“You didn’t overhear any of the conversation going on, did you, sir?”

“I did catch just a fragment of it,” said the secretary, “and, supposing as I did that it was Dr. Sheppard who was with Mr. Ackroyd, that fragment struck me as distinctly odd. As far as I can remember, the exact words were these. Mr. Ackroyd was speaking. ‘The calls on my purse have been so frequent of late’—that is what he was saying—‘of late, that I fear it is impossible for me to accede to your request....’ I went away again at once, of course, so did not hear any more. But I rather wondered because Dr. Sheppard——”

“——Does not ask for loans for himself or subscriptions for others,” I finished.

“A demand for money,” said the inspector musingly. “It may be that here we have a very important clew.” He turned to the butler. “You say, Parker, that nobody was admitted by the front door this evening?”

“That’s what I say, sir.”

“Then it seems almost certain that Mr. Ackroyd himself must have admitted this stranger. But I don’t quite see——”

The inspector went into a kind of day-dream for some minutes.

“One thing’s clear,” he said at length, rousing himself from his absorption. “Mr. Ackroyd was alive and well at nine-thirty. That is the last moment at which he is known to have been alive.”

Parker gave vent to an apologetic cough which brought the inspector’s eyes on him at once.

“Well?” he said sharply.