46 



On Hie Homoeomorphism of Mineral Species 



as mentioned. These forms, as observed, differ from the unit 

 prisms, either by the ratio 1 : 2 or 2 : 3, ratios of the simplest kind. 

 The trimetric species are naturally divided into four grand 

 groups, differing in the angle of the unit vertical prism (angle 

 I: I of the tables, oo P: oo P of Naumann), as follows: — 



1. Angle /: / from 901° to 95°. 



2. Angle /: / near L02°, or from 98° to 105°. 



3. Angle /: / near 110°. 



4. Angle /: /near 120°. 



It will be shown that these specific values of the angle / : / 

 are dependent on a principle of the most fundamental cha- 

 racter. The third Group may, however, belong with the second, 

 as remarked upon beyond. 



The angles mentioned in the table are the obtuse angle of the 

 prism /: /(column 1), and the summit angle of the unit ma- 

 crodome and brachydome (17 and li or P <» and P <x> ).* 



r—^y-^—K 



* To avoid any ambiguity in the angles referred to in the following pages, and 

 render the subject intelligible to those who may not be familiar with crystallo- 

 graphic language, a few explanations are here given. The annexed figure repre- 

 sents a rectangular prism with replaced edges and 

 angles, and the three axes a, b, c. is the basal 

 plane of the prism ; it the larger lateral plane, pa- 

 rallel to the longer lateral axis, or macrodiagonal, c ; 

 ii the smaller lateral plane parallel to the shorter 

 lateral axis, or braehydi agonal, b. /are planes on 

 the vertical edges of the rectangular prism, which 

 when extended so as to meet one another, would 

 form a vertical rhombic prism, having its axes b, c 

 in the ratio of lb ; \c. It is therefore the unit or 

 fundamental vertical prism. 11 are planes parallel 

 to the longer lateral axis, c, having for the axes a, b, 

 the ratio la: 16; extended upward they form a 

 dome, called the macrodome. The planes H, in a 

 similar manner, constitute a brachydome, or dome 



parallel to the shorter lateral axis, and having the ratio la : U. These two 



