To "muster out" means to be discharged from military service. We have a few pages (copied from microfilm) from a ledger book that lists approximately 400 names of mostly Atlantic County veterans of the US Civil War.
The ledger book pages list, in columns: date of muster, regiment, rank, name, city of residence, married or single, whether or not the solder had a widowed mother, date of discharge and if the solder was listed as a deserter.