168 Mohs’ System (^'Crystallography 
simple forms and combinations, without being compelled to have 
recourse to plates for explanation. As all that we have hitherto 
been examining, is derived from the principal series of rhom- 
boids, we must select some member of that series to be the basis 
of designation. It is most natural to choose that term accord- 
ing to which the cleavage is determined. In calcareous-spar, 
this is P, Fig. 2. PI. VIII. Let us designate this species by r, 
then is g (Fig. 3. PL VIII.) — (Fig. 5. PI. VIII.) 
r= r + 1 ; w (Fig. 6. PI. VIII.) = 7' + 2; r (Fig. 12. PI. VIII.) 
= (py ; y (Fig. H.) = (p)'" ; ^ (Fig. 42. H.) =: (p + 1)' ; 
t (Fig. 48.) — (p — 2)"; c (Fig. 12.) = r + oo ; o (Fig. 31.) 
— r — cx; u (Fig. 10.) — p -f- oo, &c. If it is required to desig- 
nate combinations, the signs of the simple forms are placed toge- 
ther in the same order as the terms of the several series : The li- 
mits stand last. Fig. 7. PI. VIII. for example, is marked by r. r-f 1 ; 
Fig. 1 0. rrr r.p -j- 00 ; Fig. 11. = r. (p)" ; Fig. 1 2. == r. r oo ; 
Fig. 7. PL VIII. r -f- 00 . r — oo ; Fig. 26. = r. (p)"^ r-i-oo; 
Fig. 35. —r — 1 . (p)". r -j- 00 ; Fig. 46. r=r. r-fl . (p)"- (j?-f 1)'; 
Fig. 50. — r — 1. r -f 1. (jt? — 2.)". (/?)". r-i-oo ; Fig. 1. 
PL VIII. = r — l.r. r-j- I.r-f2.r-f3.(j9 — 2)"'. (p -f- 1)'. 
(py"> (p + 1)". This mode of designation has the advantage 
not only of representing all the simple forms which enter into 
the combination, but also of expressing their mutual propor- 
tions ; so that upon finding merely the dimensions of a single 
form, a calculation may immediately be grounded on it. 
44. Fou7'-sided Pyramids^ with square bases. Their Seides and 
Limits . — Besides the forms already noticed, no other can be de- 
rived from the rhomboid. Hence, no other is capable of entering 
into combination with the rhomboid^ or with any form derived from 
it. If, however, we take a four-sided pyramid^ having a square 
bas(^ Fig. 14. PL VIII., and treat it as described, (in 12, and 17^ 
we shall obtain a series of four-sided pyramids with square bases, 
which will proceed according to the powers of ^2, and whose 
limits will be rectangular four-sided prisms. As the horizontal 
projections of two consecutive pyramids are not parallel to each 
other, these prisms must be regarded as in two different posi- 
tions. 
45. Examples. — Nature demonstrates the existence of this 
series within its limits, in the case of Zircon, Tungsten, Vesu- 
