of the different Systems of Crystallisation. 100 
oretical names, systemata singulaxia homoedrica , and singulaxia 
hemiedrica , the two first subdivisions of the general case, which 
comprehend the systemata singulaxia. 
You are aware that we do not yet know by observation, the 
tetartoedral system as a subdivision of the spheroedral one, and 
that it is only by abstraction that M. Mohs and I have ^treated 
of the solid tetarto-edre spheroidal , or solidum-tetarto-spheroe - 
dricum. I have done this in my Memoir of 1815, in relation 
to a third case of the hemispheroedral system, which is possible, 
also, or geometrically admissible, and of which I have described 
the general form, under the name of Leucitoides tournees 
(gedrehte Leucitoide,) or solidum Leucitoides detortum. I have 
since found for them a still more expressive name, viz. grenat- 
dysedre , since we may consider them as Rhomboidal or Grenatoe- 
dral Dodecaedrons , having a bevel on each face. I have pointed 
out in my memoir of 1815, the interesting difference of these 
solids, to be turned to the right or to the left, which gives always 
solids opposite or different, and similar to one another in oppo- 
site directions* I have likewise pointed out the reality of these 
opposite solids among crystals, and their frequent occurrence 
even, in a Memoir on the most ordinary double crystals of Fel- 
spar, viz. those of Carlsbad, inserted in the Neues Journal der 
Chimie und Physik de M. Schweigger, tom. xi. 
There now remain only those systems which are not founded 
on three axes only, like all the preceding, but on the relation be- 
tween a principal axis and three others equal and perpendicular 
to one another and to the first, and, consequently, forming al- 
ways with each other an angle of 60°. This case will be called 
in general, Systems terno-singulaxe. It contains, as you know, 
two great subdivisions, viz. the homoedral and thehemiedral. The 
first is what I call sechsgliedrig , or systenia senarium ; as, for 
example, Quartz , in its ordinary form, then Beryl , Apatite , &c. 
The second form is the Rhomboedral System , which, by analogy 
with the preceding, I call drei-und-dreigliedrig , or sy sterna terna- 
rium. It would be useless to adduce examples so well known 
as carbonate of lime, &c. There certainly, however, exist other 
subdivisions, to make this fourth case general. Quartz itself 
forms one of them, which is, in reality, hemiedral, but in an- 
other sense, and after a quite different law, from the Rhomboe- 
