The 1850 US Census for Sangerfield, Oneida, NY shows:
Dwelling #84, Family #91
Thomas Burnham, 63, no occupation, born CT
Seth Burnham, 32, furnaceman, real estate $3,500, born NY
Candace Burnham, 22, born NY
Harrison Burnham, 5/12, born NY
Achsa R., 21, born NY
Spence Gibson, 20, furnaceman, born NY
NOTE: Spence Gibson is actually Spencer Gibson, brother of Candace (Gibson) Barnum, shown above, wife of Seth Barnum. Harrison and Achsa are family names associated with the Gibson line.
'The Barnum Family' gives a date of 29 Oct 1785.
In addition to the graves of Thomas and his wife Lucretia, Dix Cemetery also contains a grave marked "Barnum, Two babies, of Thomas & Lucretia (Beckwith) Barnum (no names/dates).