42 



University of California. 



I Vol. :s. 



90° Ti . The reflection from the prismatic faces were, by 

 means of the centering and ad justing' tables, brought to revolve 

 directly in the line of the vertical crosshair, on turning 1", and 

 the crystal thus brought into true polar position, because a 

 plane normal to the prismatic zone would then be at 7? . The 

 reading on V for the clinopinacoid is the v for this circle, 

 which would be different for each crystal. Owing to imperfect 

 centering or other causes, readings on V or on H for certain 

 faces vary, when they should be the same; consequently both v 

 and h can be corrected by averaging the different readings. 



When the reflection of each face is brought at the intersec- 

 tion of the crosshairs, two readings, one on V = r, and one on 

 H = //, are made; the face is then defined by two angular 

 coordinates, 4> = t t'o and p = h — //,,. 



Symbols p q. — In place of the three indices of Miller for a 

 terminal form, Goldschmidt uses the two indices p and q, and 

 tor calculations, and in the gnomonic projection, the two indices 

 are preferable. The indices of Miller are readily transposed into 

 those of Goldschmidt by making the last one equal to unity and 

 not expressing it; thus 522 (Miller) becomes fl (Gdt). Fur- 

 thermore 001 = 0, 100 = xO, 010 = Ooo, 110 = go, 210 — 

 2 co = ^T 00 ' = '~ Xj ~y- When p and q are equal, but one is 

 expressed, thus 331 = 3. The zonal relations of forms are 

 better shown by the two symbols, because all forms having the 

 same p, or the same q., lie in the same straight line or zone; for 

 example, it can be seen that the forms f f, £f, ff are 

 tautozonal, whereas their Miller equivalents (564), (296), 

 (8.15.10) do not show this relation so well. 



Gnomonic Projection. — This projection shows the points of 

 intersection of the face-normals, drawn from the center of the 

 crystal, upon a plane lying preferably normal to the prismatic 

 zone and at a unit's distance from the center of the crystal. If 

 h is the distance of this plane above the center and is equal to 

 the c-axis, and r is the length of the base normal, then in crys- 

 tals with rectilinear axes r = h — 1. In monoclinic crystals 

 the base is oblique to the plane of projection, and with h = 1, 



r is equal to ^~g' = "sj^ ; whence it follows that with r = 1, 

 then h = sin f*. 



