Upon the application of the owners of three-fourths of the privately owned lands in any township covered by public-land surveys, more than 50 per centum of the area of which townships is privately owned, accompanied by a deposit with the Secretary of the Interior, or such officer as he may designate, of the proportionate estimated cost, inclusive of the necessary work, of the resurvey or retracement of all the privately owned lands in said township, the Secretary, or such officer as he may designate, shall be authorized in his discretion to cause to be made a resurvey or retracement of the lines of said township and to set permanent corners and monuments in accordance with the laws and regulations governing surveys and resurveys of public lands. The sum so deposited shall be held by the Secretary of the Interior or such officer as he may designate, and may be expended in payment of the cost of such survey, including field and office work, and any excess over the cost of such survey and the expenses incident thereto shall be repaid pro rata to the persons making said deposits or their legal representatives. The proportionate cost of the field and office work for the resurvey or retracement of any public lands in such township shall be paid from the current appropriation for the survey and resurvey of public lands, in addition to the portion of such appropriation otherwise allowed by law for resurveys and retracements. Similar resurveys and retracements may be made on the application, accompanied by the requisite deposit, of any court of competent jurisdiction, the returns of such resurvey or retracement to be submitted to the court. The Secretary of the Interior is authorized to make all necessary rules and regulations to carry this section into full force and effect.