How do this cartoon and letter explain why northerners lost interest in reconstruction

Well, there's no cartoon or letter, but many Northerners lost interest in reconstruction because their attempts to protect former slaves failed, and a lot of slaves ended up as sharecroppers, which wasn't really any different to slavery.  Basically, the slaves were still uneducated, poor, in the South, and didn't have any more rights than before reconstruction because of black codes (Jim Crow laws) and sharecropping.

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Answer for apex - the reformation