Why was it important for the Confederacy top defend Richmond, Virginia?

It was important for the Confederacy to defend Richmond, Virginia because Richmond was the seat of the Confederate government (its capital). The loss of Richmond would be the Union equivalent of losing Washington D.C. to the Confederates. It was widely considered that the capture of the other side's capital would signal the end of the Civil War.

separate but equal was a legal doctrine in united states constitutional law according to which racial segregation did not violate the fourteenth amendment to the united states constitution, which guaranteed "equal protection" under the law to all people. under the doctrine, as long as the facilities provided to each race were equal, state and local governments could require that services, facilities, public accommodations, housing, medical care, education, employment, and transportation be segregated by race, which was already the case throughout the states of the former confederacy. the phrase was derived from a louisiana law of 1890, although the law actually used the phrase "equal but separate

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i would say that the politicial parties from state to state varies.