240 Proceedings of the Royal Society 
only tetartohedral forms are TrirTihl and K7rhM, — i.e., they are all de- 
rived from the hemihedral forms with parallel faces. 
Also Trirlikl can only exist when all the indices li^ h, I are finite, and 
Kirhhl can only exist when all the indices are finite or one zero. 
When hhl are all finite, TnrTikl consists of any pair of parallel 
faces of the form likl and Kirlikl of any pair of inclined faces of the 
form hhl. When one of the indices is zero, Kirhld consists of any 
single face of the form hhl. 
13. Hemihedral forms with inclined faces, derived from the 
rhombohedron or scalenohedron, have only been observed in the 
following minerals, — 
Cronstedtite. 
Phenakite. 
Pyrargyrite. 
Quartz. 
Tourmaline. 
In these minerals alone, therefore, do the tetartohedral forms 
KTrhhl occur. 
Hemihedral forms with parallel faces, derived from the scaleno- 
hedron, have only been observed in the following minerals, — 
Dolomite. 
Dioptase. 
Phenakite. 
The tetartohedral forms kirhhl occur, therefore, only in these 
minerals. 
Hemihedral forms with parallel faces, derived from scalene- 
hedra, occur also in apatite. But in this mineral, two scalenohedra, 
inverse with respect to each other, always occur together on the 
same specimen, and when one scalenohedron is hemihedral the 
other is so also. Hence the hemihedral forms in this mineral cor- 
respond to hemihedral and not to tetartohedral forms in the pris- 
matic system. 
14. Let a^, a^, be the new angular elements of crystals of the 
rhombohedral system when transferred to the prismatic system. 
Let = 100, 110 ; = 010, 011 ; a, = 001, 101. 
Then tan a, = % tan a,, = tan a. = % : 
h ^ c " a ’ 
