Should a vacancy exist simultaneously from any cause hereinabove provided for in three commissionerships, so as to leave no quorum of the board to fill same, an election to fill the vacancies shall be called by the remaining commissioners, to be held not less than 20 nor more than 30 days from the occurrence of the third vacancy. Notice of the election and of the time of holding the same shall be given by one publication at least 15 days in advance of same in one or more newspapers in the city at the expense of the city. The commissioners chosen at this election shall qualify as speedily as possible thereafter. They shall serve for the unexpired portions of the terms of their predecessors.