The county court of each of the counties out of which the new county is proposed to be formed, at its first session after the notice mentioned in the next preceding section has been published, as required by said section, shall order a survey of the whole county, and of that portion thereof proposed to be included in the new county, to be made by the surveyor of such county, if there be one, and if not by some other competent surveyor, in order to ascertain the number of square miles in the county, as well as in that portion thereof proposed to be included in such new county. Such court shall also appoint some one or more competent person or persons to take a census of the population of such county, and of that part thereof proposed to be included in such new county, in order to ascertain whether or not there will remain in such county a population of six thousand after the creation of such new county. It shall be the duty of the surveyor so directed or appointed to make such survey, and of the person or persons so appointed to take the census, as soon as their fees are paid or secured to be paid in a manner satisfactory to them to proceed in the shortest time practicable to make such survey and take such census and make report thereof to the county court by which they were appointed; and the surveyor shall return and file with his report two fair plats and certificates of the survey made by him showing the metes and bounds of the county and the number of square miles of territory contained therein, and the number of square miles contained within that portion thereof proposed to be included in the new county, and the metes and bounds thereof. The return of such survey and census shall be noted in the records of the court, and such reports shall be filed and preserved by the clerk of such court in his office, and a notice in writing that such return of the survey and census has been made shall be sent to the county court of the other county out of which such new county is proposed to be formed.