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Share-Based Compensation (Narrative) (Details) - USD ($) $ / shares in Units, $ in Thousands | 3 Months Ended
--- | ---
Nov. 30, 2024 | Nov. 30, 2023
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |
Share-based compensation expense | $ 1,900 | $ 1,600
Share withheld for payroll tax obligations | $ 1,450 | $ 1,575
Restricted Stock Units [Member] |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |
Shares to be settled in cash | 3,516 | 2,861
Weighted average grant-date stock price of awards to be settled in cash | $ 121.16 | $ 120.59
Performance Stock Units [Member] |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |
Vesting period | 3 years |
Performance Stock Units [Member] | Minimum [Member] |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |
Percentage of awards actually earned | 0.00% |
Performance Stock Units [Member] | Maximum [Member] |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |
Percentage of awards actually earned | 200.00% |

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