434 ON EQUIVALENT VOLUMES. [XVI. 







density was the mean of those of its constituents ; thus imply- 

 ing that this union, unlike that observed in gases, is juxtapo- 

 sition, and not interpenetration. This system of formulas has 

 introduced such difficulties into the study of the relations be- 

 fore us, that we find Mr. Dana led to the conclusion that " the 

 elemental molecules are not combined together or united with 

 one another, in a compound, but that under their mutual influ- 

 ence each is changed alike, and becomes 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, as in the case of vapors, are directly as their densities, 

 and the equivalents of mineral species are as much more ele- 

 vated 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, and 

 the variations in the volume of different carbonates, as observed 

 by Kopp, indicate the existence of several homologous genera, 

 which are isomorphous. 



The researches of Playfair and Joule have led them to the 

 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 vol- 

 ume coincides with that obtained by multiplying the volume 

 of ice (9.8 for HO with an equivalent weight of 9) by the 

 number of equivalents of water. This result is thus explained ; 

 water in these salts is in the same state of condensation as in 

 ice, and 24 HO thus condensed would occupy the volume of 

 24 X 9.8 = 235, which is identical with that of the rhombic 

 phosphate, as 20 X 9.8 = 198 is with that of the carbonate 

 of soda, C 2 Na20 fl ,20HO. Alum, crystallizing with 24 HO, 

 has a volume which is greater than that of phosphate of soda, 

 and, according to Playfair and Joule, equals that of the water 

 * American Journal of Science (2), Vol. IX. p. 245. 



