The novel opens with the introduction of its title characters. The heroine is "the superb Virginia St. John," a celebrated beauty, famous for being famous. At the age of thirty she is the newlywed wife of an English bishop. The hero (the term has to be applied satirically) is Prof. Paul Darnley, a prominent intellectual:
"He had written three volumes on the origin of life, which he had spent seven years in looking for in hay and cheese; he had written five volumes on the entozoa of the pig, and two volumes of lectures, as a corollary to these, on the sublimity of human heroism and the whole duty of man. He was renowned all over Europe and America as a complete embodiment of enlightened modern thinking. He criticised everything; he took nothing on trust, except the unspeakable sublimity of the human race and its august terrestrial destinies."
Both characters are traveling abroad the steamship Australasian, sailing from Melbourne to London; Virginia is on her way to Chausible Island to meet her new husband, while Paul is journeying home to his elderly wife, whom he has been avoiding for the past eighteen months. (Mrs. Prof. Darnley has an irrational determination to convince her atheist and materialist husband of the existence of Hell.) On the voyage, Paul lectures on his value system, which is essentially Comte's "Religion of Humanity," and manages to convince many passengers and crew of the truth of his outlook (though Virginia does not listen to him).
An approaching storm inspires the crew to load the ship's cutter with survival supplies, including tinned meats and cases of champagne. The storm passes, but the ship's boiler suddenly explodes; the Australasian quickly sinks with the loss of almost all on board.
Yet Paul and Virginia manage to reach a nearby island in the cutter. (Shipwreck on a deserted island, as a start for a new and better society, is a staple in the utopian genre   as in the Spensonia books of Thomas Spence, among other possible examples.) Paul finds a deserted house built from wreckage; it is a comfortable and neatly furnished cottage, and the two survivors move in. Virginia is deeply distraught over their recent tragedy   but her state of mind improves when she realizes that the largest trunk in her luggage is on the cutter. The tinned meats and champagne also come in handy.
Two other survivors appear: an English clergyman who has been converted to Positivism by Paul, and an elderly woman. The latter soon dies, giving Paul and the clergyman opportunity to debate the meaning of her death from the Positivist viewpoint. Paul keeps himself busy searching for the missing link. Liberated from the trammels of traditional culture and belief, Paul confidently expects instant attainment of the sublime happiness that is the natural state of free human beings.
The clergyman proves to be an inconvenient convert, however; he spends his time getting drunk and trying to kiss Virginia, and Paul's intellectual arguments have little influence on him. Physical intimidation is more effective, since the clergyman is both a "coward" and a "weakling." When the drunken clergyman falls off a cliff, Paul meditates on the utilitarian aspects of his death. Paul eventually converts Virginia; she gives up her religious faith, and replaces it with a sexual desire for Paul   which the intellectual Paul finds very uncomfortable. In her new commitment to "glorious truth," Virginia snoops through all of Paul's private papers, and discovers his secret: he himself was once a clergyman.
By the final chapter of the story, Paul is reduced to baying at the moon. His howls attract the notice of another couple. The woman turns out to be Paul's wife, who has come searching for her errant husband. And the man is Virginia's husband the Bishop. It happens that the island on which Paul and Virginia landed is none other than Chausible Island, her destination, and the cottage they've been occupying was prepared by the Bishop for Virginia. At the end of the book, Paul discovers that his wife has attained her goal, and that he now believes in Hell.
Output: What do Paul and the clergyman do when the old woman on the island dies?