quarter day (n.)
mid-15c., "day that begins a quarter of the year," designated as days when rents were paid and contracts and leases began or expired, from quarter (n.1). They were, in England, Lady day (March 25), Midsummer day (June 24), Michaelmas day (Sept. 29), and Christmas day (Dec. 25); in Scotland, keeping closer to the pre-Christian Celtic calendar, they were Candlemas (Feb. 2), Whitsunday (May 15), Lammas (Aug. 1), and Martinmas (Nov. 11). Quarter in the sense "period of three months; one of the four divisions of a year" is recorded from late 14c. Related: Quarter days.