652 



Blake — Solving Crystal Problems. 



the several zones. One projection plot may have few or 

 no intermediate fractional plane positions, and again 

 another plot may have a general converging trend of the 

 zone rows, and have many fractional plane positions, 

 bnt notwithstanding this, we may easily trace the pres- 

 ence of equal spacings. 



In the past, the axial system was applied to rectangu- 

 lar forms with apparent success, and such success prob- 

 ably led to the original adoption of the system of refer- 

 ring the planes to axes, but we find that when we have to 

 deal with oblique crystals, the axial method of referring 

 the planes leads to confusion, and this indicates that the 

 axial plan of reckoning the planes is not of universal 

 application. It is altogether probable that the symbols 

 of the planes as at present understood may eventually 

 be replaced by an entirely different form of notation. 

 Farther on, some mention will be found relating to this 

 matter. 



Fig. 1. 



Fig. 2. 











/ 001 



%4 1 



q" 



q' 



c 



Qlo fi/ ~- ^ 



<2 



b 



e 



a 



We will show by means of a diagram this want of gen- 

 eral adaptability of the axial system. First, we give a 

 rectangular zone occurring on potassium sulphate. Fig. 

 1 represents one quadrant of this zone. The angles and 

 symbols for the planes are taken from Tutton's Crys- 

 tallography, 1911. The cut shows the crystal planes of 

 this zone edge-on as in a cross section, and it also gives 

 the direction of the planes. Lines are drawn from point 

 e on the axis b leading upward to the right. These 

 lines are made parallel to the plane edges, and are drawn 

 for the purpose of showing the relative lengths or para- 

 meters they cut off on the axes b and c, and these lengths 

 are found to be in the ratio of 1, 2, and 3, which corre- 

 spond correctly with the symbols Oil, 021, and 031. A 

 line which may be considered as a tangent line has been 



