All transferred territory is liable for its proportion of the excess indebtedness of the original county above the value of its county buildings and of the balance of funds in its treasury. The share shall be based upon the last assessment, and the value of the buildings, unless agreed upon by the respective county boards, shall be fixed by the sworn appraisal of three disinterested citizens, none of whom shall be a resident or taxpayer in either county, and who shall be appointed by the governor, upon the written application of the board of either county. The appraisal shall be in writing, subscribed and verified by at least two appraisers, and filed in the office of the secretary of state, and shall be final and conclusive. Within five days after the filing of the appraisal, the secretary of state shall transmit to the auditor of each of the counties a certified copy of the appraisal, application, appointment and oath.