Hereafter in cities of the second class, when an ordinance or resolution shall have been duly enacted under the provisions of the act¹ to which this is a supplement, said ordinance or resolution shall be certified by the clerk of council, and shall be recorded in a book provided by the city for that purpose, which book shall be at all times open to public inspection. Within ten days after any ordinance or resolution becomes a law, the same shall be published twice in each of the official newspapers of such city, together with the volume and page of the book in which the same is recorded, and the date of its becoming a law: Provided, Said publication shall not include and of the attesting signatures, except that of the mayor: And further provided, That instead of publishing an ordinance or resolution in full, an abstract thereof or the title thereof, as council may determine with reference, in any case, to its place of record, shall be a sufficient publication thereof.