by Means of Graphical Methods. 



255 



fig-nre 5, its vertical axis orientated so that it corresponds with 

 the axis joining the north and south poles ; then from the cen- 

 ter of the sphere lines, normals are supposed to extend out, 

 at right angles to the several crystal faces, until they touch the 

 surface of the sphere, where they locate points, known as the 

 poles of the faces. Figure 5 was plotted with much care in 

 clinographic projection, and was made partlj^ with the idea of 

 putting on record a good figure illustrating the simple prin- 

 ciples of the spherical projection. A combination of cube «, 

 octahedron <?, and dodecahedron d is shown, with normals ex- 

 tending to the surface of an imaginary sphere. The projected 



great circles, uniting the poles of the faces, are shown in the 

 figure as ellipses. The figure well illustrates the important 

 principle, that the normals to a series of faces which are in a 

 zone all lie in one plane, and touch the sphere on an arc of a 

 great circle. The length of arc between the poles of any two 

 faces, as measured on a great circle, is the same as the angle 

 between the normals, hence the same as between the faces as 

 measured with the reflection goniometer. Wire models con- 

 structed on the principles shown in figure 5 are very helpful 

 to beginners. 



For studying crystals, it is convenient to make use of the 

 stereographic projection. Generally the poles of one hemi- 

 sphere only (the upper) are represented, the projection being 

 made on the horizontal plane, or plane of the equator. The 



