Mr. and Mrs. Charles Hull; quiet elderly people; first visit to hotel. Henry M. Gillespie, Locke, N. Y. Middle-aged man; new guest. C. F. Willard, Chicago; been going to hotel for ten years; vouched for by hotel people. Armed with the list, Average Jones went to the Hotel Denton and spent a busy morning. “I’ve had a little talk with the hotel servants,” said he to Kirby, when the latter called to make inquiries. “Mr. Henry M. Gillespie, of Locke, New York, had room 168. It’s on the same floor with Mrs. Hale’s suite, at the farther end of the hall. He had only one piece of luggage, a suitcase marked H. M. G. That information I got from the porter. He left his room in perfect order except for one thing: one of the knobs on the headboard of the old fashioned bed was broken off short. He didn’t mention the matter to the hotel people.” “What do you make of that?” “It was a stout knob. Only a considerable effort of strength exerted in a peculiar way would have broken it as it was broken. There was something unusual going on in room 168, all right.” “Then you think Henry M. Gillespie, of Locke, New York, is our man.” “No,” said Average Jones. The Westerner’s square jaw fell. “Why not?” “Because there’s no such person as Henry M. Gillespie, of Locke, New York. I’ve just sent there and found out.” Three stones of the fire-blue necklace returned on the current of advertised appeal. One was brought in by the night bartender of a “sporting” club. He had bought it from a man who had picked it up in a gutter; just where, the finder couldn’t remember. For the second a South Brooklyn pawnbroker demanded (and received) an exorbitant reward. A florist in Greenwich, Connecticut, contributed the last. With that patient attention to detail which is the A. B. C. of detective work, Average Jones traced down these apparently incongruous wanderings of the stones and then followed them all, back to Mrs. Hale’s fire-escape.