Section 21. If they fail so to agree, the directors may petition the department to fix the route in said city or town; and the department, after notice to said board of aldermen or selectmen, shall hear the parties, and fix the route in such city or town, and make a certificate setting forth the route as fixed by it, which shall be certified by its clerk to the directors. The costs of the petition shall be paid by the directors. All variations from the route first proposed shall be made upon the map.