\ 



300 On Crystallography. 



supplement of 50° 46' 6", which is the half of the primitive 

 an^le D PD' (fig. 39 D). 



6. Finally, the polyhedron shares with the metastatic va- 

 riety the property in virtue of which the mutual incidence 

 of the faces which correspond in this variety with the tra- 

 pezoids c' p a d, c' p a" b'y are equal to those of the rhombs 

 of the primitive form. These are the different ratios which 

 have suggested the name of analogical given to the poly- 

 hedron in question. 



We now see to what all the different metamorphoses be- 

 long under which the primitive form is presented in secon- 

 dary crystals, whether simple or compound. Sometimes 

 the decrements are performed at once on all the edges, as 

 in the dodecahedron with rhombic planes, cited above, or 

 on all the angles, as in the octahedron originating from 

 the cube. At times they take place only on certain edges 

 or certain angles. At others there is an uniformity bcT 

 twcen them, so that there is only a single law by one, two, 

 three, &c., ranges, and which acts on different edges or on 

 different angles, as it is also still observed in the solids, of 

 which we shall speak presently. Occasionally the law varies 

 from one edge to the other, or from one angle to the other ; 

 and this is what happens in particular when the nucleus has 

 not a symmetrical form, as when it is a parallelopipedon, 

 the faces of which differ by their respective inclinations, or 

 by the measurements of their angles. In certain cases the 

 decrements on the edges concur with the decrements on 

 the angles to produce the same crystalline form. It also 

 happens sometimes, that the same edge, or the same 

 angle, undergoes several laws of decrement which succeed 

 each other. Finally, there is a multitude of cases in 

 which the secondary crystal preserves faces parallel to those 

 of the primitive form, and which are combined with the 

 faces produced by the decrements, in order to modify the 

 figure of this crystal. 



If amidst this diversity of laws, sometimes solitary, and 

 sometimes marching as it were by groups round the 

 same primitive form, the number of ranges subtracted 

 was in itself very variable; if, for example, there were de- 

 crements by twenty, thirty, forty, or more ranges, as 

 may be imagined, the multitude of forms which might ex- 

 ist in each species of mineral would befit to overwhelm the 

 imagination, and the study of crystallography would present 

 an immense labyrinth, which, in spite of the clue furnished 

 by theory, could with difficulty be unravelled. But the 

 power which produces the subtractions seems to have a 



very 



