MINEEALOGY; WITH A CLASSIFICATION OF SILICATES. 89 



various species. Attempts to devise structural formulas for these very complex silicates 

 appear in the present state of our knowledge of their constitution to be premature, and at 

 the same time unnecessary. 



§ 126. "We have seen in our studies of the volume of mineral species two cases ; the 

 first being that in which, in analogous compounds, the density varies with the unit- 

 weight, so that the species compared have identical unit-volumes; and the second, that 

 in which species, otherwise analogous, have such densities as give very unlike unit- 

 volumes,— a fact showing the existence of progressive or homologous series of polymères, 

 as illustrated in the case of many silicates and carbon-spars. Examples of these differences 

 are seen in the chlorids of potassium and sodium, the latter of which itself presents 

 remarkable ditferences in density. Thus, while the numerous determinations for potas- 

 sium-chlorid do not vary very miich from a specific gravity of 1.99, the careful observa- 

 tions of different experimenters with sodium-chlorid, show variations from 2.011 by Play- 

 fair and Joule, to 2.15-2.16 by Stolba, 2.195-2.204 by Deville, and 2.24-2.26 by Mohs and 

 Filhol.' With these various determinations of density before us, says Henry Wurtz, "we 

 are forced to infer the existence of four modifications of sodium-chlorid," while he adds, 

 " common salt is far from being alone among saline combinations in its passage into divers 

 modifications or allotropes. On the contrary, the circiimstance is almost universal among 

 salts, throughout the whole range of chemistry." It would seem, in fact, that such varia- 

 tions in specific gravity in a homogeneous solid (like those in the specific gravity of a vapor 

 or gas, at constant pressure and temperature,) can have but one meaning ; which is, that 

 these sodium-chlorids of different densities are so many distinct species, related to each 

 other as fibrolite to cyanite, as lyncurite to zircon, and as tridymite to cjuartz. 



§ 12Y. All siich allotropie variations in compound species, which are marked not only 

 by differences of density, but in many cases, if not in all, by differences in hardness and 

 in chemical relations, are, by Henry Wurtz conceived to be, "dependent on a variability 

 through a certain — sometimes not very narrow — range of diameters of one eiement, 

 always the basylic or electropositive of a group — in salts, therefore, always the metallic 

 base." According to him, the volumes of elemental molecules, that of oxygen excepted, 

 " are expressed by c[uantities having at the temperature of ice-fusion the relations of even 

 cubes of a series of whole numbers, of which series the number pertaining to the molecule 

 of ice at this temperature is 2*1." This, he adds, is " a standard volume in nature, to which 

 the volumes of all licjuid and solid bodies may be compared when at the same tempera- 

 ture." The cube roots of these numbers are by Wurtz, designated as " molecular dia- 

 meters," and the variations in specific gravity in the different forms of sodium-chlorid, are 

 explained by supposing the diameters of one or more of the sodium molecules in a complex 

 gToup including 4NaCl., to A'ary from 23 to 24 and 25, the diameter of the chlorine 

 molecules remaining invariable." This method enables him, by admitting more or less 

 complex groups, in which the similar elemental molecules have varying diameters, to 

 approximate closely to the densities of liquid and solid species. 



§ 128. To such a scheme it may be objected that it involves the notion of pre-existing 

 elements or groups of elements, dissimilar to each other as well as to the species under 



' Constants of Nature, by F. VV. Clarke. Part i. 30. 



-' Geometrical Cbemistry, by Henry Wurtz, pp. 72, 1876; reprinted from tlie American Chemist, March, 1876. 



Sec. III., 1885. 12. 



