"The Adventure of the Lion's Mane" is one of the most baffling of the Sherlock Holmes stories. Doyle himself claimed to like it -- indeed, to regard it as one of his best on the basis of its plot -- but almost no one else really knows what to make of it. The case is undeniably interesting, but Holmes's solution seems not only to be impossible, it seems to be based on a reason that cannot be taken seriously, and, to top it all off, we can't blame it on Watson because it is also weird in being written entirely from Holmes's point of view (Holmes is in retirement, so Watson isn't around to write it).
Holmes is living the quiet life beekeeping in Sussex, at a place near the beach that has regular lagoons form that attract swimmers. July 1907 sees a particularly nice gale that has especially filled the pools, and Holmes is taking a walk along the cliff when he meets up with Harry Stackhurst, who is headmaster of nearby prep school and is heading out for a swim with Fitzroy McPherson, the science teacher, who had already gone ahead. They are suddenly arrested by the sight of McPherson, about fifty yards away, coming up the sole path in the cliffs from the beach, staggering, crying out, and collapsing. They rush forward and discover that he is nearly dead, with "glazed sunken eyes" and "livid cheeks". His last words are (apparently) "the Lion's Mane". He is wearing only his trousers and an overcoat. Around his body is a mesh-like set of lines. They are joined by Ian Murdoch, a maths teacher at the school. They send him to get the police, and Holmes retraces McPherson's steps. McPherson was clearly the only person who had taken the path that morning. McPherson's towel is folded and dry on the rock, "so that it would seem that, after all, he had never entered the water", although bare footprints as well as shoeprints suggest that he had prepared to do so. The beach is deserted "save that two or three dark figures could be seen far away moving towards the village of Fulworth." They seem too far away and on the wrong side of the lagoon to be connected to the crime. There are "two or three fishingboats" that are "at no great distance", who can be questioned later. When he returns, he finds that there is a note from a woman in the dead man's pockets.
You can read the summary of the rest of the story at Wikipedia, if you don't have access to the story itself. Suffice it to say that the evidence points to Murdoch until Holmes argues, on the basis of a book, that McPherson was actually killed by a Lion's Mane jellyfish, and they do indeed find one hiding in the lagoon. Holmes ends the story criticizing himself for being misled by the dry towel.
So far, so good; one can see how this would make the structure of a mystery story. But nothing in it actually adds up. A few of the more obvious points:
* The Lion's Mane is a large jellyfish; McPherson can't have had the serious wounds he had unless he had been in the water where the jellyfish could reach him. (When Murdoch is later stung by it, he was well in the water and had to swim to shore.) But Holmes concludes that the dry towel shows that McPherson never entered the water; this is what he claims misled him. But Holmes was there when McPherson had died, just coming up from the lagoon; if McPherson had been in the water, he would have already known it from McPherson's body. The stings were not on McPherson's legs, as if he had dipped just part of himself in; they were on his torso. Sherlock Holmes does not need to find an indirect clue in order to tell whether a man he was with had just been in the water or not. This point is particularly salient given that at one point, Holmes describes the situation as, "he had returned without bathing, or at any rate without drying himself." That would be a very curious thing to say if you already knew that the man was dry.
* When Holmes first sees the fishing boats, he says they were "at no great distance" and they can examine them later. They never examine them. When the inspector mentions them later as a possible consideration, Holmes says, "No, no, they were too far out." Perhaps the fishing boat matter came up in the briefly mentioned inquest -- but the inspector would certainly have been aware of it, if they had. It's technically possible, I suppose, for boats to be "at no great distance" and "too far out" at the same time; but it's curious for one person to say both without any further explanation.
* The solution to the mystery lies in a book called Out of Doors, by John George Wood. It's a real book, and Wood does discuss his encounters with the Lion's Mane jellyfish. Holmes's summary if it in the story is accurate. But there are two features of Wood's story that are strange for our purposes; one of them Holmes not only mentions but arguably emphasizes, and the other of which he strangely leaves out. The one he mentions is that Wood says that his face at the end of the ordeal was "all white, wrinkled, and shrivelled, with cold perspiration standing in large drops over the surface". McPherson before he died is said to have had "glazed sunken eyes and dreadful livid cheeks". 'Livid' is the opposite of 'white'.
* The second puzzling thing is that Wood says, "The slightest touch of the clothes was agony". McPherson's wounding seems to be more serious than Wood's, but he is wearing an overcoat. What is more, the overcoat is just around his shoulders (it falls off on its own when Holmes and Stackhurst are examining him), despite the fact that he has been scrambling up a path in extraordinary agony. So you are attacked by a jellyfish and are in extraordinary agony; you take the time to put your overcoat on, despite the fact that it makes the agony even worse, and you keep it on while you scramble up the hill, occasionally falling. Maybe, but it seems a stretch.
* Murdoch once threw McPherson's dog through a window -- not out the window, literally through the plate-glass -- in a dispute; they then later became friends, as if a man is ever going to become genuine friends with someone who deliberately tried to kill his dog. This is all the more strange given that there is an entire portion of the story about the dog, in which we learn how loyal and faithful the dog is, which suggests that McPherson and his dog were quite close. And, of course, it gets even stranger given that McPherson and Murdoch were both interested in the same woman. And, moreover, despite the fact that everyone ends up insisting on it, the first description of Murdoch is that he was "so taciturn and aloof that none can be said to have been his friend". Yet three people -- Stackhurst, Maud Bellamy, and Ian Murdoch -- go out of their way to insist that Murdoch and McPherson were friends.
This is enough to be going on with for the moment. The difficulty of all of this is further compounded by the fact that mystery stories are not written on the principle of Chekhov's gun -- that's a rule for drama, and is only applicable to the story to the extent it approximates stage-drama -- but on the principle of misdirection. There are always misleading details, so it's a question of which strange details are really important. We could accept the explanation in the story without any question, despite many other oddities, if it weren't for the key point that Holmes goes out of his way multiple times to emphasize -- the water. If you assumed that a jellyfish in the water could attack a man out of the water, and do so on such a scale as McPherson is attacked, you could certainly swallow everything else. An advantage is that McPherson's death is explained; and if you pick anyone else as responsible, the jellyfish either has to be the weapon (which seems unreliable) or was used to cover the actual reason for McPherson's death (which seems rather complicated). But there are so many oddities to swallow, and there seems no way that McPherson could have been stung by the jellyfish and not obviously have been in the water.
And it's so odd to put the solution to the mystery in the title of the mystery. It's as if "The Adventure of Silver Blaze" were instead called "The Adventure of the Horse's Trainer". (I once had an idea for a story called, "The Butler Did It", in which it is obvious from the beginning that the butler did it and the problem is just proving it, but that's half a joke.)
If you don't accept the explanation in the story, we have to play the Great Game, and there are two paths to take. The explanation could be exoteric, drawing solely on the characters in the story and what we are told about them, or esoteric, and move more widely, and more wildly, through the canon and related history. Exoterically, the culprit(s) can only be significant characters actually on the stage in the story, and there are only a limited number of possibilities. Who is responsible for the death of Fitzroy McPherson?
(1) Fitzroy McPherson. It seems a baroque, agonizing, and unreliable way to commit suicide (if that was the intent), but McPherson is the only one who is known for sure to have been on the scene. He also knew what killed him; since he's a science teacher, he could well have know it just by sight. Holmes suggests that McPherson knew it was a Lion's Mane because he saw it floating on the water, but if he did that before being stung, he wouldn't have drawn close enough to be stung so badly. If it was afterward, though, he would still had to have been in the water. Unless he arranged to use the jellyfish filaments to sting himself; McPherson is the only one who could certainly have gotten himself stung without getting very wet.
(2) Harry Stackhurst. Our entire timetable depends from the beginning on Stackhurst; he is, he says, going to meet McPherson for a swim, McPherson having gone ahead. McPherson never confirms this because he is dead, but the rest of the reasoning depends on there having been very little time because McPherson was only a bit ahead of Stackhurst. The primary difficulty with Stackhurst being the principal suspect is that Holmes is clear that only McPherson had been up or down the only path. But if one took Stackhurst to be an accomplice, some possibilities open up. The dark figures on the beach and the fishing boats are ruled out because they are too far. 'Too far' is not a matter of distance but of time. Different timeline, different possibilities. You could imagine him accosting Holmes in the attempt to make sure he wasn't going down to the lagoon, and being shocked when, instead of already being dead, McPherson comes clambering up the path. Stackhurst is alone with McPherson's body for an extended period of time, when Murdoch is sent to the police and Holmes is investigating the scene; Holmes only finds the note from Maud in the pockets after he returns. Stackhurst is strangely irate at finding Murdoch hanging around Maud Bellamy's house. A number of oddities in the story are due to Stackhurst. But it's hard to make anything definite cohere around him.
(3) Ian Murdoch. Everything points originally to Murdoch, so he's the easy case. What's more, not much actually rules him out as responsible. Suspicion moves from him when Holmes convinces everyone that the weapon that killed McPherson was the living Lion's Mane -- and that's about it. The reason he wasn't arrested immediately was timeline issues -- he was supposedly keeping students late. Stackhurst establishes that element of the timeline, as well; Murdoch tells us no more than that he was late and not on the beach. Nobody seems to have checked the alibi. When Holmes is convincing the inspector of the futility of arresting Murdoch, he says, "he can surely prove an alibi", which is an odd thing to say if it were already obvious that he had one. When Stackhurst notes that it was mere chance that there weren't any students with McPherson, Holmes asks the interesting question, "Was it mere chance?" and then Stackhurst tells us why Murdoch was late. It's weird that Murdoch goes swimming in the same lagoon in which both McPherson and McPherson's dog had already died. We have only the word of Ian and Maud that Ian was OK with Maud being McPherson's fiancee.
(4) Maud Bellamy. I've always thought interesting that Maud knows Holmes by sight despite the fact that they had never met, a fact that Holmes notes explicitly. It's Maud who tells us that she was engaged to McPherson, although this appears to be confirmed by a comment made by Ian in passing; the engagement was a secret -- we are told. The difficulty with Maud as a suspect is that we have relatively little to work with; most of what we know about her is indirect.
(5) Tom and William Bellamy. We don't know much about father or son, but we do know a few things of interest. Tom Bellamy is a former fisherman, so he could handle a boat. William Bellamy is very strong, and fact that is potentially significant given that it is emphasized that, despite his bad heart, McPherson was so strong that "No single person could ever have inflicted such an outrage upon him" (according to Maud) and that it is impossible that Ian "could single-handed have inflicted this outrage upon a man quite as strong as himself" (Holmes). If any of the Bellamys are responsible, however, it seems that they cannot be the only ones involved.
There is one more.
(6) Sherlock Holmes. It seems a cheat even to suggest. But this story is unusual in that Holmes himself is telling it. Holmes was in the vicinity. Holmes alone is the reason why we think nobody else was on the path that morning. Holmes already knew about the Lion's Mane. When McPherson is indistinctly slurring words it is Holmes, and Holmes alone, who insists that he said "Lion's Mane". He does a great deal to convince everyone that Murdoch didn't do it. There are inconsistencies in Holmes's comments and behavior that could raise questions. And if he did do it, the interaction with the inspector at the end of the story could very well be read as ironic.
If we take the esoteric path, on the other hand, the sky is the limit. One could well imagine that Holmes is hinting at something he can't actually say -- that perhaps he saves Murdoch in order to save someone else, or perhaps there is something more sinister going on, in which he needs to quell the suspicions of those really responsible. But, of course, one can make up stories all day; the difficulty is making them all fit properly with what we know.