514 On Crystallography, 



of this nucleus (fig. 7) ; whence it follows, that these same 

 borders or edges are parting lines of the decrements, w hich 

 in this case take place onlv with respect to them, without 

 any relation to ihe upper ei'ges. 



Now it is eaj>y to conceive, that the edges of the lamina 

 of superposition form ahogether a^* manv triangles, EsO, 

 I/O, bli'O. Jicc, resting on those pariing lines; and as 

 these lines are >ix in niimhf r, there will be twelve triangles, 

 six in the upper part and as many in the lower; and all 

 these triangles will be scalene, on account of the ohlujuily 

 of the parting lines. 



Witli respect to the upper cdces of the laminae of super- 

 position, they not only unilergo no decrernent, hut it is 

 even necessary that they should he prolonged, remaining 

 always contiguous to the axis of the crystal, in order ihat 

 the nucleus may contiinie to be enveloped towards its two 

 suuimits, as in a state in which il might increase without 

 changing its lorm. 



It IS also to calculation combiiu'd with observation that 

 it belongs lo determine the law of decrement on which the 

 dodecahedron (lepe^d^. Now if we suppose that this law 

 acts by one range, v\e prove that in this case the two faces 

 produced on both sides of tlie same edge would he on the 

 same plane, and, besides, that they would he parallel to the 

 axis; which could not agree with the present case. There- 

 fore the simplest hypothesis u Inch occurs is thatofadcTr 

 crenient by two courses in hreailth. Now in this case cal- 

 culation demonstratt:-, that the dodecahedron ar.smg from 

 this law ought to have two remarkable properties; the one 

 is, that the obtuse angle SEO of any one of its faces has 

 precisely the same measure wiih the obtuse angle of the 

 nucleus, ?'. e. it is 101*' 32' 13" ; the other consists in the 

 respective inclinations of the faces of the dodecahedron at 

 the meeting of the most salient cdues; for instance, the in- 

 clination of 5 I O on ?! K is equaTto thai of two adjacent 

 faces towards the same summit of the nucleus, i, e, it is 

 104° 98' 'lO". Now (he mechanical measurement of the 

 angles equally leads to the same degrees, and shows that 

 the suppo,ed law is in truth the law of naturp. It is this 

 kind ot translation or metastasis of the angles of the primi- 

 tive form on the secondary crystal, which has suggested the 

 name oi melastalic given to ihe variety in question. 



Fig. 17 (PI. HI) will fully illustVafe the explanation 

 which we have just given. It represents only the kind of 

 "upper pyramid added to the nucleus, whieh being thus 

 partly uncovered, enables us to comprehend more easily thp' 



progress 



