hy Means of GrajMcal Methods. 



269 



between 001 and 210, determined by the intersections of zones. 

 Their distances from 001 being measured with the stereo- 

 graphic scale, the slopes may be plotted either from x' to the 

 right or, better, from the center, and their intersections with 

 the vertical radius, or the perpendicular erected at x' to the 

 left, then determined. The distances from 001 to the several 

 poles, measured with the stereographic scale, were found to be 

 as follows : 



Form 215 214 213 212 211 421 



Measured, 24° 5' 29° W 36° 55^ 48° 10' m° 00' 77° IW 

 Calculated, 24 5 29 12 36 42 48 11 65 54 77 23 



Two methods for determining the symbol of a hexocta- 

 hedron, observed in combination with the cube on crystals of 



fluorite from Weardale, Durham, England, are indicated by 

 figure 17. K^o zones were encountered in measuring the crys- 

 tal, hence two measurements were necessary for determining 

 the form, those made being between two hexoctahedron faces 

 adjoining a cube, 21° 13', and from cube to hexoctahedron, 

 24° 19'. Starting from the center of a- stereographic projec- 

 tion, the poles of eight faces of the hexoctahedron must lie on 

 a small circle drawn about 001 with a radius of 24° 19', which 

 may be taken from the stereographic scale. Moreover, the 

 poles of the hexoctahedron must lie symmetrically on either 

 side of a radius passing through 111, distant 10° 36' (half of 

 21° 13') from the pole of a possible truncating face, or 79° 24' 

 (the complement of 10° 36') from 110 and 110 ; accordingly 

 the point p was located at 10° 36' from the center on the radius 

 to 110, and, taking the radius 79° 24' from scale J^o. 2 of the 



Am. Jour. Sci.— Fourth Series, Yol. XIY, No. 82 — October, 1902. 

 19 



