"That's why I remarked mat the case explained itself. There is only one explanation that can account for it. When I was meditating over this astonishing behavior of X, I said, 'Why did he eat Depping's dinner?' Morley Standish triumphandy replied, 'Because he was hungry.' But it didn't seem to occur to anybody that X was hungry because X had come from some distance away, and in a hurry. It did not seem plain that people who eat normal dinners in the neighborhood of The Grange are not apt to behave in this fashion.
The corollary to this not-very complifcated deduction is that X not only came from some distance away, but was so thoroughly intimate with Depping that he (or she) could sit down and eat a dinner like that without ever thinking twice about it. It's the sort of thing you might do with a dose relative, but few other people. You have only to ask yourself, 'How many people were close enough to Depping to fit into this picture?' And on top of that you will inquire about the key. How many people would have a key which fitted Depping's balcony door? Depping locked it when he went out, and X had to get in."
"Yes, but X might have come in the front door—" Morgan was beginning, when he saw the flaw and stopped. "I see. It would be the same whichever door was used. X could'nt ring and be let in by the valet."
"Certainly not for the purpose in mind," said Dr. Fell; "that is, murdering Depping. Now, to the combination of these two things, a person with keys to the house yet living a great distance away, is added another significant circumstance… After his attempted murder of Spinelli, Depping returned. It was then he discovered that somewhere on the way he had lost his key to the balcony door. He went up, looked through the window, and saw X in possession. Would he have revealed himself so readily to some member of the neighborhood; gone into conversation; agreed to the scheme for walking in the front door; unless the person inside had been… who? And the answer that occurred to me in my innocence was: a daughter, who, being a daughter, he thought would not betray him. The fact that she was his mistress I didn't know, but the rule still works.
"Now we come to that mysterious eight of swords. The curious part there was that not only was there nobody there who knew what it meant, but that nobody had ever heard of Depping's interest in the occult. He never mentioned it, he never played with fortune-telling packs, though his bookshelves were stuffed with works on the subject… I filed away the idea, still wondering, when — as soon as Spinelli appeared on the scene— he recognized it. It was definitely a part of Depping's dark past. The murderer, then, was somebody who had known Depping in America; or, at least, known something of Depping that nobody else did.
"With my growing suspicion of the daughter in my mind, I tried to couple it with this fact. It was corroboration, even though it had never entered my head to suspect the daughter of being anything else than she pretended until Spinelli and Langdon were on the scene.
"I noticed how all references to the daughter were scrupulously kept out of their talk. What Langdon did was to hint at a 'mysterious woman' with whom Depping was going to run away: Why did he do that?
Then Spinelli made a slip and revealed that he knew the amount of Depping's estate. Whatever you deduce from this, you will admit that these two — between them — knew something about Depping's past life out of which they both believed they could make capital.
"Spinelli I could understand, because I believed he knew who the killer was. But what could both of them have known, which would be of profit? What had Langdon found out? And the first faint suggestion began to come to me, though I didn't believe it. This daughter, who didn't live with her father, although— vide Morley Standish — he was 'always worrying about her, and what she was doing’; this card of the taroc that Depping only used in America, and whose painting in water color suggested a woman; this queer attitude of the lawyer…
"For, you see, if Betty Depping were not really his daughter, it would be an excellent thing for Langdon. I mean blackmail. 'Split half the estate with me, or you get none.' And it would fit in exactly…"