Whenever there is reason to believe that the population of any city of the class named in section 1 hereof has been reduced to less than 350 bona fide inhabitants, any member of the board of supervisors of the county in which such city is located may petition the circuit court jurisdiction for the appointment of a suitable person to take a census of such city. A copy of such petition shall be served upon the mayor of such city at least 5 days before such petition shall come on to be heard by the circuit judge of such circuit, together with a copy of an order to show cause why such census should not be taken, which in all such cases shall be issued by the judge having jurisdiction thereof, and returnable not later than 15 days from the date of the issuance thereof. Upon the return of such order to show cause, any resident of such city or county shall be entitled to be heard either in support of or as opposed to the taking of such census. If satisfied on such hearing that there is good reason to believe that the population of such city is less than 350 bona fide inhabitants, it shall be the duty of the circuit judge to direct the county clerk of such county to appoint a resident elector of the county, not a resident of such city, to enumerate the inhabitants of such city. Such enumeration shall be taken within 30 days after such appointment has been made and accepted.