The term 'plumed military hat' is often used to refer to a SHAKO, a type of hat that was popular among European and American military forces during the 19th century. The SHAKO is a tall, cylindrical hat with a visor and a plume or feather on top. It was typically made of leather or felt and was often decorated with metal ornaments. The SHAKO was widely used by infantry, cavalry, and artillery units in many countries, including France, Britain, and the United States.