Correction, I believe their first engagement was at Jackson with the wounded brought back to Milldale in Warren County for treatment. Note Alexander of the 9th New Hampshire.

S. Judson ALEXANDER was born on 23 JUN 1837 in Hopkinton, Merrimack County, New Hampshire. He died on 23 JUL 1863 at Milldale, Warren County, Mississippi. He enlisted in the Ninth Regiment, Company B, N.H. Volunteers; commissioned Captain August 10 1862. Died of wounds.
http://freepages.genealogy.rootsweb.ancestry.com/~colby/colbyfam/b12.html

………

Samuel Judson Alexander

Residence Concord NH; 25 years old.
Enlisted on 7/24/1862 as a Captain.
On 7/24/1862 he was commissioned into "B" Co. NH 9th Infantry
He died of wounds on 7/23/1863 at Snyder's Bluff, MS**
He was listed as:
* Wounded 7/13/1863 Jackson, MS (Severely)
Other Information:
born in Hopkinton, NH

** Believe Milldale which is not that far from Snyder’s Bluff

Sources used by Historical Data Systems, Inc.:
- Register of Soldiers and Sailors of New Hampshire 1861-65
- Official Records of the War of Rebellion