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The scientist spoke in a tone of perpetual annoyance; but a long acquaintance had taught the reporter that it was what he said and not the manner of its saying that was to be heeded.

      “Imagination, Mr. Hatch, is the single connecting link between man and the infinite,” The Thinking Machine was saying. “It is the one quality which distinguishes us from what we are pleased to call the brute creation, for we have the same passions, the same appetites, and the same desires. It is the most valuable adjunct to the scientific mind, because it is the basis of all scientific progress. It is the thing which temporarily bridges gaps and makes it possible to solve all material problems—not some, but all of them. We can achieve nothing until we imagine it. Just so far as the human brain can imagine it can comprehend. It fails only to comprehend the eternal purpose, the Omnipotent Will, because it cannot imagine it. For imagination has a limit, Mr. Hatch, and beyond that we are not to go—beyond that is Divinity.”

      This wasn’t at all what Hatch had come to hear, but he listened with a sort of fascination.

      “The first intelligent being,” the irritated voice went on, “had to imagine that when two were added to two there would be a result. He found it was four, he proved it was four, and instantly it became immutable—a point in logic, a thing by which we may solve problems. Thus two and two make four, not sometimes, but all the time.”

      “I had always supposed that imagination was limitless,” Hatch ventured for a moment, “that it knows no bounds.”

      The Thinking Machine squinted at him coldly.

      “On the contrary,” he declared, “it has a boundary beyond which the mind of man merely reels, staggers, collapses. I’ll take you there.” He spoke as if it were just around the corner. “By aid of a microscope of far less power than the one there, the atomic or molecular theory was formulated. You know that—it is that all matter is composed of atoms. Now, imagination suggested and logic immutably demonstrates that the atoms themselves are composed of other atoms, and that those atoms in turn are composed of still others, ad infinitum. They are merely invisible, and imagination—I am not now stating a belief, but citing an example of what imagination can do—imagination can make us see the possibility of each of those atoms, down to infinity, being inhabited, being in itself a world relatively as distant from its fellows as we are from the moon. We can even imagine what those inhabitants would look like.”

      He paused a minute; Hatch blinked several times.

      “But the boundary lies the other way—through the telescope,” continued the scientist. “The most powerful glass ever devised has brought no suggestion of the end of the universe. It only brings more millions of worlds, invisible to the naked eye into sight. The stronger the glass, the more hopeless the task of even conjecturing the end, and here, too, the imagination can apply the atomic theory, and logic will support it. In other words, atoms make matter, matter makes the world, which is an inconceivably tiny speck in our solar system, an atom; therefore, all the millions and millions of worlds are mere atoms, infinitesimal parts of some far greater scheme. What greater scheme? There is the end of imagination! There the mind stops!”

      The immensity of the conception made Hatch gasp a little. He sat silent for a long time, awed, oppressed. Never before in his life had he felt of so little consequence.

      “Now, Mr. Hatch, as to this little problem that is annoying you,” continued The Thinking Machine, and the matter-of-fact tone was a great relief. “What I have said has had, of course, no bearing on it, except in so far as it demonstrates that imagination is necessary to solve a problem, that all material problems may be solved, and that, in meeting them, logic is the lever. It is a fixed quantity; its simplest rules have enabled me to solve petty affairs for you in the past, so—”

      The reporter came to himself with a start. Then he laid before this master brain the circumstances which cast so strange a mystery about the death by violence of Johann Wagner, junk-dealer, in the home of Franklin Phillips, millionaire. But his information was only from the time the police came into the affair. Mr. Phillips, Doctor Perdue and Mr. Matsumi alone knew of the ringing of the bell.

      “The blood-spot on one of the bells,” Hatch told the scientist in conclusion, “may be the mark of a hand, but its significance doesn’t appear. Just now the police are working on two queer points which they developed. First, Detective Mallory recognized the dead man as ‘Old Dutch’ Wagner, long suspected of conducting a ‘fence’—that is, receiving and disposing of stolen goods; and second, one of the servants in the Phillips’ household, Giles Francis, has disappeared. He hasn’t been seen since eleven o’clock on the night before the body was found, and then he was in bed sound asleep. Every article of his clothing, except a pair of shoes, trousers, and pajamas, was left behind.”

      The Thinking Machine turned away from the laboratory table and sank into a chair. For a long time he sat with his enormous yellow head thrown back and his slender, white fingers pressed tip to tip.

      “If Wagner was shot through the heart,” he said at last, “we know that death was instantaneous; therefore he could not have made the blood-mark on the bell.” It seemed to be a statement of fact. “But why should there be such a mark on the bell?”

      “Detective Mallory thinks that—” began the reporter.

      “Oh, never mind what he thinks!” interrupted the other testily. “What time was the body found?”

      “About half-past nine yesterday morning.”

      “Anything stolen?”

      “Nothing. The body was simply there, the window open and the door locked, and there was the blood-mark on the bell.”

      There was a pause. Cobwebby lines appeared on the broad forehead of the scientist and the squint eyes narrowed down to mere slits. Hatch was watching him curiously.

      “What does Mr. Phillips say about it?” asked The Thinking Machine. He was still staring upward and his thin lips were drawn into a straight line.

      “He is ill, just how ill we don’t know,” responded the newspaper man. “Doctor Perdue has, so far, not permitted the police to question him.”

      The scientist lowered his eyes quickly.

      “What’s the matter with him?” he demanded.

      “I don’t know. Doctor Perdue has declined to make any statement.”

      Half an hour later The Thinking Machine and Hatch called at the Phillips’ house. They met Doctor Perdue coming out. His face was grave and preoccupied; his professional air of jocundity was wholly absent. He shook hands with The Thinking Machine, whom he had met years before beside an operating-table, and reëntered the house with him. Together the three went to the little room—the scene of the tragedy.

      The Japanese gong still swung over the desk. The crabbed little scientist went straight to it, and for five minutes devoted his undivided attention to a study of the splotch on the fifth bell. From the expression of his face Hatch could gather nothing. What the scientist saw might or might not have been illuminating. Was the splotch the mark of a hand? If it were, Hatch argued, it offered no clew, as the intricate lines of the flesh were smeared together, obliterated.

      Next The Thinking Machine critically glanced about him, and finally threw open the window facing east. For a long time he stood silently squinting out; and, save for the minute lines in his forehead, there was no indication whatever of his mental workings. The little room was on the second floor and jutted out at right angles across a narrow alley which ran beneath them to the kitchen in the back. The dead-wall of the next building was only four feet from the Phillips’ wall, and was without windows, so it was easily seen how a man, unobserved, might climb up from below despite an arc-light above the wide front door of an apartment-house across the street, visible in the vista of the alley.

      “Do you happen to know, Perdue,” asked The Thinking Machine at last, “if this west window was ever opened?”

      “Never,” replied the physician. “Detective Mallory questioned the servants about it. It seems that the kitchen is beneath, somewhat

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