The mystery takes place at a chateau: "The Glandier - ancient Glandierum - was so called from the quantity of glands (acorns) which, in all times, had been gathered in that neighborhood." A standard French word, from the Old French glant, from the Latin glandem.
"Having explained so far, I cannot refrain from making one further reflexion." When one ponders or considers a subject, the common term is that one "reflects" on the matter, but it is unexpected to see reflexion (or reflection) used in the noun form in this manner. A reflection in a mirror, certainly, but as used here I was quite startled.
Now consider these unusual contractions:
"I have n't had them arrested."I think I've listed a number of unusual contractions in my reviews of John Dickson Carr books, written in the 1930s. This contracting of not to n't, unjoined to the verb is from decades earlier. I don't know if this was common usage by copy editors of the time or not.
"Are n't you satisfied?"
"A keeper is as much a servant as any other, is n't he?"
"But I've made him understand that his face does n't please me..."
"When we were in complete darkness, he lit a wax vesta..." Vesta was the Roman goddess of the hearth and the home, so I suppose the application of the name to a match is quite appropriate, though nowadays archaic.
"When I left my chamber, at half-past ten, my father was already at work in the laboratory. We worked together till midday. We then took half-an-hour's walk in the park, as we were accustomed to do, before breakfasting at the chateau." Literally this makes logical sense; if you skip the morning meal and break your fast in the afternoon, that meal would be your "break-fast," but it does sound odd to the modern reader.
"Mademoiselle Stangerson threw a fichu shawl over her shoulders..." A French novelist applies a French term: "Borrowed from French fichu (“(noun) triangular scarf; (adjective) got up, put together”) (in the sense of something thrown on without much thought), from ficher (“to drive something (such as a nail) by its point”), ultimately from Latin fīgō (“to fasten, fix; to pierce, transfix; to drive (a nail)”)"
Related: Pildomatist (from Leroux' Phantom of the Opera)