21)2 On Crystallography, 



which represents the base of a compound molecule, is cqur- 

 valent to three bases of simple molecules, afnd as the line 

 O py which correspontis to the height of a lamina of super- 

 position, contains two ridges of simple molecules. We 

 shall even conceive that the decrenient relative to the face 

 EO A' H is produced by three ranges in height of double 

 molecules, because c Op x" contains two bases of simple 

 molecules, and as O w is equal to three ridges of simple 

 molecules. Finally, in the decrement which acts on 

 lOA'K, there is a subtraction of a single range of triple 

 molecules in one sense and double ones in another. 



Between these three decrements, that which it would 

 seem most natural to adopt as the principal is the second, 

 which takes place on the face E O A' H, because it is the 

 one whose direction is least removed from that of the dia- 

 gonal which runs from A' to E'; or, if we please, because 

 it is formed by double molecules, and consequently less 

 compounded than those which are subtracted in virtue of 

 the two other dtcrcments. It is true that its measurement 

 in the direction of the height is greater than that of the 

 other decrements. But less regard ought to be paid to this 

 element, which is common to it with the ordinary decre- 

 ments, than to the differences which separate them. 



We shall now give som.e examples of intermediate de- 

 crements. Let O I I'O' (fig. 34) be one of the faces of a 

 cubical nucleus. Let us conceive a decrement which takes 

 place on all the angles by subtractions of double molecules. 

 In this case the edges of the lamina; of superposition will 

 be directed like the lines diiy km, ah, eh, Sec, on t lit: 

 hypothesis of their being a single range subtracted. 



Let E 1' (fig. 35) be the cubical nucleus. Let us sup- 

 pose that the decrements are made parallel to the lines km, 

 Im, kr, Ir, always by subtractions of di)uWe molecules, 

 but in such a manner that there are three ranges subtracted 

 in the direction of the breadth, and two in that of the. 

 height, in which case the decrements will be at once inter- 

 mediate and mixed. Let us moreover suppose that the edges 

 of the laminae of superposition, considered on the three 

 faces situated round one and the same solid angle O, have 

 transverse directions ; in such a manner that, with respect 

 to the face Oil' O', the greater number of ridges of molecules 

 are subtracted on the side 01; that with respect to the 

 faceEOO'E', it will be so on the side O O' ; and with 

 respect to the face E A I O, it will be so on the side E O. 



The effect of these various decrements will be to produce. 

 rouRd each solid angle three faces, which will he situated 



as 



