"Quite a clear print, you see," repeated Mrs. Marlow brightly. "No spot there. You must have been thinking of another."

"Aye, just so," replied Allerdyke absentmindedly. "Another, yes, of course. Aye, to be sure—you're right. No spot on that, certainly."

He was talking aimlessly, confusedly, as he turned the print over in his hand, examining it back and front. And having no excuse for keeping it, he handed it back with a keen look at its owner. What the devil, he asked himself, was this mysterious woman playing at?

"I'm going to have this mounted and framed," said Mrs. Marlow, as she put the photograph back in her bag and turned to go. "I misplaced it some time ago and couldn't lay hands on it, but I came across it by accident this morning, so now I'll take care of it."

She nodded, smiled, and went off into the sunlight outside, and Allerdyke, more puzzled than ever, walked forward into the hotel and towards the restaurant. At its door he met Fullaway, coming out, and in his usual hurry.

Fullaway started at sight of Allerdyke, button-holed him, and led him into a corner.

"Oh, I say, Allerdyke!" he said, in his bustling fashion. "Look here, a word with you. You've no objection, have you?" he went on in subdued tones, "if Van Koon and I have a try for that reward? It doesn't matter to you, or to the Princess, or to Miss Lennard, who gets the reward so long as the criminals are brought to justice and the goods found—eh? And you know fifty thousand is—what it is."

"You've got an idea?" asked Allerdyke, regarding his questioner steadily.

"Frankly, yes—an idea—a notion," answered Fullaway. "Van Koon and I have been discussing the whole affair—just now. He's a smart man, and has had experience in these things on the other side. But, of course, we don't want to give our idea away. We want to work in entire independence of the police, for instance. What we're thinking of requires patience and deep investigation. So we want to work on our own methods. See?"

"It doesn't matter to me who gets the reward—as you say," said Allerdyke slowly. "I want justice. I'm not so much concerned about the jewels as about who killed my cousin. I believe that man Lydenberg did the actual killing—but who was at Lydenberg's back? Find that out, and—"

"Exactly—exactly!" broke in Fullaway. "The very thing! Well—you understand, Allerdyke. Van Koon and I will want to keep our operations to ourselves. We don't want police interference. So, if any of these Scotland Yard chaps come to you here for talk or information, don't bring me into it. And don't expect me to tell what we're doing until we've carried out our investigations. No interim reports, you know, Allerdyke. Personally, I believe we're on the track."

"Do just what you please," replied Allerdyke. "You're not the only two who are after that reward. Go ahead—your own way."

He turned into the restaurant and ordered his lunch, and while it was being brought sat drumming his fingers on the table, staring vacantly at the people about him and wondering over the events of the morning. Rayner's, or Ramsay's, vague hint that something might suddenly clear everything up; Fullaway's announcement that he and Van Koon had put their heads together; Mrs. Perrigo's story of the French maid and the young man who led blue-ribboned pug-dogs—but all these were as nothing compared to the fact that Mrs. Marlow had actually shown him the photograph which he had until then firmly believed to lie hidden in the case of Lydenberg's watch. That beat him.

"Is my blessed memory going wrong?" he said to himself. "Did I actually print more than four copies of that thing! No—no!—I'm shot if I did. My memory never fails. I did not print off more than four. James had three; I had one. Mine's in my album upstairs. I know what James did with his. Cousin Grace has one; Wilson Firth has another; he gave the third to this Mrs. Marlow—and she's got it! Then—how the devil did that photograph, which looks to be of my taking, which I'd swear is of my taking, come to be in Lydenberg's watch? Gad—it's enough to make a man's brain turn to pap!"

He was moodily finishing his lunch when Chettle came in to find him. Allerdyke, who was in a quiet corner, beckoned the detective to a seat, and offered him a drink.

"Well?" he asked. "What's been done?"

"It's all right," answered Chettle. "I've told no more than was necessary—just what we agreed upon. To tell you the truth, our folks don't attach such tremendous importance to it—they will, of course, when you tell them your story about the photo. Just at present they merely see the obvious fact—that Lydenberg was furnished with the photo as a means of ready identification of your brother. No—at this moment they're full of the Perrigo woman's story—they think that's a sure clue—a good beginning. Somebody, they say, must own, or have owned, those pugs! Therefore they're going strong on that. Meanwhile, I'm going back to Hull for at any rate a few days."

"You've still got that watch on you?" asked Allerdyke.

"Certainly," answered Chettle, clapping his hand to his breast-pocket. "Technically speaking, it's in charge of the Hull police—it'll have to be produced there. Did you want to see it again, Mr. Allerdyke?"

"Finish your drink and come up to my sitting-room," said Allerdyke. "I'll give you a cigar up there. Yes," he added, as they left the restaurant and went upstairs. "I do want to see it again—or, rather, the photograph. You're in no hurry?"

"A good hour to spare yet," replied Chettle.

Allerdyke locked the door of the sitting-room when they were once inside it, and that done he placed a decanter, a syphon, and a glass on his table, and flanked them with a box of cigars. He waved a hospitable hand towards these comforts.

"Sit down and help yourself, Chettle," he said. "A drop of my whisky'll do you no harm—that's some I got down from home, and you'll not find its like everywhere. Light a cigar—and put a couple in your pocket to smoke in the train. Now then, let's see that photograph once more."

Chettle handed over the watch, and Allerdyke, opening the case, delicately removed the print. He sat down at the table with his back to the light, and carefully examined the thing back and front, while the detective, glass in hand, cigar in lips, and thumb in the armhole of his waistcoat, watched him appreciatively and inquisitively.

"Make aught new out of it, sir?" he asked after a while.

Instead of answering, Allerdyke laid the photograph down, went across to another table, and took from it his album. He turned its leaves over until he came to a few loose prints. He picked them up one after another and examined them. And suddenly he knew the secret. There was no longer any problem, any difficulty about that photograph. He knew—now! And with a sharp exclamation, he flung the album back to the side-table, and turned to the detective.

"Chettle!" he said. "You know me well enough to know that I can make it well worth any man's while to keep a secret until I tell him he can speak about it! What!"

"I should think so, Mr. Allerdyke," responded Chettle, readily enough.
"And if you want me to keep a secret—"

"I do—for the time being," answered Allerdyke. He sat down again and picked up the photograph which had exercised his thoughts so intensely. "I've found out the truth concerning this," he said, tapping it with his finger. "Yes, I've hit it! Listen, now—I told you I'd only made four prints of this photo, and that I knew exactly where they all were—one in my own album there, two given by James to friends in Bradford, one—as we more recently found out—given by James to Mrs. Marlow. That one—the Mrs. Marlow one—we believed to be—this—this!"

"And isn't it, Mr. Allerdyke?" asked Chettle wonderingly.

Allerdyke laughed—a laugh of relief and satisfaction.

"Less than an hour ago," he replied, "in fact, just before you came in, Mrs. Marlow showed me the photo which James gave her—showed it to me, out below there in the hall. No mistaking it! And so—when you came, I was racking my brains to rags trying to settle what this photo—this!—was. And now I know what it is—and damn me if I know whether the discovery makes things plainer or more mixed up! But—I know what this is, anyway."

"And—what is it, sir?" asked Chettle eagerly, eyeing the photo as if it were some fearful living curiosity. "What, Mr. Allerdyke?"

"Why, it's a photograph of my photograph!" almost shouted Allerdyke, with a thump of his big hand on the table. "That's the truth. This has been reproduced from mine, d'ye see? Look here—happen you don't know much about photography, but you'll follow me—I always use a certain sort of printing-out paper; I've stuck to one particular sort for years—all the photos in that album are done on that particular sort. The four prints I made of James's last photo were done on that paper. Now then—this photo, this print that you found in Lydenberg's watch, is not done on that paper—it's a totally different paper. Therefore—this is a reproduction! It is not my original print at all—it's been copied from it. See?"

Chettle, who had followed all this with concentrated attention, nodded his head several times.

"Clever—clever—clever!" he said with undisguised admiration. "Clever, indeed! That's a smart bit of work, sir. I see—I understand! Bless my soul! And what do you gather from that, Mr. Allerdyke?"

"This!" answered Allerdyke. "Just now, Mrs. Marlow said to me, speaking of her photo—the fourth print, you know—'I misplaced it some time ago,' she said, 'and couldn't lay hands on it, but I came across it accidentally this morning.' Now then, Chettle, here's the thing—somebody took that fourth print from Mrs. Marlow, reproduced it—and that—that print which you found in Lydenberg's watch is the reproduction!"

"So that," began Chettle suggestively, "so that—"

"So that the thing now is to find who it is that made the reproduction," said Allerdyke. "When we've found him—or her—I reckon we shall have found the man who's at the heart of all this. Leave that to me! Keep this a dead secret until I tell you to speak—we shall have to tell all this, and a bonny sight more, to your bosses at headquarters—off you go to Hull, and do what you have to do, and I'll get on with my work here. I said I didn't know whether this discovery makes things thicker or clearer, but, by George, it's a step forward anyway!"

Chettle put the reproduction back into the case of the watch and bestowed it safely in his pocket.

"One step forward's a good deal in a case like this, Mr. Allerdyke," he said. "What are you going to do about the next step, now?"

"Try to find out who made that reproduction," replied Allerdyke bluntly. "No easy job, either! The ground's continually shifting and changing under one's very feet. But I don't mind telling you my present theory—somebody's got information of that jewel deal from Fullaway's office, somebody who had access to his papers, somebody who managed to steal that photo of mine from Mrs. Marlow for a few days or until they could reproduce it. What I want to find now is—an idea of that somebody. And—I'll get it!—I'll move heaven and earth to get it! But—other matters. You say your folks at the Yard are going to follow up that Perrigo woman's clue? They think it important, then?"

"In the case of the Frenchwoman, yes," answered Chettle. He thrust his hand into a side-pocket and brought out a crumpled paper. "Here's a proof of the bill they're getting out," he said. "They set to work on that as soon as they'd got the information. That'll be up outside every police-station in a few hours, and it's gone out to the Press, too."

Allerdyke took the proof, still damp from the machine, and looked it over. It asked, in the usual formal language, for any information about a young man, dark, presumably a foreigner, who, about the middle of March, was in the habit of taking two pug dogs, generally bedecked with blue ribbons, into Kensington Gardens.

"There ought to be some response to that, you know, Mr. Allerdyke," remarked Chettle. "Somebody must remember and know something about that young fellow. But, upon my soul, as I said to Blindway just now, I don't know whether that bill's a mere advertisement or a—death warrant!"

"Death warrant!" exclaimed Allerdyke. "What d'you mean?"

Chettle chuckled knowingly.

"Mean," he said. "Why, this—if that young fellow who led pugs about, and talked to Mamselle Lisette in Kensington Gardens, is another of the cat's paws that this gang evidently made use of, I should say that when the gang sees he's being searched for, they'll out him, just as they outed her and Lydenberg. That's what I mean, Mr. Allerdyke—they'll do him in themselves before anybody else can get at him! See?"

Allerdyke saw. And when the detective had gone, he threw himself into a chair, lighted one of his strongest cigars, drew pen, ink, and paper to him, and began to work at his problem with a grim determination to evolve at any rate a clear theory of its possible solution.