1C2 On Crystallography. 



4. When the nucleus being a parallelopipedon is divisi- 

 ble only by planes parallel to its six faces, it is evident that 

 the integrant molecule is itself a parallelopipedon similar 

 to this nucleus. 



5. But even when the integrant molecules differ from 

 the parallelopipedon, thev are always situated in the interior 

 of the nucleus, in such a manner that being taken by small 

 groups they compose parallelopipedons ; and the decre- 

 ments which give the secondary forms are always made by 

 rows of these parallelopipedons as in the case first men- 

 tioned. 



J give the name of subtractive molecules to the small 

 parallelopipedons, divisible or not divisible, the subtraction 

 of which determines the decrements of the laminae of su- 

 perposition. 



It follows from what has been said, that the subtractive 

 molecule is a kind of unity, to which we may refer the 

 structure of all crystals in general, so that we are at liberty 

 to adhere to the data which it furnishes in the application 

 of calculation to every possible crystalline form. To know 

 afterwards if this unity be indivisible, or if it has fractional 

 parts,is a matter of observation which maybe interesting in 

 natural history, but independent of which the theory would 

 not admit of our proceeding towards the object in view. 



6. In the case where the nueleus itself differs from the 

 parallelopipedon, we may always substitute for it a solid 

 of that form, either by abstracting from some of its faces, 

 if there are more than six, or by multiplying the subdivi- 

 sions alwavs in the direction of the natural joints, if it be 

 a tetrahedron. But we frequently obtain more simple re- 

 sults, by giving the preference to the true nucleus. 



7. The decrements undergone by the laminae of super- 

 position may be effected in all imaginable directions. The 

 limits of these directions are the edges and the diagonals of 

 the faces of the nucleus. Between these two limits there 

 is an infinity of intermediate ones, according as the small 

 solids, the rows of which determine the quantity of the de- 

 crements, are considered as double, treble, quadruple, &c. 

 of the subtractive molecule. I call decrements on the edges 

 those which takq,, place parallel to the edges of the faces 

 of the nucleus ; decrements on the angles, those which take 

 place parallel to the diagonals ; and intermediary decre- 

 ments, those which are made parallel to lines comprehended 

 between the edges and the diagonals. 



I shall now successively treat of the different primitive 

 forms above mentioned, and give, relatively to each of them, 



the 



