On Crystallography, 213 



Here an important consideration for the verification of 

 the theory presents itself. If we suppose that the difflTent 

 pentagons which compose the surface of the dodecahedron 

 all uniformly depend on the different edges of the cube as 

 on so manv hinocs, so that, fur example, the two pentagons 

 ntls'V, ntOsO', are raised or lowered by the trape- 

 ziums 1 t nV , O i n 0', while they will be raised or lowered 

 in a contrary direction by the triangles I / I', OsCY, we 

 shall have an infinity of different dodecahedrons, the faces 

 of which will be so many equal and similar pentagons. 

 Among these dodecahedrons, a part of them will he possi- 

 ble in virtue of some law of decrement, and others cannot 

 be produced by any law, and will be purely geometrical 

 solids. In each dodecahedron, the incidence of the pen- 

 tagon 71 f ] s' V on the pentagon n t O sO', at the place of 

 the edge nt, which determines of itself all the other angles, 

 will have a particular measure ; and calculation proves that, 

 in the case of decrement now mentioned, this incidence 

 ought to be 126^ 52' 8". Now by measuring that which 

 corresponds with it on the dodecahedron of sulphuretted 

 iron, we find it nearly 127°: thus tlie existence of the law 

 of decrement is confirmed by the agreement of calculatioii 

 with observation. 



Wh.it we have now described also takes place with respect 

 to all the other results of the theory compared with those 

 of observation ; whence we ought to conclude, that the 

 measurement given by calculation is the true limits of the 

 approximation found by means of the goniometer; so that 

 the more carefully this instrument is constructed, the nmre 

 distinctly is the crystal defined, the observer becomes more 

 expert, and the nearer also do the results on both hands 

 aj)proach to perfect coincidence. 



The observation already made with respect to the dode- 

 cahedron with rhombic planes applies as of itself to the 

 present ca«c ; that is to say, instead of 24 decrements, viz. 

 •twelve of two courses in breadth, and the twelve others of 

 two courses in height, we can confine ourselves to the consi- 

 deration of the former twelve, only supposing their effects 

 to extend froiTi the edges of the other side, which serves 

 •them for parting lines. 



We shall give a new example borrowed from metastatic 

 carbonated lime (fisr. 6, PI. I). We have seen, when ex- 

 amining the position of the nucleus, that the edges F20, 

 O I, I K, &c., were confounded with the lower borders* 



* I c;ill iijiper rd^es, or l)()iiler, those wliicli are coilti^nions to -eacli •ium- 

 it ; and injtrinr cit/rrs, those which are opposite to the fanner, whatever 

 •■' -<)• be llic relative potitiuii of llic rlioniboid. 



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