The auditor of the old county shall give the auditor of the new county reasonable notice to meet him or her on a certain day at the county seat of the old county, or at some other convenient place, to settle upon and fix the amount which the new county shall pay. In doing so, they shall not charge either county with any share of debts arising from the erection of public buildings, or out of the construction of roads or bridges which shall be and remain, after the division, within the limits of the other county, and of the other debts they shall apportion to each county such a share of the indebtedness as may be just and equitable, taking into consideration the population of such portion of territory so forming a part of the said counties while so united, and also the relative advantages, derived from the old county organization.