A Periodic Table is an achievement that requires the player to get mahogany logs from one's Etceterian subjects.
Sufficient coins in the royal coffers combined with sufficiently high approval rating for a minimum time duration of one day are required.
37,500 coins for one day with 100% approval should yield 1 mahogany log. Players may also simply change one gatherer to mahogany before they collect their resources for this achievement to be completed.