184 Connexion between Crystalline Form and Chemical Constitution. 



silicon has turned out to be only isometric silicon, we have no 

 chance for a comparison, like that with respect to carbon. 



Anatase is probably TiO 2 , and rutile Ti 2 O 4 , the density of the 

 latter being 4*2, of the former only 3*9. The relations of Haus- 

 mannite and Braunite (p. 179, note) accord with this, the latter 

 containing two of Hausmannite. Brookite is intermediate in 

 density, and in the temperature of origin, and hence may be 

 f (TiO 2 ). It would appear, therefore, that the species of highest 

 polymerous state, rutile, forms at the highest temperature. 



4. The views illustrated sustain the conclusion that the differ- 

 ent states of elements represented above are fundamentally di- 

 stinct — that Fe in the alpha state is related to all other metals 

 that are in the same state, including K, Na (K 2 , Na 2 in the new 

 system of chemistry), as well as Mg, Ca, &c. — that Fe, Cr, Co in 

 the beta state are of the same group of elements with aluminium 

 in alumina — that Fe, Mn, Cu, Pb in the gamma state should be 

 classed with Ti, Sn. 



5. Aid is given by the principle explained toward determining 

 in many cases what are the accessory and what the dominant in- 

 gredients in a compound, and thence what should be regarded as 

 its true constitution. 



6. Crystallogeny hereby learns that quadratic or tetragonal 

 symmetry in crystals depends on quadratic symmetry, or the recur- 

 rence of fours, in the number of atoms of the negative part of a 

 compound, and hexagonal symmetry, in like manner, on the pre- 

 sence of triads or hexads of the same atoms. Moreover, on the 

 view explained, the number of atoms of the more positive ele- 

 ment or elements, in the simpler compounds at least, may be 

 just equal to that of the negative. For since 3(aRO) = R 3 3 , 

 3(/3RO) = R 2 O 3 , and 3(SRO) = R0 3 , there are in these oxides as 

 many atoms of aK, /3R, 8R as of ; and if the elements may 

 exist in these divided states, they may thus make with the the 

 crystallogenic molecule. 



The precise arrangement of the constituent atoms in a mole- 

 cule subsisting in any case, and producing the characteristics 

 and special dimensions of the crystal, yet remains to be explained. 

 This much maybe safely deduced: — that the negative atoms must 

 be grouped (and, in the systems here referred to, under quadrate 

 or hexad symmetry) at or toward one extremity of the molecule, 

 and the positive at or toward the opposite; and that the mole- 

 cule in this way derives its polarity — a characteristic abundantly 

 manifested in the formation, the forms, and the physical natures 

 of crystals, though not often apparent in mechanical effects, and 

 which is in accordance with the most fundamental of nature's 

 laws. The different constituent elements or parts of a compound 

 may differ in degree of negativity or positivity; and even the 



