In case of the division or alteration of a county as aforesaid, if the supervisors cannot agree upon a settlement, as provided in this chapter, the supervisors of either of the counties interested may apply to the circuit court for any adjoining county, for the appointment of 5 judicious men residing within a county not interested, to be commissioners for the purpose of settling and determining the matters aforesaid between such counties; and upon such application, such circuit court shall appoint such commissioners for the purpose aforesaid.