The 1st Arkansas Artillery was a battery (artillery equivalent of a company) and had no attached companies. The 1st (Stirman's) Battalion Arkansas Cavalry had no Company I. I believe the Martin's were members of the 1st (Marmaduke's) Battalion Arkansas Infantry. This organization started out as an 8-company battalion, was augmented by two companies (I and K) from Searcy County and redesignated as the 18th (Marmaduke's) Regiment Arkansas Infantry, and later redesignated as the 3rd Regiment Confederate Infantry. The regiment was in Tennessee at the time the Martin's died at Nashville. I believe the abbreviation "Batty" in their unit identification should be "Battn" -- battalion rather than battery. They were probably hospitalized at the time all this reorganization was going on, and were probably admitted when the unit was still called the 1st Arkansas Battalion. If your Martin's were from Searcy County or vicinity, that would just about make it a certainty.