Where in this or the Special Act any Question of Compensation, Expenses, Charges, or Damages, or other Matter, is referred to the Determination of any One Justice or more, it shall be lawful for any Justice, upon the Application of either Party, to summon the other Party to appear before One Justice, or before Two Justices, as the Case may require, 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 One Justice, 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 Cost of every such Inquiry shall be in the Discretion of such Justices, and they shall determine the Amount thereof.