On Crystallography. 923 



perposition*, the decr(a>ing edge of this Jamina will coin- 

 cide wiih the sniall eu^c e ??, since g n is the same diagonal 

 as fig. 31 , Thus it we draw the straiijht line g" e h, it will 

 be found to rest oa tl)e face produced by the decrenvent. 

 Now in this case g h is parallel to the axis S s, as deiiioir- 

 strated by tlie help of gcometrv ; whence it follows, that 

 the secondary faces are arrans^ed like the panes of a prism. 



If the decrement followed a more rapid pnigres*, as if it 

 took place by four courses, m which case the edge of the 

 first lamina of superposition woidd coincide with the line 

 y q, then the line g' (J ^' would indicate vhe position of 

 the faces producefl uv the decrement ; whence we see that 

 thev would rise above those of the nucleus, and would 

 conjpose the surface of a rhomboid more acute than this 

 nucleus. 



Ifj on the contrary, the decrement look place in height, 

 then the line ug" k', which we suppose to indicate the po- 

 sition of the faces produced, would be thrown towards the 

 inferior part of the axis : hence we conclude, that in this 

 case the faces of the secondary crystal, which would always 

 be a rhomboid, would be found situated in a direction con- 

 trary to those of the nucleus, i, e. they would be turned 

 towards the edges of the latter. 



The hypothesis of a decrement by two'deurses in height 

 here gives us a remarkable result, which consists in the 

 secondary rhomboid being absoluiely similar to the nucleus. 

 We shall see, when speaking of certain varieties of quartz 

 and of tournvaline, thai by confining ourselves to the con- 

 sideration of certain facets taken among those which limit 

 them, and by supposing these facets prolonged until they 

 intersect each other, we should have one of those imita- 

 tions of the primitive form given by a law of decrement. 



Let us pass to the superior angle S, and suppose at first 

 a sin/^le course Piibtracted. If, from the middle t of the 

 oblique diagonal Sp we raise t x parallel and equal to p a. 

 Ibis line will be laid on the edge of the first laniina of su- 

 perposition, since the distance between the angle S and 

 this edge is equal to an obliqe semi-diagonal of the mole- 

 cule. . The line S x h will therefore be confounded with the 

 face produced, wbicli will be perpendicular to the axis. 



A decrement more rapid, such as that which takes place 

 by two courses in breadth, would give taces inclined like 



♦ We take no notice here of the manner in which this segment is termi- 

 ■aated in its superior part up, and only couiiidcr the part situated tuward* 

 tlte angle n". 



Vol.34. No. 137. Sept. 1609. P the 



