These two men are also noted as members of Company C / 37th. Regiment. Would they be brothers of your Joel A. McPherson?

James S. McPherson - age 32 at the time of his 1862 enlistment.

John T. McPherson - age 28 at the time of his 1862 enlistment.
(He is noted as born in 1842 at these sites.)

http://mscgr.homestead.com/MSCGRMcNi.html