. Annals of the Lyceum of Natural History of New-York. Science. 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
. Annals of the Lyceum of Natural History of New-York. Science. 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 ).* 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. 0 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 braehydiagonal, 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,
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