Each county in this state shall constitute one assessment district and shall elect one assessor, whose term of office shall be four years. The assessors now in office shall serve until the expiration of the term for which they were elected, and their successors shall be elected at the general election of one thousand nine hundred thirty-six and every four years thereafter. No person shall be eligible to the office of assessor who is not a resident of the county at the time of his election. The assessor's office, properly equipped at the county seat, shall be kept open throughout the year.