3S6 Theory of Cryjlallifalhil. 



1. Trapezoidal Garnet ( Fig. 70.). 



Gtenat "h 24 faces. Daubenton Tab. Miner, edit. 1792", 

 p. 5. Grenat a 24 facettes trapszoidales. De l'lile Cryf- 

 tallograpbie, torn. ii. p. 327- 



Geomeit ebara&i Kefpeetive inclination of the trape- 

 zoids united three and three around the fame folid angle 

 D, C, G, &c. 146 26' 33"; of the trapezoids united four 

 and four around the fame folid angle u, x, r, &c. 13 1° 48' 36". 

 Angles of any oneof the trapezoids- m D u L, L = 78° 27' 46"; 

 D =5 117 2' 8"; m or u = 82" 15' 3". The value of the 

 angle L is the fame as that of the acute angle of the nucleus 

 of calcareous fpar. 



This variety refults from a feries of laminas decreafing at 

 the four edges, on all the faces of the primitive dodecaedron. 

 For the more fimplicity, let us firft confider the effect of this 

 decrement in regard to the rhombus CLGH (Jig. 68.). 

 We have juft feen that this rhombus was fuppofed to belong 

 in common to two rhomboids, which mould have for fum- 

 mitgj one, the point C, and the other, the point G. Let us 

 fuppofe that the laminae applied on this rhombus decrcafe 

 towards their four edges by fubtra&ions of a finglc range of 

 (mall rhomboids, in fuch a manner that, in regard to the. 

 two edges C L, C If, circumftances are the fame as if the 

 rhombus belonged to the rhomboid which has its fummit in 

 C; and that, .in regard to the other two edges GL, GIT, 

 the effect is the fame as if the rhombus belonged to the 

 rhomboid having its fummit in G. This difpofition is ad- 

 miffible here,' in confequenee of the particular ltrudture or 

 the dodecaedron, which permits us to obtain fmall rhom- 

 boids, fome of which have their faces parallel to the faces of 

 that with its fummit in C, and the reff to that having its 

 fummit in G*. ^n, 



* Theory h;.s concki&ed me to arrother refult, which is, that the fum 

 'of the nucleus and laminae of luperpofition, taken together in proportion 



