1. to keep watch.
2. British. to keep watch over students at an examination.
invigilance, invigilancy (noun):
Want of vigilance; neglect of watching; carelessness.
From the “News Notes” section of the October 1952 edition of The American Archivist:
Messages addressed to the Senate by Presidents Washington, John Adams, Jefferson, John Quincy Adams, Van Buren, and Polk are among documents sent to the National Archives recently by the Senate. Found recently in a supposedly empty file drawer in the attic of the capitol, the papers might have been lost forever had not the chief clerk of the Senate by chance opened the one drawer out of 780 that contained them, for the cabinets were destined for disposal. Relating chiefly to routine matters, the records fill gaps in the files of the Senate in the National Archives.