44 On the Homceomorphism of Mineral Species 



ed that one form might be a secondary to the other, that the 

 prism of Hornblende has its orthodiagonal twice that of Augite 

 in length, and that the serial relation of the forms is such that 

 they may be said to belong to one type. This point will be 

 abundantly illustrated beyond. We observe that in all the 

 comparisons made in the following tables, the only changes from 

 the forms assumed by authors made on the above principles to 

 exhibit the homoeomorphism of species, are such as depend on 

 the simple ratios, 1 : 2, 2 : 3, 3 : 2, 2 : 1. No torturing of the 

 forms has been required by employing unusual or complex 

 ratios, notwithstanding the hypothetical manner in which the 

 received fundamental forms have been in many cases assumed. 



The preceding are some of the methods that are of import- 

 ance in determining the crystallographic homologies of species. 

 It appears that the first point to be determined, is the true ver- 

 tical axis of species under comparison ; and this being ascertained, 

 the second is to fix upon the fundamental or unit vertical prism, 

 or that which shall give the relative values of the lateral axes; 

 and third, we have to determine upon a unit dome, either a ma- 

 crodome or brachydome in a trimetric species, or else the unit 

 octahedron, in order thereby to ascertain the true value of the 

 vertical axis; and fourth, to make out the serial relations of 

 forms, for a full comparison where the actual relations of the 

 axes may be doubtful. 



While studying forms by the above methods, it is also of in- 

 terest to compare them as a whole without reference to which 

 is the vertical prism ; and only by viewing them thus in every 

 different light can we fully understand their actual dimensional 

 relations. In this point of view, the results of Hausmann re- 

 specting the anhydrous sulphates and carbonates, are highly 

 interesting, although secondary in importance to comparisons 

 between the forms when placed in homologous positions. 



The position of the vertical axis derives special importance 

 from the crystallogenic nature of molecules. In a trimetric 

 molecule, if we suppose three crystallogenic axes, a vertical and 



