The term of office of each appointive member, except for initial appointments as herein specified, shall be six (6) years, beginning July 1 of the year of appointment or until his successor has been appointed and qualified. The present State Library Board shall become members of the Board of the Department and shall continue in office until their respective terms expire. The Governor shall appoint one member on or before July 1 of each year; provided that he shall make the first appointments for the following terms in the years indicated: One member for a term of one (1) year, and one member for a term of two (2) years in 1967; one member for a term of two (2) years, one member for a term of three (3) years and the member-at-large for a term of three (3) years in 1968; one member for a term of three (3) years, and one member for a term of four (4) years in 1969. After the initial appointments, terms shall be for six (6) years. Any vacancy on the Board shall be filled for the remainder of the term only and by the method of the original appointment. No person who has served a full six-year term shall be appointed to succeed himself. Members may be removed only for cause.