388 J. P. Cooke, Jr., on Atomic Ratio. 
whence we deduce the ratio 
1-40 : 1-31 : 2°76 or 1:1: 2 nearly. 
It is usual in works on mineralogy to present the results of 
analysis on the old dualistic plan, as if the mineral were forme 
by the union of various basic anhydrids. with silica. Starting 
with such data it is not, however, necessary to calculate the per 
cent of each radical in the assumed anhydrids before applying 
the above rule, because, obviously, by dividing the per cent of 
each anhydrid by its molecular weight we shall obtain the same 
quotients as before. For example, in the analysis of garnet 
cited above, where the data are given on one side in the usual 
form, we 
28 60 
Si: SiO, =19-30 : 41:35 or 19-30+-28=41°35+ 60 
and so for each of the other values, 
In the symbols of the silicates as formerly written on the 
dualistic theory the atoms of oxygen were necessarily appor- 
tioned among the different radicals in proportion to their quan- 
tivalence, although this fundamental distinction between them 
was itself overlooked. Thus the general symbol of garnet 
3RO, R,0,, 38i0, | 
our modern theories and is practically less simple. ene 
over, the “ont is far more general than the old meth 
poe 
well as with those, in which the radicals are cemented together 
by oxygen. Furthermore it is frequently useful to compare 
_ the ay inie ratios of the complex radicals which may be as 
exis’ . . . . 
Beene 
