At the time and place fixed in the notice as provided in section 31-207, the county board may again consider the question of public utility, if requested so to do by any interested party, and may also consider the advisability of such improvements, although it be found to be of public utility, and if no reconsideration is had on the question of public utility, and upon such hearing the construction of such improvements is deemed advisable, the board shall proceed to appoint three disinterested freeholders, residents of the county, who shall act as appraisers for that particular case.