The secretary must cause a notice of the filing of such petition to be published three (3) weeks in the manner of notices of special elections. The notice shall state the filing of such petition, and the names of the petitioners, a description of the lands mentioned in the said petition, and it shall notify all persons interested in or that may be affected by such change of boundaries of the district, to appear at the office of said board, at a time named in said notice, and show cause in writing, if any they have, why the lands mentioned should not be annexed to said district. The petitioners shall advance to the secretary sufficient money to pay the estimated costs of all proceedings under this chapter.