J.D. Dana on the Homeomorphism of Mineral Species. 35 
Art. V.—On the Homeomorphism of Mineral Species of the 
Trimetric System; by James D. Dana.* 
AtrHoucH many cases of homeomorphism among minerals of 
the Trimetric System have been pointed out by different investi- 
gators, no general review of the species has yet been made. 
propose, therefore, to consider the relations in form among all the 
Species, believing that in this way, and in this way alone, we 
may arrive at the true system among the homologies, and the 
principles upon which they rest. 
In the outset, it is important to ascertain what may be consid- 
ered true criterions of homology in the comparison of forms. In 
a trimetric crystal there are often several occurring prisms in the 
three axial directions, the vertical, macrodiagonal, and brachydi- 
agonal, and as either axis might be assumed to be the vertical 
axis, and either prism in each direction the fundamental prism,t 
there are wide limits as to the possible cases of homceomorphism 
that might be made out. So among rhombohedral forms, in Cal- - 
cite for example, rhombohedrons occur of a great variety of an- 
gles, and homceomorphism may be deduced between it and al- 
most any rhombohedral species, provided any one of these rhom- 
bohedrons may for the time be taken as fundamental. 
There is obviously one right position for the comparison of 
two species, and the others are wrong. Hence it is essential to 
have some basis for deciding upon this point, and especially for 
ascertaining which is the true vertical axis, in order that we may 
Ompare like axes and their planes with one another. 
{t must be admitted that there are no tests of homology which 
are of invariable application. As elsewhere in science, the rela- 
ions of species are to be ascertained rather by the general range 
of characters, than by the severe application of one single law. 
t there are important aids, and their exact value should be 
understood. . 
- Cleavage.—Cleavage is one of the most important means. 
In the trimetric system, it may take place parallel, (1) to the ax- 
dal Sections, one or all; (2) to the lateral planes of different rhom- 
bic prisms ; (3) to octahedral planes. Rm 
_ & When cleavage is parallel to one or more rhombic prisms, it 
S generally true that, (1) the vertical axis of the prism of most 
pettect cleavage is the proper vertical axis of the species, and also 
that (2) these cleavage prisms for different species are homolo- 
§0us prisms. 
* vi, 37, March, 1854. 
mi Dea clnc tes Leeteniat whch is ee iat k. the ratio 14: le. 
The f tal macrodome and brachydome have the analogous ratios la: 16, 
unit prisms. 
