Barbara North

His second wife was Barbara Slingsby (d. 1 August 1721), daughter of Sir Thomas Slingsby, 2nd Baronet, by whom he had one daughter:

1. Lady Barbara Herbert (d. 27 December 1752), married Edward (sic: William?) Dudley North on 3 October 1730

Sources

1. Miscellanies, Volume 3 By Henry Fielding. Page 336. "The Right Hon. Lady Barbara (Herbert) North, d. 27 December 1755, LM, 25:43: m. William Dudley North, of Glemham Hall (Suffolk), 1730. Half sister of the E. of Pembroke (no 289); Collin's Peerage iii. 143."
2. Peerage of England: Genealogical, Biographical, and Historical ..., Volume 3 By Arthur Collins, Sir Egerton Brydges. Page 143
3. A Genealogical and Heraldic History of the Extinct and Dormant Baronetcies ... By John Burke, Sir Bernard Burke.  Page 99.  "Cann."