If before the matters so referred shall be determined any arbiter appointed by either party die, or become incapable, the party by whom such arbiter was appointed may nominate and appoint in writing some other person to act in his place, and if for the space of seven days after notice in writing from the other party for that purpose he fail to do so, the remaining or other arbiter may proceed ex parte; and every arbiter so to be substituted as aforesaid shall have the same powers and authorities as were vested in the former arbiter at the time of such his death or disability as aforesaid.