This table and the accompanying observations were first presented to the Russian Chemical Society in March 1869. By ordering the elements according to increasing atomic weight in vertical rows so that the horizontal rows contain analogous elements, still ordered by increasing atomic weight, one obtains the following arrangement, from which a few general conclusions may be derived. 1) The elements exhibit an evident stepwise variation of properties. 2) Chemically analogous elements have either similar atomic weights or weights which increase by equal increments. 3) The arrangement according to atomic weight corresponds to the valence of the element. 4) The elements distributed most widely in nature have small atomic weights. 5) The magnitude of the atomic weight determines the properties of the element. 6) One can predict the discovery of many new elements. 7) A few atomic weights will probably require correction. 8) New analogies between elements are revealed.