Special meetings of the board shall be held only when requested by at least one-third of the members of the board, or when requested by the chairman of the board, which request shall be in writing, addressed to the clerk of the board, and specifying the time and place of such meeting, upon reception of which the clerk shall immediately transmit notice, in writing, of such meeting, to each of the members of the board. The clerk shall also cause notice of such meeting to be published in some newspaper printed in the county, if any there be. In case a vacancy arises in the office of clerk, because of death or other reason, then the request shall be addressed to the circuit clerk who shall perform the duties of the clerk pursuant to this Section.