CALCITES OF NEW YORK 55 
position of the crystal faces in space without regard to their relative develop- 
ment or crystal habit. 
2 Linear projections, which are, in a measure, diagramatic and which 
show by a system of intersecting lines, the intersection of the crystal faces 
with some assumed plane or with one another as projected on some assumed 
plane. The latter type of projection shows the relative development of 
the forms present and presents to the eye an idealized picture of the crystal 
combination. 
3. Models, which, constructed of paper, cardboard or of some easily 
workable material, present in three dimensions the idealized representation 
of the forms in relative development. 
SPHERICAL PROJECTIONS 
The method of spherical projection was introduced by F. E. Neumann! 
and later adopted by Miller. 
Stereographic projection. To develop the principles of this method 
assume the crystal of calcite shown in figure 25 to be placed with the center 
of its crystallographic axes coincident with the center of a circumscribed 
sphere of any convenient radius. From the 
common center assume radii normal to the 
faces of the upper half of the crystal. The 
points where these normals intersect: the 
surface of the sphere are known as the poles 
of the corresponding faces and accurately 
represent the relative position of the crystallo- 
graphic planes, inasmuch as they provide a 
means of measuring the angles between the 
normals, which is the supplement of the inter- 
facial angles, between any two planes. To 
reduce the above system of poles distributed over a spherical surface to 
a flat projection assume for the plane of projection the plane of the hori- 
*Neumann, F, E. Beitrage zur Kristallonomie, Berlin 1823. 
