4 iG CRYSTALLOGRAPHY. 
the cryftals; and the other forms which they often affume ration on the other five fides of the cube, as many fimi- 
may be called fecondary forms. lar pyramids will in the fame manner be formed ; which 
The primitive cryftals obtained by the above procefs will envelope the cube on every fide, 
may be divided by fedtions parallel to their different fides: It is evident, however, that the fides of thefe pyra- 
all the matter which furrounded this primitive cryftal mids will not form continued planes, but that, owing to 
may alfo be divided by lections parallel to the fides of the gradual diminution of the laminae of the cubes which 
the primitive cryftal. It follows from this, that the parts compofe them, thefe fides will referable the fteps of affair, 
detached by means of thefe fedtions are fimilar, and differ We can fuppofe, however, (what muft certainly be the 
from one another only in fize, which diminifhes in pro- cafe,) that the cubes of which the nucleus is formed are 
portion to the length that the divifton is carried. But exceedingly fmall, almoft imperceptible ; that therefore 
the divifionof the cryftals into fimilar folids has a term, a vaft number of laminae are required to form the pyra- 
beyond which we fhould come to the fmalleft particles of mids, and confequently that the channels which they 
the body, which could not be divided without chemical form are imperceptible. Now DCBE, fig. 12, being 
decompofition. It is probable, therefore, that the form the pyramid refting upon the face A B C D in fig. 7 ; and 
of the integrant particles of a body is the fame with the C B O G, fig. 12, the pyramid applied to the next face 
primitive form of its cryftals. Here, then, we have a BCGH, fig. 7, if we confider that every thing is uni¬ 
method of difcovering the form of the particles of bodies; form from E to O, fig. 12, in the manner in which the 
and if this method could be applied to all fubftances what- edges of the lamina cjfuperpnftion (as the abbe Hatty calls 
ever, it would enable us to ascertain the affinity of all bo- the laminae which compofe the pyramids) mutually pro¬ 
dies for each other by accurate calculation. It muft be jedt beyond each other, it will readily be conceived, that 
allowed, that feveral objeftions might be made to the the face CEB of the firft pyramid ought to be exadtly 
conclufions of Mr. Hauy ; but his theory is, onthe whole, in the fame plane with the face COB of the adjacent 
fo plaufible, that it would certainly be worth while to pyramid ; and that therefore the two faces together will' 
extend it, and apply it to the calculation of affinities as form one rhomb ECO B. But all the fides of the fix 
far as it is fufceptible of the application. If the cryftals pyramids amount to 24 triangles fimilar to C E B ; con- 
obtained by the above procefs be the primitive forms, it fequently they will form 12 rhombs, and the figure of 
becomes a queftion of home confequence to determine in the whole cryftal will be a dodecahedron, fimilar to that 
what manner the fecondary forms are produced. reprefented in fig. 5 and 6. 
According to Hauy, all the parts fuperadded to the The cube, before it arrives at the form of the dode- 
primitive cryftals, in order to form the fecondary cryftal, cahedron, paffes through a multitude of intermediate 
confift of plates, which dec'reafe regularly by the fub- modifications, one of which is reprefented at fig. 13. It 
fraction of one or more rows of integrant particles, in may be there feen that the fquares paeo, klqu, mnts, Sec. 
Inch a manner, that the number of thefe ranks, and con- correfpond to the fquares AB CD, D C G F, CBHG, 
fequently the form of the fecondary cryftal, may be deter- Sec. in fig. 6, and form the iuperior bafes of as many, py- 
mined by theory. To explain this, let 11s fuppofe that ramids, incomplete for want of the laminae by which 
E P, fig. 5, reprefents a dodecahedron, terminated by they ought to be terminated. The rhombufes E D L C, 
equal and fimilar rhombs; that this dodecahedron is a E C O B, See. fig. 5, by a neceffary confequence are re- 
fecondary cryftal, the primitive form of which is a cube: duced to fimple hexagons aeC/kJ}, eoBnmC, Sec. 
the fituation of this cube in the dodecahedron may be fig. 13, and the furface of the fecond. ry cryftal is corn- 
conceived from fig. 6. The fmaller diagonals DC, C G, pofed of twelve of thole hexagons and fix fquares. This 
G F, FD, of four fides of the dodecahedron, united is the cafe with the boracic fpar, allowance being made 
round the fame folid angle L, form the fquare CDFG. for fonie facets which take the place of the folid angles. 
Now there are fix folid angles, compofed of four planes, as will be feen hereafter. 
to wit, the angles L, O, E, N, R, P, fig. 5; and, con- If the decreafe of the laminae of fuperpofition took 
fequently, by making fedfions through the fmaller dia- place according to a more rapid law; if each lamina had 
gonals of the fides that form thefe angles, fix fquares on its circumference two, three, or four, rows of cubes 
will be made apparent, which are the fix fides of the pri- lefs than the inferior lamina ; in that cafe, the pyramids 
xnitive cube, three of which are reprefented in fig. 6, produced being lower, their adjacent faces would no 
CDFG, ABCD, BCGH. longer form- one plane ; and therefore the furface of the 
This cube being compofed of cubic integrant particles, fecondary cryftal would confift of twenty-four ifofceles 
each of jthe pyramids, LCDFG tor inftance,‘fig. 6, triangles, all inclined towards each other, 
which repofe upon its fides, muft alfo, according to the In this manner Mr. Hauy has (hewn, that a variety of 
theory, be compofed of fimilar cubic particles. To make fecondary cryftals are formed, and that their forms vary 
this appear, let us fuppofe that A B F G, fig. 7, is a cube by means ot llight variations in the ratio of the decrement „ 
compofed of 729 fmall cubes : each of its fides will con- To underftand this, we muft again conceive a cubic nu- 
fi ft of 81 fquares, being the external fides of as many cu- cleus, the different edges of which are fo many lines of 
bic particles, which together conftitute the cube. Upon departure to the fame number of-decrements, taking 
ABCD, one of the fides of this cube, let us apply a place at the fame time in two different ways, that is to 
fquare lamina, compofed of cubes equal to thofe of which fay, by the fubtradtion of two ranges parallel to the edges 
the primitive cryftal confifts, but which has on each fide A B, CD, fig. 7, and of one range parallel to the edges 
a row of cubes lefs than the outermoft layer of the pri- AD, B C. Let us fuppofe alfo that each lamina, being 
mitive cube. It will of courfe be compofed of 49 cubes, in thicknefs equal only to a fmall cube of the fide A B 
7 on each fide; fo that its lower bafe onfg, fig. 8, will and C D, is equal to double the fide of A D and B C„ 
fall exactly on the fquare marked with the fame letters This difpofition, in regard to the decrements proceeding 
in fig. 7. Above this lamina let us apply a fecond hnpu , from the lines DC, B C, fig. 7, is reprefented by fig. 14. 
fig. 9, compofed of 25 cubes; it will be fituated exaCtly In this hypothefis it is evident that, on account of the 
above the fquare marked with the fame letters in fig. 7. more rapid decreafe in departing from D C or A B, than 
Upon this fecond let us apply a third lamina vxyz, fig. 10, in departing from B Cor AD, the faces produced in the 
c’onfifting only of 9 cubes; fo that its bafe (hall reft upon former cafe will be more inclined to the plane ABCD, 
the letters vxyz, fig. 7. Laftly, on the middle fquare r while the faces produced in the latter will remain as it 
let us place the fmall cube r, fig. ir, which will repre- were behind ; fo that the pyramid will no longer be ter- 
lent the laft lamina. It is evident, that by this procefs minated by a fmgle cube E, fig. 12, which, on account 
a quadrangular pyramid has been formed upon the face of its extreme minutenefs, appears to be only a point, 
A BCD, fig. 7, the bafe of which is this face, and the but by the range of cubes MN ST, fig. 14, which, fup- 
vertex the cube r, fig. n. By continuing the fame ope- poling thefe cubes to be almoft infinitely finally will pre- 
1 fent 
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