VIII. — On the Homceomorphism of Mineral Species of the Tri- 

 metric System. 



By James D. Dana, of New-Haven, Conn. Honorary Member. 

 Read March 13, 1854. 



Although many cases of homceomorphism among minerals of 

 the Trimetric System have been pointed out by different inves- 

 tigators, no general review of the species in this respect has yet 

 been made. We 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 homo- 

 logies, and the principles upon which they rest. 



In the outset, it is important to ascertain what may be con- 

 sidered 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 bra- 

 chydiagonal, and as either axis might be assumed to be the ver- 

 tical axis, and either prism in each direction the fundamental 

 prism,* there are wide limits as to the possible cases of homaeo- 

 morphism that might be made out. So among rhombohedral 

 forms, in Calcite for example, rhombohedrons occur of a great va- 

 riety of angles, and homceomorphism may be deduced between 

 it and almost any rhombohedral species, provided any one of 

 these rhombohedrons may for the time be taken as funda- 

 mental. 



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 compare like axes and their planes with one another. 



* A fundamental vertical prism is one which has for its axes b, c, the ratio 

 16 : \c. The fundamental macrodome and brachydome have the analogous ratios 

 la : 16, and la : \e. These are the unit prisms. 

 MARCH, 1854. 4. Ann. Lvc. Nat. Hist. Vol. VI. 



