Chemistry and Physics. 323 



would the computed values, d. CV or CV, be equivalent to each 

 other. If the products, d. CV, were originally equivalent, then 



the quotients Q = * , where M is the simplest molecular or 



atomic weight, should be the same for all members of the same 

 series. If we have found the quotient Q 1 for one substance, then 

 from this we can obtain the actual equivalent weight d .CV = 

 Q l . M, by multiplying it by the atomic or molecular weight, and 

 by dividing this value by the specific gravity of the substance 

 under consideration we obtain the actual equivalent crystal-vol- 



ume, UVj = — ~ — . 

 cl 



d CV 

 The quotient, — ^ — , is obtained by dividing the crystal-vol- 



M 



ume by the molecular volume, -=-. The difference between the 



cl 



equivalent weights, d . CV, of a series must, since the weights 

 themselves are proportional to the molecular weights, stand in 

 the same ratio as the difference between the corresponding atomic 

 or molecular weights. This latter proposition includes, however, 

 an extension of all our previous considerations touching iso- 

 morphic bodies, possibly even a part of the morphotropic ones. 



It only remains to say a few words concerning the relations of 

 heteromorphic modifications of the same substance. It is evi- 

 dent that the molecular weight of heteromorphic modifications 

 stand in some simple rational ratio to each other, and conse- 

 quently, in connection with the above considerations, it follows 

 that the products, d. CV, must also stand in the same simple 

 ratio, or, that equivalent crystal-volumes possess equal weights. 



In presenting the results of his calculations, the author gives a 

 series of thirteen tables. Of these, seven are devoted to hetero- 

 morphic modifications of the same substance, as, for example, 

 graphite and diamond, marcasite and pyrite, calcite and arago- 

 nite, etc. In all of these cases the crystal-volume (CV), the 

 product of this by the specific gravity (d . CV) and the molecular 

 volume (MV) are given; finally, the quotient of the crystal- 

 volume divided by the molecular volume I Q = ^f?x) is deduced. 



These last values agree closely in the case of the substance in 

 each table, only showing such variations as can be explained by 

 the inaccuracy of the data available. For instance, for graphite, 

 Q = 3-732; for diamond, Q = 3*695. Again, for calcite, Q = 

 0-097295 ; for aragonite, Q = 0-09730. 



From these tables, then, it appears that the theory above devel- 

 oped is in accord with the facts; further, that in case of the com- 

 plete knowledge of one modification of a substance the determi- 

 nation of one of the quantities, CV or d, of another modification 

 is sufficient for the computation of the other. For example, as 

 soon as the axial ratio and specific gravity of graphite are known 



