164 
Mohs'* System of Crystallography 
the section may pass through the axis, but whose sides become 
equal when it passes through the middle point of that axis. A 
simple geometrical construction shews that the angles of the 
transverse section depend upon the ratio existing between the 
axis of the pyramid, and that of the rhomboid from which 
it originates ; and hence that all such pyramids as have axes in 
this ratio j give the same transverse section ; all primary pyra- 
mids, therefore, have one common transverse section ; all secon* 
dary pyramids in like manner, and all ternary pyramids : but 
the transverse section of primary pyramids is different from 
the transverse section of primary pyramids, and that again 
from the transverse section of third pyramids. 
89. Limits of their Series. — The regular six-sided prism has 
already been considered as a rhomboid with an axis infinitely 
great (2S). The question now arises : What will be the condi- 
tion of a primary, secondary, or ternary pyramid, originating 
from a rhomboid with an axis infinitely great ? Draw two sec- 
tions perpendicular to the axis of a pyramid, and so as to pass 
through the extreme points of the rhomboidal edges. The sur- 
faces of these sections will be irregular hexagons, whose angles 
have a fixed relation to those of the transverse section. Exa- 
mine now that segment of the pyramid comprised between the 
two sections just drawn. Its length, or altitude, is one-third of 
the axis of that rhomboid from which the pyramid is derived. 
Hence if the rhomboid'^s axis be infinite, the altitude of this seg-- 
ment must likewise be infinite. 
Besides those two faces, which are perpendicular to the 
axis, this segment is bounded by twelve scalene triangles. In 
proportion as the ratio of the rhomboid‘’s axis to the side of its 
horizontal projection augments, so much the nearer will two of 
the angles in each triangle approach to 1 80'",— the third to 0° : 
and when the rhomboid‘’s axis, in comparison with the side of 
its horizontal projection, becomes infinite, and the rhomboid 
thus changes into a regular six-sided prism, then the bounds 
are reached, the triangles become unlimited paraMelogramis, and 
the middle segment of the pyramid becomes an unlimited irre- 
gular twelve-sided prism. This prism will have for its base the 
transverse section of the primary pyramid, if the middle seg- 
ment in question belongs to a primary pyramid ; the transverse 
section of the secondary, when that segment belongs to a secon- 
