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and if upon such trial the House shall concur with the Senate in electing on their part same person as was elected on the part of the Senate, the person thus chosen shall be considered as duly elected a Senator, to supply the vacancy, from this State in the Congress of the United States. But if the House upon such trial shall nonconcur with the Senate, and on their part elect a person other than the one chosen by the Senate, the House shall notify the Senate there of by message, and the like proceedings shall be continued by the respective branches until an election be effected, or further attempts be considered unavailing.