Mendeleev used his periodic table of elements to

Mendeleev realized that the physical and chemical properties of elements were related to their atomic mass in a 'periodic' way, and arranged them so that groups of elements with similar properties fell into vertical columns in his table.
Mendeleev rewrote each edition of Principles of Chemistry, including all new scientific data-particularly confirmations of the periodic law-and reanalyzing difficulties that had arisen to hinder its confirmation (inert gases, radioactivity, radioactive and rare-earth elements)
he wanted to prove that he was right.