effected in pursuance of an order made otherwise than upon the application of the owners of the bridge, has caused the width between the parapets of the bridge, or the width of the approaches to it, to be increased, any additional expense thereafter incurred in consequence of the increase by the owners of that railway, canal, lock, passage or work in connection with the widening or alteration thereof under the bridge or the approaches to it shall be defrayed by one or more of the highway authorities referred to in paragraph 15 above, and any question whether any such additional expense has been so incurred or as to the amount thereof shall, in default of agreement, be determined by arbitration.