The directors shall be appointed by the mayor, and the county court or other tribunal acting in lieu thereof, of such city and county having such joint workhouse, with the approval of the council of such city and county commissioners, and shall hold their office for five years, except that at the first appointment one director shall be appointed for one year, one for two years, and one for three years, one for four years, and one for five years, and thereafter one shall be appointed annually, but all appointments shall be made in conformity with section two.