If any other school district or districts in the Town of Barton shall at any time, by their vote at a meeting duly warned for that purpose, signify their desire to become united with the Barton Academy and Graded School District, and if the Barton Academy and Graded School District, at a meeting duly warned for that purpose, shall vote to agree to such union, then the additional district, or districts, shall become and form a part of the Barton Academy and Graded School District; and such union of the districts may be made upon such terms in regard to the school property of each as may be mutually agreed upon by the districts. And by vote of the Town of Barton and consent by vote of the Academy and Graded School District, at any annual or special meeting of the Town and the district duly warned for that purpose, territory from adjoining districts may be added to the Graded School District by vote of the Town as aforesaid, and by the consent of two-thirds of the voters in the Graded School District present at any meeting legally warned for that purpose.