58 NEW YORK STATE MUSEUM 
The clinographic projection represents the crystal in parallel perspective 
and is specially valuable as presenting the aspect which shows it to the 
best advantage. 
Both orthographic and clinographic projections are used throughout 
this work, the orthographic projection, where used, being represented as 
revolved horizontally to correspond with the corresponding clinographic 
projection, as in figures 3, 4 and 5. 
MODELS 
Models of the simple forms of calcite may be constructed from paper 
or cardboard by the use of the diagram given in plate 2. This diagram is 
based upon the triangle of the horizontal diagonals of figure 7. 
To construct the face rhomb of any rhombohedron measure with a 
pair of dividers the distance from the point a to the point on the line C 
corresponding to the coefficient of R in the Naumann symbol, and lay off 
the distance from aon the line Z. Connect the point thus obtained with 
points bb’ and complete the parallelogram which will be the desired 
rhomb. 
To construct the triangular face of a second order pyramid, multiply 
the coefficient m of the Naumann symbol mP2 by 3, measure the distance 
from the point d to the corresponding number on the line C, lay off this 
distance on the line Y, and connect the point obtained with the points f {’; 
the resulting isosceles triangle will be the face of the desired pyramid. 
To construct the scalene triangle of a scalenohedron, the problem 
resolves itself into finding the lengths of the three edges of the triangle 
which may then be plotted in the ordinary way by means of arcs of circles. 
The edge Z which is that of the rhombohedron of the middle edges is 
obtained by the process described for rhombohedrons using the coefficient 
min the Naumann symbol mRn. The two polar edges are obtained in the 
following way: Lay off to the left of point O on the line Y a distance cor- 
responding to m measured on C’ and from the point thus obtained lay off 
in the directions X and Y a distance corresponding to the product of m 
and n in the symbol mRn measured on the base line at the bottom of 
