216 On Crystallography. 



The. variety in question is a rhomboid much more obtuse 

 than the niicieus, and the jiicit antiie of which is 1 1-1 18' 

 56 . Fit;;. 18 rtpiescnt? it contintd to its nucleus. In order 

 to-eviract the ialtcr at once, it is nectssary to have planes 

 trajeciinir bv the obhque diaoonals of the diflenni fa^ es of 

 the secondary rhomboid. One ol ihese sections, for in- 

 stance, thai which passes bv the diagonals drawn from a to 

 t, and from a lo u, and which nnercepts the solid angle z, 

 coincides with ihe idpe. a b dj" ot ihe nucleus. Now there 

 are six solid angles situated lateiaiiy, viz. z, c, y, on one 

 hand, and /, ??/., u, on the other. VVc shall therefore have 

 six sections arranged three and three towards each summit; 

 and as the upper solid angles alternate with the lower, the 

 sections which iniercepf. iheni preserving between them- 

 selves the same alternative, will cross so as to form six 

 rhombs, which will give the surlace of the nucleus. 



In order to conceive the structure of the secondary rhrmr 

 boid, Jet us resume the dodecahedron with rhombic planes, 

 which, as we have seen, is produced bv virtue of a decre- 

 rnent of one range of small cubes on the twelve edges of a 

 pubical nucleus. The etfect of this decrement in general is 

 to produce on both sides of every edge, likeOO', (fig. 12) 

 two triangular faces r 0', O t O', which being on a level 

 form a rhomb OrO't, the small diagonal of which is the 

 edge O O', which has served for the jiarling line. 



Let us now imagine that the nucleus is the primitive 

 rhomboid a h a J {^g. 18) of carbonated lime. Let us con- 

 ceive besides th^t the laminae of superposition decrease by 

 one range of small rhomboids similar to this nucleus, 

 but solely on the three edoes, ab, aj\ a7i, whicli join 

 around the summit a, and on those which correspond with 

 iheni in the lower part. Then, instead of twelve rhombs, 

 no more than six will be formed, the small diagonals of 

 which will be confounded, as in the other case, with the 

 edgesa/', af, an, &c. 



The other parts of the laminae of superposition, i. e. those 

 vhich are situated towards the lower edires /' (/, dJ\J.v, 

 &c., as they do not participate in the decrements, will also 

 undergo sf)n(e variations, but which will tend merely t& 

 prolong the faces produced by these decrements, so as to 

 make them imersect each other. Hence it follows, that 

 the laminae, instead of preservinsr the fiiiure of the rhomb, 

 a"? would happen if the decrement took place at once on all 

 the edg-'S, will pass successively in proportion as thev shall 

 become more renvite irom the nucleus, through the ligure 

 pf the pentagon^ and thai of the triangle. The develop- 



