Whenever the plaintiff and defendant in a writ of error pending in this court, or the appellant and appellee in an appeal, shall in vacation, by their attorneys of record, sign and file with the clerk an agreement in writing, directing the case to be dismissed, and specifying the terms on which it is to be dismissed as to costs, and shall pay to the clerk any fees that may be due to him, it shall be the duty of the clerk to enter the case dismissed, and to give to either party requesting it a copy of the agreement filed; but no mandate or other process shall issue without an order of the court.