The Treasurer, Secretary of the State and Comptroller shall, within thirty days after a vacancy election for a senator in Congress or representative in Congress, subject to the provisions of § 9-323, publicly count the votes returned, and declare what person is elected, and the Secretary of the State shall forthwith notify him by mail of his election. The Secretary of the State shall enter the returns in tabular form in books kept by him for that purpose and present a copy of the same, with the name of, and the total number of votes received by, each of the candidates for said office, to the Governor within ten days thereafter.