The secretary shall cause a notice of the filing of the petition for exclusion of lands to be published for at least once a week for two weeks in some newspaper published in the county where the office of the board is situated. If any portion of the territory asked to be excluded lies within another county or counties, the notice shall be so published in a newspaper published within each of such counties; or if no newspaper is published therein, the notice shall be posted for the same time in at least three public places in the district. In case of the posting of such notices, one of such notices shall be so posted on the lands proposed to be excluded.