of Mineral Species of the Trimetric System. 43 
The preceding table is naturally subdivided into two sections: 
I. 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 vari- 
ation from 120° in the brachydome is but small. The verti- 
cal axis typical of the groups differs therefore theoretically as 
3: /2, which is nearly as 6 to 
In section I, the axes a, b, c, have nearly or typically the ratio 
: : 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: /3: /3, 
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’. Moreover 
the angle of the vertical prism J 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 section HL, 
is the angle of the dodecahedron. ; 
In the change, therefore, in a case of dimorphism, from the 
monometric to these trimetic forms, the characteristics of the 
pe ioe molecule, or form, are to a considerable degree re- 
ine 
It is to be observed that the domes 27 and 22 for the same spe- 
cies afford nearly the angle 71°, the supplement of 109°; in fact, 
109° 28’ for 1i would give precisely the supplement 70° 32’ for 
the summit angle of 27. 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. 
If, therefore, we compare the regular octahedron with the rect- 
angular octahedron that would result from the united domes 2% 
and 27 in the species of section I, we find them nearly identical. 
We observe, further, the important fact, that the aves of the reg- 
ular octahedron correspond to diagonals between the apices of the 
basal angles of the rectangular octahedron. But these axes in 
the latter solid, cross at oblique angles equal to the angle of the 
thombic prism J, instead of at right angles ; and they correspond to 
ines between the centres of opposite lateral faces of the rhombic 
fore a long series, for the sake of comparison although often given, is not necessary 
errs at be. me with the vertical axis 
twice ag rely 4 i. —— pe oe #, ie Malt as long ; and soon. The first 
i refers always to _ 
or letter the verti is a, 
the longer or shorter Tahal ac, acourdyng as it has over it the long or short mark, 
+", 
