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Stock-based Compensation (Narrative) (Details) - USD ($) | 12 Months Ended
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Aug. 31, 2021 | Aug. 31, 2020 | Aug. 31, 2019
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |
Number of shares authorized under stock plan |  | 1,000,000 |  |
Number of shares available for grant |  | 543,700 |  |
Allocated share-based compensation expense |  | $ 9,555,000 | $ 5,358,000 | $ 4,446,000
Employee service share-based, Tax benefit from compensation expense |  | $ 2,000,000.0 | 1,200,000 | 1,000,000.0
Restricted Stock Units [Member] |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |
Granted, Number of Shares |  | 17,244 |  |
Allocated share-based compensation expense |  | $ 3,656,000 | 3,325,000 | 2,876,000
Employee service share-based, Tax benefit from compensation expense |  | 1,900,000 | $ 1,200,000 | $ 1,400,000
Compensation cost not yet recognized |  | $ 500,000 |  |
Remaining weighted-average vesting periods |  | 1 year 7 months 6 days |  |
Weighted-average grant date fair value |  | $ 208.29 | $ 184.43 | $ 163.93
Total intrinsic value of stock-based awards converted into common shares |  | $ 8,500,000 | $ 5,400,000 | $ 6,000,000.0
Market Share Units [Member] |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |
Granted, Number of Shares |  | 13,701 |  |
Allocated share-based compensation expense |  | $ 2,294,000 | 2,033,000 | 1,570,000
Employee service share-based, Tax benefit from compensation expense |  | 1,300,000 | $ 900,000 | $ 900,000
Compensation cost not yet recognized |  | $ 2,800,000 |  |
Remaining weighted-average vesting periods |  | 1 year 9 months |  |
Weighted-average grant date fair value |  | $ 184.96 | $ 216.77 | $ 177.82
Total intrinsic value of stock-based awards converted into common shares |  | $ 5,900,000 | $ 4,400,000 | $ 4,000,000.0
Expected volatility period |  | 2 years 10 months 17 days | 2 years 10 months 24 days | 2 years 10 months 24 days
Percent of original target number of vested shares |  | 100.00% |  |
Expected dividend yield |  | 0.00% | 0.00% | 0.00%
Deferred Performance Units [Member] |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |
Granted, Number of Shares |  | 0 |  |
Compensation cost not yet recognized |  | $ 0 |  |
Performance Share Units [Member] |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |
Granted, Number of Shares |  | 19,468 |  |
Allocated share-based compensation expense | [1] | $ 3,605,000 |  |
Compensation cost not yet recognized |  | $ 0 |  |
Weighted-average grant date fair value |  | $ 197.51 |  |
Vesting percentage |  | 100.00% |  |
Converted units to common shares |  | 0 |  |
Key Executives [Member] | Restricted Stock Units [Member] |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |
Vesting period |  | 3 years |  |
High Level Employees [Member] | Restricted Stock Units [Member] |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |
Vesting period |  | 3 years |  |
High Level Employees [Member] | Market Share Units [Member] |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |
Vesting period |  | 3 years |  |
Minimum [Member] | Performance Share Units [Member] |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |
Vesting percentage |  | 0.00% |  |
Maximum [Member] | Market Share Units [Member] |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |
Percent of original target number of vested shares |  | 200.00% |  |
Maximum [Member] | Performance Share Units [Member] |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |
Vesting percentage |  | 100.00% |  |
[1] | PSU awards, similar to DPU awards that were replaced by PSUs in fiscal year 2021, contain performance conditions for which accrual of expense is based on the probable outcome of the performance conditions. Vesting of DPUs related to the measurement years of both fiscal year 2020 and 2019 was deemed not probable at the end of each fiscal year. DPUs were then discontinued by the Company prior fiscal year 2021. PSUs pertaining to the measurement year of fiscal year 2021 vested at 100% since the performance conditions were fully achieved.

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- Definition The number of grants made during the period on other than stock (or unit) option plans (for example, phantom stock or unit plan, stock or unit appreciation rights plan, performance target plan). + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (c)(2)(iii)(1) -URI http://asc.fasb.org/extlink&oid=120381028&loc=d3e5070-113901 + Details
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- Definition The estimated dividend rate (a percentage of the share price) to be paid (expected dividends) to holders of the underlying shares over the option's term. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (f)(2)(iii) -URI http://asc.fasb.org/extlink&oid=120381028&loc=d3e5070-113901 + Details
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- Definition The difference between the maximum number of shares (or other type of equity) authorized for issuance under the plan (including the effects of amendments and adjustments), and the sum of: 1) the number of shares (or other type of equity) already issued upon exercise of options or other equity-based awards under the plan; and 2) shares (or other type of equity) reserved for issuance on granting of outstanding awards, net of cancellations and forfeitures, if applicable. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -URI http://asc.fasb.org/extlink&oid=120381028&loc=d3e5070-113901 + Details
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