Whenever it is desired to form a new county or counties out of one of the then existing counties, a petition praying for the formation of such new county or counties, stating and describing the territory proposed to be taken for such new county or counties, together with the name of such proposed new county or counties, signed by a majority of the legal voters residing in the territory to be taken from such county, shall be presented to the county board of such county to be affected by such division. If it appears that such new county or counties can be constitutionally formed, and each shall contain not less than four hundred and fifty square miles, it shall be the duty of such county board to make an order providing for the submission of the question of the erection of such new county or counties to a vote of the people of the county to be affected, at the next succeeding general election. The notice shall be given, the votes canvassed, and the returns made up as in the case of election of county officers. The form of the ballot to be used in the determination of such question shall be as follows: For new county, and Against new county.