The classical Quenya name for the eighth month of the year, a time of hot sunshine in the later part of summer (and indeed the Elvish word for 'hot' gave this month its name). Úrimë followed the seventh month, Cermië, and was followed in turn by the ninth month, Yavannië. The period of Úrimë was known as Wedmath by the Hobbits, and was approximately equivalent to modern August.
The Sindarin name for this period was Úrui (with the same derivation as Úrimë). It was introduced as a month of thirty days in the calendar of Númenor, the King's Reckoning, and on that system it ran from modern 24 July to 22 August. When the calendar of the Dúnedain was revised by Mardil, his new Stewards' Reckoning caused the month of Úrimë to move by a day, so that it now ran, on a modern calendar, from 23 July to 21 August.
In earlier editions of The Lord of the Rings, the names Úrimë and Úrui were shown with an unaccented initial 'U' (that is, as Urimë and Urui). Later editions have standardised the spelling to include an acute accent on the 'U' in both cases.