48 J. D. Dana on the Homeomorphism 
I. Angle of macrodome near 60°, and brachydome near 71°. 
II. Angle of macrodome 70° to 75°, or near the brachydome 
of Section I. . 
Ill. Angle of macrodome 83° to 90, or near the brachydome 
of Section Il. 
IV. Angle of macrodome 114° to 120°. 
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 intermediate 
between I and III, the macrodome corresponding with the bra- 
chydome 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 27 as 1i, 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° 32’, 
both monometric angles, necessarily imply a vertical prism of 
101° 34’.. Hence the important fact, that prisms approximating 
to 101° 34’ are of common occurrence, and a necessary result @ 
the relations pointed out to Monometric forms. ‘This affords a 
sufficient 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 J: J. Such prisms have approximately 
a:b cee 1 oe s/s. 
Valentinite affords an interesting exemplification of the gene- 
ral principle. Oxyd of antimony is a known example of dimor- 
phism, occurring in regular octahedrons as Senarmontite and in 
rhombic prisms as Valentinite. It would 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° 58’, which gives 
for the prism with half the macrodiagonal, 103° 30’,—a relation 
like that between hornblende and augite. The three unit prisms, 
103° 30’, 58° 17’, 70° 32’, very nearly correspond to the typical 
value of the axes 1: v4: v4. 
It is of interest in this connexion to compare Epistilbite with 
Valentinite. It presents the vertical prism 135°, corresponding to 
136° 58’ of Valentinite; and there is a macrodome of 109° 46, 
whence another macrodome 2i == 70° 50’, or very nearly the an- 
gle of the brachydome of Valentinite. It gives for 72 the angle 
100° 58’, as mentioned in the table. The occurrence of these 
Monometric angles has, beyond doubt, a profound significance. 
e hereby perceive in what respect Section II is related to Sec- 
tions Land III. The oscillations from the typical angles of the 
group amount to about 5°. : 
