The Genealogical Record of the Barnum Family states that Heman may be the son of Ebenezer Barnum and Elizabeth Skiff, but also calls Zenus (born 1760) the last son of that marriage. The same source notes that Heman had brothers Thomas and Daniel. If the dates given are correct, Heman Barnum married for the first time at the age of 30, and for the second time at the age of 61.
Descendant Jeanee Thompson writes: It is a guess on my part that Heman is the son of Francis and Anne, but the recurrence of the names Francis, Daniel and Thomas strongly suggest the link, along with the sale price for their property in Hinesburg purchased from Francis of Dorset. Heman and family were in Franklin, Vermont by 1800.
There was another Heman Barnum in Ferrisburg, Addison County, born about 1785, too young to own the land in Hinesburg. Addison County had eleven Barnum households in 1800 (Barnabas, John, Joseph, Richard, Abijah, Eben, Samuel, Moses, Stephen, Seth and Elihu). The younger Heman was probably from one of these lines. He married Lydia Rogers and stayed in Ferrisburg with at least two children: Joseph and Sarah.
The children’s names listed below are taken from Franklin, VT, vital records. Because of the 1810 and 1820 censuses, I think a good number would be 5 sons, four daughters for Heman and his first wife. I also am guessing that after his first wife died, Heman married Mary almost immediately because of the young children, and they had at least two children, Daniel and Thomas.
1790: No Heman, but Daniel is in Hinesburg, Chittenden Co., VT. His household consists of two adult males, one adult female.
1800: Hinesburg, Daniel lives with an adult female and two children. Franklin Co., VT. Heman has three sons, 1 daughter (none would be Heman, Jr.)
1810: Franklin: Three sons, Three daughters, one adult male, one adult female.
1820: Franklin: Harmen Burnham: 3 males under 10; 1 male 10-16; one male 16-26; one male over 45. One female under 10; one female 10-16; one female 16-26; one female over 45.
1830: 2 males less than five, one 5-10, one 10-15, he is 60-70; 1 female 15-20, 1 female 40-50.
1840: 2 children less than five, one 5-10, one 10-15, one 20-30, Heman, Jr. and his wife at 30-40, and Heman Sr. at 70-80.
1850 Franklin: There is a 24-year-old blacksmith named Daniel Barnum. A little farther down is a 22 year old Thomas Barnum, a laborer for Lorenzo Olds, blacksmith. Heman Barnum (Jr.) age 42, a farmer, along with his wife A__lia, age 41 and four children from 1 - 16, Lorenzo, Elizabeth, Rodney and Harley. There is a Michael Burnim with wife Angelina and five children. These could be Heman's children, but some are pretty young. They could also be his older sons' children.
1860: Heman (Jr.) is still there with wife Rachel and the two youngest from the last census. Lorenzo is nearby with wife Betsy.
Prior to 1777 the area constituting the present-day state of Vermont was claimed by three British colonies. The Province of Massachusetts Bay claimed the land on the basis of the 1629 charter of the Massachusetts Bay Colony, the Province of New York claimed Vermont based on land granted to the Duke of York (later King James II) in 1664, and the Province of New Hampshire, whose western limits had never been determined, also claimed Vermont. On 18 January 1777 the area was constituted as New Connecticut, and on 2 June of that same year it became the Independent State of Vermont. It joined the Union as the 14th state on 4 March 1791.