I 



Oa Crfittdiagraphg. ?3 1 



»lnict«re, which is that of crystals whose primitive form 

 is the regular hexahedral prism. Let A D be always (fig. 40) 

 cue of the bases of this prism subdivided into sniaJ! 

 triangles which are the bases of so many mo!<?cu!es. Ii is 

 evident that any two given triangles adjoinilig the other, 

 siich as A p iy A O i, compose a rhombus, and conse^ 

 tjuently the two prisms to which they belong inrax by tJiear 

 union a prism with rhomboidai bases, which is one of the 

 kinds of paralieiopitx;don. 



Let us now imagiue that tlie triangular prisms, whicli 

 are the elenieiit* oi these paraSlelopipedons, are invariably 

 connected with each other. We may substitute for the 

 arraugeuient represented in fig. 40, that of fig. 41 merely 

 composed of rhombuses, which will be th.e bases of so many 

 i>aral!e{opipedons. 



Now if vxe suppose a series of l^m'in^ piled up on the l»es- 

 agou ABCDFG, and which undergo, for example, oa 

 their different rdgcs, subtractions of one range of parailclo- 

 pipcdons similar to those now in question, these edii;es witt 

 l>e successively arranged hke the sides of hexagons il^nrk, 

 kuxyge, Sic: hence we see that the quantity in whicii 

 each lamina shall exceed the following one will he a simii 

 of parillelopipedons, or prisms with rhouilwidal, bases ; and 

 it is easy to judge that the result of the decrement, sup- 

 posing thai the latter attains its limit, will be a straia:{it 

 hcxabcdral pvraiiiid, which will have as a base the hesagoa 

 ABCDFG. 



All the other different prinaitive forms of the paralielopi- 

 pedon give analogous results. We might even substitute 

 for each of these forms a nucleus similar to the small pa- 

 rallelopipedon, which are assemblages of tetrahedrons or 

 triangJilar prisms ; and we should also succeed inexplaliiJiis: 

 the secondary forms by laws of decrement referred to tins 

 nucleus, which would also be given by mechanical di- 

 visitui. We shall use it in this manner with respect to 

 quartz, because in this case the substitution of the paralle- 

 lopipedon for thfc bipyraniidal dodecahedron lead? to mure 

 simple decrenjents for certain varieties*. 



I shaH 



• We are acquainted witli cryrtals wlioce mechanical division gives first 

 a priiin with riuimboiti.J ha-cs winch have difi'crtnt ahgips of lao" and C0». 

 Tlii> {insni may be MtciWitilt sulidivided in tbii dirtctioii of one of ihe di.r- 

 govuils of it', biise*: from which it reaulis that we might also extract inune- 

 dialcly iroin iht ujcdiulary cryaiaia liexalicdral prism ; hut which woula nor 

 lit regular. la these casci we «lull adopt the prism with rhombuidal baaii 

 tur the Diicieus, because this form, besides being simpler, has a ciiiuacter of 



rcjjularitjr 



