On Crystallography. £1^ 



placed in the interior between the panes and the axis. This 

 is what takes place in certain crystals, the prism of which 

 is very short, and resembles a hexagonal lamina. 



We shall conclude by an exan)pie drawn from analogical 

 carbonated lime, represented in fig. 39, PI. V. This va- 

 riety lias its surface composed of twenty-four trapezoids, six 

 of which are vertical, such a.s da b c, d a' b' cf, he, twelve 

 others, such as (f p a d, c' p a" h' , Sec, arranged by sixes oa 

 both sides of ihe preceding, and six terminal, such ASpap' s, 

 arran2;cd by threes round each summit. 



The former trapezoids result from the same law which 

 gives the six panes of the regular hexahedral prism (h'g. l) ; 

 the second are owing to the law which gives the carbonated 

 metastatic lime (figs. 6, 7, and \7). By comparing fig. 39 

 with fig. 6, we see that the vertical faces cut those of the 

 metastatic crystal in such a manner that they intercept the 

 solid lateral angles E, 0,I,K, Sec, (figs. 6 and 7). Finally, 

 the terminal fnces proceed from a (lecremcnt similar to that 

 which produces the equiaxis carbonated lime (fig. ]8). 



We cannot help being agreeably surprised, when we sub- 

 mit to calculation the form of this polyhedron, to see the 

 relations of its diflerent parts successively presented, either 

 between each other, or with those of several other crystals. 



1. In each vertical trapezoid abed (fig, 3y A), the up- 

 per triangle b a d \s equilateral, and its height an is doubly 

 the hcieht c n of th.e inferior triangle. 



2. Ill each terminal trapezoid psp"a" {',l}{. 39 B), the 

 upper triangle/? 5 p" is similar to the half of one of the 

 faces of the cqinaxis rhomboid, by a consequence of the 

 law of decrenjcnts ; and the li.lerior pff'/j" is similar to 

 the half of one of the faces of the inverse rhomboid, which 

 arises from the manner in which the plane of the trapezoid 

 is cut by the planes of the adjacent faces. It results that 

 the heights a'' r, sr of the triangles which subdivide this 

 trapezoid, are also to each other in the ratio of two to one, 

 as in the trape£oid abed (fig. 39 A). 



3. In each intermediate trapezoid c'pad (fig. 39 C), 

 the trianele padxi equal and similar to the f(Kuth part 

 PAD (fig. 39 D) of the primitive rhombus DPD'F'; 

 go lliat the anijle « (fig. 39 C) is straight, the angle dp a 

 30' 4(j' G", h.iff of the angle D I'D' flit:, 39 D),"and the 

 angle adp (fig. 39 C) 39-" 13' b\", half o'f the an^le PDP' 

 (fig. 39 D). 



4. The incidence of c' pad (fig. 39) on a' b' c' d is 

 precisely 135°, supplement to the half ol the rightanglc. 



b. The incidence of p sp' a" on c'/j d b' is isg" 13' 54", 



eupplcnu-nt 



