No person shall be eligible to the office of member of the Legislature unless on the date of the general election at which he is elected, or on the date of his appointment he is a registered voter, has attained the age of twenty-one years and has resided within the district from which he is elected for the term of one year next before his election, unless he shall have been absent on the public business of the United States or of this State. And no person elected as aforesaid shall hold his office after he shall have removed from such district.