Whenever it shall become necessary to construct, widen, or protect any highway under the provisions hereof, the road protection commission shall make publication for thirty days in some newspaper published in the county wherein such improvements are made, setting forth the commencement and termination, with a general outline of the nature and extent thereof. When any owner of land or other person shall claim compensation for land taken for such purpose, or for damage sustained by the construction, widening, improvement, or protection of such road or highway, he shall petition the board of supervisors in writing within thirty days after the expiration of the time provided for such publication, setting forth the nature and character of the damages claimed. Thereupon the board shall, on five days’ notice to petitioner, go on the premises and assess the damages sustained by him. The finding of the board shall be in writing, signed by the members agreeing to it, and must be entered on the minutes at the next meeting; but if the damages sustained and claimed be less than the cost of assessing, the board may allow the same without inquiry.