One of the appointive members shall be appointed for a term of two years, one for a term of four years and one for a term of six years. The successor to each of the appointive members shall be appointed for a term of six years, and in case of a vacancy, the Governor is authorized to appoint a successor for the remainder of the unexpired term. The ex officio members shall serve so long as they hold their respective offices or positions which entitle them to ex officio membership on said board of directors. (1953, c. 1129, s. 3.)