Within 30 days after a vacancy occurs in the office of president of the senate or speaker of the house of representatives, the senate or house of representatives, as the case may be, shall select a successor from among its members. If the senate or house is not in session when such a vacancy occurs, the branch concerned shall assemble at the state house not sooner than 7 days nor later than 30 days after the vacancy occurs on a date determined by the second ranking officer of the branch concerned. The clerk of that branch shall notify the members of the branch of the vacancy and the date on which selection of a successor is to take place.