The viewers shall make report of their proceedings to the next term of said court, and shall, in such report, assess the damages on behalf of the person entitled thereto, if any, in their opinion, will ensue from such extension. The report shall also be accompanied with a plot or draft of the drain or drains by them laid out, specifying whether the same shall be surface or under drains. The expense of the said view shall be paid by the persons applying for the same.