386 J. P. Cooke, Jr., on Atomic Ratio. 
Art. XXXIX.—Atomic Ratio ; by Jostan P. Cooxs, Jr. 
Tux so-called oxygen ratio, used by mineralogists, when 
interpreted by the new chemical philosophy, is simply the ratio 
tween the total quantivalences of the several classes of radi- 
cals, which enter into the composition of a mineral. Inde 
its whole value as a specific character in mineralogy depends 
upon the fact that it expresses this fundamental relation be- 
tween the different atoms, which are associated in the molecules 
of the compound, and we propose therefore to call it the 
Atomic Ratio. 
_ The possible hydrates of silicon may be represented by the 
general formula 
| oH 0 281)—mH,O=H ,. 0, 42,088. 0,; 
and every silicate may be regarded as derived from the corres- 
— hydrate by replacing the hydrogen atoms to a greater or 
ess extent. Thus the composition of garnet is proven best by* 
ii vi iv 
: R,, [R,] 380, ,8i, : 
in which R may be either Ca, Mg, Fe, Mn or Cr, and [R, ] either 
TAL I es] or [Cr,]. Garnets have been analyzed, in which 
1ese several radicals are mixed together in every conceivable 
way consistent with this general formula, to which they all 
conform. This formula expresses all that is constant so far as 
the composition of the mineral is concerned, and the constant 
element is merely a definite ratio between the quantivalences, 
or atomicities, of the several classes of radicals taken collect- 
ively. In the last analysis this ratio is the one specific charac- 
ter, which distinguishes many mineral species, and hence 1ts 
importance in the science of mineralogy. 
When the general formula of a mineral is given we can 
easily calculate the atomic ratio. We have simply to multiply 
the number of atoms of each radical by its quantivalence 4 
ind the simplest ratio between these products, and this rule 
olds in whatever form the symbol may be written. Thus the 
* The system ot notation di i in the author’s work 
ga Chin Panag een panel aan : 
sists in writing the symbols in a linear form and separating by commas the se 
radicals, which, although uni € same central or determinant atom, ae 
independent of each other, Figures below the symbols indicate in 
dent atoms, exeept when the symbol is énclosed in brackets. These yt 
ms are united among themselves to form a compound erage 
in which the several affinities of the principal radicals a7 
number of dashes required becomes Ppoonvententtt large 
Roman numerals. The Roman numerals above the symbols 
quantivalence of the radicals. 
Ls 
Mace at 5 gi 
se ihe eae er re aac 
