§ 39. Filling vacancies in office of officer appointed by governor and senate. A vacancy which shall occur during the session of the senate, in the office of an officer appointed by the governor by and with the advice and consent of the senate, shall be filled in the same manner as an original appointment. Such a vacancy occurring or existing while the senate is not in session, including offices in which officers are holding over pursuant to the provisions of section five of this chapter or any other law, and offices vacant during the session of the senate, shall be filled by the governor for a term which shall expire upon the appointment and qualification of a successor but in any event such term shall expire at the end of twenty days from the commencement of the next meeting of the senate.