q^nd Mineralogy. 163 
ters '5 " 5 It is a property of this series, that any two conse- 
cutive members, such as {p + 1 )" and {p + 2 )', or {p *f S)' 
and -h 1 )'", produce with each other parallel edges of com- 
bination, as r and a?. Fig. 13. PL VIII., in calcareous-spar. If 
P (Fig. 13.) is put ~r; then is r (of the figure) = (^)" and 
0 ? n (jp -f- 1 )' ; that is to say, the former is a secondary pyra- 
mid, depending on the rhomboid P r= r, the latter a primary 
pyramid of the rhomboid r -{- 1 (3S). Another property 
of the series is, that if any two of its terms are distant from each 
other by 5, or 11 , or 17, or generally by Qn — 1 terms {n be- 
ing any whole number) ; the edges of combination belonging to 
those two are horizontal, when the combination itself is placed 
in an upright position. In the example presented by Fig. 48, 
PI. xxvii. Ilaiiy, where r and t are pyramids of this sort ; r (of 
the figure) is = (p)", and t—(^p — 2 ) ; so that = 1 ; and 
in the general series, five terms are wanting between the pair con- 
nected together. 
36. Examples. — The following minerals afford proof that 
such series of pyramids actually exist. Calcareous-spar, (^p — 2 
t. Fig. 48. ; ( py (Monteiro in the Journal des Mines J ?* ( /?)"-» 
r, Fig. 1^. PI. VIII. ; {^py\y. Fig. 22. ; (;? + 1)', Fig. 42. 
{p -j- 1)", 5 Fig. 1. PI. VIII. ; (^ + 2)' (Haiiy, in the Journal 
des Mines ). Tourmaline, (^p — 1"), x. Fig. 123. PI. lii. ; (p)" 
(Haiiy in t. hi. des Annales du Museum ) ; (p)"', u. Fig. 124. 
Emerald, {p — 2)'" (Rome de VIsle, tab.^v. 2 nde suite. Fig. 103.) 
Red silver, {p 2)", t. Fig. 13. PI. Ixiv. (like several in this spe- 
cies not accurately drawn) ; {p)’', h. Fig. 14. Iron-glance, 
(^p — S)'" lies between P and n. Fig. 8 . PL VIlI. ; it is found 
in the collection of the Institute. 
37 . Scalene six-sided Pyramids of the accompanying Series.—^ 
The rhomboids of the accompanying series have, in like man- 
ner, their scalene six-sided pyramids, which depend upon them, 
but which do not follow the same laws as the pyramids of the 
principal series. They seldom appear in nature. We pass 
them by at present, for the sake of brevitj^ 
38. Transverse section of the scalene six-sided pyramid. — A 
section perpendicular to the scalene six-sided pyramid'^s axis, and 
meeting the rhomboidal edges (32.), is called a transverse sec- 
tion. This transverse section is in the form of an irregular duo- 
decagon, whose angles are unchangeable, at what point soever 
1.2 
