26 NEW YORK STATE MUSEUM 
rhombohedron increases the polar angles approach more nearly equality, 
equality being reached in the prism of the second order which is one of the 
limiting forms of every series of scalenohedrons. The other limit of the 
series 1s reached when the vertical length of the scalenohedron becomes that 
of its rhombohedron of the middle edges. In combination with other forms 
scalenohedrons develop crystal faces of unsymmetric outline. The faces 
like those of the pyramids of the second order are symmetrical in adjacent 
vertical pairs. If the hexagon which represents the horizontal projection 
of any scalenohedron be divided by planes passed through the horizontal 
axes into sextants as in figure 14 the unshaded portions of the figure will 
represent the positive sextants and the shaded portions: the negative sex- 
tants, above the zigzag line of the middle edges. The planes of positive 
scalenohedrons le in pairs in the positive sextants and those of negative 
scalenohedrons in the negative sextants. 
SYMBOLS 
Naumann’s system of symbols. The system of crystal nomenclature 
proposed by Naumann,’ which is now in quite general use, has for its general 
feature the use of certain capital letters preceded and followed by numbers, 
which numbers indicate the ratio of axial intercepts. In the case of the 
hexagonal system the capital letters used are P and R. The capital letter 
R indicates the fundamental rhombohedron. Coefficients placed in front 
of R, as for example 3R, 4R, 16R indicate respectively positive rhombo- 
hedrons whose length as compared with the vertical unit for calcite (.8543) 
are respectively 3, 4 and 16 times. In the same way negative rhombo- 
hedrons designated as —$R, —2R, —{R, —5R have vertical mtercepts 
respectively 4, 2, $ and 5 times the unit vertical length. The basal 
pinacoid and the prism of the first order are limit forms of the rhombo- 
hedron series and are consequently designated respectively 0R and oR. 
1 For examples of the symmetry of scalenohedrons in combination compare plate 11, 
figure 4; plate 21, figure 3. 
2 Naumann, C. F. Lehrbuch der Krystallographic. Leipzig 1829. 
