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Share-Based Compensation (Details) - USD ($)
$ / shares in Units, shares in Thousands, $ in Millions
3 Months Ended 6 Months Ended
Mar. 31, 2019
Mar. 31, 2018
Mar. 31, 2019
Mar. 31, 2018
Share-Based Compensation (Textual) [Abstract]        
Pre-tax share-based compensation expense $ 10.8 $ 10.2 $ 21.8 $ 18.8
Stock options        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Grants (in shares)     946 856
Wtd. Avg. Share Fair Value (usd per share)     $ 32.48 $ 35.51
Performance shares        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Grants (in shares)     57 40
Wtd. Avg. Share Fair Value (usd per share)     $ 155.04 $ 219.04
Restricted stock and restricted stock units        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Grants (in shares)     41 34
Wtd. Avg. Share Fair Value (usd per share)     $ 171.03 $ 192.50
Unrestricted stock        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Grants (in shares)     6 7
Wtd. Avg. Share Fair Value (usd per share)     $ 183.02 $ 183.76