CALCULATION OF VOLUME RELATIONS. 209 



repeated the work in order to verify it. The following well-known principle 

 was employed: 



The volume of the original compound is to the volume of the compound 

 produced directly as their molecular iveights and indirectly as their specific 

 gravities. 



Under this general principle are two cases: 



Case 1. Where one solid compound alters into another solid compound. 

 This case is illustrated by the well-known changes of limestone to dolomite. 

 In this change we have 2CaC0 3 replaced by MgCa(C0 3 ) 2 . The molecular 

 weight of 2CaC0 3 is 198.62. The molecular weight of MgCa(C0 3 ) 2 is 

 182.96. The specific gravity of calcite may be taken as 2.7135 ; of dolomite, 

 as 2.85. The compound proportion is therefore as follows: 



V:V ! 



198. 62 : 182. 96 

 ■ 2. 85 : 2. 7135 



or the volume of the dolomite is 87.70 per cent of that of the calcite; 

 or, therefore, there is a decrease in volume of 12.30 per cent. 



Case 2. This has three phases: (a) where two or more solid compounds 

 unite to produce a single solid compound ; (b) where a single solid 

 compound breaks up, producing two or more compounds, and (c) 

 where two or more solid compounds unite to produce two or more solid 

 compounds. In this case the method of calculation is slightly different 

 from case 1. The molecular weights of each of the compounds represented 

 in the equations are divided by the specific gravities of the respective 

 compounds. This gives their relative volumes. In phase (a) the volume 

 of the resultant single compound is divided by the sum of the volumes of 

 the producing compounds, and this gives the percentage of change. In 

 phase (b) the sum of the volumes of the resultant compounds is divided by 

 the volume of the original compound. In phase (c) the sum of the volumes 

 of the resultant compounds is divided by the sum of the volumes of the 

 original compounds. These different phases are so similar in method that 

 it is necessary only to illustrate one of them. The first phase is illustrated 

 by the formation of wollastonite by the union of calcite and quartz, the 

 reaction being: 



CaC0 3 +Si0 2 =CaSi0 3 +C0 2 . 



The molecular weights of the three solid compounds are, respectively, 

 mon xlvii — (M 14 



