The following family history was written by Felix Grundy Buchanan (1844-?), of "Rich Valley" Virginia. Buchanan's text is based on the family Bible of his great great grandfather, Alexander. The narrative was sent to William Buchanan of Glade Springs, Virginia and is commonly found in family histories on the internet. The specific version given here was probably taken from Blakeman, 1978. (Obvious typos corrected. See also Notebook:James Buchanan.)
Alexander Buchanan, native of Ireland, had two sons who came to America about the beginning of the 18th century, settled in Chester County, Nottingham Township, Pennsylvania. Their names were James and Archibald.
"James Buchanan came to Augusta County, Virginia, and married Martha Allison of the same county. Their children were:
George and David were the children of James Buchanan’s second wife, Mary Resido,  and I have heard they went to Tennessee.
My great-grandfather Robert Buchanan came to Wythe County as an early settler of this part of the state. My grandfather was a son of Robert and Magaret McCutchan Buchanan; his name was Alexander. His wife was Margaret Walker, both of Wythe, but died in Smyth.
My father was James Augustus Buchanan and my mother Mary Glenn Thomas. Father thought your family and his were the same but could not trace the relationship. I send you this paper. You may find something in your old Bible that will throw some light on it.