How did Alan and David become friends again in Kidnapped?

On the face of it, it's amazing that David and Alan should be friends at all, given their huge political differences. Yet somehow they're drawn together, sticking with each other through thick and thin, despite all the many trials and tribulations they're forced to endure.
But there are limits. And we find out just what those limits are in the climax to the story in chapter 24. David is extremely angry at Alan for losing their money. To make matters worse, David's not in the best of health, so he has an additional reason for being well and truly brassed off. Alan foolishly tips him over the edge by indulging in some anti-Whig taunts. Ordinarily, David would brush off his good friend's barbs, but not now.
For now, in his fevered, angry state, he lashes out at Alan, challenging him to a duel. Wisely, Alan turns down David's challenge. As for David, he doesn't apologize for his rash actions, but he attempts to reconcile himself to his bosom buddy by asking for forgiveness. Alan happily does so, while also expressing his admiration for David's fighting qualities.