The county court shall hold its first term on the first Monday in the calendar month next succeeding the election and qualification of the county judge and shall hold a term beginning on the first Monday in every alternate month thereafter; provided, that should the time at which any term of any such court is fixed conflict with the time of holding the circuit court for the county then the term of the county court shall begin on the Monday succeeding the time for the final adjournment of the circuit court. The county court shall continue in session at each of its terms until the business before it has been disposed of. It shall be open for the trial of cases, civil and criminal, from the beginning to the end of each of its terms.