The term of office of the members of the board is four years, and they shall hold office until the appointment and qualification of their successors. The terms of the members of the board in office when this section takes effect shall expire as follows:
Three members January 15, 1960.
Two members January 15, 1961.
Three members January 15, 1962.
Two members January 15, 1963.
The terms shall expire in the same relative order as to each member as the term for which he holds office before this section takes effect.