If an appeal has been taken from a judgment of a trial court or before the taking of an appeal if the time therefor has not expired, the trial court in which the judgment was rendered may allow the taking of the depositions of witnesses to perpetuate their testimony for use in the event of further proceedings in the trial court. In such case the party who desires to perpetuate the testimony may make a motion in the trial court for leave to take the depositions, upon the same notice and service thereof as if the action was pending in the trial court. The motion shall show (a) the names and addresses of the persons to be examined and the substance of the testimony which he expects to elicit from each; (b) the reasons for perpetuating their testimony. If the court finds that the perpetuation of the testimony is proper to avoid a failure or delay of justice, it may make an order allowing the depositions to be taken and may make orders of the character provided for by Rules 34 and 35, and thereupon the depositions may be taken and used in the same manner and under the same conditions as are prescribed in these rules for depositions taken in actions pending in the trial court.