488 ON DRAWING CRYSTALS 
squares. (Plate XV. Fig. 1.*) It will form the first mem- 
ber of a series of problems, to be considered in two sections, 
referring to the method of projecting the simple forms, and 
the combinations, in which they are found in nature. 
Section I. 
Of the Projections of Simple Forms. 
Problem I. To draw a Hexahedron. 
Suppose one of the faces of the hexahedron (Fig. 1.) to 
be perpendicular to the visual ray. Its projection upon 
another plane perpendicular to the same line will also be a 
square, equal to the above mentioned face of the hexahe- 
dron. Suppose this square (Fig. %) to revolve round a line 
M N, parallel to C D ; the points A and B will appear de- 
pressed in the lines A C and B D, while the length of C D 
remains unaltered ; the projection of the square, therefore, 
assumes the appearance of a rectangular parallelogram. 
But in the hexahedron (Fig. 1.) at the same time, the face 
C D E F is turned round C D, and the projection of the 
two faces assumes the figure of two parallelograms (Fig. 3.) 
If we still continue to revolve the solid in the same way, the 
projection of A C and B D will diminish in length, while 
that of C E and D F increases till it becomes equal to C D, 
when the face CDEF (Fig. 4.) is brought into a plane 
perpendicular to the visual ray. 
If the horizontal line M N is not parallel to C D, Fig. 5., 
the revolution round it cannot give rise to any rectangular 
• For the figures which accompany this paper I have been indebted to 
Robert Allan, Esq. younger of Laurieston. They have been carefully exe- 
cuted in conformity to the rules which they serve to illustrate. 
