The Mayor is hereby authorized to select certain streets and alleys where sled coasting may be permitted subject to supervision and inspection as provided in this article, such selection to be made from time to time after careful study and consideration with the cooperation of the Police and Fire Departments and with a view to the safety and general welfare of the citizens affected thereby. In making such selections, the Mayor shall have the discretion to designate what parts of such streets or alleys, or both, may be used for coasting, and may rescind and change such selections from time to time as he deems advisable.