"How long did it take to build a coherent table of chemical elements?"
Dimitri Ivanovitch Mendeleev invented the periodic table of elements. The table contained elements that had not yet been discovered but have subsequently by later scientists. A very interesting story found here;
http://www.zephyrus.co.uk/dimitrimendeleev.html
The periodic table is still being updated and revised. All of science is continuously being updated and revised.