A NATURAL SYSTEM IN MINERALOGY. 79 
sity, has been maintained alike on dynamical and on chemical grounds from the time of 
Favre and Silbermann in 1847, to that of Louis Henry and of Spencer Pickering in 1885, 
and was taught by the writer in 1853, in the essay already quoted. | 
§ 19. If then, as maintained by the writer since 1853, “the doctrine of chemical equi- 
valents” is reducible to that of “the equivalency of volumes,” and applies not only to 
“the chemical changes of gases” but “ to all liquid and solid species ; ” if the production 
of these by the condensation of vapors is a chemical process giving rise to polymers, the 
equivalent weights of which are as much more elevated as their densities are greater than 
those of the vapors which combine to form them, it would seem, as has already been said, 
that the application of the atomic hypothesis to explain the law of definite proportions 
and the chemical process becomes not only unnecessary but misleading. According to this 
hypothesis, which conceives molecules to be built of atoms, and masses of molecules, the 
different ratios in unlike species between the combining weight of the chemical unit or 
molecule (as deduced from the chemical analysis and from the vapor-density), and the 
specific gravity of the mass, are supposed to represent the relative dimensions of the mole- 
cules. Hence, the values got by dividing these combining weights by the specific gravity 
have been called * molecular volumes.” The number of such chemical molecules required 
to build up a physical molecule of constant volume would, according to this hypothesis, 
be inversely as their size. If, however, as all the phenomena of chemistry show, the 
formation of higher and more complex species is by condensation, or, in other words, by 
identification of volume, and not by juxtaposition, it follows that the so-called molecular 
volumes are really the numbers representing the relative amount of contraction of the 
respective substances in passing from the gaseous to the liquid or solid state, and are the 
reciprocals of the coefficients of condensation of the assumed chemical units. 
$ 20. Thus, when steam at 100° and 760 millimeters pressure, with a formula, as 
deduced from its density, of H,O, and a combining weight of 18, (H — 1) is converted into 
water of the same temperature, 1,628 volumes of it are condensed into a single volume, 
having a specific gravity of 0.9588, which at 4 becomes 1.0000. Water is thus 1,628(H,0), 
and the weight of its volume at the temperature of formation as compared with an equal 
volume of hydrogen gas—in other words its equivalent weight—is 1,628X18 — 29,304 
(or 29,244 if H,0 — 17.9633), which corresponds to a specific gravity of 1.0000 at 4. 
The hydrocarbon C,H,, = 58, condenses to a liquid having an observed density of 0.600, 
which corresponds to an equivalent weight, as compared with that of water, of 17,516, or 
approximately 303(C,H,,), but while the reciprocal of condensation (or so-called molecular 
volume) of water—18, that of the liquid hydrocarbon is 600 : 1000: : 58 : 962, which 
value, multiplied by the co-efficient, 303 = 29,251; the calculated density being 0.599. 
The chemical unit or so-called molecule for both of these species is fixed by the density of 
their vapor. 
§ 21. If now for calcite, which is not volatilized but undergoes heterogeneous 
decomposition by heat, we assume, as the chemical unit, CCaO, = 100, with a specific 
gravity of 2,735, we find for its so-called molecular volume, or reciprocal of condensation, 
100 + 2.735 = 35.56. The combining weight of calcite as deduced from this specific gravity 
is 79,922, which gives for calcite the formula 800(CCaO,) = 80,000, while 800X35.56 = 
29,248, very nearly the equivalent weight of water. The specific gravity of some of the 
purest forms of calcite is, according to Breithaupt, 2.74, and upwards; it is not impro- 
