The Example of Claudius W Sears Demonstrates that the New Orleans Academy of Sciences Attracted 'Fellows' from Across the South

Claudius W Spears was a general in the Confederate Army and later taught mathematics at the University of Mississippi.  From Wikipedia:

Sears resigned his commission from the U.S. Army on October, 10, 1842. Following a short stint teaching at St. Thomas's Hall at Holly Springs in Marshall County, Mississippi, he moved to Louisiana and was the professor of mathematics at the University of Louisiana (known now as Tulane) in New Orleans from 1845 to 1859.  Sears then was a professor at Louisiana University from 1859 into 1860, teaching both math as well as physics. He returned to St. Thomas's Hall in 1860 to serve as its president until 1861

The implications are clearly that we may need to cast a wider net for the identity of this 'R S Walker.'