Thanks for the info. Didn't know William & Mary Puryear moved all over the South, nor did I know that Walter Randall was born in Alabama and Thomas Jefferson in Mississippi. My source of information was a detailed Puryear family history posted on the Internet by John L. (Jay) Puryear, which also had a different birth order. That website and this family is found at http://familytreemaker.genealogy.com/users/p/u/r/John-L-Puryear/GENE10-0017.html#child124http://familytreemaker.genealogy.com/users/p/u/r/John-L-Puryear/GENE10-0017.html#child124.
I think you list the order as James Monroe first, followed by William Edmond, Walter Randall, Thomas Jefferson, and finally John. The Puryear history lists James Monroe first in 1841, followed by William Edmond in 1843, John in 1845, Thomas Jefferson in 1848 (all in Tennessee) and finally Walter Randall about 1850 (not sure of date) in Texas. I guess none of that matters a whit, but were you aware of this website and discrepancy?
"Uncle" John Pitt and Walter Randall Puryear were in the Texas Cavalry, Giddings Battalion, Carrington's Co. This cavalry formed late, I think in 1864, took part in the last battle of the Civil War, the battle of Palmetto Ranch (actually fought after the war was over and which the Confederates won), and surrendered to the Union at New Orleans after that battle. I found both of their names on a prisoner of war list. Both were privates.