Blake — Solving Crystal Problems. 653 



drawn on this diagram (fig. 1) parallel to b e for the 

 purpose of showing its intersection with the normals, 

 and the intersection points are marked by dots. It will 

 be seen that the dots are equally spaced, and that the 

 spaces measured from the dots to the axis c correspond 

 to the above given ratios. 



We cannot manage an oblique zone by the axial plan 

 with equal success. Take, for example, the oblique zone 

 of epidote shown in fig. 2. The angles are taken from 

 Dana's Mineralogy 1906, and the same lettering is used 

 for the planes as well as the same length is given the 

 axes, which are marked off on the diagram by two finely 

 dotted lines, which cut off portions of the two oblique 

 axes a, and c, and should thus outline the unit oblique 

 octahedron. We find, however, that neither one of these 

 dotted lines comes parallel to the plane edge e or 101, or 

 to the plane edge r or 101, as it should, and no other 

 selection of axial lengths will bring about, simultane- 

 ously, both of these parallel positions. 



The application of the tangent equal space system is 

 shown on this same diagram, fig. 2. The trial tangent 

 line, drawn for the purpose of this comparison, is made 

 parallel to the line a b, and its intersection with the plane 

 normals is shown by equally spaced dots. Thus the 

 equal spacing method of managing an oblique zone works 

 successfully, although two of the intersection points 

 happen to be lacking in this particular case. 



We will now illustrate a part the plotting sphere can 

 take in making a general study of the relations of the 

 planes of the crystal. For this purpose three species of 

 feldspar have been in part projected by the use of the 

 sphere. 



Obthoclase is a monoclinic potash feldspar. The 

 angles given by Des Cloiseaux, together with his stereo- 

 graphic projection, were used as a basis for the six 

 gnomonic projections shown in ^.g. 3. The first mem- 

 ber of this. series of six is based on the same prismatic 

 zone that was adopted by Des Cloiseaux in his stereo- 

 graphic projection, see Min. 1862. We find on compar- 

 ing the first and second members in this series of plots, 

 that there is a most striking similarity of form to be 

 seen in the figures developed by the normal intersections 

 with the tangent planes, and to all appearance there are 

 identical spacings in these two figures, except that the 



Am. Jour. Sci.— Fourth Series, Vol. XLVI, No. 275.— November, 1918. 

 30 



