276 Penfield — Solution of Prohlems in Crystallography 



and then constructing a small circle s' c' about d at a distance 

 of 24° W. A chord from h at right angles to the radius 

 through z was found to intersect the front radius at ^a. 

 The slope of z, measured with the stereographic scale, was 

 54° lh\ calculated 54° 16', and a line at this angle intersects 

 the perpendicular from z' at a distance equal to ^c. The 

 parameter relation of z is therefore %a \h : ^c^ gi'^ing as the 

 indices 324. In addition to the lines needed for the graphical 

 solution of the foregoing problem, numerous zones are shown 

 in figure 23 which were easily determined by means of the 

 great circle protractor. The figure indicates that, starting 

 with the poles of m (110) and o (Oil), it would have been a 

 simple matter to have determined the location of the poles and 

 the symbols of all the forms by no other means than zonal 

 relations. 



MoNocLiNic System. 



The graphical methods employed in this system may be 

 illustrated by pyroxene, a crystal of which is represented in 

 orthographic and clinographic projection in figure 24. The 

 figure, which represents a common habit of pyroxene from 

 northern ]N"ew York and Canada, was drawn • by Mr. H. H. 

 Robinson. As fundamental measurements the following were 

 chosen: mA7n, 110a110 = 92° 50'; a A c= 100 A 001 = 74° 15'; 

 and dAs, 101 A HI = 29° 35'. In stereographic projection, 

 figure 25, the location of the poles of the prism m and of the 

 base c, the latter by means of the stereographic scale, need no 

 special comment. The construction of the great circles through 

 T/i and c is then an easy matter, and the angles which they 

 make at e with the vertical diameter are equivalent to r of 

 figures 6 and 8. The measurement of r, 47° 30', was made on 

 the great circle GC 2X 90° from c."^ Since ;-, figure 6, is 90° 

 in the monoclinic system, the tangent of r must equal the 

 len2:th of the a axis ; hence r was laid off from J, and a deter- 

 mined as 1-093, calculated 1*092. Since d As^lT 35', iM 

 must be the complementary angle, 60° 25' ; hence the pole of 

 s was located by the intersection of a small circle (60° 25' 

 from V) with the great circle through c and m. Great circles 

 through a and s and h and s were then drawn, thus determin- 

 ing the poles of j? and d. The angle ;r, compare figures 6 and 8, 

 was measured on the great circle (diameter) at 90° from a^ and 

 found to be 30° 35' ; hence, referring to figure 6, since a is 

 90°, the tangent of tt must equal the length of the c axis, 

 which, when plotted from J, was found to be 0*592, calculated 

 0*589. The arcs mp and nic^ measured with the small circle 



* This Journal (4), xi, p. 18, 1901. 



