Theory of Cryjlallifation. 29? 



The firft decrement is the fame as that which produces the 

 rhomboidal iron ore already mentioned. The fecond has 

 this property, that, if its efTed were complete, it would give 

 a dodecaedron of ifofceles triangles, or compofed of two 

 right pyramids united at their bafes. In the cafe of any 

 other decrement by two, four or more ranges, the faces of 

 the dodecaedron would be fcalene triangles. 



The triangles of the fummits are frequently furrowed by 

 ftriae, parallel to the bafes g «, dn, g d, of the fe triangles, 

 and which point out the direction of the decrement. 



Analogical Calcareous Spar (Fig. 53 ). 

 De l'lfle Cryjlal.'ographie, torn. i. p. 543, pi. 4, fig. 36. 

 Gecmei- cha'acl. Inclination of any one, i me h> of the tra- 

 pezoids of the fummits to the corre '"ponding vertical trape- 

 zoid ecpg 1 6° 33' 54"; angles of the fame trapezoid, 

 i= ir 4 ° 18' 56'; e= 75 31' 20"; m or h = 85 4' 52". 

 Angles of the trapezoid e hog, e = 9c ; — 1 27 25' 5 3" ; 

 g ss 67 47 r 44" ; h = 74 46' 23" ; of the trapezoid cegp t 

 t = bo°;p = 9 8 3 12' 46" i c or g = !oo° 53' 37". 



Geomet. propert. 1. In each vertical trapezoid the triangle 

 ceg is equilateral. 2. The height ex of this triangle is 

 double the height p x of the oppofite triangle cpg. 3. In 

 the trapezoid ehog and the others fimilarly fituated the 

 angle h e g is a right angle. 4. If the diagonal g h be drawn, 

 the triangle h eg will be fimilar to any one a of (fig. 4.") of 

 thofe which would be produced by drawing, in the primitive 

 Thombus, the two diagonals bf y ad. 5 If in the trapezoid 

 /mi h, or any other fituated at the fummits, the diagonals ei t 

 mh t be drawn, the height el of the inferior triangle m e h 

 will be double the height il of the fuperior triangle mib, 

 6. The triangle m ih is fimilar to a half of the rhombus of 

 very obtufe fpar, divided b/ the horizontal diagonal; and 

 the triangle me h is fimilar to a half of the rhombus of the 



acute fpar, divided in the fame manner* 



The. 



