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The answer was a chorus of affirmation accompanied by some startling facial expressions.

"Did Mr. and Mrs. Morey employ any servants?"

"No," was the reply. "They had their meals in the cafe below most of the time. There is no housekeeping in these apartments at all."

"How many persons live in the building?"

"A hundred I should say."

"There is a great deal of passing to and fro, then?"

"Certainly. It was rather unusual that so few persons passed in and out last night and this morning, and certainly Mrs. Morey and her husband were not among them if that's what you're trying to find out."

The Thinking Machine glanced at the physician who was standing by silently.

"How long do you make it that she's been dead?" he asked.

"At least twelve hours," replied the physician. "Possibly longer."

"Yes, nearer fourteen, I imagine."

Abruptly he left the group and walked through the apartment and back again slowly. As he re-entered the room where the body lay, the door from the hall opened and Dr. Prescott entered, followed by Hutchinson Hatch. The Thinking Machine led the surgeon straight to the body and drew the cloth down from the face. Dr. Prescott started back with an exclamation of astonishment, recognition.

"There's no doubt about it at all in your mind?" inquired the scientist.

"Not the slightest," replied Dr. Prescott positively. "It's the same woman."

"Yet, look here!"

With a quick movement The Thinking Machine drew down the cloth still more. Dr. Prescott, together with those who had no idea of what to expect, peered down at the body. After one glance the surgeon dropped on his knees and examined closely the dead left hand. The fore-finger was off at the first joint. Dr. Prescott stared, stared incredulously. After a moment his eyes left the maimed hand and settled again on her face.

"I have never seen-never dreamed-of such a startling--" he began.

"That settles it all, of course," interrupted The Thinking Machine. "It solves and proves the problem at once. Now, Mr. Mallory, if we can go to your office or some place where we will be undisturbed I will--"

"But who killed her?" demanded the detective abruptly.

"I have the photograph of her murderer in my pocket," returned The Thinking Machine. "Also a photograph of an accomplice."

Detective Mallory, Dr. Prescott, The Thinking Machine, Hutchinson Hatch, and the apartment house physician were seated in the front room of the Morey apartments with all doors closed against prying, inquisitive eyes. At the scientist's request Dr. Prescott repeated the circumstances leading up to the removal of a woman's left fore-finger, and there The Thinking Machine took up the story.

"Suppose, Mr. Mallory," and the scientist turned to the detective, "a woman should walk into your office and say she must have a finger cut off, what would you think?"

"I'd think she was crazy," was the prompt reply.

"Naturally, in your position," The Thinking Machine went on, "you are acquainted with many strange happenings. Wouldn't this one instantly suggest something to you. Something that was to happen months off."

Detective Mallory considered it wisely, but was silent.

"Well here," declared The Thinking Machine. "A woman whom we now know to be Mrs. Morey wanted her finger cut off. It instantly suggested three, four, five, a dozen possibilities. Of course only one, or possibly two in combination, could be true. Therefore which one? A little logic now to prove that two and two always make four-not some times but all the time.

"Naturally the first supposition was insanity. We pass that as absurd on its face. Then disease-a taint of leprosy perhaps which had been visible on the left fore-finger. I tested for that, and that was eliminated. Three strong reasons for desiring the finger off, either of which is strongly probable, remained. The fact that the woman was English unmistakably was obvious. From the mark of a wedding ring on her glove and a corresponding mark on her finger-she wore no such ring-we could safely surmise that she was married. These were the two first facts I learned. Substantiative evidence that she was married and not a widow came partly from her extreme youth and the lack of mourning in her attire.

"Then Mr. Hatch followed her, learned her name, where she lived, and later the fact that she had arrived with her husband on a steamer a day or so before they took apartments here. This was proof that she was English, and proof that she had a husband. They came over on the steamer as Mr. and Mrs. David Girardeau-here they were Mr. and Mrs. Frederick Chevedon Morey. Why this difference in name? The circumstance in itself pointed to irregularity-crime committed or contemplated. Other things made me think it was merely contemplated and that it could be prevented; for then the absence of every fact gave me no intimation that there would be murder. Then came the murder presumably of-Mrs. Morey?"

"Isn't it Mrs. Morey?" demanded the detective.

"Mr. Hatch recognized the woman as the one he had followed, I recognized her as the one on whom there had been an operation, Dr. Prescott also recognized her," continued the Thinking Machine. "To convince myself, after I had found the manner of death, that it was the woman, I looked at her left hand. I found that the fore-finger was gone-it had been removed by a skilled surgeon at the first joint. And this fact instantly showed me that the dead woman was not Mrs. Morey at all, but somebody else; and incidentally cleared up the entire affair."

"How?" demanded the detective. "I thought you just said that you had helped cut off her fore-finger."

"Dr. Prescott and I cut off that finger yesterday," replied The Thinking Machine calmly. "The finger of the dead woman had been cut off months, perhaps years, ago."

There was blank amazement on Detective Mallory's face, and Hatch was staring straight into the squint eyes of the scientist. Vaguely, as through a mist, he was beginning to account for many things which had been hitherto inexplicable.

"The perfectly healed wound on the hand eliminated every possibility but one," The Thinking Machine resumed. "Previously I had been informed that Mrs. Morey did not-or said she did not-play the piano. I had seen the bare possibility of an immense insurance on her hands, and some trick to defraud an insurance company by marring one. Of course against this was the fact that she had offered to pay a large sum for the operation; that their expenses here must have been enormous, so I was beginning to doubt the tenability of this supposition. The fact that the dead woman's finger was off removed that possibility completely, as it also removed the possibility of a crime of some sort in which there might have been left behind a tell-tale print of that fore-finger. If there had been a serious crime with the trace of the finger as evidence, its removal would have been necessary to her.

"Then the one thing remained-that is that Mrs. Morey or whatever her name is-was in a conspiracy with her husband to get possession of certain properties, perhaps a title-remember she is English-by sacrificing that finger so that identification might be in accordance with the description of an heir whom she was to impersonate. We may well believe that she was provided with the necessary documentary evidence, and we know conclusively-we don't conjecture but we know-that the dead woman in there is the woman whose rights were to have been stolen by the so-called Mrs. Morey."

"But that is Mrs. Morey, isn't it?" demanded the detective again.

"No," was the sharp retort. "The perfect resemblance to Mrs. Morey and the finger removed long ago makes that clear. There is, I imagine, a relationship between them-perhaps they are cousins. I can hardly believe they are twins because the necessity, then of one impersonating the other to obtain either money or a title, would not have existed so palpably although it is possible that Mrs. Morey, if disinherited or disowned, would have resorted to such a course. This dead woman is Miss-Miss--" and he glanced at the back of a photograph, "Miss Evelyn Rossmore, and she has evidently been living in this city for some time. This is her picture, and it was made at least a year ago by Harkinson here. Perhaps he can give you her address as well."

There was silence for several minutes. Each member of the little group was turning over the stated facts mentally, and Detective Mallory was staring at the photograph, studying the handwriting on the back.

"But how did she come here-like this?" Hatch inquired.

"You remember, Mr. Hatch, when you followed Mrs. Morey here you told me she dressed again and went out?" asked the scientist in turn. "It was not Mrs. Morey you saw then-she was ill and I knew it from the operation-it was Miss Rossmore. The manager says a hundred persons live in this house-that there is a great deal of passing in and out. Can't you see that when there is such a startling resemblance Miss Rossmore could pass in and out at will and always be mistaken for Mrs. Morey? That no one would ever notice the difference?"

"But who killed her?" asked Detective Mallory, curiously. "How? Why?"

"Morey killed her," said The Thinking Machine flatly and he produced two other photographs from his pocket. "There's his picture and his wife's picture for identification purposes. How did he kill her? We can fairly presume that first he tricked her into drinking the acid, then perhaps she was screaming with the pain of it, and he choked her to death. I imagined first he was a large, powerful man because his grip on her throat was so powerful that he ruptured the jugular inside; but instead of that he plays the piano a great deal, which would give him the hand-power to choke her. And why? We can suppose only that it was because she had in some way learned of their purpose. That would have established the motive. The crowning delicacy of the affair was Morey's act in leaving his keys with the manager here. He did not anticipate that the apartments would be entered for several days-after they were safely away-while there was a chance that if neither of them had been seen here and their disappearance was unexplained the rooms would have been opened to ascertain why. That is all, I think."

"Except to catch Morey and his wife," said the detective grimly.

"Easily done with those photographs," said The Thinking Machine. "I imagine, if this murder is kept out of the newspapers for a couple of hours you can find them about to sail for Europe. Suppose you try the line they came over on?"

It was just three hours later that the accused man and wife were taken prisoner. They had just engaged passage on the steamer which sailed at half-past four o'clock. Their trial was a famous one and resulted in conviction after an astonishing story of an attempt to seize an estate and title belonging rightfully to Miss Evelyn Rossmore who had mysteriously disappeared years before.

PROBLEM OF THE VANISHING MAN.

There was a feverish restlessness in the merciless gray eyes, an unpleasant frown on his brow, as Charles Duer Carroll paused on the curb in front of a tall down town office building and stared moodily across the busy street into nothingness. Carroll was a remarkable looking young man in many ways. He was young,-only thirty,-and physically every line of his body expressed power, sturdiness rather than youth, force rather than grace. He was blessed too with an indomitable, uncompromising jaw, the jaw of a fighting man. The chin was square, the lips thin, avaricious perhaps, the nose slightly hooked, the cheek bones high. In general his appearance was that of a keenly alert man who is never surprised; who chooses his way and pursues it aggressively without haste, without mercy, and without mistakes.

Despite his youth,-it may have been because of it,-Carroll was president and active head of the great brokerage concern, the Carroll-Swayne-McPartland Company, with general offices on the fourth floor of this huge building behind him. He held that responsible position by right of being the grandson of its founder, old Nick Carroll. Upon his retirement from active business a year previously the old man, a wrinkled, venomous image of the young, had banged his desk with lusty fist and so declared it-Charlie Carroll was to be his successor. There had been heartburnings, objections, violent protests even; but the old man owned five thousand of the ten thousand shares of the company, and-Charles Duer Carroll was president.

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