The narrator's main story takes place in the summer of 1797, when the Indomitable joins a naval fleet in the Mediterranean. The narrator explains that not long before there had been a wave of mutinies on British naval ships, including the catastrophic Nore Mutiny, which continued for much longer than most. It was only put down eventually due to the "unswerving loyalty of the marine corps," and because some of those involved in the mutiny became loyal again.
The navy relies on a culture of loyalty, with sailors obediently following their captains. Mutiny is thus extremely dangerous for individual ships and for the navy at large. It can only be put down by its opposite, "unswerving loyalty."
The narrator compares the Nore Mutiny to a contagious fever that affects a healthy man. Like a fever, mutiny spread insidiously among normally loyal sailors. Nonetheless, some of those who had mutinied were able to make up for their behavior by serving valiantly afterwards, earning heroic victories for Admiral Nelson against Napoleon's fleets.
Mutiny spreads through the ties of comradeship that bind sailors—as one turns against the captain the ties of comradeship help turn others, setting up a kind of tension between loyalty to comrades and loyalty to captain. In the case of the Nore Mutiny, justice did not need to be served via punishment, as the sailors served valiantly after the mutiny was put down.