218 J. D. Dana’s Mineralogical Contributions. 
In Sphene there are 3 of oxygen within the brackets as in the 
other species. The usual formula is 2¢aSi+Ga'tis. But the rela- 
tion in form to Euclase sustains the above mode of writing it. 
(Ca+Ti) Si? is equivalent to (#) sit, since R=RO+RO?; so that sphene 
is essentially a silicate of the common form, or of iin which 
partof #iis replaced by Ca. Some chemists write for the ses- 
quioxyd Brannite Mo+Mn, and others adopt the same form for 
other sesquioxyds, denying the existence of a proper sesquioxyd. 
re are but few anhydrous silicates, in which the bases ex- 
ceed the silica in oxygen. These are Sillimanite, Kyanite, An- 
dalusite, Topaz, Staurotide, with Tourmaline, Euclase and 
Sphene. Andalusite, Topaz and Kyanite, have the same formula 
mst; in Sillimanite we have both &18i*, and i ai; and in Stau- 
rotide, home@omorphous with topaz and andalusite, * ai’, Hence 
the ratio of silica varies in the same species from 3 to # (and per- 
haps to 1) and in the same homeeomorphous group, from 3 to 3. 
The formulas of Euclase, Datholite and Sphene, are therefore 
essentially of one type. And if this be true, then ‘Bei (under 
which.we include (R*,# or B)Si") is trimorphous. (1.) Triclinic 
in Kyanite and Sillimanite ; (2.) monoclinic in Sphene, ete; 
(3.) érimetric in Andalusite, Topaz. G. Rose considers Kyanite 
and Sillimanite distinct in form. But the angles of Sillimanite 
observed are too doubtful to enable us to decide upon this point, 
Beryl and Eudialyte.—These species are shown to be closely 
homeomorphous on page 211. 
The formula of Beryl is (4Be+3%1) 8i?; that of Endialyte, 
(§R?+}2r) Sit. We also add that Pyrosmalite and Dioptase have 
the ratio 1:2, if the water and also the chlorid in the former be 
excluded. 
Groups of Anhydrous Silicates among minerals. —Making the 
ratio between the oxygen of all the bases, and that of the silica 
of fundamental value, the anhydrous silicates among minerals 
— into i groups, presenting the ratios 1:3, 1:2, 1: 12, 
21, 1:($-—3 -3. ips 
I. Ratio 1:3. This includes Edelforsite, Ca Si, and Mancinile, 
Zn Si, both species of somewhat doubtful existence. 
IL Ratio 1:2. Includes Wollastonite, Augite, Spodumene, 
Wichtyne, Beryl, Eudialyte. a 
Iif, Ratio 1:14. Includes Eulytine, Bis Si*. 
1V. Ratio 1:1. Includes—_ 
1. Trimetric, _ Chrysolite, ete. R3 i Tephroite, Mn3Si 
2. Hexagonal. .Phenacite, Bei Willemite, 225i 
