The Andhra Pradesh and Madras (Alteration of Boundaries) Act, 1959
9. Bye-election to fill the additional seat.-
(1) As soon as may be after the appointed day, a bye-election shall be held to fill the additional seat allotted to the State of Madras in the Council of States by virtue of section 8.
(2) The term of office of the member elected to the Council of States in pursuance of this section shall expire on the 2nd day of April, 1962.