If, at the time of the filing of the petition, or at any time subsequent thereto, it shall be made to appear to the court, or the judge thereof in vacation, by affidavit or otherwise, that the owner or owners of the whole or any share of any tract or tracts of land affected or within the bounds of the proposed drainage district, whose names are unknown, and cannot, after due diligence, be ascertained by the petitioners, the court or the judge thereof, shall order a notice in the nature of a summons to be given to all such persons by publication of the petition, or of the substance thereof, and describing generally the tract or tracts of land as to which the owner or owners are unknown, with the order of the court or the judge thereof thereon, in some newspaper published in the county wherein the land is located or in any city within the geographical limits of the county. If no newspaper shall be published in the county or city, then in some newspaper designated in the order of the court or the judge thereof, and a copy of such publication shall also be posted in at least three conspicuous places within the boundaries of the proposed district, and at the courthouse door of the county. Such publication in a newspaper shall be made once a week for four successive weeks.