Whenever the owners of the greater part of the lands or buildings abutting upon any street, lane, or alley, or part thereof in said City, shall present their petition in writing to the City Council, praying that such street, land, or alley, or part thereof as specified be graded, paved, or macadamized, curbed and guttered, and that a sidewalk or the sidewalks thereof be constructed or repaired, or paved or laid with flagging or such other material as may be ordered by the City Council, or that either one or more of such improvements be made, the City Council may order and direct that such improvements be made.