In chapter 5 of The Hound of the Baskervilles, Sherlock Holmes's investigation is hampered by three broken threads—that is to say, potential leads that end up going nowhere.
The first of these threads is a telegram that arrives just before dinner. In it, Holmes is informed by Sir Henry Baskerville that Barrymore is at the Hall. This is a setback for Holmes, as it proves that Barrymore could not have been the man following Baskerville around London.
Along with the first telegram comes a second one, which, like the first, represents a broken lead. The second telegram is from Cartwright, who tells Holmes that he has been unable to trace the cut sheet from The Times despite having visited no fewer than twenty-three hotels. This proves that no one from the newspaper has been following Sir Henry.
Holmes remains undeterred, however. In fact, he claims that there's nothing more stimulating than a case like this, where everything goes against you. Which is just as well, really, because he's in for another disappointment.
Holmes and Watson track down the cabman who drove the elusive spy. But in what is yet another broken thread, yet another lead that goes nowhere, the two are shocked to discover that the name the spy gave to the cabman was none other than Sherlock Holmes.