I have no need of proof. The laws of nature, unlike the laws of grammar, admit of no exception. - Dmitri Mendeleev

1. The elements, if arranged according to their atomic weights, exhibit an evident periodicity of properties.
2. Elements which are similar as regards their chemical properties have atomic weights which are either of nearly the same value (e.g., platinum, iridium, osmium) or which increase regularly (e.g., potassium, rubidium, caesium).
3. The arrangement of the elements, or of groups of elements in the order of their atomic weights corresponds to their so-called valencies as well as, to some extent, to their distinctive chemical properties--as is apparent among other series in that of lithium, beryllium, barium, carbon, nitrogen, oxygen and iron [sic. The printed speech in J. Chem. Soc. says barium and iron. Obviously boron (B) and fluorine (F) are meant. Mendeleev's 1869 paper lists the symbols B and F rather than the names of the elements.--CJG]
4. The elements which are the most widely diffused have small atomic weights.
5. The magnitude of the atomic weight determines the character of the element just as the magnitude of the molecule determines the character of a compound body.
6. We must expect the discovery of many yet unknown elements, for example, elements analogous to aluminium and silicon, whose atomic weight would be between 65 and 75.
7. The atomic weight of an element may sometimes be amended by a knowledge of those of the contiguous elements. Thus, the atomic weight of tellurium must lie between 123 and 126, and cannot be 128.
8. Certain characteristic properties of the elements can be foretold from their atomic weights.
...[R]elations ...exist between the atomic weights of dissimilar elements ...hitherto ...neglected. I believe that the solution of some of the most important problems of our science lies in researches of this kind. To-day, 20 years after the above conclusions were formulated, they may still be considered as expressing the essence of the now well-known periodic law.

I suppose when my unknown elements are found, more people will pay us attention.

I wish to establish some sort of system not guided by chance but by some sort of definite and exact principle.