What follows has to be one of the most painstaking murder investigations in fiction. Theodore Roosevelt, who was in fact police commissioner in ‘96, asks his friend Laszlo Kreizler, a brilliant “alienist” (a quaint name for psychologist), to head the investigation. Kreizler assembles a team which could be a model of late-Victorian P.C.: a New York Times reporter familiar with the criminal underworld, an ambitious young woman in T.R.’s office, two smart Jewish cops, a large black man on Kreizler’s payroll and a street-savvy kid who is about the same age as the victims. First, they pore over what little literature exists on serial killers. They make an eerie visit to a psychopathic killer in Sing Sing and go to Sioux country, where their suspect may have learned about mutilation from the Indians. They descend more than once into the darkest comers of the city, where young men with “painted” faces sell their bodies. But mostly they wait for the next killing.

It’s uncomfortable to call a book about the murder of children entertaining, but this one is undeniably engrossing, despite the grisliness. A sense of delicacy has certainly not discouraged Hollywood, which is paying Carr $500,000 for film rights. For readers made squeamish by the gore, “The Alienist” does have diversions. Carr’s descriptions of New York-nights at the opera, dinners at Delmonico’s, encounters with J. P. Morgan-are so authentic that he was able to pass the manuscript off as nonfiction. Eventually he confessed, but the publishers decided to go ahead with the book. They knew that it is something far more impressive than a recounting of an actual case: it is a product of Carr’s own extraordinary imagination.