If the other party shall not, by notice served upon an officer of the first moving party within twenty days of the service of such first notice, appoint its arbitrator to arbitrate the dispute or differences specified, then the first moving party shall have the right without further notice to appoint a second arbitrator, who shall be a disinterested person with precisely the same force and effect as if said second arbitrator has been appointed by the other party. In the event that the two arbitrators fail to appoint a third arbitrator within twenty days of the appointment of the second arbitrator, either arbitrator may apply to a Judge of any court of maritime jurisdiction in the city above-mentioned for the appointment of a third arbitrator,