114 THE CANADIAN NATURALIST. [Dec. 



of definite proportions, in what is only an expression of that law 

 in a higher form. 



The principle of polymer ism is exemplified in related mineral 

 species, such as meionite 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 intel- 

 ligible if we adopt for these species high equivalent weights and 

 complex molecules. The hardness of these isomeric or allotro- 

 pic species, and their indifference to chemical reagents, increases 

 with their condensation, or, in other words, varies inversely as their 

 empirical equivalent volumes ; so that we here find a direct 

 relation between chemical and physical properties. 



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 Play fair 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 in- 

 genious but fallacious speculations of Dr. Macvicar, who has 

 arbitrarily assumed comparatively high equivalent weights for 

 mineral species, and has then endeavoured, by conjectures as to 

 the architecture of crystalline molecules, to establish relations 

 between his complex formulas and the regular solids of geo- 

 metry, are curious but unsuccessful attempts to solve some of the 

 problems whose significance I have endeavoured to set forth. 

 I am convinced that no geometrical groupings of atoms, such as 

 are imagined by Macvicar, and by Gaudin, can ever give us an 

 insight into the way in which nature builds up her units, by 

 interpenetration and identification, and not juxtaposition of the 

 chemical elements. 



None of the above points are presented as new, though they are 

 all, I believe, original with myself, and have been, from time 

 to time brought forward, and maintained, with numerous illus- 

 trations, chiefly in the American Journal of Science, since March, 

 1853, when my paper on the Theory of Chemical Changes and 

 Equivalent Volumes, was there published. I have however 

 thought it well to present these views in a connected form, as 

 exemplifying my notion of some of the principles which must form 

 the basis of a true mineralogical classification. 



