Should the second election, as provided for in s. 138.07, be necessary to select the place as county seat of any county in this state, the clerk of the circuit court shall prepare the ballot as aforesaid, dropping the names or name of all places voted for in the first election except the two places receiving the highest vote in the same, and no other places shall be voted for nor shall the vote of any other place or places be counted or considered by the county commissioners in canvassing the result of such election.