Simpler Methods in Crystallography. 339 



a line from 12.7.0 to c, and intersecting it by a line from 

 12.0.4 or 301 to h. Again, 6.10.3 is found by intersections 

 from 6.10.0 or 350 to c with 603 or 201 to a. In Crystallo- 

 graphy these forms, which cut all three axes, are denoted by 

 the general symbol {hhl). The poles of the zones in which 

 these forms lie are not in any one of the planes of symmetry 

 of the crystal. 



40. The cases referred to embrace between them all those 

 regarding which any difficulty is likely to be experienced by 

 the beginner. In concluding this part of the paper, I would 

 very strongly advise those who wish to master this important 

 section of Crystallography to patiently follow these instruc- 

 tions. In the end, it will be evident that much mathematical 

 work of a really useful kind has been done, and that, too, 

 by the very simplest means possible under the circumstances. 

 It is an excellent plan to make a large gnomonogram of the 

 Cubic System, making the base a metre in width, and the 

 other side those of a square, of which the base line is the 

 diagonal. The point of contact with the spherical surface 

 may be conveniently assumed to be on the middle of a per- 

 pendicular from the apex (c) of the triangle, and to repre- 

 sent the octahedron (111) o. Take c at the top, h at the 

 right hand lower corner, and a on the left, m in the middle 

 of the base line. With patience, and careful drawing of 

 lines, the whole of all the indices up to fractions as high as 

 |-|ths may be laid down simply by using intersection lines 

 from and to the various cardinal positions already referred 

 to. A map so constructed is a most valuable auxiliary to 

 practical work afterwards. 



41. The gnomonogram possesses many advantages over 

 any of the other projections, most especially in regard to 

 the facility it affords of drawing zones, and in readily 

 determining the directions of intersections between any two 

 faces. But it represents only one-eighth of the sphere of 

 projection, or only one-twelfth in the case of the Ehombo- 

 hedral System. Moreover, for the Monosymmetric System 

 two separate gnomonograms are needed, and for the Anorthic 

 four, and in both these cases the construction is much less 



