Allerdyke, who could not exist without fresh air and exercise, went for a stroll before breakfast when he was in London—­he usually chose the Embankment, as being the nearest convenient open space, and thither he now repaired, thinking things over.  There were many new features of this affair to think about, but the one of the previous night now occupied his thoughts to the exclusion of the others.  What was this woman doing, coming—­with evident secrecy—­out of one set of rooms, and entering another at that late hour?  He wanted to know—­he must find out—­and he would find out with ease,—­and indirectly, from Fullaway.

Fullaway always took his breakfast at a certain table in a certain corner of the coffee-room at the hotel; there Allerdyke had sometimes joined him.  He found the American there, steadily eating, when he returned from his walk, and he dropped into a chair at his side with a casual remark about the fine morning.

“Didn’t set eyes on you last night at all,” he went on, as he picked up his napkin.  “Off somewhere, eh?”

“Spent the evening out,” answered Fullaway.  “Not often I do, but I did—­for once in a way.  Van Koon and I (you don’t know Van Koon, do you?—­he’s a fellow countryman of mine, stopping here for the summer, and a very clever man) we dined at the Carlton, and then went to the Haymarket Theatre.  I was going to ask you to join us, Allerdyke, but you were out and hadn’t come in by the time we had to go.”

“Thank you—­no, I didn’t get in until seven o’clock or so,” answered Allerdyke.  “So I’d a quiet evening.”

“No news, I suppose?” asked Fullaway, going vigorously forward with his breakfast.  “Heard nothing from the police authorities?”

“Nothing,” replied Allerdyke.  “I suppose they’re doing things in their own way, as usual.”

“Just so,” assented Fullaway.  “Well, it’s an odd thing to me that nobody comes forward to make some sort of a shot at that reward!  Most extraordinary that the man of the Eastbourne Terrace affair should have been able to get clean away without anybody in London having seen him—­or at any rate that the people who must have seen him are unable to connect him with the murder of that woman.  Extraordinary!”

“It’s all extraordinary,” said Allerdyke.  He took up a newspaper which Fullaway had thrown down and began to talk of some subject that caught his eye, until Fullaway rose, pleaded business, and went off to his rooms upstairs.  When he had gone Allerdyke reconsidered matters.  So Fullaway had been out the night before, had he—­dining out, and at a theatre?  Then, of course, it would be quite midnight before he got in.  Therefore, presumably, he did not know that his secretary was about his rooms—­and entering and leaving another suite close by.  No—­Fullaway knew nothing—­that seemed certain.

The remembrance of what he had seen sent Allerdyke, as soon as he had breakfasted, to the hall of the hotel, and to the register of guests.  There was no one at the register at that moment, and he turned the pages at his leisure until he came to what he wanted.  And there it was—­in plain black and white—­