“Hum-m-m! I see! So, then, you really do not know if there actually was a woman or a girl at all? Any idea where the persons were supposed to live?”

“Yes. They hired a room on the top floor of a house adjoining the Ocean Billow Hotel, sir. At least, Reggie—that’s my youngest son, Mr. Cleek—saw Greta go in there and look down from one of the top floor windows one day when he was on his way home from school. He spoke to her about it at the dinner table that night, and she said that that was where her ‘pensioners lived.’”

“Pretty good neighbourhood that, by Jove! for people who were ‘pensioners’ to be living in,” commented Cleek. “The Ocean Billow Hotel is a modern establishment—lifts, electric lights, liveried attendants, and caters to people of substance and standing.”

“Yes,” admitted Beachman. “When I was suspended, sir, during the examination and this house taken over by Sir Charles, I took Mrs. Beachman and Reggie there, and we have remained at the place, nominally under guard, ever since. You see, being convenient and in a straight line, so to speak, it offered extra advantages in case of my being summoned here at a moment’s notice.”

“H’m! Yes! I see!” said Cleek, stroking his chin. “In a straight line from here, eh? House next door would, of course, offer the same advantages; and from a room on the top floor a wire-tapping device——Yes, just so! I think, Sophie, I think I smell a very large mouse, my dear, and I shan’t be surprised if we’ve hit upon the place of reception for your messages the very first shot.”

“Messages, Mr. Cleek? Messages?” interposed Sir Charles. “You surely do not mean to infer that the woman telegraphed messages from this house? Do you forget, then, that there is no instrument, no wire, attached to the place?”

Cleek puckered up his brows. For the moment he had forgotten that fact.

“Still, there are wires passing over it, Sir Charles,” he said presently; “and if a means of communication with those were established, the ‘tapper’ at the other end could receive messages easily. She is a devil of ingenuity is Sophie. I wouldn’t put it beyond her and her confederates to have rigged up a transmitting instrument of some sort which the woman could carry on her person and attach to the wire when needed.”

Here Sir Charles threw in something which he felt to be in the nature of a facer.

“Quite so,” he admitted. “But do not forget, Mr. Cleek, that the deflected message was sent last night, and that the woman was not then in this house.”