At a cafe in Switzerland, two Gestapo agents plot with a man disguised as an old bookseller to abduct Dr. Franz Tobel (William Post Jr.), the inventor of a new bomb sight. However, the bookseller is really Holmes (Basil Rathbone), who sends the Nazis after decoys while he and Tobel drive to a rendezvous with an RAF plane that takes them to London. They go to 221B Baker Street, where Watson (Nigel Bruce) pulls a gun on them, but Mrs. Hudson (Mary Gordon) recognizes Holmes's voice. Holmes leaves to make arrangements with government representative Sir Reginald Bailey (Holmes Herbert), and Tobel sneaks out while Watson is asleep. He goes to see his sweetheart, Charlotte Eberli (Kaaren Verne), and gives her a message which, if anything happens to him, she's to give to Holmes. The message is in a version of the stick-figure code from the Holmes story "The Adventure of the Dancing Men". On his way back from Charlotte's, Tobel is struck on the head, but a policeman rescues him. Back at 221B, Holmes deduces that Tobel has been with a girl, and even describes her based on clues left on Tobel's clothing.The next day, a test of Tobel's bomb sight is a huge success. Tobel will supply it to the RAF, but insists that he will arrange all production, so no one besides himself will know the secret of the invention. The authorities reluctantly agree not to interfere, and will rely on Holmes to protect Tobel unofficially. Tobel brings a gift-wrapped package to fellow scientist Prof. Frederic Hoffner (Henry Victor). It's the prototype of the part of the bomb sight he'll be producing. Three other scientists will produce the other parts, all unknown to anyone other than Tobel. Soon, Scotland Yard reports that Tobel is missing. Holmes tracks down his secret office, but all they find there is some gift wrapping and the scent of an expensive perfume. Holmes deduces that Tobel called his lady love from 221B that first night and has the call traced. When Holmes visits her, Charlotte hands him the envelope Tobel left, but now it only contains a note - "We meet again, Mr. Holmes." It must have been switched by the "electrician" who came to Charlotte's apartment. From her description, Holmes realizes that he's up against Prof. Moriarty (Lionel Atwill).Holmes disguises himself as a thug formerly in Moriarty's employ and roams Soho until an old sailor leads him to one of Moriarty's places of business. The master criminal won't back down from his plans of treason, and has Holmes put in the false bottom of a sea chest, so he can be dumped in the ocean. Meanwhile a "beggar" (Michael Mark) who followed Holmes to Moriarty's place reports back to Watson and Inspector Lestrade (Dennis Hoey). They see Moriarty's two henchmen carrying away the sea chest. Amazingly, Lestrade figures out the false bottom trick and rescues Holmes. Back at Charlotte's, he takes the sheet of paper that was underneath the one on which Tobel wrote his coded message and finds away to reveal the message from it. Watson recognizes the substitution cypher from the earlier case, but it takes Holmes to figure out the variation that Tobel used. Decoded, the message gives the names and addresses of 3 of the 4 scientists (which is enough for Holmes to deduce Tobel's entire scheme). The final name is gibberish - obviously coded differently. Moriarty has had the message longer, and has already murdered the first three scientists and taken the prototypes of their components. The final name has him stumped - as he's busy trying unsuccessfully to torture it out of Tobel. Holmes realizes that the final name and address, of Prof. Hoffner, were coded in mirror image. Not long after, Moriarty comes to the same realization, and sends men to grab Hoffner (who will be more useful alive than the others) and the final component.When the thugs return, Moriarty opens the package, only to find a note - "We meet again, Professor." Of course, the captured scientist is really Holmes in disguise. Unknown to Moriarty and his men, while they were grabbing the fake professor, the real one went to their car and attached a device that would drip luminous paint on the street. Although they are delayed by a false trail at one point, Watson and the police are able to track Holmes to Moriarty's supposedly impregnable hideout. Meanwhile, Moriarty is open about his intention to murder Holmes, but the latter mocks his lack of originality in means of death. If their positions were reversed, he says, he'd put a needle in Moriarty and start slowly removing his blood, so Moriarty would die by inches, fully conscious the entire time. "The needle to the last, eh Holmes?" says Moriarty, but of course he can't resist inflicting this very form of death on the detective. This elaborate process gives Lestrade and Watson time to arrive and rescue Holmes. Nearby, a gunfight breaks out when police attempt to rescue Tobel, and Moriarty escapes in the confusion. Holmes, though weakened, has anticipated Moriarty and has a gun on him. However, Moriarty runs through his special escape tunnel, complete with a trap door that will send anyone following Moriarty plunging sixty feet into the sewers below. As soon as he disappears, we hear a long scream and a splash. Unfortunately for Moriarty, Holmes had found the trap door and left it open.In an epilog, Holmes and his companions watch RAF bombers on their way to Germany, equipped with the new bomb sight. Charlotte is now Mrs. Tobel. Holmes waxes Shakespearean, quoting from John of Gaunt's "Sceptred Isle" speech in Richard II.
Output: Question: Who is Sherlock Holmes nemesis?, Answer: Professor Moriarty.