On Crystallography. 461 



language, already extremely concise, from every thing enig- 

 matical, and because in the case particularly when the form 

 was composed of a great number oF facets, which would 

 necessarily imply a proportional complication in the expres- 

 sion of the sign, beginners would be embarrassed to make 

 the relation between one and the other. 



To obviate this difficulty, I thought it right to place un- 

 der the different letters which compose the sign, those 

 which correspond with them on the figure. By means of 

 this addition the sign of the bibinary feldspar is presented 



as follows : G- M T I P, This is the method which I shall 



use in the course of this work, with respect to all the cry- 

 italline forms, adding to each sign a kind of guide, which 

 will serve for recovering its form, however complicated it 

 niav be. 



We shall pass to the parallelopipedons of a more regular 

 •form, and in the first place consider the cases in which they 

 differ from the rhomboid. We shall suppose that each of 

 them is nothing else than that of fig. 48 ; the form of 

 which has varied so as to become more symmetrical. As 

 a consequence of tliis variation, certain solid or salient an- 

 gles, which were different on the first parallelopipcdou, have, 

 hcx'onie equal. All that tak'*s place on one is repeated on 

 tlie other, and ihev consetjuently ought to be marked with 

 the same letter. It is tlius that, in algebra, certain general 

 solutions are simplified in the particular cases where a 

 quantity, which we had at first supposed different from an- 

 other law, becomes equal. 



Let us conceive, fur eximple, that the primitive form is 

 a straight prism, which has for bases oblique-angled pa- 

 rallelograms, one side of which is loncrer than the other. 

 We shall have (fig. 4S.) 0=A, I = E, &c. We shall 

 eubstitute, ihcrelore, on both occasions, the second letter 

 for the first, as we see on fig. 53. 



By continuing to run over the various modifications of 

 the paralle'opipedon, we shall see th^m pass bv different 

 degrees of simplicity, which will determine new equahties 

 between the klleis indicative of their angles and of their 

 edges ; and we shall have successively. 



For the obrKjuc prism with rhombic bases, the expres- 

 sion represented in \\z. 54. 



For the straight prism with rectangular bases, that which 

 we see in fig. 35. 



For the straight prism with rhombic bases, that of 

 .fijf. 56. 



For 



