On the Drawing of Figures of Crystals. al 
quently one is sufficient,) ascertains with perfect confidence, every 
other angle in the crystal. Consequently if these edges were in- 
correctly represented, the figure would be comparatively useless and 
unintelligible, and often would prove worse than useless, by leading 
to incorrect deductions. | 
Since these deductions depend on the parallelisms of edges, the 
following principle is of fundamental importance in the drawing of 
erystals; edges which are parallel in the crystal should be repre- 
sented in the figure as parallel. Figures projected with this prin- 
ciple in view, though with no attempt to attain mathematical accu- 
racy, will be valuable to the science. Yet a knowledge of mathe- 
matical crystallography, greatly facilitates the application of this prin- 
ciple. Crystals are often imperfect and the intersections of planes are 
indistinct, and consequently the exact limits of the planes and the 
direction of their mutual intersections cannot be observed. ‘They 
are also frequently so much distorted that some planes are oblitera- 
ted by the extension of others, and generally it is desirable to intro- 
duce in the figure, the plane or planes which may. have been thus ob- 
literated. These and other difficulties can only be surmounted by 
applying the principles of mathematical crystallography, which af- 
ford expressions for the planes indicating their exact situation.* 
3. In the projection of crystals, the eye is supposed to be at an 
infinite distance, so that the rays of light fall from it on the crystal 
in parallel lines; otherwise the more distant parts of parallel edges 
should converge, as in the ordinary sketches of scenery. If parallel 
lines were drawn from the vertices of the solid angles of a crystal, 
to a board placed behind it, and the points thus formed on the board, 
were connected by straight lines, as in the crystal, a representation 
of the crystal would be formed, constructed according to the mode 
of projection employed in crystallography. The plane on which the 
crystal is projected, is termed the plane of projection. ‘This plane 
may be at right angles with the vertical axis, may pass through the 
_ vertical axis, or may intersect it at an oblique angle. ‘These differ- 
ent positions give rise, respectively, to the horizontal, vertical and 
* With but an imperfect knowledge of these principles, it becomes a simple pro- 
cess to project the axes of their relative dimensions and exact obliquity, and after 
this preparation, to lay off with accuracy, the situation and intersections of the 
various secondary planes. Indeed, the projection of the axes in each of the sys- 
tems of classification excepting perhaps the elinate, may be easily understood 
without any acquaintance with mathematical erystallography, and the subsequent 
construction of the secondary forms requires only a familiarity with the system of 
crystallographic notation. 
