For the story, the author created a society known as the 'Honorable Society of Ananias', intending to write a series of stories in that setting, but only one resulted.
The time is the year 2144. The four members of the Society meet for lunch once a month at which one of the members tells a story. The story must be a complex and fantastic lie, but one which sounds like the truth. Other members are free to heckle and attack the supposed veracity of the tale.
At one meeting, Gilbert Hayes, a guest, requests that he be allowed to tell a story. His tale is that, as an astronomer, he discovered fifteen years ago a planet with no gravitational field and undiscovered by other astronomers. Described by Hayes as a 'super-neutron', he claims that it is heading for the Sun and will strike in a few hours, destroying the Sun (and Earth).
The story Hayes weaves involves complex astronomical observations and theories, and at the end of the tale, he calmly observes that the supposed planet is about to enter the solar system and destroy the planets one by one. He hands around pieces of exposed film-negative, through which the members gaze into the sky and see - or think they see - a small dark spot against the sun.
Earth is of course not destroyed and Hayes believes this has happened because the Sun contains enough cadmium to absorb the super-neutron.
Out of sheer relief, the members vote him in as Perpetual President of the Society, but the former President has misgivings. He thinks that the story was in fact true and that therefore Hayes should have been disqualified.