In any case of the violation of an ordinance of the said City, in which there is a judgment by the Mayor of imprisonment for more than ten days, or for a fine of more than ten dollars, an appeal shall lie, at the instance of the person against whom such judgment is rendered, to the Circuit Court of Mason County. Such appeal shall not be granted by the Mayor unless within ten days from the date of the judgment, such person shall enter into a recognizance, with security deemed sufficient, to appear before the said Court on the first day of the next term thereof, to answer for the offense against the City with which he stands charged, and not thence depart without leave of said Court. The provisions of chapter one hundred and sixty-two of the code of West Virginia, relating to recognizances in criminal cases, shall be applicable to the recognizances contemplated by this section; but any money recovered thereon, or by virtue thereof, shall inure to the said City.