and Mineralogy. 1.61 
ramids dependent on the accompanying series, (25.), are as yet 
unknown. 
29. Their Limits. — On rhomboids of infinitely great or infi- 
nitely small axes, there depend, in like manner, isosceles six-sided 
pyramids of infinitely great or infinitely small axes. They also 
are regular six-sided prisms, distinguished from the preceding 
by their different position in combinations. These prisms con- 
stitute, moreover, the limits of the isosceles six-sided pyramids; 
30. Di-rhomhoid. — Bisect those edges of the rhomboid which 
do not meet the axis. Connect the points of bisection and the 
summits of the rhomboid by straight lines, and through these 
lines, extend cutting planes which may take away from the rhom- 
boid segments, such asjf/:' ^ Fig. 10. PL VIII. The remainder 
will be an isosceles six-sided pyramid, represented , in Fig. 9. 
PI. VIII. This pyramid must not be confounded with the pre- 
ceding (26.), because it has not the same proportions to the rhom- 
boid from which it originates. If we suppose that a rhomboid, 
as Fig. 10. combines with itself in a position different by 60% the 
pyramid will in like manner originate from this union. The fi- 
gure, in consequence of its origin therefore not a simple form; 
but as it manifests in all respects the same relations as the simple 
rliomboid, it will henceforth be named a di-rhomhoid, 
31. Examples . — In calcar eous-spar^ § (Fig* H* PL VIII.) is an 
isosceles six-sided pyramid. If these pyramids are designated 
generally by /? + w, and hence that one which depends upon 
P = r, by j?; upon r ~f 1, hjp + 1, and so on; then is ^ —p -f- 2; 
in other words, it depends upon the rhomboid r -{- 2, which is 
marked by m. In apatitej let ^ be a di-rhomboid (30.) = r ; 
then i& x ^p ; r ~p — 1. In quartz^ let .9 be = r ; then is P 
and z.^p — 1 ; m z=:p -f 1. In corundum, ( Tableau Compa^ 
ratf), let P be ~ u ; then is r (of the figure) h=:p-^l. 
In emerald, let 5 be — r; then u:=.p, and t—p — 1. In redl 
silver, let P be — r; then is m — y?, and r (of the figure =:p -f 1. 
In sidphate of iron, let P be = r ; then is ^ — jt?. Examples of a 
six-sided prism forming the limits of the pyramid are to be seen 
imt of the calcareous-spar, m of the apatite, r of the quartz, s 
of the corundum, z of the iron-glance, n of the red silver, and 
s of the sulphate of iron. 
32. Scalene six-sided pyramids. — I^et any rhomboid be placed 
VOL. III. NO. 5. JULY 1820. 
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