CALCITES OF NEW YORK 27 
The combination shown in figure 11 is made up of the forms—R, R and 
—2R. The planes of the prism of the second order which are each perpen- 
dicular to one horizontal axis, intercept the two remaining horizontal axes 
at a distance from the center which is twice their unit lengths... The 
Naumann symbol for the prism of the second order is #P2. A pyramid 
of the second order is designated by the symbol P2 preceded by a 
coefficient which indicates the vertical intercepts compared with the unit 
value of the vertical axis for calcite. Thus, the series of pyramids shown 
in figure 5.are represented by the symbols #P2, 3P2 and.3P2. Low values 
of the coefficient represent flat or obtuse pyramids of the second order and 
high values steep or acute pyramids. A scalenohedron is designated in the 
Naumann system of symbols by the symbol of the rhombohedron of its 
middle edges followed by a numeral which indicates the relative vertical 
length of the scalenohedron compared with that of its rhombohedron of the 
middle edges. The series of positive scalenohedrons shown in figure 12 are 
designated by the symbols R3, R2 and R3, R being the symbol of the 
rhombohedron of their middle edges. Inthe same way the negative scaleno- 
hedron shown in figure 13, which has for its rhombohedron of the middle 
edges the negative rhombohedron —}R and which is three times the 
vertical length of that rhombohedron, is designated by the symbol —}R3. 
The system of nomenclature employed by J. D. Dana in his earlier 
editions is very closely allied to that of Naumann. The prism oR of 
Naumann is indicated by i (infinity) in Dana’s symbols, «P2 by i —2 etc. 
ies pyramids, 22, 222) 4P2 of Naumann become ;—2, 2—2, 4 —2 
etc., of Dana. In the symbol for rhombohedrons, Dana omits the capital 
letter R, substituting for it the numeral 1 in the case of the fundamental 
rhombohedron; thus R, 4R, —4R, —2R etc., become in Dana’s symbols 
1, 4, —4, —2 etc. The same is applied to the scalenohedrons, the numer- 
als indicating the vertical intercepts in Naumann being used as exponents 
by Dana; thus R3 becomes 1’, +R5 becomes 1°, —$R3 becomes —#’ etc. 
1 This property of the regular hexagon is subject of easy demonstration and may be 
found in every elementary textbook on geometry. 
