An update to Jim Dixon's post: that New York Herald link no longer works. The new link is https://www.loc.gov/item/sn83030313/1843-05-11/ed-1/.

I haven't had time to look over the whole thing, but it is largely accurate. The Somers was a very new ship (she was making only her second voyage, the first having been a sort of shakedown cruise). She was extremely fast for the time, although functionally obsolete -- she didn't have an engine. She was extremely overcrowded, with a complement of boys being trained for sea. The three men were hung for allegedly planning mutiny. The leader, Philip Spencer, was 18 years old, a ne'er-do-well who had flunked out of two colleges and been forced off two previous ships but was still in the navy because his father, who was a cabinet secretary, had pulled strings. The evidence against him came mostly from the purser's assistant, a man named Wales. In addition to Spencer, two experienced sailors, Cromwell and Small, were hung. The evidence against them was even more indirect -- indeed, it is likely that Cromwell's only crime was that he was a very cruel man and everyone was willing to testify against him.

The event is described as "the only mutiny in the history of the United States navy." There was no mutiny, although one may have been planned. Spencer certainly thought about it; he admitted to an obsession with the idea.

It should be noted that, under the laws of war of the time, a sailor could not be executed except by order of a court-martial. Captain Mackenzie did not have the authority to order a court-martial (roughly speaking, it took someone two grades higher). Nor did he conduct one. He told his junior officers to make some recommendations. They recommended death. Mackenzie, who may have put them up to it and was certainly a sadist who liked to watch people die (he regularly attended, and wrote descriptions of, executions) and who ordered an extraordinary number of floggings, of course turned the recommendation into an illegal order. Despite this, he was acquitted by court-martial, although the charges were declared "not proved" rather than "not true."