48 S. L. Pen field — Crystal Drawing. 



b of the orthographic projection above will intersect the axis 

 at one-third of its length. 



The principle involved in the projection of the clinographic 

 b axis, as given above, is very simple. Imagine a sphere with 

 two points fixed on its equator corresponding to A and p of 

 figure 13, and theu a chord Ap through the two points ; it 

 then follows that a series of chords parallel to Ap drawn 

 through the 5°, 10°, 15°, etc., graduation points of the meridian 

 through A would all emerge from the imaginary sphere on a 

 meridian Me, figure 13, passing through p, at points 5°, 10°, 

 15°, etc., from the equator. By drawing two chords, xx and 

 yy\ as in figure 13, or a third zz' so as to make more certain 

 of the intersection, any desired point on the meridian through 

 p is quickly found. In figure 13 a combination of the prisms 

 m (110) and M (110) and the base c (001) has been drawn. 



It may be said concerning the protractor that it has been 

 plotted on a large scale to insure accuracy, and that lengths 

 corresponding to one-third those of the axes will generally be 

 found convenient for drawing simple crystal figures. In con- 

 nection with the protractor it is recommended to use a scale, 

 corresponding to figure 15, printed or drawn on tracing cloth 

 or paper. When the outer lines of such a scale are adjusted 

 between the five degree graduation marks of the ellipses, the 

 intermediate lines will serve to subdivide the space into fifths, 

 or degrees. 



Projection of the Axes of twinned Crystals. — The axial pro- 

 tractor furnishes a ready means for plotting the axes of twin 

 crystals, a problem which at times presents considerable diffi- 

 culty, especially to beginners, hence two examples may be cited 

 explaining the uses of the protractor. In staurolite, twins 

 according to a pyramid are common, and in the example chosen 

 it will be assumed that a face having the symbol 232 ( — ■§«: 

 b : — fc) is the twinning plane. The data employed in plotting 

 the axes are the axial lengths, a : b : c= 0*473 : 1 : 0'683, and the 

 </> and p anglesof the twinning plane; ^ = 010^230 = 54° 37' 

 and p — 001 ^232 = 60° 31'. To insure accuracy in plotting, 

 the full lengths of the axes of the protractor have been 

 regarded as unity. In figure 16 the axial lengths —a and 



