Discrete structers

Sir Arthur de Templar was paid 9 gold coins for the information he provided in the last known location of the Holy Grail. Soon later, from highly trusted sources, he learns that one of the 9 gold coins is not fully gold (it has some admixture of other elements and so its weight differs, either heavier or lighter, from the weight of the other 8 true gold coins). Sir Arthur pays a visit to his closest friend drug-maker Mr. Drugless and within a few seconds they identify the fake coin. Legend says that they used just an old weighing device (shown in figure) and could identify the fake coin in only 3 weighings. A weighing is an operation of putting k coins on one plate of the device and k other coins on the other plate (k = 1, 2, 3, ...) and checking if the device is in equilibrium, and if not, which plate is heavier or lighter. Repeat and clearly describe the procedure used by Sir Arthur and Mr. Drugless for identifying the fake coin among 9 gold coins in just 3 weighings