of the Trimetric /System. 55 



In section I. the angles of the domes oscillate from or about 

 the monometric angles 60° and 70° 32'. In section III., 90° is 

 nearly a mean between the angles of the domes. In section 

 IV., 120° is a similar mean for the domes. Section II. is inter- 

 mediate between I. and III., the macrodome corresponding with 

 the brachydome of section I., and the brachydome with the 

 macrodome of section III. The vertical axis in section III. is 

 two thirds that of section I. ; and by taking §* as \l, the two 

 groups would coalesce. The vertical axis of section IV. is about 

 two fifths of that of I. 



In section I. a macrodome of 60° and a brachydome of 70° 

 82', both Monometric angles, necessarily imply a vertical prism of 

 101° 84'. Hence the important fact, that prisms approximating 

 to 101° 34' are of common occurrence^ and a necessary result of the 

 relations pointed out to Monometric forms. This affords a suffi- 

 cient reason for the occurrence of so many species near 102° in 

 angle, just as there are many near 90°, and gives special im- 

 portance to this value of /; /. Such prisms have approxi- 

 mately 



a x b : c = 1 : y/§ : y/h> 



Valentinite affords an interesting exemplification of the gene- 

 ral principle. Oxyd of antimony is a known example of, di- 

 morphism, occurring in regular octahedrons as Senarmontile, and 

 in rhombic prisms as Valentinite. It might hardly be expected 

 that the latter should retain closely any of the angles of the 

 former; and yet there is a brachydome having exactly the 

 angle 70° 32'. The cleavage vertical prism has the angle 136° 

 20', which gives for the prism with half the macrodiagonal, 

 102° 36',— a relation like that between Hornblende and Augite. 

 The three unit prisms, 102° 36', 59° 4', 70° 32', very nearly 

 correspond to the typical value of the axes 1 : Vi : V%- 



It is of interest in this connexion to compare EpistUbite with 

 Valentinite. It presents the vertical prism 135°, corresponding 

 to 136° 20' of Valentinite ; and there is a macrodome of 109° 



