The Secretary of Agriculture is authorized in his discretion to accept, on behalf of the United States, title to any lands held in private or State ownership within the townships described in section 37 of this title, and in exchange therefor may patent not to exceed an equal value of national forest land in the State of Montana, surveyed and nonmineral in character, or the Secretary of Agriculture may authorize the grantor to cut and remove not to exceed an equal value of timber within the national forests of said State, the values in each case to be determined by the Secretary of Agriculture: Provided, That before any such exchange is effected, notice of the contemplated exchange reciting the lands involved shall be published once each week for four successive weeks in some newspaper of general circulation in the county or counties in which may be situated the lands to be accepted and in some like newspaper published in any county in which may be situated any lands or timber to be given in such exchange. Timber given in exchange shall be cut and removed from national forests under the laws and regulations relating to the national forests and under the direction and supervision and in accordance with the requirements of the Secretary of Agriculture.