In case of a vacancy in the office of United States Senator from death, resignation or otherwise, the Governor may fill the place by appointment which shall be for the period of time intervening between the date of such appointment and January third following the next succeeding general election. But in the event any such vacancy shall occur less than one hundred days prior to any general election, the appointment shall be for the period of time intervening between the date of such appointment and January third following the second general election next succeeding. The Governor shall within five days after any such appointment order an election to be held in connection with and at the time of the general election immediately preceding the expiration date of such appointment if at the expiration of such appointment an unexpired term shall remain.