of Mineral Species of the Trimetric System. AY 
solids of the trimetric system. And when the cleavage prism is 
rhombic, there is better reason for regarding the lateral axes as 
oblique in their intersections, than rectangular. The subject of 
twin crystals affords evidence that this is not mere hypothesis ;* 
and additional proof is shown beyond in the relations of the 
domes to the angles of the regular octahedron. And still another 
argument may be derived from the relations of the domes in an- 
le to the vertical prism. If such views may be adopted, it must 
obviously be essential to correct comparisons of form between 
species, that the vertical axis should be determined on the best 
possible data. 
The preceding remarks are offered as introductory to the fol- 
lowing tables of the values of the axes and principal prisms in 
trimetric mineral species. I have endeavored to apply with fidel- 
ity the principles that have been briefly reviewed. The unit 
prisms, as has been stated, are not in all instances those assumed 
as such by other authors; but although they are in general well 
entitled to be so regarded, they are not all supposed to be the 
unit prisms, as has been explained by referring to Hornblende 
and Augite as examples. An exhibition of the mathematical re- 
lations of the forms is the main point in view. ehever we 
have placed in the columns of unit prisms, angles usually re- 
garded as those of other prisms, it is stated by a mention of the 
form to which they have been commonly referred. Thus, under 
Chrysolite, the prism taken as 17 is $7 of most writers, as men- 
tioned. ‘These forms, as observed, differ from the unit prisms, 
either by the ratio 1 : 2 or 2: 3, ratios of the simplest kind. 
he trimetric species are naturally divided into four grand 
groups, differing in the angle of the fundamental or unit vertical 
pews (angle J: I of the tables, o P : » P of Naumann), as fol- 
0) 
1. Angle I: I from 904° to 95°. 
2. Angle I: I near 102°, or from 98° to 105°. 
3. Angle I: J near 110°. 
A. Angle I; I near 120°. 
It will be shown that these specific values of the angle J: i 
are dependent on a principle of the most fundamental character. 
The third Group may however belong with the d as re- 
marked upon beyond. ; 
The angles mentioned in the table are the obtuse angle of the 
Prism J: J (column 1), and the summit angle of the unit macro- 
dome and brachydome (1i and 12 or P@ and P  ).f 
* See : ; ; 
t To fet cpt tereey Miner@lee referred to in the following pages, and 
render the subject intelligible to those who may tot be familiar with crystallo- 
Sraphic language, a few explanations are here given. The annexed figure represents 
Szconp Senms, Vol, XVIII, No. 52.—July, 1854. 6 
