212 4 On Crystallography^. 



We call decrements in breadth those \w which, as well as- 

 ill the preceding, each lamina has only the height of a 

 molecule ; so that their whole effect hy one, two, three, Sec, 

 courses, is in the way of breadth. Decrements in height are 

 those in which each lamina, exceeding only the following 

 one bva single course ip the direction of the breadth, mav 

 have a height double, triple, quadruple, &c., to that of a 

 molecule: this is expressed by saying that the decrement 

 takes place by two courses, three courses, &c. in height. 



The two kinds of decrement which we have mentioned 

 are combined together in the following example taken from 

 sulphuretted iron (ferruginous pyrites) with twelve penta- 

 gonal faces (fjg. 14). 



This variety has also for its nucleus a cube, the position 

 of which with regard to the dodecahedron is sensible by 

 the bare inspection of fig. 15. We there see that the por- 

 tions superadded to the nucleus, instead of being pyramids, 

 as in the preceding case, are species of wedges which have 

 tor their external faces two trapeziuins, suchasOIp^, 

 AE/J g, and two isoscele triangles l^p o, A q I. 



Let us conceive that the decrements are here made bv two 

 ranses in breadth, between the edges O I and AE, I I' and 

 00', EO and E'O', and in a similar manner and at the same 

 time on the opposite squares they are made by two ranges 

 in height between the edges EOandAI, O I and O' T, 

 O O' and E E', by which we see that these decrements take 

 place on the different faces of the cube, according to three 

 directions which cross each other at right angles. Then 

 the decrement bv two ranks in breadth, tending to produce 

 ■ a more inclined i'nce than that which results from the de- 

 crement by two ranks in height, each pile of decreasing 

 ]amina> will no longer end in a polni, but in a cuneiform 

 solid (fig. 16) ; i. e. it will be terminated by an edgep^ or 

 t n ; and if vve compare the directions of these two edges 

 with that of the edge r s (figs. 14 and 15) which terminates 

 the pile raised on the face E O O' E' of the nucleus, it will 

 be easy to see that th.ese three edges are perpendicular to 

 each other in consequence of the traverse directions which 

 the decrements take. 



Besides, each trapezium, such as Op ^ I (figs. 15 and 

 16) bcintj; on the same plane with the triangle OH which 

 belongA to the adjacent pile, the union of these two figures 

 will form a pentagon p O t I q; whence it follows that the 

 solid will be terminated by twelve equal and similar penta-- 

 gonal faces, on account of the regular form of the nucleus 

 and the symmetry of the dtfcicmenls. ^ 



Here 



