(1) The submission shall be by written agreement, general or special, specifying what demands are to be submitted, the names of the arbitrators or the manner of their selection, but not necessarily that of the umpire, and the court by which the judgment on their award is to be rendered, and if such written agreement requires one (1) of the parties to name an arbitrator and such party fails to do so, the court by which the judgment on the award is to be rendered shall on such failure so to name an arbitrator, upon the petition of the opposite party, appoint such arbitrator.
(2) The agreement may specify that the submission be entered of record in any court of law or equity, or, in cases within its jurisdiction, before a judge of the court of general sessions.