The County Court shall, when petitioned under the provisions of the preceding section, appoint commissioners as in case of an application for laying out a highway. Such commissioners shall notify the petitioners and one of the trustees of said Village of the time and place of hearing, and shall examine the premises and the circumstances of the case, and make a new appraisal; and the Court, on their report, may set aside the former assessment of damages and render judgment for such sum as appears just; and, if the sum is greater than the sum before allowed, the Court may tax cost for the petitioner; otherwise the Village shall recover its cost. But if no proceedings for reassessment are instituted, as approved by the last preceding section, within the time therein limited, then the award of damages or assessment for benefit shall be established as valid, and shall be collectible.