Members of Council shall be elected at the regular municipal election in the year 1961 and every second year thereafter. Their terms shall be for a period of two (2) years and shall commence and they shall assume office on the first day of January, following their election, and shall serve out their terms or until their successors are elected and qualified, whichever occurs last. If any members of Council elected at large shall fail to qualify, then an equal number of the councilmen elected at large who were not reelected and whose terms are expiring shall continue to hold office until the expiration of the term of the councilman who failed to qualify or until a vacancy occurs. The councilmen-at-large to hold over shall be selected on the basis of the number of votes cast for each at the election at which they were most recently chosen, selecting first such councilman for whom the largest number of votes was so cast and continuing therefrom in decreasing order of such number of votes. Councilmen-at-large who were appointed to fill vacancies shall be selected in the order in which they were so appointed but shall rank behind Councilmen-at-large who were elected to such position.