4SS ./. M. Blake — Plotting Crystal Zones on Paper. 



our present purpose. Such omissions occur in many similar 

 descriptions. These wanted elements can only be supplied by 

 a further study of the original crystals. 



We begin our zone plot by first drawing a circle, and we dot 

 the position of the normals of the planes on this circle by 

 means of a protractor. We now draw radii through these 

 normal points. Then we take a scale of equal parts and rotate 

 it in the plane of the paper, and at the same time move it out 

 and in from the center until we have the equal spaces on the 

 scale coinciding with the extended radii. The straight edge of 

 the scale will now represent a tangent line, and the distance of 

 this line from the center will be the radius, and one of , the 

 equal spaces so developed divided by the radius, will give a 

 tangent ratio commonly known as the axial ratio. This ratio 

 will be that between the two axes that are included in the 

 selected zone. 



Guided by our zone plot, we may reach further accuracy up 

 to the limit we have secured by our goniometer measurements, 

 by taking the values from a table of natural tangents. Planes 

 which do not fall into the system of equal spacing as shown 

 on the plot, will be open to the suspicion of being false entries, 

 and so, also, complex fractional indices should be subject to 

 inquiry. The latter may be due to the position of the selected 

 axes, or to the adopted axial lengths. At the same time, frac- 

 tional indices are not impossible. The half spaces that are 

 shown on fig. 2 appear to belong to the general make up of the 

 crystal. The positions of some of the fractional planes have 

 been dotted, but the letters designating them have been omitted 

 in fig. 2. 



Fig. 1 gives the zone of epidote that contains the inclined 

 axis. The horizontal line within the circle represents the 

 plotted tangent line on which the equal spacing is developed 

 by the intersection of the radii with the equally spaced scale. 

 The inner circle gives the symbols from Decloiseaux, and the 

 outer circle, the symbols from Dana's Mineralogy. The radii 

 are drawn on fig. 1 to show the equal spacing characteristic. 

 These radii are also marked on the marginal ring in fig. 2. 



These two diagrams differ in this way. Fig. 1 shows the 

 plane of the plotting paper with the radii drawn upon it. 

 The plane in fig. 2 is parallel to this plane and is the plane b of 

 Dana, and the plane g' of Decloiseaux. On this plane b, is a 

 projection of all the planes of the crystal whose normals pierce 

 this plane at the points lettered on the diagram. The normals 

 of the zone which is being plotted are parallel to this plane b 

 and do not pierce it, and their position is marked on the mar- 

 gin near the circle in fig. 2. 



Decloiseaux's stereographic projection is much confused by 



