On Crystallography. 123 



ihe method of calculating the results of all the laws of de- 

 crements of which it is susceptible. I shall begin with 

 the parallelopipedon, which is as it were the term of com- 

 parison to which the other forms refer. 



1 . Theory of the Parallelopipedon. 



8. Let AG (fig. 1, PI. IX) be a parallelopipedon, the faces 

 of which may have whatever respective dimensions and 

 measurements of angles we please. Let us conceive this 

 solid subdivided, by plans secting parallel to its different faces, 

 into a multitude of elementary parallelopipedons which 

 will be the integrant molecules. Each of the same faces 

 will be separated in its turn into a certain number of small 

 parallelograms, which will be the exterior faces of as many 

 molecules. 



If we choose any two of the six faces in question, pro- 

 vided they are opposite, we may consider the solid as an 

 assemblage of lamina? distinguished by the secting plans 

 parallel to these very faces. 



9. Let us now imagine pew laminae formed of small 

 parallelopipedons similar and equal to the foregoing, which 

 are placed as if in steps above various faces of Ihe generator 

 parallelopipedon, in such a manner that the facets in con- 

 tact coincide exactly, like what takes place in the interior 

 of this solid. Here there are three cases to be distinguished. 

 The first is that in which the laminae extend by their edges 

 so as to envelop completely the generator parallelopiptvion, 

 which wilf grow without changing its form. The second 

 is that in which the laminae would remain on a level by their 

 edges with the faces adjacent to the generator parallelopipe- 

 don, in which case it is easy to see that thev would form 

 re entering angles at the places of the ridges DC, BC, CG, 

 &c. In the third case, the laminae will go on decreasing, 

 following certain directions, in such a manner that each 

 will be exceeded by the foregoing in a quantity equal to 

 one or more rows, either in breadth or height. 



Of thee three cases, the first is relative to the primitive 

 forms given immediately by crystallization, and admits of 

 no difficulty. The second is foreign to Our views, because 

 nature presents us with no exampleof it in simple crystals. 

 We shall dwell at some length upon the third, which is. 

 properly the object of the theory. 



10. Let us conceive in the first place that the decrements 

 are produced in breadth on all the ridges by subtraction of 

 an equal number of rows, and let us confide ourselves for 



the 



