The merculite rocket was a type of ship-mounted rocket-propelled weapon used by the Talarians on board their warships and cargo carriers in the 24th century. They were considered obsolete by Federation standards of the time.
In 2364, the merculite rockets of the freighter Batris were used to destroy the IKS T'Acog after it had lowered its shields by three Klingon criminals who had stolen the Talarian freighter. (TNG: "Heart of Glory")
In 2367, the captain of the Talarian warship Q'Maire, Endar, powered up the weapons of his ship, neutral particle weapons, X-ray lasers and merculite rockets in order to "convince" the crew of the USS Enterprise-D to return his adopted Human son, Jono. The weapons were however not a match for the defenses of Federation starships, like the Enterprise. (TNG: "Suddenly Human")