Theory of CrjJlallifaUon. $3t 



tine, the cafe in which the two tetraedra repofe on the faces 

 dbe, fgp, of the oetaedron; the other, that iri which 

 they would refl on the faces bfg, dep. It is thence feen, 

 that whatever may be the two folid angles of the cube af- 

 fumed for the points of departure, we {hall always have the 

 fame oclaedron, with two tetraedra contiguous by their fum- 

 mits to the two folid angles in queftion ; and as there are 

 eight of thefe folid angles, the central oclaedron will be cir- 

 cumfcribed by eight tetraedra, which will reft on its faces. 

 The fame effect will take place if we continue the divifion 

 always parallel to the flrft fections. Each face of the oc- 

 taedron, then, however fmall we may fuppofe that oclaedron 

 to be, adheres to a face of the tetraedron, and reciprocally. 

 Each tetraedron then is enveloped bv four oetaedra. 



The ftructure I have here explained is that of fparry fiuor. 

 By dividing a cube of this fubftance we may, atpleafure, ex- 

 tract rhomboids, having the angles formed by their planes 

 equal to 120' or regular oetaedra, or tetraedra, equally re- 

 gular. There are a fmall number of other fubftances, fuch 

 as rock cryftal*, carbonate of lead (fparry lead), £ce. which 

 being mechanically • .vend the term at which we 



ihould have a f\ pipedoii, give alfo parts 



of various different forms afforted together in a manner even 

 more complex than in fparry fluor. Thefe mixt ftru&ures 

 neceffarily occafion unce ng the real figure of 



the integral moleculae which belong to the fubftances in quef- 

 tion. I .have, however, obferved that the tetraedron is al- 

 ways one of thofe folids which concur to the formation of 

 fmall rhomboids or parallelopipedons that would be drawn 

 from the cryftal by a firft divifion. On the other hand, there 

 are fubftances, which, being divided in all poffible directions, 

 refolve themfelves only into tetraedra. Of this number are 

 garnet, blend, and tourmaline. I ftiall foon give examples 

 of this refult of the mechanical divifion. 



*' M.mui es de l'Acad. des Sci nces, An 1786, p. 78. 



In 



