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There isn't a whole lot of action over the next four chapters, which are devoted entirely to the prosecutor's speech. The narrator informs us that he seems to be nervous and feverish, and actually dies nine months later of consumption (d'oh). But we'll give you the broad strokes of his argument here.
First, the prosecutor doesn't address the crime itself, but instead goes on about how Russian morality has declined to the point that society is used to something like the Karamazov affair. He cites a quote from famous Russian writer Nikolai Gogol's novel Dead Souls, a book everyone there is sure to recognize: "Ah, troika, bird-troika, who invented you!" The troika, or carriage, serves as a metaphor for Russia as a whole, and he suggests that this Russia-troika is being pulled into insanity by people like the Karamazovs. (Scattered applause here.)
Next the prosecutor paints his own psychological profile of all of the Karamazovs, starting with the father, then on to Ivan, Alyosha, and finally Dmitri. Yup, even goody-two-shoes Alyosha is depicted as clutching onto the monastic life as an escape from his deep Karamazovian corruption. A line about Alyosha perhaps sinking either into "mysticism" or "chauvinism" draws some applause.
Then the prosecutor goes back to the theme of Russia and states that, actually, "we are all Karamazovs," capable of both high idealism (as seen in Alyosha) and total degradation (as seen in Fyodor). Interestingly, he cites a quote from Rakitin on this point.
Then Kirillovich suddenly seems to remember that there is a crime to prosecute and says, "incidentally," that he thinks it goes against Dmitri's unstable nature to save and sew up 1,500 roubles in an amulet.
After dismissing the dispute over Dmitri's inheritance as irrelevant, the prosecutor goes on to the medical opinions about Dmitri's state of mind.