294 On Cryst.'tliographij. 



tion preserve the same distances between them ns on fia;. 3 1 . 

 This solid IS circumscribed Jo its nuclcusj which is that oF 

 carbonated lime ; a /; o' (fii;". 37) indicates the direction ot" 

 a section which would be parallel to the face S Gg" G', 

 and which is indicated by the same letters (fig. 31), and we 

 easily conceive that the edges of this section should be 

 lineally disposed like those of the same lamina of superpo- 

 sition. The paradoxical carbonated lime discovered by M. 

 Tonnellier is similar to this dodecahedron, abstraction 

 being made of some additional iacets. 



We find here that the nucleus touches the secondary 

 crystal by its lateral angles only, winch are situated in the 

 ridges B S', D.s', C/, &c., whereas in metastatic carbon^ 

 ateu hnie, which is a dodecahedron of the same kind, i. e, 

 with scalene triangular faces, the lateral ridges ot the nu-- 

 cleus are confounded with those which correspond with 

 BC, CD, DF, &c. 



This leads us to an hypothesis which will prove a remark-^ 

 able properly in the paradoxical dodecahedron. If we ima- 

 gine six trenchant planes, one of which passes by the points 

 C, D, F; a second by the points B, C, D ; a third by the 

 points G, B, //, &c., which is a way of dividing the crystal 

 analogous to that employed to extract the nucleus from the 

 metastatic, we shall also obtain a rhomboid, but which will 

 exist in imagination only, since the crystal does not sub- 

 rnit to this kind of division. Now it is demonstrated by 

 calculation that this rhomboid is similar to that of inverse 

 carbonated lime, tlie aut^^Ie of which at the summit is 

 73° 31' 20'. - 



Besides, if we consider this rhomboid as a ficlitious nu- 

 cleus, we find that the dodecahedron might be, so far as it 

 is concerned, a secondary form, which would result from 

 a. decrement by three ranges on the inferior edges. 



Let us'resmne the true nucleus, and conceive that the 

 intermediate decrement, instead of being produced by one 

 range of double molecuks, as in the paradoxical solid, takes 

 place by five ranges in breadth and four in height. Then 

 the secondary crystal becomes similar to the metastatic 

 itself; and if this result is never to be met with in nature, 

 the eye would be the more easily deceived by it, as the 

 hypothetical nucleus would be presented under the ap- 

 pearance of a real nucleus. 



We see by these details, to which I could give a much 

 greater latitude, that the intermediate laws, the existence 

 of which is in other respects hitherto confined to a trifling 



number 



