How did chemists begin the process of organizing elements?

The first person to organize the periodic table was chemist Dimitri Mendeleiv. He ordered the elements by mass number and organized them in columns and rows. These columns and rows shared similar characteristics both fisical and chemical. Back then there were only 60 or so discovered elements of the 118 that exist today. Mendeleiv left some blank spaces in between elements, predicting that future scientists would find elements to fill this spaces and these would have similar characteristics as the one around it. both of these predictions were right. However, he admitted that his method or organization may be wrong for he could have calculated the mass number incorrectly. Then another scientist named Henry Moseley found that he could reorganize the table by the atomic number and still be able to group elements by their characteristics.
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Density and pressure