Whenever the quantity of public land remaining unsold in any land district is reduced to a number of acres less than one hundred thousand, it shall be the duty of the Secretary of the Interior to discontinue the land office of such district; and if any land in any such district remains unsold at the time of the discontinuance of a land office, the same shall be subject to sale at some one of the existing land offices most convenient to the district in which the land office has been discontinued, of which the Secretary of the Interior shall give notice.