fourth smartest man in London, and for daring I am not sure that he has not a claim to be third. I have known something of him before. (p. 13)

Holmes notices that he has dirt on his trouser knees, so he assumes that he has been kneeling.  There are few reasons for a grown man to kneel, so Holmes taps his stick to see if the ground is hollow.  He then uses this information to deduce that the men plan to rob the bank by digging a tunnel under it from the shop.  He then calls the police, they wait, and the men are caught when they do exactly what Holmes said they would.

Much of the pleasure we derive from reading Arthur Conan Doyle's stories about Sherlock Holmes comes from enjoying Holmes' extraordinary displays of powers of observation and deduction. In the story "The Red-Headed League," we encounter these powers early on when Holmes remarks to Watson:

Beyond the obvious facts that he has at some time done manual labour, that he takes snuff, that he is a Freemason, that he has been in China, and that he has done a considerable amount of writing lately, I can deduce nothing else.

Of course these facts are not obvious to Watson, and in his explanation of how he arrived at his conclusions, Holmes establishes his expertise and reveals his methods. The first skill he uses is one of close observation of details (in many cases with his iconic magnifying glass). The second is having built up a storehouse of facts (such as knowledge of tattoos and tobacco products) which allow him to deduce facts about people and evidence that the less well-informed might miss. Finally, he uses logic, unprejudiced by conventional preconceptions.

One characteristic of Holmes' method is that it is based on analysis, on taking time to think through a problem and formulate matters to be investigated, rather than simply leaping in and starting to investigate at random. After Holmes takes on the case we read the following bit of dialogue:

"What are you going to do, then?" I [Watson] asked.

"To smoke," he [Holmes] answered. "It is quite a three-pipe problem, and I beg that you won't speak to me for fifty minutes." 

Once Holmes has worked out the problem in his mind, he decides to investigate in person. The focus of his investigation is elimination of wrong answers until the only one left is the correct one, or as is famously said in The Sign of the Four, "when you have eliminated the impossible, whatever remains, however improbable, must be the truth." The final stage in the crime-solving process is apprehension of the criminal.

 “Beyond the obvious facts that he has at some time done manual labour, that he takes snuff, that he is a Freemason, that he has been in China, and that he has done a considerable amount of writing lately, I can deduce nothing else.”

Once his reasoning is revealed as relying on his powers of observation his client is less bewildered –

Mr. Jabez Wilson laughed heavily. “Well, I never!” said he. “I thought at first that you had done something clever, but I see that there was nothing in it after all.”

He carefully ascertains that a young man prepared to work for half wages must have another motive for working at the pawnbrokers, and he summarises his observations at the end-

“You see, Watson,” he explained …“it was perfectly obvious from the first that the only possible object of this rather fantastic business of the advertisement of the League, and the copying of the Encyclopaedia, must be to get this not over-bright pawnbroker out of the way for a number of hours every day. It was a curious way of managing it, but, really, it would be difficult to suggest a better. The method was no doubt suggested to Clay's ingenious mind by the colour of his accomplice's hair. The £4 a week was a lure which must draw him, and what was it to them, who were playing for thousands? They put in the advertisement, one rogue has the temporary office, the other rogue incites the man to apply for it, and together they manage to secure his absence every morning in the week. From the time that I heard of the assistant having come for half wages, it was obvious to me that he had some strong motive for securing the situation.”

As ever, Holmes companion Watson is as impressed as the audience at Holmes’ powers of deduction-

“You reasoned it out beautifully,” I exclaimed in unfeigned admiration. “It is so long a chain, and yet every link rings true.”