270 Penfield — Solution of Problems in Crystallography 



sheets, a small circle through j? was constructed which inter- 

 sected the small circle prex^iouslj drawn at the point marked 

 317. Through the point thus found a radius was drawn, which 

 intersected the divided circle at 18° 25^ and from 010 a line 

 at right angles to the radius was drawn, thus determining the 

 intercept ^ on the first axis, as also the base-line Oy. The 

 angle of cube on hexoctahedron is 21° 19^, hence a line drawn 

 from the center at this angle was found to meet the perpendic- 

 ular from y' at O'lll, determined by scale JSTo. 4 of the printed 

 sheets, or practically jth of the radius, the true value being 

 O'llS ; hence the axial relation of the face under consideration 

 is ^a : a : ja, the indices being 317. 



It is always an advantage to plot near the periphery of a 

 stereographic projection, where the spaces between degrees 

 are larger than near the center; therefore a solution, similar to 

 the one just given, but made about 100, is also shown in figure 

 17. The small circle with radius 21° 19', taken from scale 

 ISTo. 2, was first drawn about 100. All points on the zone 100 

 to Oil are 90° from Oil, hence the desired polejnay be located 

 by means of a small circle constructed about Oil at a distance 

 of 79° 21'. To do this, two points were located on the hori- 

 zontal diameter at 79° 21^ from Oil, to the right and left, 

 making use of scale E'o. 3 of the printed sheets. One of these 

 points is at s, figure 17, the other too far to the left to be 

 shown, and through them the small circle so was con- 

 structed, which intersects the small circle previously drawn at 

 the desired point, marked 713. To find the symbol, the radius 

 through the pole 713, and the chord from 010 at right angles 

 to it, were drawn ; thus the intercept on the first axis was found 

 to be 0*111 or \. By means of the stereographic scale the dis- 

 tance from 001 to the pole 713 was found to be 67°, and this 

 angle plotted from the center intersects the perpendicular from 

 x' at 0'333 or ^. The axial relation is therefore \a : a : -}(Z, 

 the indices being 713. The distance from 713 to 317, meas- 

 ured with the small circle protractor, was found to be 43° 15', 

 theory 43° 13'. 



Tetragonal System. 



In this system the problem presents itself of finding from 

 one fundamental measurement the length of the vertical axis, 

 and from interfacial angles the symbols of occurring forms. 

 The example chosen for illustration is a crystal of octahedrite 

 from Brazil, given to the writer by Professor Groth of Munich. 

 The crystal, shown in figure 18 in orthographic* and clino- 



* The orthograpliic projection is represented as revolved 18° 26' about the 

 vertical axis, the reason for which will be explained in an article now in 

 preparation. 



