THE 
LONDON, EDINBURGH anv DUBLIN 
‘PHILOSOPHICAL MAGAZINE 
AND 
JOURNAL OF SCIENCE. 
[FOURTH SERIES.] 
MAY 1860. 
XLIII. Crystallographic Notices. By W. H. Mitisr, M.A., 
F.R.S., Professor of Mineralogy in the University of Cambridge*. 
On the Employment of the Stereographic Projection of the 
Sphere in Crystallography. 
." the Philosophical Magazine for July 1859, it is shown that 
the properties of anharmonic ratios may be used with 
advantage in constructing the gnomonic projection of the sphere 
by which Neumann represents crystallme forms, and also in 
constructing the projection applied to the same purpose by- 
Quenstedt. I was unable, at that time, to extend the method 
to the representation of crystalline forms, according to Neumann’s 
method, by the stereographic projection. Subsequently, however, 
I have ascertained that it is equally applicable to the stereographic 
projection, leading to a construction by which the centre of the 
projection of any zone-circle may be readily determined. Hence, 
having given the centre and radius of the primitive, the radius 
of the projection of a zone-circle may be found, being the hypo- 
thenuse of a right-angled triangle one side of which is the radius 
of the primitive, and the other side the distance of the centre of 
the projection of the zone-circle from that of the primitive. The 
construction for finding the magnitude of a line or angle from 
that of the anharmonic ratio into which it enters, will be found 
in art. 13 of the paper in the Philosophical Magazine referred 
to above. 
Let P, Q, R,S be the centres of the projections of four zone- 
circles K P, K Q, K R, KS passing through the point A; K the 
projection of K; efg, pqgr the symbols of AP, KAR; hkl, 
uvw the symbols of the poles Q, Sin the zone-circles K.Q, KS, 
* Communicated by the Author. 
Phil, Mag. 8. 4. Vol. 19, No. 128, May 1860. Z 
