660 Blake — Solving Crystal Problems. 



reaching a rational explanation of all that relates to 

 crystal growth. 



A general examination and measurement of many 

 crystals tends to show that each crystal form has allot- 

 ted to it a limited number of planes. A gnomonic pro- 

 jection of a certain crystal might appear to suggest the 

 need of additional planes in order to carry out the sym- 

 metry and balance. The experiment mentioned in this 

 Journal, May 1915, in which crystal surfaces- were 

 regrown, was designed to favor the development of all 

 possible planes, but this plan does not extend the limit 

 to any great extent. There are various forms of hemi- 

 hedrism in which certain planes are suppressed, and 

 there is a probability that by means of a series of 

 gnomonic projections, we may get an insight into some 

 of the reasons why certain planes should have the 

 precedence. 



A potash alum sphere was polished and grown. Two 

 additional planes not commonly noticed were thus 

 developed, and when plotted, these planes harmonized 

 and took their places in gnomonic projections of alum 

 made on the cubic, the octahedral, and the dodecahedral 

 planes. But there are planes that have been credited to 

 the monometric system that would not have thus har- 

 monized; but structural differences occur in different 

 nonometric species, as shown for instance in the cubic 

 and the octahedral cleavages, and in other ways. 

 • The use of the plotting sphere for locating and study- 

 ing the relations of the crystal planes was adopted by 

 the writer in 1864. The appearance of an article which 

 was probably in the Analen der Physic und Chemie, 

 which gave the gnomonic projections of sulphate of cop- 

 per and datholite, that showed the equal spacing fea- 

 ture, turned his attention to the importance of making 

 such projections as a help in crystal study, and the 

 experiment of using a plotting sphere to reduce the 

 amount of preliminary work in making gnomonic pro- 

 jections proved so successful even with the imperfect 

 apparatus at first used, that a carefully shaped sphere 

 was constructed by the writer early in 1865. This 

 sphere is described in article 4. 



The first article of this series was published in 1866. 

 It related to the importance of measuring complete 

 crystal zones. This method of measuring was intended 



