Certainly no problem that ever came to the attention of The Thinking Machine required in a greater degree subtlety of mind, exquisite analytical sense, and precise knowledge of the marvels of science than did that singular series of events which began with the death of the Honorable Violet Danbury, only daughter and sole heir of the late Sir Duval Danbury, of Leamington, England. In this case The Thinking Machine — more properly, Professor Augustus S.

F. X. Van Dusen, Ph. D., M. D., F. R. S., et cetera, et cetera — brought to bear upon an extraordinary mystery of crime that intangible genius of logic which had made him the court of last appeal in his profession. “Logic is inexorable,” he has said; and no greater proof of his assertion was possible than in this instance where literally he seemed to pluck a solution of the riddle from the void.

Shortly after eleven o’clock on the morning of Thursday, May 4, Miss Danbury was found dead, sitting in the drawing-room of apartments she was temporarily occupying in a big family hotel on Beacon Street. She was richly gowned, just as she had come from the opera the night before; her marble-white bosom and arms aglitter with jewels. On her face, dark in death as are the faces of those who die of strangulation, was an expression of unspeakable terror. Her parted lips were slightly bruised, as if from a light blow; in her left cheek was an insignificant, bloodless wound. On the floor at her feet was a shattered goblet. There was nothing else unusual, no disorder, no sign of a struggle. Obviously she had been dead for several hours.

All these things considered, the snap judgement of the police — specifically, the snap judgement of Detective Mallory, of the bureau of criminal investigation — was suicide by poison. Miss Danbury had poured some deadly drug into a goblet, sat down, drained it off, and died. Simple and obvious enough. But the darkness in her face? Oh, that! Probably some effect of a poison he didn’t happen to be acquainted with. But it looked as if she might have been strangled! Pooh! Pooh! There were no marks on her neck, of fingers or anything else. Suicide, that’s what it was — the autopsy would disclose the nature of the poison.

Cursory questions of the usual nature were asked and answered. Had Miss Danbury lived alone? No; she had a companion upon whom, too, devolved the duties of chaperon — a Mrs. Cecelia Montgomery. Where was she? She’d left the city the day before to visit friends in Concord; the manager of the hotel had telegraphed the facts to her. No servants? No. She had availed herself of the service in the hotel. Who had last seem Miss Danbury alive? The elevator attendant the night before, when she had returned form the opera, about half past eleven o’clock. Had she gone alone? No. She had been accompanied by Professor Charles Meredith, of the university. He had returned with her, and left her at the elevator.

“How did she come to know Professor Meredith?” Mallory inquired. “Friend, relative —”

“I don’t know,” said the hotel manager. “She knew a great many people here. She’d only been in the city two months this time, but once, three years ago, she spent six months here.”

“Any particular reason for her coming over? Business, for instance, or merely a visit?”

“Merely a visit, I imagine.”

The front door swung open, and there entered at the moment a middle-aged man, sharp-featured, rather spare, brisk in his movements, and distinctly well groomed. He went straight to the inquiry desk.

“Will you please phone to Miss Danbury, and ask her if she will join Mr. Herbert Willing for luncheon at the country club?” he requested. “Tell her I am below with my motor.”

At mention of Miss Danbury’s name both Mallory and the house manager turned. The boy behind the inquiry desk glanced at the detective blankly. Mr. Willing rapped upon the desk sharply.

“Well, well?” he demanded impatiently. “Are you asleep?”

“Good morning, Mr. Willing,” Mallory greeted him.

“Hello, Mallory,” and Mr. Willing turned to face him. “What are you doing here?”

“You don’t know that Miss Danbury is”— the detective paused a little —“is dead?”

“Dead!” Mr. Willing gasped. “Dead!” he repeated incredulously. “What are you talking about?” He seized Mallory by the arm, and shook him. “Miss Danbury is —”

“Dead,” the detective assured him again. “She probably committed suicide. She was found in her apartments two hours ago.”

For half a minute Mr. Willing continued to stare at him as if without comprehension, then he dropped weakly into a chair, with his head in his hands. When he glanced up again there was deep grief in his keen face.

“It’s my fault,” he said simply. “I feel like a murderer. I gave her some bad news yesterday, but I didn’t dream she would —” He stopped.

“Bad news?” Mallory urged.

“I’ve been doing some legal work for her,” Mr. Willing explained. “She’s been trying to sell a huge estate in England, and just at the moment the deal seemed assured it fell through. I— I suppose it was a mistake to tell her. This morning I received another offer from an unexpected quarter, and I came by to inform her of it.” He stared tensely into Mallory’s face for a moment without speaking. “I feel like her murderer!” he said again.

“But I don’t understand why the failure of the deal —” the detective began; then: “She was rich, wasn’t she? What did it matter particularly if the deal did fail?”

“Rich, yes; but land poor,” the lawyer elucidated. “The estates to which she held title were frightfully involved. She had jewels and all those things, but see how simply she lived. She was actually in need of money. It would take me an hour to make you understand. How did she die? When? What was the manner of her death?”

Detective Mallory placed before him those facts he had, and finally went away with him in his motor car to see Professor Meredith at the university. Nothing bearing on the case developed as the result of that interview. Mr. Meredith seemed greatly shocked, and explained that his acquaintance with Miss Danbury dated some weeks back, and friendship had grown out of it through a mutual love of music. He had accompanied her to the opera half a dozen times.

“Suicide!” the detective declared, as he came away. “Obviously suicide by poison.”

On the following day he discovered for the first time that the obvious is not necessarily true. The autopsy revealed absolutely no trace of poison, either in the body or clinging to the shattered goblet, carefully gathered up and examined. The heart was normal, showing neither constriction nor dilation, as would have been the case had poison been swallowed, or even inhaled.

“It’s the small wound in her cheek, then,” Mallory asserted. “Maybe she didn’t swallow or inhale poison — she injected it directly into her blood through that wound.”

“No,” one of the examining physicians pointed out. “Even that way the heart would have shown constriction or dilation.”

“Oh, maybe not,” Mallory argued hopefully.

“Besides,” the physician went on, “that wound was made after death. That is proven by the fact that it did not bleed.” His brow clouded in perplexity. “There doesn’t seem to be the slightest reason for that wound, anyway. It’s really a hole, you know. It goes straight through her cheek. It looks as if it might have been made with a large hatpin.”

The detective was staring at him. If that wound had been made after death, certainly Miss Danbury didn’t make it — she had been murdered! And not murdered for robbery, since her jewels had been undisturbed.

“Straight through her cheek!” he repeated blankly. “By George! Say, if it wasn’t poison, what killed her?”

The three examining physicians exchanged glances.

“I don’t know that I can make you understand,” said one. “She died of absence of air in her lungs, if you follow me.”

“Absence of air — well, that’s illuminating!” the detective sneered heavily. “You mean she was strangled, or choked to death?”

“I mean precisely what I say,” was the reply. “She was not strangled — there is no mark on her throat; or choked — there is no obstruction in her throat. Literally she died of absence of air in her lungs.”

Mallory stood silently glowering at them. A fine lot of physicians, these!

“Let’s understand one another,” he said at last. “Miss Danbury did not die a natural death?”

“No!” emphatically.

“She wasn’t poisoned? Or strangled? Or shot? Or stabbed? Or run over by a truck? Or blown up by dynamite? Or kicked by a mule? Nor,” he concluded, “did she fall from an aeroplane?”

“No.”

“In other words, she just quit living?”

“Something like that,” the physician admitted. He seemed to be seeking a means of making himself more explicit. “You know the old nursery theory that a cat will suck a sleeping baby’s breath?” he asked. “Well, the death of Miss Danbury was like that, if you understand. It is as if some great animal or — or thing had —” He stopped.

Detective Mallory was an able man, the ablest, perhaps, in the bureau of criminal investigation, but a yellow primrose by the river’s brim was to him a yellow primrose, nothing more. He lacked imagination, a common fault of that type of sleuth who combines, more or less happily, a number eleven shoe and a number six hat. The only vital thing he had to go on was the fact that Miss Danbury was dead — murdered, in some mysterious, uncanny way. Vampires were something like that, weren’t they? He shuddered a little.

“Regular vampire sort of thing,” the youngest of the three physicians remarked, echoing the thought in the detective’s mind. “They’re supposed to make a slight wound, and —”

Detective Mallory didn’t hear the remainder of it. He turned abruptly, and left the room.

On the following Monday morning, one Henry Sumner, a longshoreman in Atlantic Avenue, was found dead sitting in his squalid room. On his face, dark in death, as are the faces of those who die of strangulation, was an expression of unspeakable terror. His parted lips were slightly bruised, as if from a light blow; in his left cheek was an insignificant, bloodless wound. On the floor at his feet was a shattered drinking glass!

’Twas Hutchinson Hatch, newspaper reporter, long, lean, and rather prepossessing in appearance, who brought this double mystery to the attention of The Thinking Machine. Martha, the eminent scientist’s one servant, admitted the newspaper man, and he went straight to the laboratory. As he opened the door The Thinking Machine turned testily from his worktable.

“Oh, it’s you, Mr. Hatch. Glad to see you. Sit down. What is it?” That was his idea of extreme cordiality.

“If you can spare me five minutes?” the reporter began apologetically.

“What is it?” repeated The Thinking Machine, without raising his eyes.

“I wish I knew,” the reporter said ruefully. “Two persons are dead — two persons as widely apart as the poles, at least in social position, have been murdered in precisely the same manner, and it seems impossible that —”

“Nothing is impossible,” The Thinking Machine interrupted, in the tone of perpetual irritation which seemed to be a part of him. “You annoy me when you say it.”

“It seems highly improbable,” Hatch corrected himself, “that there can be the remotest connection between the crimes, yet —”

“You’re wasting words,” the crabbed little scientist declared impatiently. “Begin at the beginning. Who was murdered? When? How? Why? What was the manner of death?”

“Taking the last question first,” the reporter explained, “we have the most singular part of the problem. No one can say the manner of death, not even the physicians.”

“Oh!” For the first time The Thinking Machine lifted his petulant, squinting, narrowed eyes, and stared into the face of the newspaper man. “Oh!” he said again. “Go on.”

As Hatch talked, the lure of a material problem laid hold of the master mind, and after a little The Thinking Machine dropped into a chair. With his great, grotesque head tilted back, his eyes turned steadily upward, and slender fingers placed precisely tip to tip, he listened in silence to the end.

“We come now,” said the newspaper man, “to the inexplicable after developments. We have proven that Mrs. Cecelia Montgomery, Miss Danbury’s companion, did not go to Concord to visit friends; as a matter of fact, she is missing. The police have been able to find no trace of her, and today are sending out a general alarm. Naturally, her absence at this particular moment is suspicious. It is possible to conjecture her connection with the death of Miss Danbury, but what about —”

“Never mind conjecture,” the scientist broke in curtly. “Facts, facts!”

“Further,” and Hatch’s bewilderment was evident on his face, “mysterious things have been happening in the rooms where Miss Danbury and this man Henry Sumner were found dead. Miss Danbury was found dead last Thursday. Immediately after the body was removed, Detective Mallory ordered her room locked, his idea being that nothing should be disturbed at least for the present, because of the strange circumstances surrounding her death. When the nature of the Henry Sumner affair became known, and the similarity of the cases recognized, he gave the same order regarding Sumner’s room.”

Hatch stopped, and stared vainly into the pallid, wizened face of the scientist. A curious little chill ran down his spinal column.

“Some time Tuesday night,” he continued, after a moment, “Miss Danbury’s room was entered and ransacked; and some time that same night Henry Sumner’s room was entered and ransacked. This morning, Wednesday, a clearly defined hand print in blood was found in Miss Danbury’s room. It was on the wooden top of a dressing table. It seemed to be a woman’s hand. Also, an indistinguishable smudge of blood, which may have been a hand print, was found in Sumner’s room!” He paused; The Thinking Machine’s countenance was inscrutable. “What possible connection can there be between this young woman of the aristocracy, and this — this longshoreman? Why should —”

“What chair,” questioned The Thinking Machine, “does Professor Meredith hold in the university?”

“Greek,” was the reply.

“Who is Mr. Willing?”

“One of the leading lawyers of the city.”

“Did you see Miss Danbury’s body?”

“Yes.”

“Did she have a large mouth, or a small mouth?”

The irrelevancy of the questions, to say nothing of their disjointedness, brought a look of astonishment to Hatch’s face; and he was a young man who was rarely astonished by the curious methods of The Thinking Machine. Always he had found that the scientist approached a problem from a new angle.

“I should say a small mouth,” he ventured. “Her lips were bruised as if — as if something round, say the size of a twenty-five-cent piece, had been crushed against them. There was a queer, drawn, caved-in look to her mouth and cheeks.”

“Naturally,” commented The Thinking Machine enigmatically. “And Sumner’s was the same?”

“Precisely. You say ‘naturally.’ Do you mean —” There was eagerness in the reporter’s question.

It passed unanswered. For half a minute The Thinking Machine continued to stare into nothingness. Finally:

“I dare say Sumner was of the English type? His name is English?”

“Yes; a splendid physical man, a hard drinker, I hear, as well as a hard worker.”

Again a pause.

“You don’t happen to know if Professor Meredith is now or ever has been particularly interested in physics — that is, in natural philosophy?”

“I do not.”

“Please find out immediately,” the scientist directed tersely. “Willing has handled some legal business for Miss Danbury. Learn what you can from him to the general end of establishing some connection, a relationship possibly, between Henry Sumner and the Honorable Violet Danbury. That, at the moment, is the most important thing to do. Neither of them may have been aware of the relationship, if relationship it was, yet it may have existed. If it doesn’t exist, there’s only one answer to the problem.”

“And that is?” Hatch asked.

“The murders are the work of a madman,” was the tart rejoinder. “There’s no mystery, of course, in the manner of the deaths of these two.”

“No mystery?” the reporter echoed blankly. “Do you mean you know how they —”

“Certainly I know, and you know. The examining physicians know, only they don’t know that they know.” Suddenly his tone became didactic. “Knowledge that can’t be applied is utterly useless,” he said. “The real difference between a great mind and a mediocre mind is only that the great mind applies its knowledge.” He was silent a moment. “The only problem remaining here is to find the person who was aware of the many advantages of this method of murder.”

“Advantages?” Hatch was puzzled.

“From the viewpoint of the murderer there is always a good way and a bad way to kill a person,” the scientist told him. “This particular murderer chose a way that was swift, silent, simple, and sure as the march of time. There was no scream, no struggle, no pistol shot, no poison to be traced, nothing to be seen except —”

“The hole in the left cheek, perhaps?”

“Quite right, and that leaves no clew. As a matter of fact, the only clew we have at all is the certainty that the murderer, man or woman, is well acquainted with physics, or natural philosophy.”

“Then you think,” the newspaper man’s eyes were about to start from his head, “that Professor Meredith —”

“I think nothing,” The Thinking Machine declared briefly. “I want to know what he knows of physics, as I said; also I want to know if there is any connection between Miss Danbury and the longshoreman. If you’ll attend to —”

Abruptly the laboratory door opened and Martha entered, pallid, frightened, her hands shaking.

“Something most peculiar, sir,” she stammered in her excitement.

“Well?” the little scientist questioned.

“I do believe,” said Martha, “that I’m a-going to faint!”

And as an evidence of good faith she did, crumpling up in a little heap before their astonished eyes.

“Dear me! Dear me!” exclaimed The Thinking Machine petulantly. “Of all the inconsiderate things! Why couldn’t she have told us before she did that?”

It was a labor of fifteen minutes to bring Martha around, and then weakly she explained what had happened. She had answered a ring of the telephone, and some one had asked for Professor Van Dusen. She inquired the name of the person talking.

“Never mind that,” came the reply. “Is he there? Can I see him?”

“You’ll have to explain what you want, sir,” Martha had told him. “He always has to know.”

“Tell him I know who murdered Miss Danbury and Henry Sumner,” came over the wire. “If he’ll receive me I’ll be right up.”

“And then, sir,” Martha explained to The Thinking Machine, “something must have happened at the other end, sir. I heard another man’s voice, then a sort of a choking sound, sir, and then they cursed me, sir. I didn’t hear an............