Other Ranks Busby. The regiments of the Royal Horse Artillery (RHA), dating from 1793, are part of the Royal Regiment of Artillery (commonly termed Royal Artillery) of the British Army. The Busby headdress is the English name for a head-dress made of fur, worn by Hungarian hussars. In Great Britain hussar and RHA busbies are cylindrical in shape, with a bag. The RHA wore these with the cords tied around the busby and with just the white plume at the front and lacking any other badge.