232 T.S. Hunt on the Theory of Chemical Changes. 
composed of one equivalent of each of these carbonates, or of 
two to three, as the case might be, while its density was the 
mean of those of its constituents; thus implying that this union, 
unlike that observed in gases, is juxtaposition, and not interpene- 
tration. This system of formulas has introduced such difficulties 
into the study of the relations before us, that we find Mr. D 
led to the conclusion that ‘the elemental molecules are not com> 
bined together or united with one another, in a compound, but 
that under their mutual influence, each is changed alike, and be- 
comes a mean result of the molecular forces in action.’* 
The solution of these difficulties is very simple, and will have 
been inferred from the plan of our inquiry. It is found in the 
principle that all species crystallizing in the same shape, have 
the same equivalent volume ; so that their equivalent weights, a 
in the case of vapors, are directly as their densities, and the equiv 
alents of mineral species are as much more elevated than those 
of the carbon series, as their specific gravities are higher. ~The 
rhombohedral carbonates must be represented as salts having from 
twelve to eighteen equivalents of base, replaceable so as to give 
rise to a great number of species, aud the variations in the vo 
ume of different carbonates, as observed by Kopp, indicate the 
existence of several homologous genera, which are jsomorphous. 
The researches of Playfair and Joule have led them to 
conclusion that in some hydrated salts which crystallize with 
twenty and twenty-four equivalents of water, as the carbonate, 
the triphosphates and triarseniates of soda, the calculated volume, 
coincides with that obtained by multiplying the volume © ee 
9°8 for HO with an equivalent weight of 9;) by the number of 
equivalents of water. This result is thus explained; wate! . 
these salts isin the same state of condensation as in Ice, 
24HO thus condensed would occupy the volume of 24x98= 
235, which is identical with that of the rhombic phosphate, @® 
20 x9:'8=198- is with that of the carbonate of soda, C2NasOs, 
20HO. Alum, crystallizing with 24 HO, has a volume nee 
greater than that of phosphate of soda, and according to Play! 
‘aud Joule, equals that of the water in the state of ice, with he 
addition of the bases, the acid being excluded.f In reality, 1 
“equivalent volume of alum is to that of the rhombic phosphate : 
270:235, and 24HO crystallizing in the monometric i 
would have the same volume as alum, with a specific gravity 
about ‘8, giving for HO, 11-25 instead of 9°8. eee 
_ What are called the atomic volumes of crystallized ener 
the comparative volumes of their crystals. In the rhomboh™ 
system, the length of the vertical axis being constant, the volUR® 
et ae ee 
, ae aN CEREW TY ecw s PST SEN So ol Ree 
* This Journal, [2], vol. ix, p. 245. 48, 
wah rn Soc. Quar, Journai, | p. 139, cited in Liebig and Kopp’s An- Rep, 1847 
