Theory of CrjjlalVfiat'iort . 383 



parallelopipedons ; and theory has the advantage of being able 

 togeneralife its object, by connecting with one facl: that mul- 

 titude of facts which by their diverfity ieem to be little fuf- 

 ceptible of concurring in a common point. 



What has been here faid will be better illuftrated by a 

 few examples of the manner in which we may reduce to the 

 theory of the parallelopipedon that of the forms different 

 from thatfolid. 



Cryjlals, the molecule of which are tetraedra with ifofceles 

 triangular faces. 



Garnet. 



I. Primitive garnet (fig. 68.) Grenata douze faces. Dau- 



benton Tab. Mine r. edit. 1792^.5. Grenat dodeca s :Jre a plans 

 rhombes. De 1'Ifle Cryjlallographie, torn. ii. p. 322. var. 1. 



Geomet. characl. Refpeclive inclination of any two of the 

 faces of the dodecaedron 120°. Angles of the rhombus 

 CLGH, C or G = 109° 28' 16"; L or II --= 78° 31' 44". 



Though garnets of the primitive form be in general vi- 

 treous on the fradturcs, there are perceived on them, how- 

 ever, lamina? fituated parallel to the rhombufes which com- 

 pote their furface. Let us fuppofe the dodecaedron divided 

 in the direction of its laminae, and, for the greater fimplicity, 

 let us make the fe&ions pafs through the centre. One of 

 thefe fecYions, viz. that which will be parallel to the two 

 rhombufes DLFN, B HO R, will concur with a hexagon 

 which would pafs through the points E, C, G, P, T, A, by 

 making the tour of the cryftal. A feeond fe&ion parallel to 

 the two rhombufes GLFP, BEAR, will coincide with 

 another hexagon fhewn by the points D, C, H, O, I, N. If 

 the divifion be continued parallel to the other eight rhom- 

 bufes, taken two and two, we fhall find that the planes of 

 the fecYions will be confounded with four new hexagons ana- 

 logous to the preceding. But by renaming all thefe hexa- 

 gons it is feen that their fides correfpond, fome of them with 



the 



