フォールン・ティンバーズの戦い
Recognizing his bravery and fighting skill, Adair's superiors promoted him to lieutenant colonel. He was assigned to the command of Charles Scott, who would eventually serve as Kentucky's fourth governor. He assisted in the construction of Fort Greeneville in 1794, forwarding supplies to Anthony Wayne during his operations which ended in a decisive victory at the Battle of Fallen Timbers.