Hall of the 9th would not appear to be Reuben of the 4th as their period of enlistment coincide. However, Reuben may very well have later been exchanged and enlisted in the 18th Cavalry. Look at their unit thumbnail sketches and note the counties where they were raised. This might narrow your search.

George Martin

Private R. Hall, enlisted in (New) Company G, 9th Mississippi Infantry on September 8, 1862 at Jasper County, Mississippi, reported as deserter December 8, 1862, no further records

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Reuben T. Hall, age 36, 5' 7", hazel eyes, dark complexion, resident of Panola Company, Mississippi, enlisted as a Private in Company A, 4th Mississippi Infantry, date not stated, captured at Spring Port, Mississippi, n.d., paroled at Oxford, Mississippi December 23, 1862, no further records

4th Regiment, Mississippi Infantry

4th Infantry Regiment was organized at Grenada, Mississippi in April, 1861. Many of its members were recruited in Attala, Grenada, Lafayette, and Carroll counties. It moved to Tennessee where a detachment was captured at Fort Henry and the regiment at Fort Donelson. After being exchanged, the unit was assigned to S.D. Lee's and Baldwin's Brigade, Department of Mississippi and East Louisiana. It participated in the conflicts at Chickasaw Bayou,Port Gibson, and Big Black River Bridge, then was captured at Vicksburg. Again exchanged, it was attached to General Baldwin's and Sears' Brigade and fought with the Army of Tennessee from Cassville to Nashville. Later it shared in the defense of Mobile. This regiment was organized with 787 officers and men and totalled 279 in October, 1862. It reported 4 casualties at Chickasaw Bayou, 47 at Kenesaw Mountain, 29 at the Chattahoochee River , and 26 at Atlanta. Few surrendered in May, 1865. The field officers were Colonels Thomas N. Adaire, Joseph Drake, and Pierre S. Layton; Lieutenant Colonel Joseph J. Gee, and Major Thomas P. Nelson.

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18th Regiment, Mississippi Cavalry

18th Cavalry Battalion [also called 18th Regiment] was organized during the late fall of 1862 with eight companies. Many of the men were recruited in Smith, Coahoma, and Sunflower counties. The unit served in Chalmers', R. McCulloch's, Slemon's Brigade, then returned to McCulloch's, and finally Starke's Brigade. It skirmished in various conflicts in Tennessee and Mississippi. The battalion contained 225 effectives in October, 1863 and reported 6 casualties at Collierville and 51 in the expedition from Memphis into Mississippi. It ended the war in Mississippi with only a few officers and men. The field officers were Colonel Alex. H. Chalmers, Lieutenant Colonel J. Waverly Smith, and Major William R. Mitchell.