viscounty

noun

1. The territory administered by a viscount as (notably royal) official
2. An estate held (as fief or nominally) with the title of viscount

   “His grace made a surrender to the crown, in 1706, of the titles conferred upon his father, and obtained a new grant of those honors, dated 17th of June, 1706, extending the remaindership to his heirs male or female, descended from William, first Earl of Queensberry, leaving the marquesate and earldom of Queensberry, with the viscounty of Drumlanrig, and barony of Douglas, of Hawick and Tibbers, untouched, and to descend according to the original patents of creation.”