CRYSTALLOGRAPHY. 



-^omboidal bafes, fituated in fuch a manner, that the faceS 

 \ D, a d, anfl Q,Vt, c d, are vertical, and B, D, are the 

 lite angles of the bafe, and that thefe proceed in an afcend- 

 X direftion from A to C. Let us fuppofe alfo, that the 

 •ifm is cut into two equal parts by a plane which pafles 

 -ough the diagonals drawn from B to D, and from b to d, 

 _ r.d that the one half remained fixed, whiUl the other is 

 riverfed without being feparated from the former. The 

 (, -yftal will then be prefented under the afpeft feen in /^. 

 ^ , , where the triangle t>, d', c, which was one of the halves 

 the inferior bafe,^^. 60, is now fituated in the upper part, 

 ;. 61, and forms a falient angle or projefting edge with 

 r'i^ triangle A B D. Whilft the triangle B D C,/^. 61, 

 > iiich was one of the halves of the fuperior bafe,_^. 60, is 

 uafported into the lower part,_/f^. 61, and forms are-enter- 

 - angle with the triangle a ^ </, we may eafily conceive 

 t the plane of junftion T>^, bd, of the two halves of a 

 jmboid is fituated like a plane drawn, formed by a decre- 

 ■nt on one range or other of the edges A. a, C c,Jig. 60, 

 J ;.;;d thus the manner in which thefe halves join is in ftrift 

 relation with the ftrufture. 



Now if we imagine a fecondary form, which has for its 

 nucleus a fimilar prifm to the above, and if v/e fuppofe that 

 it has been cut in the direftion of the plane D B, ^ (/, and that 

 one of the halves has been reverfed asin_/ff. 61, the arrange- 

 ment may be fuch, that there will ftill be a re-entering angle 

 at one termination, and a falient angle at the other, refulting 

 from the mutual incidences of the faces produced by the 

 decrements. 



In certain cafes, the plane of junftion on which the two 

 halves of the cryftals are joined is fituated parallel to one of 

 the faces of the nucleus, and the arrangement does not 

 admit of prefenting a re-entering angle oppofite to a falient 

 one. 



Thefe cryftals which are here defcribed are called by 

 Haiiy keir.yiropes, or half reverfed. Rome de Lifle has 

 called fuch cryftals marles. 



Another accident extremely common is the manner in 

 which cryftals in groups are inferted into each other. This 

 kind of penetration is fubjeft to many diverfities ; but on 

 accurate examination, we fhall find that they are fubjeft to 

 certain laws always analogous to thofe of ftrufture, and that 

 thefe cryftals, inftead of being precipitated confufedly on each 

 other, have a certain kind of arrangement. In illuftration 

 of this, let Plate V.fg. 62. be a cube, and M N /- an equila- 

 tecal triangular facet, produced by a decrement of one range 

 round the angle A : let us fuppofe a fecond cube modified 

 in the fame manner, and attached to the former by a facet 

 refulting from a fimilar decrement ; we ftiall have the com- 

 bination reprefented_;?^. 63. 



We mav alfo conceive that one of thefe cubes, for inftance 

 the lower one, is increafed in all its dimenfions, except in 

 thofe places where the other forms an obftacle to its pro- 

 grefs. As the increment continues increafing, it will more 

 and more envelope the upper cryftal, and may finifti by 

 covering it entirely. We obferve cryftals funk into each 

 other at different degrees of depth, Ijut always in fuch a 

 manner, that their plane of junftion has a pofition analogous 

 to planes refulting from decrement ; fo that both follow 

 their common progrefs to this plane, which fervcs as their 

 refpeftive limit. Cubes of fluor fpar inferted into each 

 other have the laminje of each extended without interruption, 

 until they are ftopped by the common plane of junftion. 



The example here ftated relates to a very fimple and 

 ./egular law of decrement. But frequently the laws which 

 determine the plan_e of junftion are more or let complicated, 

 and there are a few wliich are rather exij-aordrnary. W hen 



two prifms crofs towards the middle of their axis, there are 

 two planes of junftion which unite croffing each other as 

 in the mineral called ftaurotide, and thefe planes have pofi- 

 tions analogous to thofe which would be determined by the 

 known laws of decrement. 



In the preceding theory of cryftallography it has been 

 conftantly fuppof«d, that the lamina: compofing cryftals of 

 the fame fpecies proceed from a common nucleus^ undergo- 

 ing decrements fubjeft to certain laws, on which the forms 

 of thefe fecondary cryftals depend. But this, fays Haiiy, 

 is only a conception adopted to make us more eafily perceive 

 the mutual relations of the forms we are treating of. Pro- 

 perly fpeaking, a cryftal taken as a whole is only a regular 

 group of fimilar molecules. It does not commence by a 

 nucleus of a fize proportioned toyw'hat it afterwards acquires, 

 or that which we can extraft from it by mechanical divifion ; 

 and the laminse which cover this nucleus are not applied 

 fucceffively over each other in which the theory confiders 

 them. The proof of this is, that among crj'ftals of different 

 fizes that are often attached to the fame fupport, thofe 

 which can only be diftinguiftied with the microfcope are as 

 complete as the largeft ; from whence it follows that they 

 have the fame ftrufture, that is to fay, they have already 

 within them a fmall nucleus proportioned to their diameter, 

 and enveloped by the rcquifite number of decreafing lammas 

 to form the faces of the fecondarj- cryftal. We muft there- 

 fore conceive, that from the firft commencement a cryftal 

 fimilar to the rhomboidal dodecahedron is already a fmall 

 dodecahedron, and contains a cubical nucleus proportionally 

 fmall, and that this kind of embryo continues to increafe with- 

 out changing its form by the addition of new lamini on all 

 the fides, fo that the nucleus increafes on its part, always pre- 

 ferving the fame relation vnth the entire cryftal. 



We fhall render this idea diftinft by a conftniftion whicli 

 refers to the dodecahedron, and reprefented by a plane figure. 

 What is faid of this figure may eafily be apphed to a ioUd, 

 fince we can always conceive a plane figure to be a feftion 

 made in a fohd : let t s,z s", Plate V.fg. 59. A, be an affcm- 

 blage of fmall fquares, in which the fquare B N, D G, com- 

 pofed of forty-nine fquares, reprefents a feftion of the nucleus, 

 and the extreme fquare Ip i bfc s, &c. the fteps formed by the 

 laminas of fuperpofition. We may conceive that the affemblage 

 commenced by the fquare B N, D G, and that different piles 

 of fmall fquares are afterwards applied on each of the fides 

 of the central fquare ; for inftance, on the fide B N, the five 

 fquares comprehended between _/' and h, afterwards the three 

 fquares contained between c and c, and then the fquare s. 

 This progrefs correfponds with what would take place if 

 the dodecahedron commenced with a cube proportioned to 

 its volume, and wliich afterwards increafed by an addition of 

 laminae conftantly decreafing. 



But we may alfo fuppofe, that the affemblage of molecules 

 commenced as reprefented Plate V.^. 59. C, in which the 

 fquare B N, D G,is only compofed of nine molecules, and had 

 on each fide of it only a fingle fquare, st, t' a. If we refer 

 this affemblage in imagination to the folid, of which it is a 

 feftion, we (hall eafily perceive that this folid had for its 

 nucleus a cube compofed of twcnty-feven molecules, and 

 that each face compofed of nine fquares had placed on 

 the middle one a little cube, fo that the decrement of one 

 range is already feen in the initial dodecahedron. 



By the addition of new fquares, this affemblage %vill 

 become that of B, fg. 59, in which the central fquare 

 B N, D G, is formed of twenty-five fmall fquares, and fup- 

 ports on each of its fides a range of three fquares, belides 

 the terminal fquares s I, s'a. Here we have already two 

 laminx of fuperpofition inftead of one only. Laftly, by a 

 5 L 2 nu-thcr 



