The value of all patented lands within said monument offered for exchange, and the value of the lands of the United States to be given in exchange therefor, shall be ascertained in such manner as the Secretary of the Interior may direct; and the owners of such privately owned lands within said monument shall, before any exchange is effective, furnish the Secretary of the Interior evidence satisfactory to him of title to the patented lands offered in exchange; and lands conveyed to the United States under section 444 of this title shall be and remain a part of the Petrified Forest National Monument.