Connexion between Crystalline Form and Chemical Constitution. 1 79 



Regarding the atom of oxygen as double in its fundamental 

 nature, the number of atoms of oxygen (or the negative ele- 

 ment) in the protoxides is 2 ; in the sesquioxides 6, or a mul- 

 tiple of 3 ; in the deutoxides 4. 



It appears, from a survey of all hexagonal and tetragonal com- 

 pounds, to be a general fact that the number of atoms of the 

 negative element is 3, or a multiple of 3, in the former ; and 2, 

 4, or a multiple of 4, in the latter; and that consequently the 

 hexagonal and tetragonal systems are based on these numbers 

 respectively, their symmetry being a consequence of it. 



1. Tetragonal species, and the number 4. — Among unisilicates 

 (the silicates which have the ratio 1 : 1 between the oxygen of 

 the bases and silica (Si0 2 ),and the number of atoms of oxygen 4, 

 or its multiple) tetragonal species are common; while none occur 

 among the bisilicates, in which the ratio is 1 : 2, and the number 

 of atoms of oxygen is 3, or its multiple. There are none also 

 among the anhydrous carbonates, which likewise have the oxygen- 

 ratio 1 : 2. But among these bisilicates and carbonates there 



are examples of hexagonal species. The compounds CaW 



(Scheelite), PbW (Scheeletine), PbMo (Wulfenite), Y 3 f (xeno- 

 time) are tetragonal, the last having 8 of oxygen (or 16 if doubled) 

 and the others 4. Matlockite (PbCl + PbO) is tetragonal, while 

 PbI + 2PbOis hexagonal, and PbCl-f2PbO is orthorhombic. 



Cerasine (PbCl + PbC) is tetragonal ; and the number of atoms 

 of the negative elements, O, CI, is 4. Hausmannite is tetra- 

 gonal, and, with the usual formula Mn Mn, has 40. Yet the for- 

 mula is better written Mn 2 Mn; for this corresponds with its close 



relation in form to the RO 2 or deutoxide group, while MnMn is 

 a formula of the isometric spinel group. Similarly the tetra- 

 gonal species chalcopyrite has the formula 2(€u, Fe)S + FeS 2 . 

 Braunite, taking the most recent formula for it, that of Rammels- 

 berg, (Mn, Si) 2 O 3 , is apparently an exception. Its composition, 



as Rammelsberg shows, corresponds to 3Mn + Mn + Si ; and this 

 formula has 120, which is a multiple of 3, and satisfies the prin- 

 ciple under illustration. But the true arrangement of the con- 

 stituents makes it not a sesquioxide, as above, but a deutoxide 

 like Hausmannite, which it approaches in its tetragonal form ; 



for the formula may be 2Mn 2 Mn + MnSi, which is equivalent 

 to 2 of Hausmannite and 1 of a silicate analogous to the tetra- 

 gonal species zircon (ZrSi)*. The deutoxide of manganese, 



* Hausmannite approaches more closely the anatase form of TiO 2 than 

 the rutile form, the angle between O and the plane made \-i in anatase 



