On Crystallography i 2ll 



the supposition that the cubic nucleus has ori each of its 

 edges 17 ridges rf molecules ; v.i-.euce it follows, that each 

 of iis faces is composed of 289 facets of molecules, and 

 that the whole solid is equal to 4<j!3 molecules. On this 

 hypothesis, there are eight Iaiiiina2 of superposition, the 

 last of which is reduced to a sunplc cube, whose edt>es de-' 

 terminc tiic numbers of molecules which form the series 

 15, 1.^, II, 9, 7, 5, 3, I, the ditTt-rence being 2, because 

 there is one course subtracted from each extremity. 



Now if instead of thi> coarse kind of masonrv, which 

 has the advantage of speaking to the eye, we substitute in 

 our imaginaiion the infinuely delicate architecture of na- 

 ture, we must conceive the nucleus as being composed of 

 an incomparably grater number of imperceptible cubes. In 

 this case the number of laminae of superposition will also 

 be beyond comparison greater than on the preceding hvpo- 

 thesis. By a necessary consequence, the furrows which 

 form these lamina; l)y the alternate projecting and re-en- 

 tering of their edges will not be cognizab'e bv our senses ; 

 and this is what takes |)lace in the polvhedia which cr\stal- 

 lization has produced at ease, witliout being disturbed in 

 its progress. 



We may remark that instead of twenty-four decrements, 

 which act two and two from one side to ihe other of each 

 ridge, we may limit ourselves to adu'it only twelve, by 

 considering each of the twelve others as beinsr the continua- 

 tion of the former. For instance, we may suppose that 

 decrements act directly towards the four edoes of the basis 

 AEOI, (fig. 12) and towards those of the inferior basis, 

 in order to produce the two pyramids which have their sum- 

 mits in s and in /, and that with respect to the other 

 faces of the cube, they act solely towards the two edi!,es I T, 

 0', and towards the opposite edges behind the cube, to 

 produce secondary faces situated like I M', 0/0'. On 

 this hypothesis, if we conceive that the eflects of the decre- 

 ments are prolonged from the other side of the edires which 

 have served them as parting lines in such a nianner that 

 these prolongations, combining with the faces produced by 

 llie immediate action of ihc decrements, circumscribe a 

 space, we shall evidently have the same dodecahedron. 

 We shall afterwards sec the utility of this remark. 



If the luminae applied on the cube decreased on all sides 

 by two or more courses, then the pyramids being more el- 

 liptical, and their adjacent faces being no hjiiijer two and 

 tAo on the same plane;, the secondary crystal would be 

 Ictiiiiuuled by 24 distinct triangles. 



O a We 



