Share-Based Compensation (Narrative) (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	May 31, 2024	May 31, 2023	May 31, 2024	May 31, 2023
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Share-based compensation expense	$ 1.6	$ 1.7	$ 5.1	$ 4.8