On Crystallog raphy. S 1 5 



progress and effects of decrement by two courses. Each 

 edge of this nucleus has been divided into ten ; \vhenc?e it 

 follows that every face is an assemblage of a hundred aniall 

 rhombs, which are the external facets of as many molecules. 

 This construction requires but eight laminse of superposi- 

 tion for each of the same faces ; and these laminse being 

 united together three and three in the places which corre- 

 spond to the upper edges of the nucleus, form kinds of de- 

 creasing envelopes which are successively generated, and the 

 last of which is composed of eight small rhonil)()ids. If we 

 consider the position of the line Ks whicHi represents one 

 of the terminating edges, composed of all the solid angles 

 which -are contiguous to it, we shall remark that the geo- 

 metrical summit s of the dodecahedron is situated a little 

 above the physical summit s'^ : but this difference is con- 

 sidered as nothing, on account of its extreme minuteness. 



What we have said as to increments assumed by the laminse 

 "of superposition towards their upper edges, in continuing to 

 envelop the crystal on this same side, is a consequence of 

 this general principle, namely, that the portions of laniinjse, 

 situated out of the reach of the decrements, extend, by mu- 

 tually retrieving themselves, in such a manner as to avoid the 

 re-entering angles which seem excluded by the crystalliza- 

 tion, at least in solitary crystals *. But we may abstract 

 these simply auxiliary variations, as the effect of decre- 

 ments only determines the form of the secondary crystal. 

 It is even sufficient to take the decrements at their oritjin, 

 in order to have as many planes; and these again being 

 afterwards extended in idea until they meet, lead to the 

 complete form of the polyhedron which they tend to pro- 

 duce. Hence it is thus that we confine ourselves to the 

 consideration of the initial effect of decrements, in calcula- 

 tion of which the progress is always much more simple and 

 expeditious than that of reasoning. 



It is useful, however, to be also able to give a distinct 

 account of all the details relative to the structure of a cry- 

 stal, so that, if we have at our disposal a certain number of 

 small solids similar to molecules, we may arrange them 

 around a given nucleus, and thus produce an artificial imi- 

 tation of crystallization. I shall therclore, in a final ex- 

 ample taken from t^/zir/r/s-carbonattd lime, follow lamina 

 by lamina the progressive route of the decrements, and in 

 >iome measure give the svnthegis of the structure. 



• Rt entfiing; angles, when thoy exist in crysiaU, arc ;iccid<nts occasioiiMl 

 \>y \>L^^■uiiiu■ circuiiUiCanccit, ui' which we shall hereafter xiitfak. 



O 4 The 



