CALCITES OF NEW YORK 23 
of second order are of unsymmetrical outline but lke those of the prism 
of the second order they are symmetrical in adjacent pairs to vertical planes 
passing through the terminal edges [see pl. 10, fig. 1-5]. 
Rhombohedrons. Returning to the consideration of the fundamental 
rhombohedron assume the diagonals of rhombic faces to be drawn as shown 
in figure 7. It is plain from the vertical projection of figure 7 (upper half 
of figure) that the horizontal diagonals, in this case the long diagonals, of 
the rhombic faces form two equilateral triangles having their centers in the 
vertical axis. If two planes be passed perpendicular to the vertical axis 
and intersecting the rhombohedron in these two triangles, as shown in the 
figure, it is clear that the distance between the planes is equal to the distance 
of each from the nearest vertex; that is the planes through the horizontal 
diagonals divide the vertical axis into three equal parts. The triangles 
referred to may be designated as the triangles of the horizontal diagonals. 
Assume now, a vertical line the length of which is some proportion of the 
vertical axis of calcite, as3. If this line be divided into thirds by hort- 
zontal planes upon which the triangles of the horizontal diagonals be con- 
structed and the vertexes joined as shown in figure 8, the resulting solid 
will be a rhembohedron having the same vertical projection as figure 7 and 
the vertical length of which is 3 times that of the fundamental rhombo- 
hedron. Similarly any number of rhombohedrons may be developed having 
various vertical intercepts the ratios of which are limited by the law of 
rational indexes. The rhombohedrons of this series are designated as 
positive. Up to the present there have been recorded 29 positive rhombo- 
hedrons for calcite the flattest of which has a vertical length of } the vertical 
ratio and the steepest of which has a vertical length of 28 times the same 
ratio. The limits of this series are the basal pinacoid having a vertical 
intercept of 0 and the prism of the first order having a vertical intercept of 
oo, the latter forms being respectively parallel to the basal axes and to 
the vertical axis [see fig. 3, 4]. 
Assuming the position of the triangles of the horizontal diagonals to 
be reversed, a series of rhombohedrons may be developed in the same 
