and Mineralogy. 171 
examples of the former case, o and x of the latter. The limits 
of these series are oblique-angled four-sided prisms, whose axis, 
if the pyramid is in its upright position, are vertical^ as M and 
I in the figure referred to. By this derivation, however, we 
also obtain prisms, whose axes (the fundamental oblique-based 
four-sided prism being in its upright position,) lie horizontally, 
and are parallel to the diagonals of the oblique-base, as Fig. 6. 
and 9. PI. Ixii., or as d and o, Fig. 112. PI. xxxv. When 
one of their angles becomes 180°, these prisms have the pro- 
perty of changing into parallel planes, as is represented by s. 
Fig. 116. PI. xxxv. and by s and h. Fig. 118. PL xxxvi. in hea- 
vy-spar. If the faces of these prisms appear in combination 
with each other, they produce a rectangular four-sided prism, 
which, as such, that is to say, viewed from the extremities in 
the direction of its axis, must be regarded as a combination. 
From the union of two horizontal prisms, a form results which 
some crystallographers have named a four-sided pyramid, with 
a longish rectangular base, (Fig. 72. PI. Ixix.) 
58. Great variety in the Proportions. — Whatever was above 
established respecting the rhomboid and pyramid with square 
base, may in like manner be established with regard to such 
forms as are derived from the four-sided pyramid with an ob- 
lique base. The only circumstance deserving notice at present 
is, that, although the difference of figure among the forms de- 
rived from the four-sided oblique-based pyramid, is not so great 
as in the two former cases, (here, indeed, we find nothing but 
four-sided oblique based pyramids and oblique-angled piisms) ; 
yet the variety of these forms, in respect of their mutual pro- 
portions, seems to be much greater. Nature makes use of them 
most abundantly in the mineral kingdom ; nearly a half of all 
the known species assume these forms. The cleavage of mine- 
rals has an exact analogy with their outward form, in so far as 
that is regular ; and the forms derived from four-sided pyra- 
mids with oblong bases, furnish much striking information 
about the various relatious of this property ; they will diffuse 
still more light over it, when they have been examined in a 
more strict and complete manner than has yet happened. 
54. Hexahedron, and the Forms that result from it.^A mul- 
titude of forms yet remain which are not connected with any of 
