Crystalline Form and Chemical Constitution. 183 



ber of atoms of oxygen so as to reduce the oxygen in all the 

 above formulas to 10), may be viewed as containing the basic 

 element in as many different states as there are grades of the 

 above compounds. For convenience these states may be desig- 

 nated by using the Greek letters as follows : — 



„ , f~RO R 2 3 RO 2 RO 3 RO 5 



formulae . -^ R0 R ^ ^ Q ^ Q ^ Q 



States of fR rJ R^ R^ R^ 



Basic element \aR /3R 7R 8R eR 



or the alpha, beta, gamma, delta, and epsilon states. It is observed 

 that3RO = R 3 3 ; 3(j3RO) = R 2 O 3 ; 2( 7 R0)=R0 2 ; 3( 7 R0) = 

 §R0 2 ; 3(8RO) — RO 3 , and so on; in other words, the one 

 molecule R 2 3 corresponds to three of /3R0; and in 3 (/3R0) 

 there are as many atoms of the basic element /3R as of 0. 



Now if a sesquioxide occurs in isometric crystals, as is supposed 

 to be true of Fe 2 3 (but reasonably doubted), that sesquioxide 

 is not Fe 2 O 3 , but may be Fe| 0. This is but the converse of 

 the conclusion stated above, that if a protoxide occurs in hexa- 

 gonal crystals, it is not then RO, but may be R 3 O 3 . So in 

 other cases : if oxide of tin had an isometric as well as a tetra- 

 gonal form, the former in the crystalline state should be Siii 0, 

 and only the latter SnO 2 . A metal in the different states R, 

 R2, R, has accordingly the same isomorphic power; and so 

 also 2R, 2R 2 , 2R^; and 3R, 3R* 3 3R,. Hence under the 

 principle explained, 



RO, RfO, RiO should be alike isometric in crystallization. 



2(R0),' 2(R|0), 2(RaO) may be tetragonal 



3(R0), 3(R|0), 3(R^0) may be hexagonal 



Quartz, which is hexagonal silica, should, according to the 

 above, be 3(SixO), or else 6(8^0), and not 2(SixO) = Si0 2 . 

 SiO 2 is hence unknown in the crystalline state ; and if ever ob- 

 tained crystallized it will in all probability have one of the forms 

 of TiO 2 . Common uncrystallizing silica, or opal silica, low in 

 density, may be silica in the isometric form, or Si^O, but with 

 so feeble crystallizing power as never to exhibit anything but the 

 so-called colloid condition. Whether isometric silicon, crystals 

 of which have been obtained artificially, is simply silicon in the 

 alpha state or not cannot be at once decided ; for it is probable 

 that diamond, which is isometric carbon, is equivalent to C 4 , its 

 density, and the product of the atomic weight by the specific 

 heat, indicating this relation to graphite*. As " graphitoidal " 



* For this inference with regard to the equivalent of carbon in the dia- 

 mond I am indebted to Professor G. F. Barker, who offered it while I was 

 explaining to him the views contained in this paper. 



