C. Palache — Crystal Measurement^ etc. 



283 



The discussion of the results may proceed directly, but is 

 simplified and hastened by the use of the graphical method. 

 This is based upon the gnomonic projection. In this projec- 

 tion the crystal faces are represented by the points of intersec- 

 tion of the face-normals with a plane tangent to the sphere of 

 projection and preferably normal to the chief zone of the crys- 

 tal. Thus in general the plane of projection is chosen parallel 

 to the vertical circle Y of the goniometer, that is, normal to 

 the prism zone of the crystal as usually mounted. 



1 "^ 



"^1 



+r 



i 



"^S\ / 



X 



\ 



' V\ 





x^ 



y^ * 



- 



■^-x 









Figure 4 shows a gnomonic projection. 8 is the projection 

 of the pole face or the face normal to the prism zone. The 

 circle described about s as center (Grundkreis) has a radius, r^ 

 equal to the distance from the crystal center to the plane of 

 projection. X and Y are the projections of the axes a and h. 

 \i r^\ and SY is taken as first meridian, then the position of 

 a face, /", is given directly in the projection by its angular 

 (polar) coordinates d= tg p and <^. Or it may be located by 

 the rectangular coordinates derived from the first, 



a; = sm<^ tg p. 

 y = coscf> tg p. 



The values for x and y may be calculated for each face from 

 its (f^ and p^ and plotted on ruled paper very rapidly, and this 

 projection gives a direct picture of the crystal showing its 

 degree of symmetry and the relations of its faces. Both 

 measurement and projection are the same for all systems, and, 

 if unknown before, the symmetry of the crystal may be found 

 from the projection. 



If the distance from crystal center to plane of projection 

 {= r) be taken as unity, and axis c equal to r, then in the rec- 

 tangular systems the values of x and y for the unit form which 

 are measured in the directions of the a and h axes respectively, 



