Other (Income) Expense, Net (Schedule of Other (Income) Expense, Net) (Details) - USD ($) $ in Thousands	12 Months Ended
	Sep. 30, 2024	Sep. 30, 2023	Sep. 30, 2022
Equity interest in the earnings of the JV	$ (41,191)	$ (36,846)	$ (18,193)
Net (gain) loss on sales of assets and businesses	(457)	1,491	(1,775)
Gain on non-recurring matter related to a previous acquisition	(4,803)
Rent income	(347)	(360)	(672)
Net (gain) loss on investments in deferred compensation program	(6,571)	(3,265)	6,295
Other components of net periodic pension and other postretirement benefit, excluding service cost and interest expense	11,764	10,547	11,572
Other	(2,035)	(764)	(774)
Other (income) expense, net	$ (67,168)	$ (50,291)	$ (26,691)