The case of Stephen Baker Barnum, the patriarch of this family, is unique in that he apparently changed the spelling of his surname to Burnham later in life. That change is particularly interesting since the two surnames are quite distinct in the historical record and no other connection has been found between them.
Although no published documentation has been found to connect John Henry Burnham and Stephen Baker Barnum, John Henry is reliably considered to have been a son of Stephen and his wife Martha Hill, based upon the following information:
1) Both John Henry Burnham and Stephen Baker Barnum were natives of Connecticut.
2) A male child of the correct age to be John Henry was enumerated as a member of the family of Stephen Baker Barnum in the 1820 and 1830 censuses, and those ages do not coincide with either the ages of Stephen´s other sons or with those of any known relatives.
3) Sometime in the early 1830s, Stephen Baker Barnum changed his family's surname to Burnham and moved with them to Thompsonville, Sullivan County, New York.
4) Both John Henry Burnham and Stephen Baker Barnum/Burnham settled in the same area of Sullivan County in the 1830s and there are connections between their families and neighbors.
5) John Henry was a carpenter who arrived in Sullivan County about 1835, at the same time as Stephen and Martha arrived there and changed the family surname to Burnham.
6) In his death notice in the Republican Watchman of Monticello, New York, John Henry was referred to as a captain; there was a letter held at the Monticello, New York, post office for a Captain Burnham in 1846.
7) Careful research has revealed no evidence of another Barnum or Burnham family that included a son named John who was born during the same period and later married a woman named Maryette [Stanton].
8) Likewise, research has revealed no evidence of another Barnum family whose surname was changed to Burnham.
9) A Y-DNA test through Family Tree DNA has confirmed that the descendants of John Henry Burnham are related to several Barnum families but not to any Burnham family.
As mentioned above, John Henry Burnham, a carpenter, arrived in Sullivan County about 1835.
He was elected to the school board in 1844.
In the 1860 US Census for Fallsburgh, Sullivan, New York, the family of John H. Burnham was enumerated as follows:
Dwelling #949; Family #919
John H. Burnham, 49, Mail, Carpenter, Real property $400, Personal property $60, b. Connecticut
Maryette Burnham, 42, Female, b. Connecticut
John L. Burnham, 18, Male, Carpenter, b. New York, Attended school within the year
Seth Burnham, 15, Male, b. New York, Attended school within the year
Frank Burnham, 10, Male, b. New York, Attended school within the year
Eliza Stanton, 73, Female, b. New York
Note: Eliza Stanton was Maryette's mother. Enumerated next door was the family of William A. Baker; the Baker and Burnham families intermarried.
By the time of the 1870 census for the same place, John Henry had died and his widow Maryette was living with their son John Lewis. As in 1860, the family of William A. Baker was living next door.
John Henry died 5 October 1863 and was referred to as Captain Burnham in his death notice.
His death notice appeared in the Republican Watchman and Jeffersonian Democrat of Monticello, New York, on 14 October 1863 and read as follows: In Fallsburgh, on the morning of Oct. the 5th of consumption, Capt. John H. Burnham, aged 52 years, 6 months and 21 days.