3?o Theory of Cryftall'ifathn. 



five angles will produce twenty faces, which, taken four 

 and four, will be equally on a level, which will make, in 

 the whole, fix diftincl faces,- fituated as thofe of the cube 

 (Jig. 60.) ; fo that the refult will be precifely the fame as in 

 jthe cafe of the rhomboid confidered is nucleus. 



In whatever manner w .' to fubdivide either the 



cube, the rhombus, or the o&aedron, we {bail always have 

 folids of two forms, that is to fay, pftaedra and tetraedra, 

 without ever being able to reduce the refult of the divifion to 

 unity. But the molecules of a cryilal being neceflarily fimi- 

 lar, it appeared to me probable that the firucture was as it 

 were interfperfed with a multitude of fmall vacuities, occu- 

 pied either by the water of cryftaliifation or by fome other 

 iubffance ; fo that, if it were poffible to carry the divifion to 

 its limits, one of the two kinds of folids in quefiion would 

 difappear, and the whole cryftal would be found compofed 

 only of moleculae of the other form. 



This idea is the more admiflible, as each oftaedron being 

 enveloped bv eight tetraedra, and each tetraedron beinor 

 equally enveloped by four oelaedra, whichever of the forms 

 we imagine to be fuppre'Tcd, the folids that remain will join 

 exactly by their edges ; fo that, in this rdpect, there will be 

 continuity and uniformity throughout the whole extent of 

 the mafs. The manner in which each octaedron is enve- 

 loped by eight tetraedra may be readily conceived, if we take 

 care that in dividing the cube (Jig. 60.) only by the fix fec- 

 tions given by the rhombus, we may depart at pleafure from 

 any two, a, s ; 0, h ; c, n 5 /', >■, cf the eight folid angles, 

 provided that thefe two angles be oppofite to each other. But 

 if we depart from the angles a, s, the rhomboid will have 

 the pofition fhewn fg. 62. On the other hand, if we de- 

 part from the folid angles 0. b, thefe angles will become the 

 fummits of a new rhomboid (fg, 64.) compofed of the fame 

 pftaedron as that of fg. 63, with two new tetraedra applied 

 on the faces h (if, egp (fg.6^.)^ which were unoccupied 

 On -\r- rhomboid of fg, 6%. Figures 65 and 66 reprefent, 

 9 one, 



