When the public interests will be benefited thereby, the Secretary of Agriculture is authorized in his discretion to accept on behalf of the United States title to any lands within the exterior boundaries of the national forests which, in his opinion, are chiefly valuable for national-forest purposes, and in exchange therefor may patent not to exceed an equal value of such national-forest land, in the same State, surveyed and nonmineral in character, or he may authorize the grantor to cut and remove an equal value of timber within the national forests of the same State; the values in each case to be determined by him. 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 such exchanges shall be cut and removed 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. Lands conveyed to the United States under this section and section 486 of this title shall, upon acceptance of title, become parts of the national forest within whose exterior boundaries they are located.