170 
Mohs’ System of Crystalhgraiihy 
50. Examples. — Nature displays the existence and the li- 
mits of this series of eight-sided pyramids in the following ex- 
amples. In zircon., Fig. 1 4 and 15. PI. VIII. let P be = ; then 
IS x = (jpy^ that is to say, the simple form that arises from aug- 
menting the faces f is the primary scalene eight-sided pyramid, 
originating from the four-sided square-based one, designated by 
P ; and the axis of the former is consequently equal to three times 
that of the latter. In this same mineral are likewise found {p)” 
and as the Institute’s collection exemplifies. In Vesiivlan, 
let o be =p ; then is — (^ — 1)' ; 5 = (p)' ; x = (p)" ; and 
7i = (p -f go)', or Ji is the eight-sided prism with unequal 
angles, which forms the limit of the first scalene eight-sided 
pyramid. In Tinstone, lei 0 be==:p; then is .^ = (py"; r — 
(p -f 00 )'". In the Transactions of the Geological Society, 
(Vol. ii. PL 15. seq.) the fifth modification is = (p -f- 00 ). Haiiy, 
in the Tableau Comparatlf p. 302, describes the same form in 
Rutile, and marks it by li, (Tab. ii. Fig. 31.) In yellow lead- 
spar also, we find (p -}- co)'" marked by r. 
51. Summary of these Fomis and Combinations. — What- 
ever was above established (41. — 43.) respecting those forms 
which originate in rhomboids, may also be applied to those 
forms which originated in four-sided square-based pyramids. 
The remarkable analogy which exists in all points between the 
one class and the other, contributes not a little to augment the 
interest arising from the study of both. The latter, like the 
former, constitute among themselves a group, and produce 
symmetrical combinations, into which they admit nothing that 
cannot be derived fro7n the fundamental form, in the mode al- 
ready explained. 
52. Four-sided Pyramids with oblique Bases. Their Li- 
mits and Series. — A similar group will result, if, with some 
very slight alterations, we apply the process of derivation, ex- 
plained above, (12. and 17-), to a four-sided pyramid with an 
oblique base, like Fig. 1. PI. Ixii., or such as would originate 
from augmenting the faces o, (PI. xliv. Fig. 37.) From that 
operation several series of four-sided oblique-based p^amids 
arise ; in some of which the transverse section at right angles 
to the axis, is similar to the transverse section of the original 
pyramid, in others not : o and s (Pi. xliv. Fig. 42.) present 
