104 Chronicles of Science. [ Jan., 
been worked out by the American mineralogist, Professor Dana.* 
Hitherto we have been unable to explain why a given substance 
should crystallize in a certain definite system in preference to any 
other; wliy, for example, a piece of tin-stone should invariably 
crystallize in forms belonging to the tetragonal system rather than 
in those of the other crystallographic groups. Dana shows that 
this symmetry of form is immediately connected with the chemical 
constitution of the mineral. Taking, as an example, this tetragonal 
or pyramidal system, we may remind the reader that the solids 
belonging to this order are bounded by 4, 8, or 16 sides; and 
hence the symmetry of the forms is characterized by the number 4, 
or a multiple of 4. Now it is found that in most minerals belong- 
ing to this system the number of atoms of the electro-negative or 
non-metallic element is in like manner 4, or a multiple or submul- 
tiple of that number. Hence a piece of tin-stone crystallizes in 
tetragonal forms, in virtue of its constitution as a binoxide, Sn O, ; 
the number of atoms of the electro-negative oxygen being 2, a 
submultiple of 4. So again, zircon, wulfenite, scheelite, and schee- 
litine, are all tetragonal species, each containing 4 atoms of oxygen, 
their formule being respectively—Zr O, 81 O,; Pb O, MO,; Ca O, 
WO,; and PbO, WO,: or, combining the oxygen of the acid with 
that of the base, according to the fashion of modern chemists, their 
composition may be expressed by the following formule, which more 
clearly show the 4 atoms of the element in question—Zr SO,, 
Pb MO,, Ca WO,, and Pb WO,,. 
Turning to the hexagonal or rhombohedral system, we find the 
relations to be equally curious. The symmetry of this system is 
related to the number 6; its prisms, pyramids, and other forms, 
being bounded by 3, 6, 12, or 24 sides. Here the number of atoms 
of the electro-negative element is consequently 3, or a multiple of 3. 
Thus, the sapphire and the ruby—varieties of crystallized alumina 
—assume hexagonal forms, since alumina is a sesquioxide containing 
3 atoms of oxygen, Al, O,. In like manner specular iron-ore is 
hexagonal, being a sesquioxide of iron, Fe, O,. The same is the 
case with the large class of rhombohedral carbonates, including 
those of lime, magnesia, and the protoxides of iron, manganese, and 
zine; forming the species known respectively as calcite, magnesite, 
chalybite, diallogite, and calamine (Ca CO,, Mg CO,, Fe CO,, 
Mn CO,, Zn CO,.) 
While the professor thus establishes his position with regard to 
the tetragonal and hexagonal systems, he is by no means so happy 
in his attempts to deal with the other orders. In the cubic system 
the number of atoms of the electro-negative element appears to be 
* “On a Connection between Crystalline Form and Chemical Composition, with 
sss sek a therefrom.’’— Silliman’s Journal,’ xliy., No. 130, p. 89; ‘Phil. 
Mag.,’ p. 178. 
