182 Prof. J. D. Dana on a Connexion between 



and while the former may be simply ZnS, the latter should be 

 Zn 3 S 3 ; and so for the hexagonal sulphide of Fe, Ni, Cd, we 

 should have Fe 3 S 3 (troilite, pyrrhotine) ; Ni 3 S 3 (Millerite) ; 

 Cd 3 S 3 (Greenockite) ; and similarly Ni 3 As 3 (copper nickel) ; 

 Ni 3 Sb 3 (Breithauptite). 



3. Isometric system. — The number of atoms of the negative 

 element in isometric species appears to be either 1, 2, 3, 4, or a 

 multiple of 3 or 4 ; and this diversity accords with the twofold 

 nature of a cube; that is, (1) an equiaxial square prism, and (2) 

 (if a diagonal be made vertical) a rhombohedron of 90° ; for it 

 has this double relation to other forms. Accordingly, isometric 

 forms occur among protoxides, protosulphides, protochlorides, 

 &c. ; also deutoxides; also unisilicates ; in leucite, analcime; 

 also in 



Mg 3 B 4 , or boracite; As; Sb ; NaCl; KlSr; Nafir; NiC"l + 6aq; 



CuCl + 6aq; CoBr + 6aq; AmCl + SnCl 2 ; KCy + AgCy ; 



3NaG-f6i'@*-f-9aq; the alums, which have 160 besides 



240 in the water; NaAc + 2UAc; NaW + WW. 



Important chemical and crystallographic conclusions flow from 

 the principle which has been explained, if it is sustained, as we 

 believe, by the facts. A few only are briefly touched upon. 



1. It follows that the hexagonal state of the elements may be 

 one corresponding to 3R, or SnR, that while zinc in the isometric 

 state, if such exists (about which there is no doubt), is Zn, in 

 the hexagonal it may be Zn 3 , the same state in which it exists 

 in hexagonal oxide of zinc. So also Pd, As, Sb may represent 

 the isometric state of the elements palladium, arsenic, antimony; 

 but Pd 3 , As 3 , Sb 3 the hexagonal, and so for other cases. 



2. The oxide of copper, CuO, which may also be written 

 CuO 2 , is dimorphous, it occurring both in isometric and ortho- 

 rhombic forms ; and the orthorhombic form is closely isomor- 

 phous with TiO 2 in Brookite — /: / and /: -J in the oxide of cop- 

 per being respectively 99° 39' and 126° 29', and in Brookite 

 99° 50' and 126° 15'. This relation to TiO 2 shows that the 

 orthorhombic state of the cupric oxide should have the formula 

 CuO 2 , or that of a deutoxide, and the isometric alone that of 

 CuO. And it indicates further that the element copper may 

 exist theoretically, if not actually, in two corresponding polyme- 

 rous states. 



3. As long since illustrated by Laurent, the protoxides RO, 

 sesquioxides R 2 O 3 , deutoxides RO 2 , and other grades of oxides 

 RO 3 , RO 5 (and the same in corresponding chlorides, sulphides, 

 &c), in which 1 part of oxygen balances, in its affinity, 1, §, J;, 

 &c. parts of the basic element (as is seen on dividing by the num- 



