Section 18. There shall be a state board of retirement serving in the department for the purpose of administering the state employees' retirement system established under the provisions of chapter thirty-two. Such board shall consist of five members as follows: the state treasurer who shall be a member ex officio and who shall serve as chairman, a second member who shall be appointed by the treasurer, a third and fourth member who shall be elected by the members in or retired from service of such system from among their numbers in such manner and for such term, not exceeding three years, as the commission shall determine, and a fifth member who shall not be an employee, a retiree, or official of the commonwealth and shall be chosen by the other four for a term of three years. Future elections of the third and fourth member shall be held under the supervision of such retirement board and the term of the third and fourth member shall be so arranged as not to expire in the year of expiration of the term of the third and fourth member. If a fifth member is not chosen by the other four members within thirty days after the expiration of the term of the fifth member, the governor shall appoint a fifth member for a term of three years. Each member of such retirement board shall continue to hold office until the expiration of his term and until the qualification of his successor. Upon the expiration of the term of office of any elected, chosen or appointed member or in case of a vacancy in any of said offices, his successor shall be elected, chosen or appointed as aforesaid for a three-year term or for the unexpired portion thereof, as the case may be, except that in no event shall the term of the third and fourth member expire in the same year as the term of the fifth member.