440 CONSTITUTION AND VOLUME OF MINERAL SPECIES. [XVIL 



oxides of ferricum, chromicum, and aluminicum, having two 

 thirds the equivalents ordinarily assigned to these metals, and 

 represented by fe, cr, and al; so that Fe 2 3 becomes 3feO, 

 capable of replacing 3MgO, or 3FeO. In the same way arsenic 

 and antimony, in one third their usual equivalents, may be rep- 

 resented by as and sb ; As0 8 then becomes 3asO. Silica, Si0 8 , 

 may also be written as 3siO, and by this means all these oxides 

 may be reduced to the type M 2 2 . 



We have further asserted that, for species crystallizing in the 

 same form, the density varies directly as the equivalent weight, 

 so that the quantities obtained in dividing the one by the 

 other, and known as the atomic or equivalent volumes, will be 

 equal Such a relation is already recognized between species 

 of the same genus, and we now propose, having fixed an 

 equivalent weight for one species, to calculate, from their den- 

 sities, those of the species isomorphous with it, and to show 

 from the formulas corresponding to these equivalent weights 

 that the different genera thus related are homologous, or ex- 

 hibit other intimate relations. 



[In developing the subject in the paper of which the above 

 is the introduction, I began by considering the volume of some 

 artificial salts the density of which has been carefully deter- 

 mined by Playfair and Joule, as given in their elaborate me- 

 moir on Atomic Volumes. The volume of the four prismatic 

 arseniates and phosphates of soda, with 24HO, was found by 

 them to be from 233.0 to 235.6; while that of four alums, 

 with the same number of equivalents of water, varied from 

 271.6 to 280.5 ; the presumption, for obvious reasons, being in 

 each case in favor of the greater density, and hence of the 

 lesser volumes. With the alums were compared the equivalent 

 volumes of the chlorides of sodium and potassium, calculated 

 from their ordinary formulas, and the conclusion reached that 

 the crystals of these salts possess equivalent weights which are 

 such multiples of NaCl and KC1 as would give an equiva- 

 lent volume equal to that found for the alums, or more proba- 

 bly some multiple of the latter. With the volume of the 

 arseniates and phosphates of soda was also compared that of 



