159 
and Mineralogy. 
23. The limits hy themselves not in Forms of infinite 
dimensions are not exhibited by nature. The limits appear, 
therefore, only in combinations. The complete regular six-sid- 
ed prism, as displayed in nature, is a combination of both limit- 
ing forms. 
24. Ccmjirmation hy experiment. — Nature confirms the law 
of this rhomboidal series within its limits in all minerals that as- 
sume such forms. In calcareous-spar^ of which all the figures in 
PI. VIII. are .varieties, let P Fig. 2. be represented by r ; that i& 
to say, by tlie rhomboid which constitutes the basis of derivation, 
and whose axis has been put = 1; then is g~r — 1, Fig. 3. ; 
/;=T-M,Fig.5 .; 77 Z — r -f 2, Fig. 6 . All these rhomboids have 
pretty exactly the dimensions which they would have if calculated 
according to the foregoing proportions from the rhomboid P, es- 
timated = 104° ,28'. If, in place of that number, we employ 
1Q5° 5', the result of numerous measurements instituted for this 
purpose, the dimensions of the derived rhomboids calculated upon 
this supposition agree still more exactly with nature., c (Fig. 7.) 
PI. VIII.) is = r -j- 00 in combination with o = r — oo. Again, 
in tourmaline, let P be r ; then is 7 i=:r — ?!; o = r-f- 1 4 r (of 
the figure) = r -p 2 ; I and Z' — r -|- 00 , and h—r — 00 . In 
chahasie, let P be =: r ; then is w =: r — 1 ; r (of the figure) 
z=zr — 1. In dioptase, P does not appear as a crystal, but 
merely as a cleavage form. If P is made = r ; then is r (of 
the figure) = r -f 1 : s in this species is not r + oo, as what 
follows ( 29 .) will shew. In red silver, let P be — r ; then 
is^=:r — 5 = r — 2; ^ori = r-|-l; h and o=:r-|- 00 and 
r — 00 : n is not r-j- 00 , (29.), but of the same nature with s in 
dioptase. In iron-glance, let P be = r ; then is s—r — 2, 
(r — 1 and r -p 1 exist in nature, but are not noticed by Haiiy). 
Lastly, in sulphate of iron, let P be = ?*; then is r (of the fi- 
gure) — 1; o=rr-pl; and n — r — 00 . Besides these ex- 
amples, nature affords many other proofs in favour of this se- 
ries : they are not contained in the figures of the Traite; hence 
5 = r -p 3 belongs to our Fig. 1. Plate VIII 
* All the figures in the text not referred to in our Plate VIII, are to be found 
in Haliy’s Mineralogy. 
