"Demse Carrell: A Study" by Nancy B. Fratt.
... "No record has been found of Demse's first marriage to Frances, maiden name unknown, or of the birth of their oldest son, Daniel, both probably in the early 1730s. Daniel is, however, considered the child of Frances as he was later listed in several long-term leases. With the emphasis on "lawfully begotten" heirs in those days, Daniel would probably have been excluded had he been born out of wedlock. ...
... On 13 December 1744, John Sanford Sr., of Westmoreland executed a lease to Demse Carrel of Troro Parish, Fairfax County, for 100 acres in that parish. This agreement was for the "lives of him the said Demse Carrel, Frances Carrel his wife, & Daniel Carrel his Eldest son."* Later, Willoughby Newton of Westmoreland gave a lease to William Remey of Fairfax County, 20 September 1747, for 150 acres, also in Truro Parish. This was for the lives of William, Ann Omohundro his mother, and Daniel, the son of Dempsey Carroll.** A partially proven deed in Loudoun County, dated 24 December 1766, refers to the Newton lease of land, formerly in Fairfax but by 1757 in Cameron Parish, Loudoun County. Newton agreed to add the name of William Porter Carroll, son of Denisy, to that lease on 17 October 1758.*** ...
... [Children of Demse Carrell] 1. Daniel, eldest son, b. 1730-35, may have predeceased his father or may have d. Fairfax County 1787; no further data ...
* Fairfax County Deed Book A 2, p. 542
** Fairfax County Deed Book B, No. 1, pp. 370-2.
*** Loudoun County, Original deed, also in Partially Proven Deeds Book 1, p. 805