What does woodward mean by the phrase the "magical formula of white supremacy"?

The "magical formula of white supremacy" is something that happened after the failed reconstruction by which the conservatives and radicals would reconcile in the South now that there was no strong opposition from the north. That is the way by which the white people in the south would continue to assert the dominance over the black population through oppressive laws even though the African Americans were free people. They whites not only believed they were superior but also the that the belief itself is beneficial to the structure of power.