When any owner of land or other person shall claim compensation for land taken for a public road, or for damages sustained by the construction of a road, he shall petition the board of supervisors, in writing, at the next meeting after the laying out of the road or at the meeting when the report thereof shall be returned, setting forth the nature and character of the damages claimed, whereupon the board shall, on five days’ notice to the petitioner, go upon 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.