XIX.] OBJECTS AND METHOD OF MINERALOGY. 457 



show that these polybasic salts may contain many atoms of 

 different bases, and their frequently complex and varying 

 constitution is thus rendered intelligible. In the application 

 of the principle of chemical homology, we find a ready and 

 natural explanation of those variations within certain limits, 

 occasionally met with in the composition of certain crystalline 

 silicates, sulphides, etc.; from which some have conjectured the 

 existence of a deviation from the law of definite proportions, 

 in what is only an expression of that law in a higher form. 



The principle of polymerism is exemplified in related mineral 

 species, such as rneionite and zoisite, dipyre and jadeite, horn- 

 blende and pyroxene, calcite and aragonite, opal and quartz, in 

 the zircons of different densities, and in the various forms of 

 titanic acid and of carbon, whose relations become at once in- 

 telligible if we adopt for these species high equivalent weights 

 and complex molecules. The hardness of these isomeric or 

 allotropic species, and their indifference to chemical reagents, 

 increase with their condensation, or, in other words, vary in- 

 versely as their empirical equivalent volumes ; so that we here 

 find a direct relation between chemical and physical prop- 

 erties. 



It is in these high chemical equivalents of the species, and 

 in certain ingenious but arbitrary assumptions of numbers, 

 that is to be found an explanation of the results obtained by 

 Playfair and Joule in comparing the volumes of various solid 

 species with that of ice ; whose constitution they assume to be 

 represented by HO, instead of a high multiple of this formula. 

 The recent ingenious but fallacious speculations of Br. Mac- 

 vicar, who has arbitrarily assumed comparatively high equiva- 

 lent weights for mineral species, and has then endeavored, 

 by conjectures as to the architecture of crystalline molecules, 

 to establish relations between his complex formulas and the 

 regular solids of geometry, are curious but unsuccessful at- 

 tempts to solve some of the problems whose significance I have 

 here endeavored to set forth. I am convinced that no geo- 

 metrical grouping of atoms, such as are imagined by Macvicar 

 and by Gaudin, can ever give us an insight into the way in 

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