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After Senator Jefferson Davis of Mississippi and other senators representing South Carolina, Alabama, Florida, Georgia, Louisiana, and Mississippi announced their withdrawal, the Senate debated how to define their absence without officially acknowledging the act of secession. In March 1861 the Senate declared those seats vacant. Later, the Senate formally expelled other members who withdrew.
Records of the U.S. Senate, National Archives and Records Administration
Whereas the seats... as members of the Senate have become vacant, therefore resolved that the Secretary be directed to omit their names respectively from the roll