XVI.] ON EQUIVALENT VOLUMES. 433 



solids, like those of vapors, might "be determined from their 

 specific gravities. 



A connection between equivalent weight and density is 

 evident in some allied and isomorphous species. H. Kopp, in 

 dividing the assumed equivalent weights of such bodies by 

 their specific gravities, obtained quantities which were found 

 to be equal for some of these related species. These numbers 

 evidently represent the volumes of equivalents, and in accord- 

 ance with the atomic hypothesis are said to denote the atomic 

 volumes. The inquiry of Kopp has been pursued by many 

 investigators, among whom are Schroeder, Filhol, Play fair, and 

 Joule, and, more recently, Dana. Their results show that the 

 volumes thus calculated for related species of similar crystal- 

 lization are generally identical, or sustain to each other some 

 simple ratio ; while Mr. Dana, who has compared isomorphous 

 species of unlike chemical constitution, finds that the calculated 

 volumes are often to each other as the number of equivalents 

 of elements in the formulas representing the species ; thus 

 leading to the conclusion that the real equivalent weight is 

 either a mean of that of all the elements, or some multiple of 

 it. The reason of this appears in the fact that the formulas 

 of those species in which this relation is apparent generally 

 differ in the proportions of A1 2 3 , Si0 3 , MgO, CaO, etc., and the 

 quantities obtained in dividing the equivalent weights of these 

 by the number of elements are nearly equal. If we divide by 

 the number of elements, the equivalents calculated from the 

 formulas of those species, it will be seen that the mean equiva- 

 lents vary with the specific gravity. 



These investigations have been principally confined to native 

 and artificial mineral species, and the equivalents have been 

 calculated fconi the formulas of Berzelius and Eammelsberg, 

 which express the simplest ratios deducible from analysis. 

 While in conformity with the dualistic notions, a mineral like 

 calcite or magnesite was regarded as a compound of one equiv- 

 alent of carbonic acid and one of lime or magnesia, dolomite 

 was said to be composed of one equivalent of each of these 

 carbonates, or of two to three, as the case might be, while its 

 19 BB 



