On October 1, 1937, the Governor, by and with the advice and consent of the Senate, shall appoint the members of the board of review for terms of six years, except that the terms of the members first taking office shall be two, four, and six years, respectively, as designated by the Governor at the time of their appointment. Vacancies shall be filled by the Governor for the unexpired term. The Governor shall designate one member as chairman of the board.