Yes, these dates refer to the year of James's reign, but May 23 7 James I is May 23, 1609 (the 7th year of James I's reign began 6 years after he became king, on 24 March 1609, and ends 7 years less a day after he became king, on 23 March 1610) - same principle as why the 20th century begins in year 1900 and ends in year 1999.