Simpler Methods in Crystallography. 413 



angle y (77°'37) with ca for the zone of the brachydomes. The 

 point where this line intersects the horizontal line through 

 (101) is the position of h (010). From this, as a radiant, 

 draw a line through a for the prism zone 5a, and draw lines 

 from c through M'^, m^, by the intersections of which on ha 

 produced the true positions of if (110) and m (110) are found. 

 Eule lines parallel to ca through Mm to cut he. The points 

 of intersection so found are respectively those of q (Oil), 

 k (Oil) ; and, on h^ (101), respectively, those of z (121) and s 

 (121). From these fixed points the projection of all the rest of 

 the poles of Chalcanthite follows easily enough. For example, 

 d (210) is easily determined by drawing lines from (100) to 

 (Oil) and (110) to (101). A radial from (001) through the 

 point of intersection to the prism zone gives the position 

 required. Similar lines from (110) to (101), (100) to (Oil) 

 give in like manner r (210). A line from q (Oil) through 

 p (111) to the prism zone gives the position of h (120), and 

 from the same q through s (121) gives a (130). A line from 

 m (110) through (111) gives the position of w (021) on he; 

 while V (021) is determined by a line from M (110) through 

 p (111) to the zone of he. For (310) the lines from (100) 

 to (111), (111) respectively, are intersected by lines from 

 (110) to (111), (110) to (111). Kadial lines from c through 

 these intersections to the prism zone give the points required. 

 For Axinite, the most anorthic of all crystals, a somewhat 

 different mode of working has to be adopted. The tangent 

 plane is best placed so as to touch the sphere of projection 

 at r (111). As in the case of Chalcanthite, first rule a perpen- 

 dicular line through this point, and another at right angles 

 to it, each prolonged both ways to the sides of the paper. 

 Set off M (110) and c (001) from the first projection by the 

 method previously described. Determine the distance Mm, 

 ma, mh, by the method adopted for the gnomonographic pro- 

 jection of the prism zones in the example given in Part I. 

 From M, with the radius Mh, describe an arc cutting the 

 right-hand prolongation of the horizontal line through the 

 tangent point. The point so determined is h (010), which is 

 of prime importance as a radiant point. From h draw a line 

 through M for the prism zone. Set off Ma, Mm from the 



