When, upon any application, petition or matter presented to any judge of the Superior Court for a hearing by him as a judge, notice to the adverse party of the hearing thereon is required, either by statute or in the discretion of the judge, the judge to whom such application, petition or matter has been presented may, in the order of notice issued by him, designate any other judge of the Superior Court to hear the same, the consent thereto of such other judge having first been obtained, and when any application, petition or matter is pending before any judge of the Superior Court, such application, petition or matter may be by him transferred to any other judge of the Superior Court, upon like consent first obtained, and in either case such other judge shall thereupon proceed with such application, petition or matter with the same authority as though the same had originally been presented to him or had theretofore been pending before him.