A book, well bound and indexed, to be denominated “The Docket,” shall be kept in the office of the Mayor, in which shall be noted each case brought or tried by him, together with the proceedings therein, including a statement of complaint, the summons, the return, the fact of appearance, the defense, the hearing, the judgment, the costs and, in case the judgment be one of conviction, the action taken to enforce the same; the record of such case shall be signed by the Mayor or other persons acting in his stead, and the original papers thereof, if no appeal be taken, shall be kept together and preserved in his office.