In The Ghost with the Silk Hat," three boys—Weary McGraw, Steve, and the Whale—venture into the woods near Millville and discover that someone has bought and is refurbishing the old Wiltshire Estate. Curiosity piqued, they explore the area and encounter the caretaker, Steinmann, who tells them about Wilfred Cobworth, a boy supposedly insane and kept in the estate.

Wilfred confides in the boys that he is frightened by strange noises and sightings, including a ghostly figure resembling the former owner, Mr. Wiltshire. The boys, especially Weary, suspect foul play. They devise plans to investigate further, ultimately sneaking into the estate at night. They encounter Steinmann in disguise, trying to frighten Wilfred and affirm his insanity claim.

Through their courageous efforts, the boys uncover a plot by Wilfred’s guardian, Mr. Harger, and his associates Steinmann and Gurdheim. They aim to drive Wilfred insane or have him declared as such to gain control of his inheritance. Wilfred, with the boys' help, resists the psychological assault.

The boys learn that Steinmann has been impersonating the ghost of Mr. Wiltshire to terrorize Wilfred. They expose the scheme, capturing Steinmann and bringing the conspirators to justice. Their bravery and cleverness save Wilfred from further harm, reuniting him with his supportive lawyer, Mr. Harlton.