

48 On the Homoeomorphism of Mineral Species. 



The preceding table is naturally subdivided into two sec- 

 tions : — 



J. Species having the summit angles of the domes, near 109°. 

 II. Species having the summit angles of the domes, near 120°. 



In the first of these groups there is a remarkable closeness of 

 coincidence to the angle mentioned ; and in the second, the va- 

 riation from 120° in the brachydome is but small. The verti- 

 cal axis typical of the groups differs therefore theoretically as 

 V3 : V2 , which is nearly as 6 to 5. 



In section I. the axes a, b, c, have nearly or typically the ra- 

 tio 1 : V2 : y/2. In Andalusite, the ratio is almost identical with 

 this, and 109° 28' is exactly a mean between 109° 6' and 109° 

 50', the angles given for the two domes. 



In section II. the ratio of the axes approaches 1 : V3 : VB, 

 which it is very closely in Epsomite, the domes of which are 

 nearly 120°. 



109° is approximately the angle of the regular octahedron, 

 the faces of which solid incline to one another 109° 28'. More- 

 over the angle of the vertical prism /varies but little from that 

 of a cube, or 90°. Here is an obvious relation to monometric 

 forms not to be overlooked. Moreover, the angle 120°, in sec- 

 tion II., is the angle of the dodecahedron. 



In the change, therefore, in a case of dimorphism, from the 

 monometric to these trimetric forms, the characteristics of the 

 monometric molecule, or form, are to a considerable degree re- 

 tained. 



It is to be observed that the domes 21 and 21 for the same spe- 

 cies afford nearly the angle 71°, the supplement of 109° ; in fact, 

 109° 28' for li would give precisely the supplement 70° 32' for 

 the summit angle of 21. In several of the species the occurring 

 dome is that of 70°-71°, instead of that of 109° ; so that either 

 might be taken as characteristic of the first section in Table I. 

 70° 32' is the summit angle of the regular octahedron. 



