 
dissimilar positions, having their faces directed to points dia- 
metrically opposite. It is scarcely possible that this measure 
would have been adopted if the invention of the Reflective 
Goniometer had preceded the crystallographic researches of Romé 
de V’Isle. In order to give an angle by a single reading, in 
accordance with Carangeot’s goniometer, Wollaston repeated the 
numbering of the graduation in each semicircle (a source of 
ambiguity in the recorded observations), instead of numbering 
up to 360°, as is usual in circular instruments, and introduced 
two stops and a spring which permitted the circle to turn only 
in a direction contrary to that of the numbering, and enabled 
the circle to be fixed nearly at 0° and 180°. This contrivance 
was but partially successful ; for it only gave the angle between 
two faces one of which was observed at 0° or 180°, leaving the 
other dihedral angles to be obtained by subtracting the difference 
between the corresponding readings from 180°; and in the most 
carefully constructed instruments the adjustment of the stops 
was too uncertain to fix the zero of the vernier at 0° or 180°, 
without leaving an error too large to be neglected. In the best 
goniometers now constructed the stops are omitted, and the gra- 
duation is numbered up to 360°. The difference of the readings 
