The Enforcement Acts of 1870 and 1871
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The Second Force Act, which became law in February 1871, placed administration of national elections under the control of the federal government and empowered federal judges and United States marshals to supervise local polling places. The Third Force Act, dated April 1871, empowered the president to use the armed forces to combat those who conspired to deny equal protection of the laws and to suspend habeas corpus, if necessary, to enforce the act.
https://www.senate.gov/artandhistory/history/common/generic/EnforcementActs.htm