## Abstract

The arrangements in space of the covalencies of a polyvalent atom, while they are subject to small variations seldom exceeding 5 or 10$^{\circ}$, tend to conform to quite a limited number of types. It is desirable to relate this grouping to some familiar property of the atom. The property here used is the size (in G. N. Lewis's sense) of the valency group of the central atom, and the number of shared electrons which it contains, together with that of the preceding (unshared) electronic group in the atom. The experimental results show the following relations. I. When the valency group is less than 8 we have with a covalency of 2 a linear structure (as in Cl-Hg-Cl), and with one of 3 a plane with equal angles of 120$^{\circ} $ (as in BF$_{3}$). II. With a complete octet the arrangement can be either tetrahedral or planar. When the covalency is less than 4 it is always derived from the tetrahedron, as in the triangular OH$_{2}$ and the pyramidal NH$_{3}$. The fully shared octet is always tetrahedral when the preceding group (n in the grouping (n) 8) is 2, 8, or 18. In the transitional elements where 8 < n < 18, it is tetrahedral if n is not much more than 8, and planar if it is not much less than 18; but the two series overlap. III. When there are 10 valency electrons, at least 2 of them (the "inert pair") unshared, the structure with a dicovalent atom (as in M[I$_{3}$]) is linear: that of a 4-covalent atom is found in the thallous and plumbous salts to be planar, but in tellurium tetrachloride it may be a distorted tetrahedron. IV. The peculiar 4-covalent duodecet in M[ICI$_{4}$] is planar. V. A covalency of 5 is always found to give a trigonal bipyramid. VI. Covalency 6. Three structures are theoretically possible, a trigonal prism, a trigonal antiprism, and a regular octahedron. Experimentally the octahedron is always found, except in a few giant molecules such as those with a nickel-arsenide lattice. The regular octahedron has been found with practically every possible size of the preceding group, as well as with the "inert pair" of electrons. VII. A covalency of 7 can have two different structures, one derived from the octahedron and the other from the trigonal prism. VIII. Covalency 8. The only compound examined, K$_{4}$[Mo(CN)$_{8}$], has a dodecahedral arrangement of the 8 CN groups. Nearly (but not quite) all the structures can be even more simply related to the size of the valency group by assuming that the mean positions of the electron pairs in this group are the same whether they are shared or not, the structure being linear for 4 electrons, plane symmetrical for 6, either tetrahedral or plane for 8, a trigonal bipyramid for 10, and an octahedron for 12.