38 THOMAS STERRY HUNT ON A NATURAL SYSTEM IN 



epidotes, and tourmalines, the ingenuity of miueralogical chemists has devised chemical 

 formulas often exceedingly complex and difHcultly commensurable. For all such cases I 

 hare shown that the atomic formulas already described furnish a simple solution. 



§ 33. In the atomic notation adopted by me since 1853, the ordinary chemical symbols 

 of the elements are employed to represent one part by weight of hydrogen, or eight parts 

 by weight of oxygen, and the proportions of other elements which unite with these respec- 

 tively. In other words the coefficients of the symbols of the elements, in the ordinary 

 notation are multiplied by the atomicities of tlie respective elements, for the atomic uota- 

 tatiou. The symbols in the latter are distinguished from those representing equiva- 

 lents by the use of small letters, and to prevent the confusion which might otherwise arise 

 from the absence of capital letters in the formulas, a coefficient is in all cases employed 

 after the symbol of the element ; while in constructing condensed formulas the values of 

 m may be represented by fractions. Thus, the general formula of pyroxene in the ordin- 

 ary equivalent notation being nlsi^mfi.^), if the value of n be 30, and m = (ca^mgîfej), 

 the atomic formula of pyroxene will be si6„(cai5mg„jfe5)o,w. 



§ 34. But as we have elsewhere shown (§ 21), the variable relations between silica, 

 alumina, and protoxyds, in closely related species ; the intervention of boron and titanium 

 on the one hand, and of sulphur, fluorine, and chlorine on the other, permit a further gene- 

 ralization, by which silicates are affiliated to quartz on the one hand, and to corundum and 

 spinels on the other. We thus arrive at a general atomic formula n{A+'E) in which A 

 represents an atom of silicon, boron or titanium, or of hydrogen or any metal, and E an 

 atom of oxygen or sulphur, or of fluorine, chlorine or oxysulphion. Dividing now the 

 molecular weight of the compound by n we get the value of A-l-E, which is the mean 

 weight of the individual or atomic unit of the species, whether this be oxyd, silicate, oxy- 

 fiuorid, oxychlorid or oxys^^lphid, and it is this weight, designated as P, which for each such 

 species must be the term of comparison in fixing the atomic condensation of the species. 

 The mean unit-weight thus deduced, divided by the specific gravity of the species, 

 water being unity, gives the volume, V, of the atomic unit. In silicates, the A^alue 

 of P is deduced by dividing that of the empirical atomic formula by the whole number of 

 oxygen atoms, to which, in the case of oxyfiuorids, oxychlorids or oxysulphids, the num- 

 ber of atoms of fluorine, chlorine or sulphur, is to be added. In this way only is it 

 possible to obtain direct comparisons of volume between different mineral species, as 

 was indicated in 1852, and will be fully shown in the third part of this paper.' 



§ 35. The principles hitherto maintained by the author as the basis of a natural sys- 

 tem in mineralogy, may be resumed as follows : — 



1. The conception of high equivalent or molecular weights like those of the carbon 

 series in so-called organic chemistry, extended to all mineral compounds ; as was especially 

 maintained for the carbon-spars, the spinels, and the various natural silicates, and illus- 

 trated by the hypothesis of polysilicates and polycarbonates with many atoms of base. 



' Dana, ill his inquiry into the subject of atomic vohimes in 1850 (Amer. Jour. Science, ix. 221), proposed to divide 

 the volumes deduced from the empirical chemical formulas by the number of atoms of elements in these formulas. 

 Thus (0 = 8), SiOj, Al^Oj and CaO, were, in the notation adopted by him, supposed to contain respectively four, 

 five and two elemental atoms, whereas in atomic notation they evidently correspond to three, three and one 

 oxyd-units. Hence, as 1 long since showed, the results obtained by such a discussion of atomic volumes were fiil- 

 lacidus. (Amer. .lour. Science, 1853, xvi. 214.) 



