Frances Hunter Arbuckle and Captain Matthew Arbuckle had a son, Matthew. Born December 18, 1778 in Greenbrier County, West Virginia, and died June 11, 1851 at Fort Smith, Sebastian County, Arkansas. He was buried in the Arbuckle Cemetery, Lavaca, Sebastian County, Arkansas.
United States Army Officer. He served as Colonel and commander of 7th United States Infantry Regiment, stationed at Fort Scott, Georgia. Assumed command of Ft. Smith, AR in 1822. First commander of Ft. Gibson, IT (OK) from 1824 to 1841. Last assigned to Ft. Smith, AR on March 14, 1851. He died there in June of 1851. The Arbuckle Mountains in Southern Oklahoma were named in his honor.