“Ah, but how do you know that, sir?” asked the inspector, with the air of one who puts his finger on a weak point.
“Because Miss Cross happened to mention it casually to Anthony!” Roger returned triumphantly. “I’d got as far as that in my reasoning, you see, when it occurred to me that the only possible purpose Mrs. Vane could have in delaying the death was this one, to provide herself with an alibi. If I could find out, I felt at that stage, that Mrs. Vane actually had expressed her intention of going away in the very near future, then my case was as good as clinched. And up pops Anthony with the very information I wanted!”
“So I haven’t lived in vain after all, Inspector, you see,” murmured Anthony facetiously.
“Well, hitherto I’d been working entirely on guesswork, but that seemed to give me the one bit of proof I wanted. After that it was simply a case of using one’s imagination to reconstruct what must have happened. And what did happen can be put baldly in a couple of sentences. Before Mrs. Vane’s ingenious scheme could take effect, Meadows had pushed its author over the cliff. Result, Meadows murdered Mrs. Vane and Mrs. Vane murdered Meadows, in spite of the handicap of being already dead herself. I should think that must be the first time in Scotland Yard’s history that a man had been murdered by a corpse, Inspector, isn’t it? If I wanted to make a detective story out of it and was looking for a nice lurid title, I should call it ‘The Dead Hand.’ Well, now, comments, please. What have you got to say about it all?”
“I’ll say this, sir,” replied the inspector without hesitation. “It’s as clever a bit of constructive reasoning as ever I’ve heard.”
“And the idea had never occurred to you?” pursued Roger, pleased.
“Never,” admitted the inspector handsomely. “And so after all this excitement the public is to be disappointed of an arrest, eh?”
“Well, I’m afraid so.”
There was a little silence.
“Of course it isn’t capable of what you might call proof, Mr. Sheringham, is it?” remarked the inspector thoughtfully. “Not the kind of proof to satisfy a court, I mean.”