CRYSTALLOGRAPHY. 



*ci)TekMedJg. 24. The iheory of their formation will be 

 explained as we proceed. 



1 he primitive form is not in all cafes the ultimate form 

 10 which cryftals can be reduced ; for where the primitive 

 .orm is not a parallelopiped, the divifion parallel to the 

 laces neceffarily produces forms which muft vary from that 

 of the primitive nucleus. See Plate V. ^g. 56. Crj/lallo- 

 ^raphy, which reprefents the bafe of a fix-fided prifm, divided 

 i\- feclions parallel to each of its fides: from this divifion 

 :hj ultimate form which we can ever obtain muft be that of 

 a triangular prifm ; for by carrying on the divifion we may 

 conceive the particles to become fmaller, but their form will 

 remain the fame. We have therefore obtained the form of 

 the integrant molecule. In parallelopipeds, the form of the 

 nucleus is alfo that of the molecule itfelf. 



Thus in the cube, as reprefented Plate W.Jigs. 48 and 49, 

 the divifions parallel to the fides produce a feries of fmaller 

 cubes, which muft be the form of the integrant molecule. 

 In fome inftances, the primitive forms themfelves admit of 

 divifion by laminse not parallel to that of the faces, from 

 which muft neceffarily refult a new form of the integrant 

 molecule. 



Plate II. Jig. 26. reprefents a primitive rhomboid of 

 tourmaline A E, O I, G H, A K, which is divifible both 

 in the direction of its fix faces and in that of the fhort dia- 

 gonals A O, I A', A K. Thefe latter feftions divide the 

 rhomboid into fix tetrahedrons, which are reprefented fur- 

 rounding the nucleus. Haiiy conceives, that by thefe divi- 

 fions, we obtain the form of the integrant molecule, or of 

 the ultimate integrant atom of the cryftallized mineral. It 

 has been obferved, that no proof can be advanced to con- 

 firm this conjefture, except the impodibility of altering the 

 form, how tar foever we carry the divifions ; and the obvious 

 confequence is, that if thefe divifions be carried far enough, 

 we muft at laft reduce the cryllal to its integrant particles. 

 It is not, however, neceffary to fuppofe, that the confti- 

 tuent particles themfelves have any other form than that of 

 fpheres ; becaufe all the forms of the integrant molecule, 

 which are the tetrahedron, tlie triangular prifm, and the 

 cube, may be readily conceived to be conftrufted with four, 

 fix, and eight fpherical particles, arranged in their forms 

 by cryftalline polarity. It deferves attention, that the forms 

 of the integrant molecule are the moft fimple which can 

 exift among folids with plane furfaces, being bounded re- 

 fpedtively by the fmalleft poflible number of fides, viz. 

 four, five, and fix. 



If we conceive the integrant molecules to be arranged in 

 rows, and a number of thefe rows to be arranged in the 

 fame planes, they will form lamina? of any conceivable fize. 

 Now by a fuccelfion of plates increafing in fize, the magni- 

 tude of the primitive cryftal will be increafed ; but if thefe 

 laminae decreafe in extent by one or more rows of particles, 

 the refult will be a change of form, or the produiSion of a 

 fecondary cryftal. Now the laminas may either decreafe on 

 the edges by one or more rows, or may decreafe diagonally 

 on the angles by a determinate number of rows, or the 

 decreafe may take place in fome intermediate direftion. 

 Thefe are called by Haiiy, decrements on the edges, de- 

 crements on the angles, and intermediate decrements. Some- 

 times decrements take place at once on all the edges, 

 fometimes upon all the angles, and fometimes only on cer- 

 tain edges and angles. In fome inftances the decrements 

 are uniform, and the fame number of rows decreafe from 

 the different edges or angles. Sometimes the law of decre- 

 ment varies from one edge to another, or from one angle to 

 the other ; and this happens chiefly when the nucleus has not 

 a fymmetrical form, or when it is a parallelepiped, whole 



faces differ m the refpcttive incliiiations of their faces, or 

 in the meafure of their angles. In certain cafes, the decre- 

 ments on the edges concur with thofe on the angles to pro- 

 duce the fame cryftalline form. It happens alfo, that the 

 fame edge, or the fame angle, fometimes undergoes different 

 laws of decrement that (ucceed each other ; and, finally, 

 there are a great many cafes where the fecondary cryftal 

 preferves faces parallel to thofe of the primitive form, and 

 which combine with the faces produced by the decrement, 

 to modify the figure of the cryftal. 



If, in the midft of fuch a diverfity of laws, fometimes 

 adting fohtarily, and fometimes in combination upon the 

 fame primitive form, the number of ranges fubtrafted 

 were hkewife variable ; if, for inftance, there were decre- 

 ments of twenty, thirty, forty, or a greater number of ranges 

 of molecules, of which it is ver)' poflible to conceive, the 

 multitude of forms which might exift in each mineral fpecies 

 \vpuld be fufficient to appal the imagination, and the ftudy 

 of cry ftallography would prefent an immenfe labyrinth, from 

 which even the afliftance of theory could not extricate the 

 learner. 



But the force which produces the decrements of range* 

 appears to have a very limited adlion. Generally thefe fub- 

 tractions take place by only one or two rows of molecules. 

 None have hitherto been found beyond fix rows ; but fuch 

 is the fecundity united with this fimplicity, that were we to 

 confine ourfelves to decrements by one, two, three, and 

 four rows, and to exclude thofe that are mixed or interme- 

 diate, we find that the rhomboid is fufceptible of 8,388,604 

 varieties of cryftallization. Doubtlefs many of thefe varie- 

 ties do not exift in nature ; but there is reafon to expeft 

 that difcoveries in the field of inquiry will be made for 

 many years to come. 



The tetrahedron and the triangular prifm, when they 

 occur as integrant molecules, are always airanged in fuch a 

 manner in the interior of cryftals, that, taking them in 

 groups of two, four, fix, eight, they compofe parallelo- 

 pipeds. Thefe parallelopipeds a.e, by Haiiy, named J'ub- 

 traclive molecules. They are always fubftituted in the place 

 of tetrahedrons and triangular prifms in confidering the 

 decrements where they produce the fecondary forms. 



Decrements of the Edges. — The moil fimple cafe of change 

 of form produced by the fuperpolition of decreafing lamina;, 

 is that which fuppofes ranges of molecules to be taken 

 away on all the edges of a parallelopiped, in a diieAioa 

 parallel to the edges. Yet this cafe, fo fimple in appear- 

 ance, may give rife to fonns of confidcrable complexity. 

 Thus the rhomboidal dodecahedron [Plate \\. Jig. 21. or 

 Plate III. Jig. 2%. Cryjlaliography) may be formed in this 

 way from a cubic nucleus. If the integrant molecule of 

 this fpecies be a cube, it follows that the primitive cryftal 

 E A, O I, and E' A', O' I', is formed by a congeries of cubes; 

 Suppofe thefe cubes of fuch a fize, that an edge of ths pri- 

 mitive cryftal is compofed of a row of feventeen cubes, 

 placed fide by fide, as reprefented ^_j-. 29. I O, O E : of 

 courfe each face of the primitive cryftal will be a congerie* 

 of 289 fquares, confifting of fo many integrant molecules ; 

 and the primitive cryftal or cube will be a congeries of 

 4913 cubes. Let us fuppole that a fquare furface or plate, 

 of the thicknefs of one integrant molecule, be applied to 

 every face of cube ; but that inftead of being of the fame 

 fize as the face of that cryftal it is lefs by a fiugle row of 

 molecules all round ; fo that the fides, inftead of containing 

 feventeen little cubes, contain only fifteen each (fee//. 29.); 

 of courfe this fquare will contain only 225 little cubes, in- 

 ftead of the 289 that form the furface of the primitive 

 cryftal. Upon each of thefe firft plates applied to every 



' ' ■ ' face. 



