This section of Common Sense was something Paine added after the rest of the pamphlet made its first appearance. In it, he wants to talk about the speech from the King of England that was published in America the same day his pamphlet came out.
The King's Speech made a lot of threats to the American people, telling them they'd be crushed if they kept rebelling. Paine wants to respond to this speech by telling Americans to remain brave and keep fighting.
Paine adds that at this point in American history, it doesn't really matter what the King of England says or does. America will be a free country and no one needs to listen to that old windbag anymore.
Paine makes sure to reiterate that America will never reach its full potential as an economic and military power as long as it's the colony of someone else, especially a tiny island (England) that's 4,000 miles away.
At the risk of sounding like a broken record, Paine repeats that sooner or later, America will become independent. The longer it waits, though, the bloodier its war for independence will be. At the moment he's writing, there is a very straight line leading America to independence and a crooked, complicated one leading them to reconciliation with Britain. And if the situation drags on too long, America will be ruined and neither independence nor reconciliation will be an option.
Now that violence has broken out and Britain has attacked the U.S. in a number of different ways, Paine won't allow his readers the option of thinking they should just give in to Britain. The country has come too far to back down now.
The way Paine sees it, a future America will be governed in one of three ways: 1) by a legally elected Congress, 2) by a military power, or 3) by a mob. That's why an independent America will have to form a solid Constitution that'll keep dictators from ever taking power.
America has been given a great gift in having a common enemy, because Paine is confident that the fight for independence will bind the three colonies together going into the future.
Before concluding, Paine wants to take on the arguments that have been recently published by the American Quakers, which say that peace is the only path forward and there's no point ever in going to war, since God will take care of everything.
Paine begins by saying that the religious person who wrote the Quaker pamphlet shouldn't be talking about things he knows nothing about. After all, the Quaker writer has argued that religious people should trust in God's judgment and not get involved in political affairs. But as Paine points out, this writer has directly involved himself in politics by condemning the war with Britain, whether for religious purposes or not.
Further, Paine claims that he and the Quaker writer want the same thing in the end, which is peace. Paine simply insists that fighting for American independence will result in a much longer peace in the future than surrendering will in the present.
If anything, the Quaker writer should have written his pamphlet for the British, who were in fact the first people to take up arms against Americans. They're the ones who should let things be and allow America to become independent.
Basically, the pacifist ideas of Quakerism means that these people are willing to tolerate anyone who rules over them, no matter how awful that person is.
Paine closes this Appendix with one last insult to the Quakers and pacifists who are unwilling to stand up and fight for America on religious grounds. He basically calls for all red-blooded Americans to look down on these people as irresponsible cowards with weak arguments.