Investigate psychological theories current in the late nineteenth century, and examine ways that Doyle makes use of these theories within his story. You may want to focus on a specific branch of psychology, a related field such as criminology, or the theories of one particular psychologist.
Research German composers whose music was frequently performed near the end of the nineteenth century. Use this information to speculate on the further knowledge of Sherlock Holmes's character provided by the story's reference to his musical tastes. You might also consider Italian and French music of the same time period, which Holmes dislikes. What does this contrast in Holmes's musical interests reveal about him?
Examine cultural factors in turn-of-the-century America that could account for the popularity of the Sherlock Holmes stories. You could locate specific developments in American society comparable to the British ones mentioned in this entry. Conversely, you might investigate unique characteristics of American life, thought, or tastes during this time period that would make Doyle's stories appealing to Americans for reasons that differ from those of British readers.
Research the principles of logic known as induction and deduction. Distinguish between them, and identify the elements of each demonstrated by Sherlock Holmes's reasoning in "The Red-Headed League." You might wish to judge which principle predominates in Holmes's thinking, or which most aids Holmes in solving the mystery.