On Ciystallography. 29 i 



irfoved from the base AEO I in a quantity measured by a 

 ridge Og of a molecule, is necessarily parallel to the face 

 produced by tlie decrement. It is the same with the plane 

 r t s ; from vvbich it follows, ihat if we suppress the part 

 situated above r^i, we shall have a solid on which the 

 facet r t s will represent the effect of the decrement under 

 consideration. 



Wa may now observe that the directions c g,s t (fig. 32) 

 of the laminae applied to the face I O A' K (and the same 

 may be said of the face EO A' H) in virtue of the auxiliary 

 decrement, are no longer parallel either to the rid2;e or to 

 the diagonal, but comprehended between both. A fortiori 

 the defect of parallelism will take place, if we suppose that 

 the decrement on the angle EO I of the base proceeds by 

 three, four, or more range-s. Decrements of this kind are 

 called intermcdinte; and we conceive that they may be re- 

 ferred to an inlinity of different directions, according as 

 they are more or less removed from the one or other of 

 their limits, which are the parallelism with the ridges and 

 the parallelism with the diagonals. 



In cases similar to fig. 32, we avoid the kind of com- 

 plication which would flow from the immediate considera- 

 tion of those intermediate decrements, by supposing theni 

 contained in the principal decrement. But certain crysta's 

 exist, in which the three decrements considered round one 

 and the same solid angle are ail intermediate. In this case 

 we choose the simplest for the principal, regarding the two 

 others as auxiliary. 



Fig. 33 represents a case of this kind : en, which is the 

 edge of the first of the laminai applied on AEO I, is situ- 

 ated in such a manner that on the side C^l there are three 

 edges of molecules subtracted, and on the side O E there is 

 only one: np, wiiich is the eda;e of the first of the larnin^s 

 applied on I O A' K, indicates three ridges of molecules sub- 

 tracted from O' I lengthways, and two from OA' length- 

 ways ; cp, which is the edge of the first of the laininx; 

 piled up on EO A' H, determines a subtraction of two ridges 

 on O A', and of a single one on O E. 



Now it is easy to see that things go on, rektivcly to the 

 different iaces situated around the angle O, as if the mole- 

 cules which compose the laminae of superposition, being 

 invariably tied together in clusters, formed other molecules 

 of a higher order, and as if the sul)tractions were effected 

 by ranges of these last molecules. Thus there would be on 

 ihc base A EO I a decrement of triple molecules by two 

 ranges in height ; sinec on one hand the quadribtcr c O ;« Z, 

 T 2 " which 



