Discuss Sherlock Holmes's ennui.

Watson frequently remarks in the Sherlock Holmes detective stories that the great man suffers from ennui when he doesn't have a problem to solve. This is why he sometimes uses drugs such as cocaine and morphine, which were not illegal in his day. He takes on the apparently trivial problem of Jabez Wilson partly because it gives his hypersensitive and hyperactive mind something to work on. As he tells Watson at the end of the tale:

“It saved me from ennui,” he answered, yawning. “Alas! I already feel it closing in upon me. My life is spent in one long effort to escape from the commonplaces of existence. These little problems help me to do so.”

Holmes' little problems also help the reader to escape from the commonplaces of existence.
By establishing that Holmes takes on any kind of case that interests him and saves him from boredom, Arthur Conan Doyle can write about a wider variety of characters, settings, and problems than would have been possible if Holmes only worked for clients who could pay a fee commensurate with his services. He has enough wealthy clients to earn all the money he needs. In one story, "The Adventure of the Priory School," a nobleman writes Holmes a check for six thousand pounds as a reward. This would be equivalent in buying power to at least a million of today's American dollars.
Holmes obviously does not expect to make any money off the problem brought to him by Jabez Wilson. Doyle has taken pains in many of his Sherlock Holmes stories to show that the great detective has other motives besides money for helping clients, and Wilson has probably informed him before Watson's arrival that he can't afford to pay. Holmes likes mental challenges. He also likes to help people in trouble. He sometimes finds, as he does in this story, that apparently trivial problems can have very complex ramifications and implications. At the very end of the story he tells Mr. Merryweather that he will not charge the bank for saving their French gold except to be reimbursed for some petty expenses.
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