Tbtory of Cryjiallifutiofl. 387 



The refults of the four decrements being thus' perfectly 

 fimilur to each other, the laminae of fuperpofition, applied on 

 the rhombus CLGH, and on each of the other rhombufes 

 of the dodecaedron, will form as many right quadrangular 

 pyramids, which will have for bafes thefe fame rhombufes. 

 \nfig. 71 may be feen the pyramids which reft on the three 

 rhombufes CLDE, CEBH, CGHB {fig. 68.), and 

 which have for fummits the points vi, e, s (fig. 71.) ; but 

 on account of the decrement by a Ample range, the adjacent 

 triangular faces, fuch as E m C, E s C of the two pyramids 

 that belong to the rhombufes CLDE, CEBH, are on a 

 level, and form a quadrilateral E m C s. But we had twelve 

 pyramids, and confequently forty-eight triangles. • Dividing 

 by two, we thall then have twenty-four quadrilaterals, which 

 will compofe the furface of the fecondary cryftal. But be- 

 caufe the rhomboidal bafes of the two pyramids extend more, 

 in proceeding from L to E or from H to E, than in proceed- 

 ing from D to C or from B to C, the fides m E, E s of the 

 quadrilateral will be longer than the fides C m, C s. More- 

 over, we (ball evidently have m E equal to E s, and C m 

 equal to C s. The quadrilaterals will then be trapezoids, 

 which will have their fides equal two and two. 



I am acquainted with no cryitalline form where the firiss, 

 when they exift, point out, in a more fenfible manner than 

 in this, the mechanifm of the ftru&ure. We may here 

 fee the feries of decreafing rhombufes which form each of the 

 pyramids CLDEot, CEBHj, &c. (fig. 71.), and fome- 

 times the furrows are fo deep that they produce a kind of 

 flair, the fteps of which have a more particular poliih and 

 brilliancy than thofe of their facets, which are parallel to the 

 faces CEDL, CUBE, &c. of the nucleus. 



is the latter arc applied one Upon the other, is always equal to a Cum of 

 rhomboids, though at firft view it does not appear that this fliould be the 

 cafe, accoiding to the figure of thefe lamina?, which reprefent riling pyra- 

 mids. See Mtmoiid ds lAia<i. 1789, p. 52^. 



Cca If 



