iS6 J. M. Blake — Plotting Crystal Zones on Paper. 



Art. XLIX. — Plotting Crystal Zones on Paper ; 

 by John M. Blake. (Article 3.) 



Many years ago the writer became interested in the study of 

 crystals, and took up the subject of the relative lengths of the 

 crystal axes as one step that might lead toward a better under- 

 standing of crystal laws. Leading up to the present paper he 

 wrote two others, one on zone measurement, which will be 

 found in this Journal in 18G6, and a second in May, 1915, this 

 second paper relating to the growing of suspended crystals for 

 the purpose of showing the proportional development of 'the 

 planes on different members of an isomorphous group. To 

 supplement this was mentioned the brief growing of polished 

 crystal spheres of a salt with the object of bringing out the 

 maximum number of planes belonging to the species, some of 

 which planes may have been undeveloped by the first treatment. 



The mystery connected with the irrational axial lengths 

 appears not to have been solved up to this day, and that this 

 mystery still exists must be laid in great part to the difficulty 

 in making exact measurements. These measurements as a rule 

 may vary ten minutes or more in angle, and under these con- 

 ditions, it seemed useless to depend upon the ordinary methods 

 of utilizing such measurements for the purpose of solving our 

 problem. 



The evident need of greater accuracy led the writer to adopt 

 several methods for improving and facilitating work on crys- 

 tals. In part, these methods were original. It was hoped that 

 by attacking the problem in different ways, some progress 

 might be made in the solution of the axial question. One of 

 these methods is here described. The experimental trials with 

 these methods have thus far been limited mostly to the ortho- 

 rhombic and the oblique systems of crystals. 



It appears to be generally accepted that the length of the 

 axes of a crystal belonging to these systems cannot be expressed 

 in whole numbers, or by a vulgar fraction. These axial lengths 

 may be square roots multiplied by some rational quantity. The 

 parameters or the lengths cut off on the axes by the planes of 

 the crystal are generally considered to have the relation of 

 simple rational numbers when compared with one another. 



Variations in angle are mostly due to what are called vicinal 

 planes. These planes and the related curved surfaces have 

 been regarded as secondary and as superposed on the ideally 

 perfect crystal. This, however, may be regarded as a tenta- 

 tive supposition. These vicinal planes and the related curved 

 surfaces are doubtless subject to certain laws by themselves, 



