, OnO-yslallography. 295 



nuniUer of cases, produce forms equally simple with those 

 whK-h originate from the ordinary laws, and that tUeir the- 

 ory even leads to results v/hich would deserve to be foUov^'cd 

 and developed as a simple object of curiositv. 



Secondary COMPOUND Forms. — We call simple secon- 

 dary forms, those which proceed from a single law of de- 

 creiDent, the effect of which masks the nucleus, which 

 touches their surface only on rertain points or certain 

 ridges; and compoiind secovdary forms, those whicli proceed 

 from several simultaneous laws of decrement, or from a 

 single law which ha-s not attained its limit; so that there 

 r^eniain faces, parallel to those of the nucleus, and which 

 concur with the faces produced by the decrement in modi- 

 fying the fonn of the secondary crystal. 



Let us s4ippose, for example, that the law which gives 

 the octahedron originating from the ctibe (fig. !20, PI. HI), 

 is combined with that from v.liich results the dodecahedron 

 with pentagonal faces (fig. 15, Pl. II). The first vvill give 

 rise to eight faces, which will have as centres the solid angles 

 of the nucleus ; and it is easy to see that each of these 

 faces, for instance that wh..«e centre coincides with the 

 solid angle O (figs. 14 and 1 5), will he parallel to the equi- 

 lateral triangle whose sides would pass by the points p, s, t. 

 In the same way the face wh():e centre will be confounded 

 w ith the angle O' will be paralie! to the equilaternl triangle, 

 whose sides would pass by the points *■, n, p' ; but the se- 

 cond law produces faces situated like pentagons cut by the 

 aides of the triangles p s t, sn p' . Now the sections of 

 these triangles on the pcntacon tOsO'n reduce the latter 

 iflto an isoscele triangle, which has for its ba.-e the line t ?!, 

 and whose two olher sides pass, ihc onc^ by the poinrs t. s, 

 the olher by the points 7i, s. Jt is the same with thr oih'jr 

 pentagons; whence it follows that the secondary solid uiU 

 be an icosahedron terminated by eight equilateral triangles 

 and twelve iboscele triangles. 



Fig 38, PI. V, represents this icosahedron marked by 

 W'tteis whose correspondence with those of fiiis. 14 and 15 

 renders perceptible to the eye the relation between the two 

 solids; but tliis icosahedron has much greater dimensions 

 than those of the icosahedron which we obtain arlificially 

 by making sections on the eiiiht solid anycles ot the dode- 

 cahedron of fig. 14, which are confounded with those of 

 the nucleus. This increase of dimensions was ncf essary 

 for preserving to the nucleus a constant volume. We shall 

 rllu'trate this bv a more ample development. 



If we wished to obtain the nucleus of the icosahedron 

 T 4 of 



