Upon the filing of a petition of the kind described in this chapter, the clerk of the district court with whom such petition is filed shall issue a notice under the seal of the said district court fixing the time and place for the hearing upon such petition. Such notice shall be published in the official newspaper of the county for two successive weeks, the last publication to be at least ten days before the time set for hearing. Proof of the publication required by this section shall be filed in the office of the clerk of the district court on or before the date set for the hearing on such petition.