The value of patented lands within the park offered in exchange, and the value of the timber on park lands proposed to be given in exchange for such patented lands, shall be ascertained in such manner as the Secretary of the Interior may, in his discretion, direct, and all expenses incident to ascertaining such values shall be paid by the owners of said patented lands, and such owners 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 if the value of the timber on park lands exceeds the value of the patented lands deeded to the Government in the exchange such excess shall be paid to the Secretary of the Interior by the owners of the patented lands before any of the timber is removed from the park, and shall be deposited and covered into the Treasury as miscellaneous receipts. The same course shall be pursued in relation to exchange for timber standing near public roads on patented lands for timber to be exchanged on park lands. The lands conveyed to the Government under section 51 of this title shall become a part of the Yosemite National Park.