According to link below, pp 585-586, of CONFEDERATE MILITARY HISTORY, Vol. X, @1899, edited by Gen. Clement A. Evans, paragraph references Capt. J. Pinckney Smith recruiting the "Macon Cavalry" just in time to participate in the Battle of Shiloh (Apr. 1862), then were "consolidated on terms of equality" with the Brierfield Rebels not too long after Shiloh and before the Confederate Army retreated from Corinth, MS at the end of May, 1862. This conflicts with your diary entry unless there was another "Macon Cavalry."
What would have been "terms of equality"?