The contract as so modified shall provide a method of ascertaining the amount to be paid for such equipment and for the investment of the contractor in the construction of such road upon a termination by the city of such contract, and for the equipment of such existing railroad at the end of the full term of the contract. Such contract as so modified may provide for determining from time to time, in default of agreement, by arbitration or by the court, a valuation of such investment of the contractor in the construction of such road and of the equipment, or any part or portion of either thereof, for any purpose under such contract. The contract also may provide for assuring that in case a new contract for equipment, and for maintenance and operation of such existing railroad, or proposed railroad, is made after such termination, pursuant to notice, or after the expiration of the full term of such contract, that the title to and possession of the equipment so taken and the right to the possession of the railroad so constructed may be transferred directly to the new contractor upon his paying the amount so required.
N.Y. Rapid Trans. Law § 45