The Secretary of the Interior is hereby authorized, under such rules and regulations as he may prescribe, to allow any person who prior to May 27, 1924, filed an application for a permit in accordance with the provisions of the Act of February 25, 1920, to prospect for oil and gas upon lands within an Indian reservation or withdrawal created by Executive order who shall show to the satisfaction of the Secretary of the Interior that he, or the party with whom he has contracted, has done prior to January 1, 1926, any or all of the following things, to wit, expended money or labor in geologically surveying the lands covered by such application, has built a road for the benefit of such lands, or has drilled or contributed toward the drilling of the geologic structure upon which such lands are located, or who in good faith has either filed a motion for reinstatement or rehearing; or performed any other act which in the judgment of the Secretary of the Interior entitles him to equitable relief, to prospect for a period of two years from March 3, 1927, or for such further time as the Secretary of the Interior may deem reasonable or necessary for the full exploration of the land described in his application under the terms and conditions therein set out, and a substantial contribution toward the drilling of the geologic structure thereon by such applicant for a permit thereon may be considered as prospecting under the provisions hereof; and upon establishing to the satisfaction of the Secretary of the Interior that valuable deposits of oil and gas have been discovered within the limits of the land embraced in any such application, he shall be entitled to a lease for one-fourth of the land embraced in the application: Provided, That the applicant shall be granted a lease for as much as one hundred and sixty acres of said lands if there be that number of acres within the application. The area to be selected by the applicant shall be in compact form and, if surveyed, to be described by the legal subdivisions of the public land surveyed; if unsurveyed, to be surveyed by the Government at the expense of the applicant for lease in accordance with rules and regulations to be prescribed by the Secretary of the Interior, and the lands leased shall be conformed to and taken in accordance with the legal subdivisions of such surveys; deposit made to cover expense of surveys shall be deemed appropriated for that purpose, and any excess deposits may be repaid to the person or persons making such deposit or their legal representatives. Such leases shall be for a term of twenty years upon a royalty of 5 per centum in amount or value of the production and the annual payment in advance of a rental of $1 per acre, the rental paid for any one year to be credited against the royalties as they may accrue for that year, with the preferential right in the lessee to renew the same for successive periods of ten years upon such reasonable terms and conditions as may be prescribed by the Secretary of the Interior. The applicant shall also be entitled to a preference right to a lease for the remainder of the land in his application at a royalty of not less than 12½ per centum in amount or value of the production, the royalty to be determined by competitive bidding or fixed by such other methods as the Secretary of the Interior may by regulations prescribe: Provided further, That the Secretary of the Interior shall have the right to reject any or all bids.