Give examples of ethos, pathos, and logos in King's "Letter from Birmingham City Jail."

King's "Letter from Birmingham City Jail" has often been used as a model of ethos, pathos, and logos, the three pillars of argument. 

Ethos is credibility or authority. King establishes his authority from the start of the letter, writing, "I have the honor of serving as president of the Southern Christian Leadership Conference, an organization operating in every Southern state, with headquarters in Atlanta, Georgia." He also establishes his authority by comparing himself to no less of a person than the Apostle Paul, and refers to Socrates as a model, showing he is an educated man.

King uses pathos or emotional appeal when he writes: "Injustice anywhere is a threat to justice everywhere. We are caught in an inescapable network of mutuality, tied in a single garment of destiny. Whatever affects one directly affects all indirectly." He appeals to emotions with even more direct examples at the end of the letter:

I guess it is easy for those who have never felt the stinging darts of segregation to say "wait." But when you have seen vicious mobs lynch your mothers and fathers at will and drown your sisters and brothers at whim; when you have seen hate-filled policemen curse, kick, brutalize, and even kill your black brothers and sisters with impunity; when you see the vast majority of your twenty million Negro brothers smothering in an airtight cage of poverty in the midst of an affluent society; when you suddenly find your tongue twisted and your speech stammering as you seek to explain to your six-year-old daughter why she cannot go to the public amusement park that has just been advertised on television, and see tears welling up in her little eyes when she is told that Funtown is closed to colored children, and see the depressing clouds of inferiority begin to form in her little mental sky, and see her begin to distort her little personality by unconsciously developing a bitterness toward white people; when you have to concoct an answer for a five-year-old son asking in agonizing pathos, "Daddy, why do white people treat colored people so mean?"...then you will understand why we find it difficult to wait.

King also relies on logos, or facts, to explain why the civil rights movement has come to Birmingham: "Birmingham is probably the most thoroughly segregated city in the United States. Its ugly record of police brutality is known in every section of this country. Its unjust treatment of Negroes in the courts is a notorious reality. There have been more unsolved bombings of Negro homes and churches in Birmingham than in any other city in this nation. These are the hard, brutal, and unbelievable facts." 

By establishing his credibility, explaining in factual terms why he is in Birmingham, and appealing to people's emotions with examples of what racism has done to black people, he writes a strongly persuasive letter arguing for racial equality now.