_m^y^ ^^-^and on Equivalent VolmM^- '^ ^'^ "^^ §11 



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 haVf| 

 been inferred from the plan of our inquiry. It is found in tlie 

 principle that all species crystallizing in the same shape, have 

 the same equivalent volume ; so that their equivalent weights, as 

 in the case of vapours, are directly as their densities, and the equi- 

 valents of mineral species are as much more elevated than those 

 of the carbon series, as their specific gravities are higher. The 

 l<hombohedral 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, indi- 

 Oate the existence of several homologous genera, which are 

 komorphous. 



'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 volume 

 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 

 ^0 X 9-8 = 198 is with that of the carbonate of soda, C^ Na^ O^, 

 20 HO. Alum, crystallizing with 24 HO, has a volume which 

 is greater than that of phosphate of soda, and according to Play- 

 fair and Joule, equals that of the water in the state of ice, with 

 the addition of the bases, the acid being excluded f. In reality, 

 the equivalent volume of alum is to that of the rhombic phos- 

 phate as 270 : 235, and 24 HO crystallizing in the monometric 

 system, would have the same volume as alum with a specific 

 gravity of about '8, giving for HO 11*25 instead of 9*8. 



"What are called the atomic volumes of crystallized species are 

 the comparative volumes of their crystals. In the rhombohedral 

 system, the length of the vertical axis being constant, the volume 

 varies with the length of the lateral axes, or in other words, 

 increases as the rhombohedron becomes obtuse, and diminishes 

 as it becomes acute, the cube being the limit between the two. 

 So in the dimetric and trimetric systems, the length of the vertical 

 axis being unity, the volume diminishes as the base of the prism, 



* American Journal of Science [2], vol. ix. p. 245. 

 i t Chem. Soc. Quar. Journal, i. p. 139, cited in Liebig and Kopp's 'Aji^. 



Rep., 1847-48, vol. i. p. 30., .-/.^-n ,5: - ^^ • ■ .^. .»,,.. -; ii bdi 



