162 
Mohs’ System qf Crystallography 
in an upright position. Produce the axis, to any distance, 
equally on both sides of the summits. From the corners of the 
rhomboid, draw straight lines to the extremities of the produced 
axis, through every contiguous pair of those lines, and the in- 
termediate edge of the rhomboid, let planes be extended, the 
solid which those planes include will be a scalene six-sided py^ 
ramid^ (Pig- 1^- PI- VIII.) In this pyramid, the edges which 
do not meet at the summit, occupy the same position as the cor- 
responding edges of the rhomboid ; they are hence named rhom- 
hoidal edges; the others pyramidal or axis edges. Of a scalene 
six-sided pyramid, whose rhomboidal edges agree in situation 
with the same edges of a rhomboid, w^e say that it is derived 
from the rhomboid, or depends upon it. 
SS. Their proportions to the rhomboids : Their designation. 
-—Nature presents no scajene-pyramids, but such as are capable 
of uniting among themselves, or with other forms derived from 
the rhomboid, to produce symmetrical combinations. We obtain 
pyramids of this sort, if the axis of the rhomboid from which 
they are derived (S2.) is in the first place doubled; in the second 
tripled ; and in the third place quintupled. A pyramid obtain- 
ed by doubling the axis is called a primary ; by tripling it, a 
secondary ; and by quintupling it, a ternary pyramid. Prima- 
ry pyramids of this species are designated by {^p + w)' ; secon- 
dary pyramids by (p + ri)” ; ternary by (p + : so that the 
primary pyramid depending on r would be marked (y?)' ; the 
secondary (j?)" ; the ternary (y?)'" : the primary pyramid de- 
pending on r + 2 would be marked (y? S)' ; the secondary 
(jo "k ; the ternary ( -k S)"'. 
34. Series qf scalene six-sided Pyramids. — Upon any given 
rhomboid of the principal series, therefore, depend three scalene 
six-sided pyramids : upon that series itself, three pyramidal se- 
ries^ which proceed according to the law followed by the series 
of rhomboids ; that is to say, their axes increase or diminish as 
the powers of 2, the horizontal projections being equal. 
35. Different general series qf such Pyramids, and some of 
their Properties.' — Among themselves, these pyramids exhibit a 
particular series, the general expression for which will be 
{p -k ti)"', ( JO + -k 1)", (jo + -k if* the general expres- 
sipn for the pyramids be (jo -k nf^, and m signify the charac- 
