The buckle might have been dropped by a former occupant of the room.

But was that likely?
Would an object sparkling with diamonds have escaped the eyes of even a careless chambermaid?
Would it have escaped the keener eyes of James Allerdyke?
Anyhow, that question could easily be settled by finding out how long that particular room had been unoccupied before James was put into it.

A much more important question was--had the owner of the buckle been in the room between nine o'clock of the previous evening and five o'clock that morning?
Out of that, again, rose certain supplementary questions: What had she been doing there?
And most important of all--who was she?
That might possibly be solved by an inspection of the hotel register, and after he had drunk the coffee which was presently brought up to him, Allerdyke went down to the office to set about that necessary, yet problematic, task.
As he reached the big hall on the ground floor of the hotel, the manager came across to him, displaying a telegram.
"For your cousin, sir," he announced, handing it over to Allerdyke.
"Just come in." Allerdyke slowly opened the envelope, and as he unfolded the message, caught the name Franklin Fullaway at its foot-- "Let me know what time you arrive King's Cross to-day and I will meet you, highly important we should both see my prospective client at once." This message bore the same address which Allerdyke had found in the telegram discovered in James's pocket-book--Waldorf Hotel--and he determined to wire Mr.Franklin Fullaway immediately.

He sat down at a writing-table in the hall and drew a sheaf of telegraph forms towards him.

But it was not easy to compose the message which he wished to send.
He knew nothing of the man to whom he must address it, nothing of his business relations with James; he had no clear notion of what the present particular transaction was, nor how it might be connected with what had just happened.