126 T. S. Hunt — Chemical Integration. 



liquids and solids, not less than for gases and vapors, a func- 

 tion of their equivalent or integral weights. 



§ 18. The hardness and chemical indifference of solid species 

 are in like manner, as we have elsewhere endeavored to show, 

 functions of their integral weights. For the study of these 

 relations we have calculated for the species to be compared the 

 values got by the proportion d : p '. '. 1 : v, in-which d = density of 

 weight of the liquid or solid species compared with water, 

 1628(H„0) at 4° ; and p = the weight of the gaseous species (or 

 so-called molecular weight) compared with H 2 at 0° and 760 mm . 

 The relation d:p is thus that between the densities of the solid 

 (or liquid) and the gaseous species, and the. so-called molecular 

 volume = v is the reciprocal of the co-efficient of the condensa- 

 tion suffered by the gaseous in passing into the solid species. 

 The hardness and the chemical indifference of related species 

 are inverse!}' as the values of v. 



For such specie?, with more or less complex formulas, it be- 

 comes necessary to fix comparable terms for p, and in the case 

 of compound oxydized species, of which the vapor-density is 

 unknown, we have assumed, as the unit forp, a weight including 

 that of H = 10, of CI = 35-5, or of 0^-2 = 8-0. By thus adopt- 

 ing a combining weight of 8*0 for oxygen as a basis, we get a 

 unit which gives a common term of comparison for oxyds, 

 sulphids, chlorids, fluorids, and for intermediate compounds like 

 the oxysulphids and oxyfluorids common in native species. It 

 is of course a hypothetical unit, which for elemental species and, 

 for fluorids, chlorids, etc., corresponds with the normal vaporous 

 species ; but for oxydized species is some fraction thereof, as in 

 the cases of water, of spinels, and other oxyds. 



We may readily extend this system of hypothetical units to 

 silicates, carbonates, sulphates, phosphates and more complex 

 species by dividing in all cases the empirical equivalent weight 

 by twice the number of oxygen portions (O = 16'0,or more ex- 

 actly 15*9633) plus the number of chlorine or fluorine portions.* 

 We have thus, for example : 



P- 



Forsterite, . . ■ SiMg 2 4 = 140-=-8 17-50 



Calcium carbonate CCa0 3 = 100-i-6 16-66 



Calcium sulphate S0aO 4 = 136h-8 17-00 



Gypsum SCa0 4 -2(H 2 0) = l72-f-12 ... 14-33 



Apatite 3(P 2 Ca 3 O e )-CaF 2 =908-=-50. 18-.16 



* In the writer's essay on A Natural System in Mineralogy (Mineral Physi- 

 ology and Physiography, 279-401), the values of p and v have been thus deter- 

 mined. These silicates are there represented by a new notation, which employs 

 symbols in small letters to represent quantivalent ratios; the combining weights 

 of the elements being divided by their valency, and in all cases followed by their 

 coefficients. The formula of forsterite thus becomes (mgisii)o 2 , that; of ortho- 

 clase (kial 3 sii2)oi6, and that of topaz (aUsin^f 1 . 



