The Purple Cloud doesn't really hit its stride until all the people are dead. Well, all the people except the narrator, of course. It starts out with a very silly framing narrative: a gentleman gets some manuscripts from a doctor friend of his who had a patient who could see into the past and future while under hypnosis. Thus she was able to describe the story that the sole survivor of humanity writes. Apparently Shiel planned to use this frame as the basis of a series, as he hints that she also observed other interesting stories of the future and the past, but I believe that Purple Cloud is the only story of this kind that he published.
After you get past the frame, then you have to wait for everyone to die. This takes awhile. First we have to be introduced to the protagonist, also the first person narrator. He used to be a doctor, back in the day, and after some (creepy) machinations by his fiance, he's selected to join an expedition to reach the North Pole. There's a lot of build-up about how there's a bajillion dollar prize to the single man who first sets foot at latitude 90 deg., and thus the jealousies that cripple the crew, and also the prophetic ravings of a preacher who predicts that to reach the Pole will spell mankind's doom. Now, we reach here the first bit where you sort of have to bite back a WTF?!? response and continue reading: almost any exploratory expedition I've ever read about would have agreed to split the prize money between all the crew members, no matter which individual reached the Pole first--it's the only way to keep everyone from killing each other, like they end up doing here. I may have put the story down right there if I hadn't been reading this as a sort of project, but I'm glad I kept going.
So after watching his fiance commit murder and keeping silent, after 'accidentally' shooting another crew-member on the ship and then polishing off another in a duel, our hero finally reaches the Pole alone. Then he has to get back. He discovers that his immediate companions were all crushed by ice movements, but in general he doesn't suspect anything out of the ordinary until, a few months later, he finally gets back to open water and to the ship that brought the expedition to the Arctic--and of course the entire crew is dead. As are the crews of all the ships he visits afterwards. OK, now we're finally into the real story. The quality and rhythm of the prose improves remarkably at this point.
He takes control of a ship (with a luckily eternally-working air-powered engine, that’s the ‘future’ part of the story) and makes his way back to Europe and then to his native England. Here you also have to work a bit on your now creaky suspension of disbelief: whenever he stops the ship for the night and keeps no watch, he just stops, and everything's fine—he never runs into any other boats or creatures or land. How convenient.
The enormity of the tragedy doesn't truly strike him until he gets to London and finds everyone dead (no surprise by this point). In the course of his journeys he reconstructs the final days of humanity, with the eponymous Purple Cloud advancing and people fleeing before it; being herded North and West and trying to hide in caves, mines, and sealed-up houses. Their bodies are remarkably preserved, and if you have any suspension of disbelief left it's probably in a coma by this point: he believes that the Cloud had preservative properties that keep the bodies from decaying as expected, but he notes that insects are among the life forms to have survived the massacre. The thought that the insects would have long since eaten all the corpses doesn't occur to him, but to be fair he was writing ~90 years before the genesis of the Body Farm.
So the last man on Earth was a pretty evil motherfucker even while he was constrained by society. Without that, he goes nuts. He enters into a phase of dramatic arsonism, detailing the ways in which he rounded up explosives, incendiary material and fuses to burn down all of London at once--he does this in many other major cities as well. He realizes that this may not be the best thing for his soul, so to try to stave off the destructive impulses he declares himself a god-king and builds himself an almighty island temple of gold and precious materials with fountains of wine. (Yeah, suspension of disbelief has probably been bludgeoned into senselessness by now.) He alternates between periods of destruction and construction, and his ravings get quite extensive--he'll ruminate on the existence/non-existence of God in between detailing construction set-backs on his temple project.
He travels all over the world, especially whenever he gets a paranoid feeling that maybe he isn't the last one left. Mostly he vows to kill anyone else he may meet, to make sure that he's the god-king of the world. This all falls apart when he goes into Turkey to blow up a city and finds a young girl. At this point it's been around 20 years since he reached the pole (whole chunks of years are elided when he stops writing in his journal for long periods), and she appears to be about 20. And here your suspension of disbelief takes a swan dive off the highest point, never to be heard from again--you wouldn't believe the machinations Shiel has to go through to set this up.
She learns his language pretty fast, and attaches herself to him even though he goes so far as to beat her (ouch). He doesn't want to have children as he believes the human race was meant to die. She obviously doesn't feel the same way. And he can’t quite bring himself to kill her. They even try living on different continents, but eventually he gives in to her and it is implied that the human race will in some fashion survive. Sorry for the spoiler, but if you've waited 110 years, I really don't think I can be blamed for ruining things for you.
Overall, this is fascinating on many levels: for the pulp prose leading up to the genocide, for the raving prose after it, for portraying a character so evilly, and for artificially wrenching a 'happy' ending out of its wreckage. Having read this I can see how it fits into generic history a little better. Obviously Shelley had done the whole "last man on Earth" thing earlier (and also had Dr. Frankenstein and the monster end up in the Arctic wastelands), so Purple Cloud is part of a chain of stories leading all the way to Dan Simmon's recent The Terror, which tells the tale of Franklin's doomed expedition to find the Northwest Passage. In between you get John Campbell's "Who Goes There?" (later filmed as horror movie The Thing) which sets its alien shape-shifting terror in the antarctic. And in the realm of people killing off all of humanity, you get Alfred Bester's "Adam and No Eve," which goes back to primordial ooze for it's "happy ending;" one feels his story is a reaction to the artificiality of Purple Cloud's ending (although I don't know if he read it).
Is this a good book? In many ways no: at times it devolves into something terribly silly. On the other hand, in many ways yes: the raving protagonist, the anti-hero, and the use of themes and settings that come from and lead to many other generic works is at least notable. It's a pretty fast read once everyone dies, so I would say it's worth your time as a student of the genre, if not perhaps as a work of pulpy escapist paraliterature.