At any such special session, the Supreme Court, by consent of the parties or their counsel, may hear and determine any cause then ready for a hearing, or, without such consent, upon twenty days’ previous notice in writing, given by a party desiring a hearing to the adverse party, of his intention to insist on the same. The Court, at such special session, shall, after notice to the parties or their counsel from the clerk of the Court, hear any cause which, in its opinion, the public interest requires to be heard and determined. Any judgment, decree or order entered or made at such special session shall have the same effect and may be reviewed and reheard in like manner and subject to the same rules as a judgment, decree or order entered or made at a regular session.