Continuing the 1946 season of The New Adventures of Sherlock Holmes, here are the summaries for the next two episodes you mentioned. Both featured Tom Conway as Holmes and Nigel Bruce as Watson.
The Singular Affair of the Coptic Compass
Original Air Date: December 7, 1946
Summary: Sherlock Holmes returns to his lodgings to find a bizarre collection of items: a railway ticket, a Coptic compass, a half-eaten apple, and a naked corpse.
The Mystery: The crime appears designed to frame Holmes or at least cause him extreme professional embarrassment and lead to his arrest by Scotland Yard.
The Villain: The episode serves as a battle of wits against his ultimate nemesis, Professor Moriarty, who planted the murder specifically to distract Holmes while he attempted to steal a priceless jewel.
The Adventure of the Grand Old Man
Original Air Date: December 21, 1946
Summary: Holmes is hired to protect an elderly, dying playwright—the "Grand Old Man" of the title.
The Mystery: The playwright is in danger of being murdered before he can fulfill a final wish: finding the living relatives of a man from whom he had stolen a play years earlier.
Note: Although an original radio script, the story was loosely inspired by elements from Sir Arthur Conan Doyle's novel The Sig