Periodic table
Russian chemistry professor Dmitri Mendeleev and German chemist Julius Lothar Meyer independently published their periodic tables in 1869 and 1870, respectively. Mendeleev's table was his first published version; that of Meyer was an expanded version of his (Meyer's) table of 1864. They both constructed their tables by listing the elements in rows or columns in order of atomic weight and starting a new row or column when the characteristics of the elements began to repeat.
Numerology
The discovery of atomic triads, an early attempt to sort the elements into some logical order by their physical properties, was once considered a form of numerology, and yet ultimately led to the construction of the periodic table. Here the atomic weight of the lightest element and the heaviest are summed, and averaged, and the average is found to be very close to that of the intermediate weight element. This didn't work with every triplet in the same group, but worked often enough to allow later workers to create generalizations.