The Treasurer, Clerk, Constable, Tax Collector, and Superintendent of Streets and Waterworks shall annually give bonds to the City to the satisfaction of the City Council for the faithful discharge of their respective duties, and any other City officer may be required by the City Council to give similar bonds. In case any officer neglects to give bonds as above specified, after 10 days' notice from the City Council that he or she is required to do so, his or her office shall thereupon become vacant and the vacancy shall be filled as hereinbefore provided.