1862.] 193 



The following are the symbols of these groups : 

 hhk, khh, hkh 

 hhk, Jc~hh, li~kh 



hhl, khh, hkh 

 Tihk, kill, ~hkh 



kkh, Jikk, kJik 

 'k'kh, hlkk, Ihk. 



The last group is restricted to those forms of k k h whose poles lie 

 between those of 1 1 1 and 112, &c. 



The direct rhomboids are all derived from the form h k k, and 

 consist of two groups, 



hkk, khk, kkh 

 lick, khk, kkh t 

 and 



hUl, khk, kkh 

 hkk, khk, kkh. 



The form h k I furnishes four groups of hexagonal scalenohedrons. 

 1st. hkl, hlk, klh, Ikh, Ihk, khl 

 ~h~k\ ~hlk t ~klh t I kit, Ihk, khl. 



2nd. hkl, hlk, klh, Ikh, !hk, khl 

 hkl, hlk, klh t Ikh, lhk t khl. 



3rd. hl~k y hkl, Ikh, klh, 'khl, Ihk 

 lilk, hkl, Ikh, klh, khl, Ihk. 



4th. h~lk, hkl, Ikh, klh, khl, Ihk 

 ~hlk, Jikl, lk~h, klh, khl, Ihk. 



The forms of the prismatic system are then shown to be formed 

 by an analogous development of faces about the rhombic axes ; 

 making two of the faces of the rhombic dodecahedron the basal 

 pinacoids. 



In examining the Tables accompanying the paper, in which all the 

 known faces of crystals are expressed in the notation of the cubical 

 system, it will be seen that the indices are necessarily somewhat large. 



