Section 18. If jurors are to be drawn in a city, the mayor and city clerk shall meet with the aldermen at its regular place of meeting. The ballots in the jury box shall be shaken and mixed and one of the aldermen, designated by the mayor, shall, without seeing the names written thereon, openly draw a number of ballots equal to the number of jurors required. He shall announce clearly and distinctly the names of the jurors so drawn, and shall then hand the ballots drawn by him to the mayor, who shall examine and verify them. The mayor shall then hand such ballots to the city clerk, who shall announce clearly and distinctly the names upon the ballots and return the same to the jury box, after making the endorsements thereon required by law, and the names so drawn shall be recorded as part of the proceedings and shall be published if and when the proceedings are published officially. In the absence of the mayor, the chairman or president of the board of aldermen shall perform the duties required of the mayor by this section.