Whenever it shall be made to appear to the Mayor and/or Council that there are good reasons for believing that any dog within the city is mad, he or she may issue a proclamation requiring that all dogs shall, for a period to be defined in the proclamation, wear good, substantial muzzles, securely put on, so as to prevent them from biting or snapping, and any dog at large, during the period defined by the Mayor, without such muzzle, shall be taken by the Animal Warden and impounded.