Mr. Kaufman, a member of the House, from Texas, died very suddenly on the thirty-first of January. His funeral took place on the Monday following, February 3d. Mr. Kaufman was born in Pennsylvania in 1813, graduated in Princeton College in 1833, practiced law in Louisiana, and removed to Texas in 1835. The subject of most general interest in the political world is the election of United States Senator, in a number of the States, for the term commencing on the 4th of March. Several elections have taken place, and others have not been accomplished in spite of repeated ballots. In New-York, the Constitution provides for an election on the first Wednesday of February. On that day the Whig candidate, ex-Governor Hamilton Fish, received a majority of 37 in the House: the Senate, after two ineffectual ballots, adjourned. A special law will therefore be required to elect a senator. In Massachusetts, the Democratic candidate, Robert Rantoul, Jr., was elected to fill the vacancy occasioned by Mr. Webster's acceptance of a place in the Cabinet. All attempts to elect a senator for the ensuing term have failed up to this period. Mr. Sumner, the Free Soil candidate, lacked but two votes of an election on the twelfth ballot, but afterwards lost. It was finally postponed to the twenty-seventh of February. In the Ohio Legislature, ten successive ballots were cast without arriving at an election, after which the subject was indefinitely postponed. In Rhode Island, General Charles T. James, the Democratic candidate, was elected; in Florida, Stephen R. Mallory, in place of Hon. D. L. Yulee, both Democrats; and in Delaware, James A. Bayard, Democrat, in the place of Mr. Wales, the present Whig senator. Hon. Henry Dodge was reelected by the Legislature of Wisconsin, by a majority of one, on the fifth vote. In Pennsylvania, Hon. Richard Brodhead was elected in place of Mr. Sturgeon, both members of the Democratic party. Henry S. Geyer, Whig, has been elected by the State of Missouri, as United States Senator, in place of Col. Thomas H. Benton, who is superseded after an uninterrupted service of thirty years.