of the Trimetric System. 



45 



two lateral, while the vertical is at right angles to the lateral, 

 from the nature of the form, these last may either intersect at 

 right angles, corresponding to the form of a rectangular prism, 

 orat oblique angles, corresponding to the angle of a rhombic 

 prism ; that is, in other words, they may connect the centres of 

 the lateral faces of a rectangular prism or of a rhombic prism. 

 Either condition will express the forces as indicated by the form, 

 and result in the 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 rectangu- 

 lar. 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 octahe- 

 dron. And still another argument may be derived from the 

 relations of the domes in angle 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 

 fidelity the principles that have been briefly reviewed. The 

 unit prisms, as has been stated, are not in all instances those as- 

 sumed as such by other authors ; and although they are in gene- 

 ral well entitled to be so regarded, they are not all supposed to 

 be the unit prisms, as has been explained by referring to Horn- 

 blende and Augite as examples. An exhibition of the mathe- 

 matical relations of the forms is the main point in view. When- 

 ever we have placed in the columns of unit prisms, angles 

 usually regarded as those of other prisms, it is stated by a men- 

 tion of the form to which they have been commonly referred. 

 Thus, under Chrysolite, the prism taken as li is hi of most writers, 



* See the author's Treatise on Mineralogy, 4th edit., now in press. 



