When Holmes and Watson visit Saxe-Coburg Square, Holmes surprises Watson by beating on the pavement with his walking stick. Later he explains:
"I was ascertaining whether the cellar stretched out in front or behind. It was not in front."
Then he knocks on the front door of Jabez Wilson's pawnshop and asks the assistant, who calls himself Vincent Spaulding, for directions to the Strand. He later explains to Watson that he wanted to get a look at the man's knees. He saw that the knees of his trousers were worn, wrinkled and stained. From this Holmes deduces that Spaulding, whose real name is John Clay, has been burrowing in the basement. Holmes had already assumed that the whole business of the Red-Headed League was to get Wilson out of the way.
Later Holmes tells Watson:
"The only remaining point was what they were burrowing for. I walked round the corner, saw the City and Suburban Bank abutted on our friend's premises, and felt that I had solved my problem."
Holmes naturally deduces that Clay and no doubt the man who called himself Duncan Ross have been digging a tunnel in the direction of that bank.
These are the three deductions Holmes makes about what he observes at Saxe-Coburg Square. He knows Clay is digging a tunnel. He knows, from tapping on the pavement, in which direction the tunnel must be heading. And when he sees the City and Suburban Bank a short distance from Wilson's shop, he deduces that Clay and his accomplice are planning to break into the bank.
Later Holmes calls upon Scotland Yard and uses their authority to contact the chairman of the bank directors, Mr. Merryweather. While they are all waiting in the dark for Clay and his associate to break through the floor of the strongroom, Merryweather tells Watson:
"We had occasion some months ago to strengthen our resources and borrowed for that purpose 30,000 napoleons from the Bank of France....Our reserve of bullion is much larger at present than is usually kept in a single branch office, and the directors have had misgivings upon the subject.”
Jabez Wilson has told Holmes that the Red-Headed League had been dissolved that very morning. From this Holmes deduces that the thieves have just about completed their tunnel-digging and intend to loot the bank that night. The whole complicated case is successfully wrapped up in less than twenty-four hours.