Whenever it shall be made to appear to the judge of the district court of the county wherein the lands embraced within the limits of any townsite are situate, the title to which was and is vested in the probate judge of such county, by a verified petition that any lots, blocks, parts or parcels thereof have not been sold, disposed of and conveyed in the manner prescribed by law, that such lots, blocks, parts or parcels or any of them can be sold, that no board of trustees of such townsite was ever elected in the manner prescribed by law, or, if at any time a board was elected, that such board of trustees was not elected or actually acted as such board for more than two years next preceding the date of the verification of the petition, and that the petitioner or petitioners will deposit in court such sum of money as the court may order to cover all costs of procedure hereinafter mentioned in this chapter in case the lands are not sold, then the judge of such district court shall appoint, by order and decree, a board of appraisers to consist of three residents of the county wherein such townsite is situated, who shall have no interest in such unsold, undisposed of and unconveyed lots, blocks, parts and parcels of land. Each of said appraisers shall take an oath to faithfully discharge his duties as such appraiser and shall file such oath in the office of the clerk of said district court before commencing his duties as such appraiser within ten days after his appointment. In case such appraisers or any of them should fail or neglect to file his or their oath or oaths with the said clerk within the time above limited, then the judge of such district court shall appoint another or other appraisers in place of the appraiser or appraisers so failing to file his or their oath or oaths.