Theory of Cryjlullijjf'nn. 135 



For the fame reafon the triangle D P C {jig* 16") will be oa 



a level with tlie trapezium D JNI N C {Jig- 15) ; and by rca- 

 foninp; in the like manner in regard to the other pyramids, 

 j; will be conceived, thai as the Gx pyramids have for their 

 whole faces twelve trapeziums and twelve triangles, the i'ur- 

 f the fecondary folid will he compofed of twelve penta- 

 gons, which will corrcipond with the twelve rhombufes of 

 fig. -. : hut with this difference, that they will have other 

 inclinations. This iolid is represented alone fig. 19, and 

 with its cubic nucleusy?j\ 20, where it may be feen in what 

 manner it would be necefiary to proceed in order to extracl. 

 this nucleus. For example, if a lection be made pafling 

 through the points D, C, G, F, you will detach the pyramid 

 reding on the face D C G F of the nucleus, which will by 

 this faction be uncovered. » 



Among the cryftals belonging either to the fulphurc of iron 

 (martial pyrites), or the arfeniate of cobalt (the arfenical co- 

 balt ore of Tunaberg), there is found a dodeeaedron, the 

 faces of which are equal and fimilar pentagons, and its nu- 

 cleus is a cube fituated as above defcribed. But there are 

 an infinite number of poffible dodeeaeclra, which may 

 have, for faces, equal and fimilar pentagons, and will differ 

 from each other by the refpeetive inclinations of their faces. 

 Of all thefe dodecaedra, the one, the Itructure of which would 

 be fnbjected to the before-mentioned laws, gives 126° 56 1 8 ' 

 a • the angle made by the inclination of any two of its faces 

 D P R V S, C P K G L {jig. 19), at the edge of junction 

 P R, as may be eafily demonftrated by calculation*. But 

 though we cannot flatter ourfelves with the hope of attaining 

 to the pn ■ ifion of feconds, nor even to that of minutes, in 

 fame angle in dodecaedral pyrites, that mca- 

 furement taken with every poffible attention evidently ap- 

 : near totherefult given by calculation, that we 

 piaj confider that refult as the real boundary of approxima- 

 1 I by help of the inltrument, and conclude that 



Sec Lis Memoires de I' Academic d's Sciences, an nee i-te. 



theo 



