The City Council is authorized, to establish, construct, and maintain public sewers in said City; and it may assess the owners of land or buildings adjoining or abutting said streets or any portion thereof, in which such sewers may be established, so much of the expense of constructing such sewers as it shall adjudge such land or buildings to be benefited thereby; but in no case shall the expense of construction of any such sewer be assessed against the abutting owner on either side of any such street or any portion thereof in excess of one-fourth of such expense and the City shall pay one-half of such expense; provided that all sewer assessments heretofore made shall remain in full force and effect until paid or abated.