Nltn TAEIETIES OF CARBONATE OF LIME. I9I 



On the other hand, the common inverse rhomboid has its Conamonin* 

 faces turned toward the superior edges of the nucleus: and, '«f»e«l»o™- 

 having also examined what law would give the same rhom* 

 boid, with its faces answering to those of the nucleus, I was 



led by calculation to the result expressed by e. 



Let us suppose, that the common inverse rhomboid is Combinatum 

 combined in one figure with the common metastatic dode- ** 



caedron; it is evident, that its faces would answer to the 

 mast saliant edges of this dodecaedron: but in the variety Structure of 

 before us, on the contrary, they answer to the least saliant *^® pre^^** ™- 

 e;dges. Now there are two different cases, in which this may 

 take place: one is that in which the metastatic would result 



from the law D, and the inverse rhomboid from the law «; 

 the other, that in which the metastatic would be produced 

 by the intermediate decrement, and the rhomboid by the 

 decrement E* E*. Mechanical division removes all ambt*^ 

 guity by proving, that the second is the case. The faces of 

 the two solids combine, as 1 have said, with the sides of the 

 hexaedral prism, from which we can derive no indication in 

 favour of one structure, or of the oth«r. 



The stenohome carbonated lime, fig. 9, diifers from that Stenonome 

 which I have described in my treatise under the name of |^."^"*'* 

 subtractive by the addition of the facets t and it. The for- 

 mer afford a fresh example of the law of decrement, which 

 tends to produce a rhomboid similar to the nucleus. The 

 faces It It exhibit a particular case, the possibility of which i 

 had proved ; namely that in which the decrement on B, fig. 

 8, taking place by two rows, would produce a dodecaedron, 

 all the triangles of which, instead of being scalene as in the 

 other cases, would become isosceles; that is to say, the do- 

 decaedron would be composed of two right pyramids united 

 base to base. In fact we should have a dodecaedron of this 

 kind by prolonging the faces in question till all the other* 

 had disappeared. 



The angle of 151° S' 42", which measures the respective proportion* 

 incidences of the faces of this dodecaedron, is exactly dou- between the 

 ble the angle of smallest incidence of the faces of the nu- 

 cleus, 75* 31' 21". These proportions between the angles 



of 



