Upon receiving the petition, signed by a majority of the members of the board of trustees, the supervisors shall fix a time for hearing the petition, which shall be not more than 30 days thereafter, and shall cause a notice, stating the time and place of hearing, and the object of the petition in general terms, to be published for 10 days prior to the day of hearing, in some newspaper published in the library district, if there is one, and if there is no newspaper published in the library district, then in a newspaper published at the county seat of the county in which the library district or part thereof is situated.