After the men leave Lauriston Gardens, Holmes mails out a telegram and they make their way to the home of the constable, John Rance. On the cab ride over, Watson is skeptical about Holmes’ confidence in the details he provided to the detectives. Holmes explains that he knew about the cab and the horse’s shoes based on the markings that the wheel and hoofprints made on the ground, that he deduced the murderer’s height and age from his stride length, his boot type from his footprints, his long fingernails from scratches on the wall, and the Trichonopoly from its ashes. Though he believes he was correct, Holmes confesses that the florid face was more of a guess, but he refuses to tell Watson how he came to this deduction.
Holmes explains his deduction process to a skeptical Watson (and thus to the readers as well, justifying the details he had provided about the murderer. Again, Holmes hints at secret knowledge (in this case, his reason for guessing that the murderer has a “florid” face) but chooses not to explain it.
Mystified by the case, Watson asks how the men ended up in the house, how the murderer could have forced Drebber to poison himself, where the blood and the ring came from, what the murderer wanted, and why he wrote “RACHE” on the wall. Holmes tells Watson that “RACHE” (written in Gothic script, which real Germans would use only for printed, not handwritten, text) was intended to be a red herring to lead the police toward Socialist secret societies. Holmes doesn’t tell Watson any more, though, because “a conjurer gets no credit once he has explained his trick; and if I show you too much of my method of working, you will come to the conclusion that I am a very ordinary individual after all.” However, when Watson praises Holmes for bringing deduction to an exact science, Holmes is pleased, as Watson had known he would be, and reveals that the murderer and Drebber came in the same cab and walked into the house together.
Watson summarizes the main questions of the case, but Holmes, deciding not to tell Watson any more, reveals that he doesn’t tell others much information about his methods or his knowledge, because he doesn’t want to be perceived as “ordinary.” Despite his claims to the scientific rigor of deduction in his magazine article, Holmes views (or likes to view) himself partly as a kind of conjurer, or magician, always astounding his audience. Watson, however, already knows this and is able to flatter Holmes into telling him more. In this instance, Holmes and Watson briefly exchange roles, with Watson gaining the upper hand in his ability to manipulate Holmes.
The cab stops at John Rance’s house in Audley Court, a dingy place surrounded by dirty children and lines of dirty laundry. The constable seems unwilling to talk, but once Holmes takes out a gold coin Rance readily tells him about his night shift. At around one in the morning, Rance was talking with another policeman, and an hour or so later he decided to check Brixton Road, which was empty except for a cab or two. Rance knew part of Lauriston Gardens was supposed to be empty, and became suspicious when he saw a light in the window. Rance found the house empty, save for a lit candle on the mantelpiece and Drebber’s body on the floor. The constable then exited the house and sounded his whistle, attracting the attention of other policemen. At that time, the streets were empty, except for a tall, red-faced drunk man in a brown coat.
Rance’s eagerness to take a bribe is a clear example of corruption and injustice in the police force. Rance’s description of the man as tall and red-faced matches Holmes’ description of the murderer, and his mention of a cab on Brixton Road foreshadows the revelation of Jefferson Hope (a cab driver) as the murderer.
Holmes asks if the man was carrying a whip, but Rance says no, and Holmes mutters to himself that he must have left it elsewhere. Giving the constable the gold coin, Holmes declares that Rance will never be promoted, as he let the suspect, the apparently drunk man, walk free. On the cab ride back, Watson asks why the murderer would come back to the house. Holmes tells him that he came back for the ring, and that they can use the ring to draw out the murderer. He then thanks Watson for pushing him to take the case, as it is “the finest study [he] ever came across.” Calling it “a study in scarlet,” Holmes declares that it is their duty to “unravel” the “scarlet thread of murder running through the colourless skein of life.”
Holmes’ question about a whip is a hint that the murderer drives a cab. Scolding Rance for his incompetence, Holmes again displays his sense of superiority to Scotland Yard. Holmes’ enthusiastic description of murder as “scarlet thread” in a “colourless skein of life” suggests the polarity of his attitudes toward murder and toward everyday life. Whereas murder is “scarlet” — that is, vibrant and waiting to be unraveled — the “skein of life” is “colourless” and uninteresting to Holmes. Clearly he sees solving a murder as an aesthetic activity or a pleasurable puzzle more than a matter of justice.