Both Uses

conscience
in
We Shall Overcome
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And I don't make that request lightly, for, from the window where I sit, with the problems of our country, I recognize that from outside this chamber is the outraged conscience of a nation, the grave concern of many nations and the harsh judgment of history on our acts.†

conscience = feeling or appraisal of having personally behaved in a morally right or wrong manner
His actions and protests, his courage to risk safety, and even to risk his life, have awakened the conscience of this nation.†
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Definitions:

(1) (conscience)
feeling or judgment of morally right or wrong personal behavior
(2) (meaning too rare to warrant focus)