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The system of reckoning dates unique to the Hobbits of the Shire, based on the founding of that land in T.A. 1601. The Shire-hobbits reckoned this as year 1. So, years of the Third Age can be converted to Shire-years by subtracting 1600 (e.g. the Downfall of Barad-dûr occurred in III 3019, but in the Shire this was counted as the year 1419).