“That’s quite right,” the inspector agreed soothingly. “But the trouble is, you see, that in a case like this when the known facts are so precious few, it’s possible to make half-a-dozen sets of deductions from them, all quite different. For instance,” he went on with a paternal air which Roger found somewhat hard to bear, “for instance I’ve no doubt that if you gave me time, I could prove to you, just as conclusively as you’ve proved your own theory, that the real murderer is the doctor’s secretary—(what’s her name?) Miss Williamson.”
“Miss Williamson?” Roger echoed, startled out of his mild annoyance. “Good Heavens, I never thought seriously of her. You don’t really think⸺?”
“I do not, sir,” the inspector smiled. “Not for one minute. I can’t say it ever entered my mind before. But—wait a minute!” He thought rapidly for a moment, still smiling. “How’s this? Miss Williamson’s setting her cap at the doctor,—” Roger caught his breath and looked at the other narrowly, but the inspector returned his gaze with bland innocence “—but knows she can’t get him, or thinks of course that she can’t get him, till Mrs. Vane’s out of the way. You’ve seen the lady, and you probably gathered as well as I did that if Miss Williamson makes up her mind to a thing, that thing’s going to happen. She strolled over from the house to the top of the cliffs that Tuesday afternoon to get a breath of air, and sees Mrs. Vane making for the Russells’ house, alone; not a soul in sight. ‘Here’s my opportunity!’ she says, joins Mrs. Vane and easily persuades her, on some pretext or other, to accompany her down to the ledge; and there all she’s got to do is to push her over. That fits the facts all right, doesn’t it?”
“But was Miss Williamson out that afternoon?” Roger asked shrewdly.
“Oh, yes, sir,” said the inspector, with an air of mild surprise. “Didn’t you know that?”
“No,” Roger had to admit. “I didn’t.”
“Oh, yes. She went out just as I said, for a breath of air. It was a hot afternoon and the laboratory got a bit stuffy. She was on the top of the cliffs for about half-an-hour, and says she saw nobody. It was a bit before the time of the murder, but we’ve only got her word for that. If nobody saw her go out and nobody saw her come in, how are we to know she’s telling the truth? I tried to get some confirmation of her statement from the doctor, but he’s as vague as you like. Might have been the morning, so far as he remembers. Besides, he wasn’t in the laboratory all the afternoon himself; I got that from the maid who took his tea in to him there; he wasn’t there then.”
“Well, how about the coat-button? How is that going to fit in?”
“On her way down the drive,” responded the inspector glibly, “Miss Williamson noticed a coat-button lying on the ground. She recognized it as one of Miss Cross’s, and being a precise, careful sort of person, picked it up and slipped it into her pocket, meaning to give it to Miss Cross later. After the murder, however, she says to herself: ‘Well, there’s nothing to beat a murder that looks like an accident, but I’ll just make sure that if anybody is going to be suspected it shan’t be me!’ and with that she climbs down to where the body’s lying (she’s a strong, active-looking woman, so that wouldn’t give her overmuch difficulty) and puts the button in the dead woman’s hand. As for the footprints, they might just as well have been made by her as anyone else.”
“Very neat,” said Roger approvingly. “And the shoes, eh? What about them?”