Blake — Solving Crystal Problems. 661 



to facilitate plotting on the sphere, although not so men- 

 tioned in the article. At that time the new system of 

 drawing which required the use of the plotting sphere 

 had been brought into practical form and was employed 

 in making the plan-drawing of gaylussite which was 

 given in art. 5, and also the perspective drawing of the 

 same species given in the same article. Some descrip- 

 tions of other mineral species appeared in this Journal 

 at about the same period. Then for many years it 

 became necessary to discontinue the study of crystals. 

 The work was resumed about a decade ago and the 

 drawings and projections of albite were completed as 

 given in art. 3, and later some of the earlier work has 

 been reviewed and the present article, 6, includes some 

 more recent observations. 



As regards plotting spheres, hollow school globes are 

 now so well made from paper pulp, that the exercise of 

 a little more care in perfecting their shape will make 

 them excellent plotting spheres. If found necessary, 

 the spherical figure could be perfected by local abra- 

 sion. There may be a tendency to expand in damp 

 weather, and to stick in a too-closely fitted metal equato- 

 rial ring, which difficulty could probably be avoided by 

 making the ring of the same material as the sphere. 



The writer is indebted to Prof. T. L. Walker's Crys- 

 tallography 1914 for an account of an equal "pace" 

 system by Dr. Victor Goldschmidt, but in that account 

 there was no mention of the use of a plotting sphere 

 upon which to make approximate calculations. The 

 fact that the contribution from Dr. Goldschmidt is 

 along lines parallel to that of the writer, is very fortu- 

 nate, as it will help to further the cause of reform in 

 crystallographic methods, and when a more general 

 interest is awakened in crystal study, we may expect 

 that cooperative efforts will bring about a generally 

 acceptable solution of many unsolved crystal problems. 



We have endeavored in this article to give some idea 

 of the usefulness of the plotting sphere in bringing to 

 light points of importance which might otherwise easily 

 pass unnoticed. The field for this kind of exploration 

 is very large, and it has remained almost untouched. 



Observations relating to zones of planes and their 

 investigation by the tangent method, lead us to antici- 

 pate that important developments may be expected to 



