Where in this or the special Act, or any Act incorporated therewith, any Question of Damages, Charges, Expences, or other Matter is referred to the Determination of any Sheriff or Justices, it shall be lawful for the Sheriff or any Justice, upon the Application of either Party, to order the other Party to appear before such Sheriff if the Order shall be issued by the Sheriff, or before Two Justices if the Order shall have been issued by a Justice, at a Time and Place to be named in such Summons ; and upon the Appearance of such Parties, or in the Absence of any of them upon Proof of due Service of the Summons, it shall be lawful for such Sheriff or such Two Justices, as the Case may be, to hear and determine such Question, and for that Purpose to examine such Parties or any of them, and their Witnesses, on Oath; and the Expences of every such Inquiry shall be in the Discretion of such Sheriff or Justices, and he or they shall determine the Amount thereof.