56 NEW YORK STATE MUSEUM 
zontal axes which is indicated in figure 25 by the shaded portion. This 
plane intersects the surface of the sphere in a horizontal circle known as 
the fundamental circle (German, grundkreis) which passes through the 
poles of all prismatic planes. Connect the poles by a system of radiating 
a lines with the lower pole of the vertical axis; 
the points at which this system of lines 
intersects the plane of projection is shown in 
figure 26 which is known as a stereographic 
y projection of the planes of the calcite crystal 
co shown in figure 25. It is evident from 
/ figures 25 and 26: 
1 That the basal pinacoid will be pro- 
jected at the center of the fundamental 
— circle. 
Fig, 25 2 That the poles of all planes lying in 
the same zone will fall on the same great circle of the sphere. 
3 That the projections of the poles of planes lying in zones which 
include the basal pinacoid will he on radu of the fundamental circle. This 
applies to rhombohedrons and pyramids of the second order. 
In order to determine the relative positions of the pole of any plane 
such as K:-in spherical projections [fig. 26] it is sufficient to record the 
angular distance from a fixed point on the fundamental circle to the vertical 
great circle through the pole, and the angular distance measured on this great 
circle from the vertical pole (for hexagonal forms that of the basal pinacoid) 
to the pole of the given form. The first of these angles is known as ¢ and the 
second as e; they correspond respectively to geographic longitude and 
latitude, the fundamental circle corresponding to the geographic equator. 
The stereographic projection greatly facilitates the recognition of 
zonal relations and provides a graphic method of solution for many of the 
crystallographic problems.! 
‘The solution of problems in stereographic projection have been much simplified 
by the introduction of a set of stereographic protractors devised by 8. L. Penfield. Am. 
Joe, Sei, WYO, 278 Paracel 1111), 
