If any protest against such proposed work or proposed district or any other protest be sustained by said Director, he shall not thereby be prevented from commencing proceedings anew hereunder which shall embrace the same work and/or the same district or any part or parts of either or both thereof; and new proceedings may be had the same as if all such prior proceedings, no matter how many times instituted, had never been commenced.
If no protests be made against such proposed district, or if all protests made against the same be overruled by said Director, said Director shall accompany his recommendation to the Supervisors that the proposed work be ordered, with a diagram on which shall be delineated each separate parcel of land with the limits of such assessment district, the approximate dimensions of each such parcel, and its relative location to the work proposed to be done. The correctness of such diagram shall be certified by the City Engineer. Instead of said diagram said Director may accompany his said recommendation to the Supervisors with a description of such proposed district.