“Be more catholic,” urged Vance. “Consider his ironies in relation to his scientific speculations. What could be more natural than that a man who projects his mind constantly into the vast interplanet’ry reaches, and deals with light-years and infinities and hyperphysical dimensions, should sniff derisively at the infinitesimals of this life? . . . Stout fella, Arnesson. Not homey and comfortable perhaps, but dashed interestin’.”

Vance himself had taken the case with unwonted seriousness. His Menander translations had been definitely put aside. He became moody and waspish—a sure sign that his mind was busy with an absorbing problem. After dinner each night he went into his library and read for hours—not the classic and æsthetic volumes on which he generally spent his time, but such books as Bernard Hart’s “The Psychology of Insanity,” Freud’s “Der Witz und seine Beziehung zum Unbewussten,” Coriat’s “Abnormal Psychology” and “Repressed Emotions,” Lippo’s “Komik und Humor,” Daniel A. Huebsch’s “The Murder Complex,” Janet’s “Les Obsessions et la Psychasthènie,” Donath’s “Über Arithmomanie,” Riklin’s “Wish Fulfillment and Fairy Tales,” Leppman’s “Die forensische Bedeutung der Zwangsvorstellungen,” Kuno Fischer’s “Über den Witz,” Erich Wulffen’s “Kriminalpsychologie,” Hollenden’s “The Insanity of Genius,” and Groos’s “Die Spiele des Menschen.”

He spent hours going over the police reports. He called twice at the Dillards’, and on one occasion visited Mrs. Drukker in company with Belle Dillard. He had a long discussion one night with Drukker and Arnesson on de Sitter’s conception of physical space as a Lobatchewskian pseudosphere, his object being, I surmised, to acquaint himself with Drukker’s mentality. He read Drukker’s book, “World Lines in Multidimensional Continua”; and spent nearly an entire day studying Janowski’s and Tarrasch’s analyses of the Pardee gambit.

On Sunday—eight days after the murder of Robin—he said to me:

Eheu, Van! This problem is unbelievedly subtle. No ordin’ry investigation will ever probe it. It lies in a strange territ’ry of the brain; and its superficial childishness is its most terrible and bafflin’ aspect. Nor is the perpetrator going to be content with a single coup. Cock Robin’s death serves no definitive end. The perverted imagination that concocted this beastly crime is insatiable; and unless we can expose the abnormal psychological mechanism back of it there will be more grim jokes to contend with. . . .”

The very next morning his prognostication was verified. We went to Markham’s office at eleven o’clock to hear Heath’s report and to discuss further lines of action. Though nine days had passed since Robin had been found murdered, no progress had been made in the case, and the newspapers had grown bitter in their criticisms of the police and the District Attorney’s office. It was therefore with considerable depression that Markham greeted us that Monday morning. Heath had not yet arrived; but when he came a few minutes later it was obvious that he, too, was discouraged.

“We run up against a brick wall, sir, every way we turn,” he repined, when he had outlined the results of his men’s activities. “There ain’t a sign of a motive, and outside of Sperling there’s nobody on the landscape that we can hang anything on. I’m coming to the conclusion that it was some stick-up man who ambled into the archery-room that morning and messed things up.”

“ ‘Stick-up’ men, Sergeant,” countered Vance, “are deuced unimaginative, and they’re without a sense of humor; whereas the johnny who sent Robin on the long, long trail had both imagination and humor. He wasn’t content merely to kill Robin: he had to turn the act into an insane joke. Then, lest the public wouldn’t see the point, he wrote explanat’ry letters to the press.—Does that sound like the procedure of an itinerant thug?”

Heath smoked unhappily for several minutes without speaking, and at length turned a gaze of exasperated dismay upon Markham.

“There’s no sense in anything that’s breaking round this town lately,” he complained. “Just this morning a guy named Sprigg was shot in Riverside Park, up near 84th Street. Money in his pocket—nothing taken. Just shot. Young fella—student at Columbia. Lived with his parents; no enemies. Went out to take his usual walk before going to class. Found dead half an hour later by a bricklayer.” The Sergeant chewed viciously on his cigar. “Now we got that homicide to worry about; and we’ll probably get hell from the newspapers if we don’t clear it up pronto. And there’s nothing—absolutely nothing—to go on.”