Blake — Solving Crystal Problems. 651 



Aet. XXXIII. — Means of Solving Crystal Problems; by 

 John M. Blake. (Article 6.) 



In several preceding articles published in this Journal 

 the writer has drawn attention to methods by which the 

 measuring and description of crystals can be much facil- 

 itated. It would appear that the early selection of 

 methods of treating crystal problems, and subsequent too 

 close adherence to the original plan, has seriously 

 impeded the progress of crystal study, and at the same 

 time the problems involved have been made needlessly 

 complex. 



The early adoption of the theory requiring the use of 

 axes and parameters has led to the almost universal 

 practice of treating the planes singly and in pairs. This 

 practice has had the effect of diverting attention from 

 the very important relation existing between the planes 

 composing a zone as well as the equally important rela- 

 tion between the several zones enclosing a crystal form. 

 If we make a complete change in our system of studying 

 crystals, and have our work conform more especially to 

 the zone point of view, we may then dispense with the 

 use of axes, and can manage both rectangular and 

 oblique crystals with equal facility. 



It will be noted that in article 3 in this" Journal, Decem- 

 ber 1916, and in articles 4 and 5 in March and May 1917, 

 easy plotting-and-mechanical methods are employed 

 almost entirely in place of tedious and complicated alge- 

 braic work. The gnomonic projection of the crystal 

 planes opens up a promising means of crystal study. 

 When the planes are once plotted on the sphere for the 

 purpose of projection, their relative positions will be 

 rigidly held, and the whole system of planes can be 

 handled as a unit by simply moving the sphere into 

 new positions. We can then study the plane system of 

 the crystal by making various projections of the inter- 

 section points where the plane normals pierce a plane 

 tangent to the sphere. 



We find certain positions of this tangent plane where 

 the rows of normal piercing points lie in parallel equally 

 spaced lines. It is these particular positions that yield 

 interesting results. It will be seen later in anorthite, 

 that these positions occur at right angles to the axes of 



