What was Holmes 's argument to support the statement that the owner of the stick was quite young in The Hound of the Baskervilles?
To most people, the walking stick left at Holmes's apartment is precisely that: a walking stick and nothing more. But to the world's greatest detective, it's so much more than that. Once Holmes starts examining this seemingly commonplace object, he quickly deduces certain characteristics about its owner, Dr. Mortimer.
For one thing, it's clear to Holmes that Mortimer is not a very successful doctor. He arrives at this conclusion on the basis of the inscription on the walking stick: "C. C. H." Holmes establishes that this is an acronym for Charing Cross Hospital. That being the case, he makes the further deduction that Dr. Mortimer was presented with the walking-stick as a going away present when he left the hospital to start working in private practice.
If Mortimer had been a successful doctor at Charing Cross Hospital, then it is unlikely in the extreme that he would've left London to open up a country practice. At the very most, he could only have been a house-surgeon or a house-physician at the hospital, little more than a senior student. And as Mortimer left Charing Cross Hospital five years ago—the date of his departure is on the walking-stick—then one can reasonably conclude that he is a young man—under the age of thirty, to be precise.
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