At the municipal election held in such city in the year one thousand nine hundred and twenty-seven, and in every fourth year thereafter, city councilmen shall be elected in the various State senatorial districts in such city. The number of councilmen to be elected in the various State senatorial districts in such cities shall be twenty-two. They shall be elected in the various State senatorial districts of such cities in proportion to the population thereof as determined by the last United States census and each succeeding United States census. The councilmanic ratio for the election of councilman as aforesaid shall be ascertained by dividing the whole population of all the State senatorial districts of such cities by the number twenty-two. One councilman shall be elected for each such ratio, and an additional councilman shall be elected for any fractional portion of such ratio in excess of fifty per cent thereof. Every State senatorial district in such cities shall be entitled to elect as many city councilmen as it has councilmanic ratios of population as aforesaid, and an additional councilman for any fractional portion of such ratio in excess of fifty per cent thereof. The number of councilmen to be elected for each such district shall be determined and announced by the county commissioners on August first of one thousand nine hundred and twenty-seven, and of every fourth year thereafter, on the basis of population as aforesaid. Councilmen shall be nominated and elected according to law, and those receiving the highest votes shall be declared elected to the number to which each such district is entitled. Councilmen shall serve for the period of four years from the first Monday in January following their election. In cases where a vacancy exists at the time this amendment becomes effective, and hereafter whenever a vacancy shall exist or happen in the office of city councilman, the president of the council shall issue a writ of election to the proper county board of elections for a special election to fill the said vacancy, which election shall be held on a date named in the writ which shall be not less than thirty (30) days after the issuance of said writ. The president of the council may fix in such writ of election the date of the next ensuing primary, municipal or general election as the date for holding any such special election.