The board of county commissioners shall meet within the first ten days of June of each year and shall constitute a board of equalization of the assessments made within the county. The chairman of the board shall preside. The county board of equalization shall conduct a continuous day-to-day meeting, not to include Saturdays, Sundays, or legal holidays, until it has completed all duties prescribed by this chapter. The first order of business must be the equalization of assessments of property assessed by city boards of equalization. The second order of business must be the equalization of assessments of property assessed by township boards of equalization. The chairman of each city board of equalization, or the chairman’s appointed representative, and each city assessor must be present at such meeting during the first order of business. The chairman of each township board of equalization, or the chairman’s appointed representative, and each township assessor must be present at such meeting during the second order of business. Each person required by this section to attend the meeting of the county board of equalization must be compensated at a rate not to exceed ten dollars per day for each day actually and necessarily spent in attendance at such meeting plus the same mileage and expenses as are authorized for subdivision employees and officials. Such per diem and expenses must be paid by the city or township in the same manner as other city or township expenses are paid.