From the Hammonds family of West Virginia. It is said that members of the family trace the tune back to “Old Uncle Pete” Hammons, born in 1845. Burl Hammonds called the tune “Falls of Richmond,” in the plural. The title refers to the small waterfalls, or rapids, on the James River at Richmond, rather than, as some have supposed, the 1865 capitulation (or "fall") of Richmond, the capital of the Confederacy during the American Civil War (Allan Jabbour points out Richmond ‘fell’ not only in the Civil War, but in the Revolutionary War as well). The falls of the James mark the farthest navigable point on the river, leading to the development of Richmond. Recorded by Bob Carlin and the Fuzzy Mountain String Band among others.
I think I learned it from print but can't say where.
I play this tune in a medley with:
    "Boatin' Up Sandy"
    "Bonaparte Over the Alps"
    "Cold Frosty Morning"
    "Kitchen Girl"
    "Sally in the Garden"
    "Santa Anna's Retreat"