A motion to postpone a trial on the ground of the absence of evidence shall only be made upon affidavit showing the materiality of the evidence expected to be obtained, and a statement of facts showing that due diligence has been used to procure it, and also the name and residence of the witness or witnesses. The court may also require the moving party to state upon affidavit the evidence which he expects to obtain, and if the adverse party thereupon admits that such evidence would be given, and that it be considered as actually given on the trial, or offered and overruled as improper, the trial shall not be postponed. The court, when it allows the motion, may impose such conditions or terms upon the moving party as may be just.