Each ordinance enacted by the Council shall be published at leastonce, within fifteen days after its enactment, either separately or as a part of the published proceedings of the Council. All ordinances and amendments thereof shall be recorded by the Clerk in a book to be called "The Ordinance Book" and it shall be the duty of the Mayor and Clerk to authenticate such records by their official signatures thereon. The Clerk shall enter in such book, after the publication of each ordinance, the date and method of publication, which entry shall be prima facie evidence of such publication.