The Central Government may, in respect of the institutions of the categories specified in the Sixth Schedule located in a new State or in the State of Andhra Pradesh or Madras, direct that such facilities as may be specified in the direction shall be provided to the Government and the people of one or more adjoining States for such period as may be so specified; and thereupon those facilities shall be provided for the said period upon such terms and conditions as may be agreed upon between the State Governments concerned before the 31st day of March, 1957, or, if no agreement is reached by the said date, as may be fixed by order of the Central Government.