In counties of 300,000 inhabitants or less, where the county seat is entirely located within the corporate limits of a city or village, the boundaries of such county seat shall be the same as the boundaries of such city or village, as the same are now or hereafter constituted. However, the county board may by resolution adopted by a majority thereof extend the boundaries of such county seat to add to the territorial area of such county seat such unincorporated land in the county contiguous to the county seat as the resolution may describe; but in no event may such extension include any land situated more than one mile from the county seat as then existing.