218 On Crystallography . 



minae represented by figures 19 D and 19 E, observing that 

 the letters marked with an accent, in each figure, ought to 

 coincide vviih the same letters not accented in the preceding 

 figure. 



Beyond the term which answers to fiij. 19 E, thelanjinse 

 of superposition cease to envelop the interior edges of the 

 crystal, by their borders [lords) analogous to these edges 

 {aretes), and are reduced to simple triangles. This will be 

 easily conceived by considering the laminae represented by 

 figures 19 F, J9 G, I9 H, the positions of which are de- 

 termined according to the same conditions with the above. 



The numberof rhomboids which compose the different 

 laminss being always diminishing, the last lamina is reduced 

 to a simple rhomboid d' (fig. 19 I), which will attach itself 

 to that denoted by the same letter (fig. 19 H), and will 

 form the summit of one of the lateral solid anft'' '•■> of the 

 secondary rhomboid. 



We now sec the reason why the laminae of superposition 

 assume fioures successively pentagonal and triangular in 

 issuing from the nucleus. For example, every lamina de- 

 tached from the crystal (fig. 18) by a section which passes 

 between the angle z and the middle of the lines % t, z u, is 

 necessarily triangular, and has the same structure with 

 F t' R' (fig. 19 G), i. e. it is really embattled {crencUc) at 

 its basis in such a way, thai the imperceptible furrows, which 

 exist on the crystal produced by Nature at the basis of these 

 kind of laminas, are on the prolongation of those which pro- 

 ceed from the decrement towards the edges. There are 

 even crystals the surface of which, from the effect of a less 

 finished crystallization, exhibits similar furrows, which run 

 over the whole extent of the faces hi directions parallel to 

 the small diagonals. 



Decremrnits on the Angles. — The decrements which have 

 ridges {nrttes) for parting lines, and which we call decre- 

 ments on the borders [Lords], would not be sufficient to ex- 

 plain all the diversities of form presented by secondary 

 crystals. Observation and calculation prove that we must 

 also admit of decrements which have angles for points of 

 separation, and the action of which is applied parallel to 

 the diagonals. We shall call them decrements on the angles. 



In order to enable students to comprehend the method 

 which I have followed in mv inquiry into these new de- 

 crements, I shall remark, that the same substances which 

 present the dodecahedron with pentagonal planes, origi- 

 iiaiing from the cube, and which might in the san)e way 



assume 



