"The Scarlet Band" is a novella of Atlantis and a pastiche of Arthur Conan Doyle's Sherlock Holmes. It was originally published in the May 2006 issue of Analog and reprinted in Atlantis and Other Places in 2010. Although the second Atlantis story, it is chronologically set last in the series.
The English detective, Athelstan Helms, and his associate and biographer, Doctor James Walton, travel to Atlantis in the 1880s to help authorities investigate a series of murders. The victims were all critics of the House of Universal Devotion, a homegrown religion. Naturally, the authorities (and Walton) are convinced the House is responsible, but Helms isn't so certain.