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"Who is it?" demanded the detective.

"You don't happen to know all the facts in this case," continued The Thinking Machine without heeding the question. "I got them all, only after Mr. Hatch, at my suggestion, had located the thief. Originally I began where you left off. I believed you had eliminated the servants, and presumed there was not a burglary. Ultimately this led to Hawes Campbell in a manner which is of no interest to you. Then I got all the facts.

"When Mr. Hatch left his office to go to Mrs. Dillingham's, he took an automobile which happened to be passing," resumed the scientist. "It was a cab, No. 869019. Inside that cab he found, much to his astonishment, a woman-a young woman in evening dress. She made the surprising statement that the chauffeur didn't know she was there, and that she was not going anywhere-was merely riding around to collect her thoughts. And this was, please remember, about eleven o'clock at night. On its face this incident had no connection with the jewel theft; but by a singular chain of coincidences, subsequently developed, it seemed that Mr. Hatch had arrived at the solution of the mystery before he even knew the circumstances of the theft."

Detective Mallory nodded doubtfully. "But how does that connect with the--" he began.

"Subsequent developments establish a direct connection," interrupted The Thinking Machine. "We have the woman in the automobile. We shall presume that she must have had some strong motive for leaving a house at that time of night and doing the apparently purposeless things that she did do. We don't know this motive from these facts-we only know there was a motive.

"Now when you and Mr. Hatch were talking to Mrs. Dillingham, a woman entered the room. Mr. Hatch recognized her immediately as the woman in the automobile. Everything indicated that she was an intimate friend of Mrs. Dillingham's. So we pass on to the point where Mr. Hatch found that Hawes Campbell arrived at the ball early, went away again, then returned after eleven o'clock. Mr. Hatch wanted to know why he left, and went to his home to inquire. Campbell's sister met him there. She was the woman he had met in the automobile. So we have Campbell leaving the ball, immediately after the theft, say, and his sister running away from her home sometime between nine-thirty and eleven, and secreting herself in an automobile.

"Why? I have said, Mr. Mallory, that imagination-the ability to bridge gaps temporarily-is the most essential part of the logical mind. Now, if we imagine that Campbell stole the necklace, that he went home, that his sister found it out, that there was some sort of scene which terminated in her flight with the necklace, we account for absolutely every incident preceding and following Mr. Hatch's arrival at the Dillingham place.

"I have made inquiries. The Campbells are worth, not thousands, but millions. Therefore, the question. Why should Hawes Campbell steal a necklace? The answer, kleptomania. And again, it was known to the sister, who tried in her own manner to return the stolen property and avoid the scandal. When she was in the automobile, she was trying to collect her thoughts-trying to invent a way to return the necklace. It was the merest chance that Mr. Hatch happened to get into that particular vehicle.

"Now, we come to the most difficult part of the problem," and The Thinking Machine dropped back still further into the cavernous depths of his chair. "What would a frightened, perhaps hysterical, woman do with that necklace? From the fact that it has not been returned, we know that she didn't venture into the house with it, and leave it casually in any one of a hundred places where it might have been discovered without danger to herself. Yet everything indicates that she had it while in the cab. The obvious thing which suggests itself is that she hid it in the cab, intending to regain possession of it later and return it. Now, that cab number was 869019. Strangely enough, after Mr. Hatch left the cab it seems to have disappeared. The chauffeur, John Kilrain, has another cab number now, 610698-that is, auto cab No. 869019 was made to disappear by the simple act of turning the number board upside down, giving us 610698."

"Well, by George!" exclaimed Detective Mallory. No mere words would convey the reporter's astonishment; he gasped.

"Now," continued The Thinking Machine after a moment, "there are two reasons, both good, why auto cab number 869019 should have disappeared. The vital one, it seems to me, is that Kilrain discovered the necklace inside and kept it; the other is that he was threatened with arrest by the policeman who took his number for speeding, and to avoid a fine disguised the identity of his cab. There are one or two other possibilities; but if the necklace isn't found in the automobile, I should advise, not arrest, but a close watch on Kilrain, both at his home and in his intercourse with other chauffeurs at the various cab stands."

There was a rap at the door, and Martha appeared. "Did you want an automobile, sir?"

"We'll be right out," returned the scientist.

And so it came about that The Thinking Machine, Detective Mallory, and Hutchinson Hatch searched the very vitals of auto cab No. 869019, temporarily masquerading as No. 610698, while Kilrain stood by in perturbed amazement. At the end he was allowed to go.

"Remember, please, what I advised you to do," The Thinking Machine reminded Detective Mallory.

With eyes that were heavy with sleep Hutchinson Hatch crawled out of bed and answered the insistent ringing of his telephone. The crabbed voice of The Thinking Machine came over the wire, in a question.

"If Miss Campbell was so anxious to return the necklace that night, she couldn't have done better, could she, than to have handed it to a reporter who was going to the house to investigate the robbery?"

"I don't think so," Hatch replied wonderingly.

"Did you have on your overcoat that night?"

"I had it with me."

"Suppose you go look in the pockets, and--"

Hatch dropped the receiver, already inspired by the suggestion, and dragged his overcoat out of the closet. In the left hand lower pocket was a small package. He opened it with trembling fingers. There before his eyes lay the iridescent, gleaming bauble. It had been in his possession from an hour after it was stolen until this very instant. He rushed back to the telephone.

"I've got it!" he shouted.

"Silly of me not to have thought of it in the first place," came the querulous voice of The Thinking Machine. "Good night."

THE ROSWELL TIARA.

Had it not been for the personal interest of a fellow savant in the case it is hardly likely that the problem of the Roswell tiara would ever have come to the attention of The Thinking Machine. And had the problem not come to his attention it would inevitably have gone to the police. Then there would have been a scandal in high places, a disrupted home and everlasting unhappiness to at least four persons. Perhaps it was an inkling of this latter possibility that led The Thinking Machine to take initial steps in the solution of a mystery which seemed to have only an obvious ending.

When he was first approached in the matter The Thinking Machine was in his small laboratory from which had gone forth truths that shocked and partially readjusted at least three of the exact sciences. His enormous head, with its long yellow hair, bobbed up and down over a little world of chemical apparatus, and the narrow, squint eyes peered with disagreeable satisfaction at a blue flame which spouted from a brazier. Martha, an aged woman who was the scientist's household staff, entered. She was not tall yet she towered commandingly above the slight figure of her eminent master. Professor Van Dusen turned to her impatiently.

"Well? Well?" he demanded shortly.

Martha handed him two cards. On one was the name Charles Wingate Field, and on the other Mrs. Richard Watson Roswell. Charles Wingate Field was a name to juggle with in astronomy-The Thinking Machine knew him well; the name of the woman was strange to him.

"The gentleman said it was very important," Martha explained, "and the poor lady was crying."

"What about?" snapped the scientist.

"Lord, sir, I didn't ask her," exclaimed Martha.

"I'll be there in a moment."

A few minutes later The Thinking Machine appeared at the door of the little reception room, which he regarded as a sort of useless glory, and the two persons there arose to meet him. One was a woman apparently of forty-five years, richly gowned, splendid of figure and with a distinct, matured beauty. Her eyes showed she had been weeping but now her tears were dried and she caught herself staring curiously at the pallid face, the keen blue eyes and the long slender hands of the scientist. The other person was Mr. Field.

There was an introduction and the scientist motioned them to seats. He himself dropped into a large cushioned chair, and looked from one to the other with a question in his eyes.

"I have been telling Mrs. Roswell some of the things you have done, Van Dusen," began Mr. Field. "Now I have brought her to you because here is a mystery, a problem, an abstruse problem, and it isn't the kind of thing one cares to take to the police. If you--"

"If Mrs. Roswell will tell me about it?" interrupted the scientist. He seemed to withdraw even further into the big chair. With head tilted back, eyes squinting steadily upward and white fingers pressed tip to tip he waited.

"Briefly," said Mrs. Roswell, "it has to do with the disappearance of a single small gem from a diamond tiara which I had locked in a vault-a vault of which no living person knew the combination except myself. Because of family reasons I could not go to the police, and--"

"Please begin at the beginning," requested The Thinking Machine. "Remember I know nothing whatever of you or your circumstances."

It was not unnatural that Mrs. Roswell should be surprised. Her social reign was supreme, her name was constantly to be seen in the newspapers, her entertainments were gorgeous, her social doings on an elaborate scale. She glanced at Mr. Field inquiringly, and he nodded.

"My first husband was Sidney Grantham, an Englishman," she explained. "Seven years ago he left me a widow with one child-a son Arthur-now twenty-two years old and just out of Harvard. Mr. Grantham died intestate and his whole fortune together with the family jewels, came to me and my son. The tiara was among these jewels.

"A year ago I was married to Mr. Roswell. He, too, is a man of wealth, with one daughter, Jeanette, now nineteen years old. We live on Commonwealth Avenue and while there are many servants I know it impossible--"

"Nothing is impossible, Madam," interposed The Thinking Machine positively. "Don't say that please. It annoys me exceedingly."

Mrs. Roswell stared at him a moment then resumed:

"My bed room is on the second floor. Adjoining and connecting with it is the bed room of my step-daughter. This connecting door is always left unlocked because she is timid and nervous. I keep the door from my room into the hall bolted at night and Jeanette keeps the hall door of her room similarly fastened. The windows, too, are always secured at night in both rooms.

"My maid and my daughter's maid both sleep in the servants' quarters. I arranged for this because, as I was about to state, I keep about half a million dollars worth of jewels in my bed room locked in a small vault built into the wall. This little vault opens with a combination. Not one person knows that combination except myself. It so happens that the man who set it is dead.

"Last night, Thursday, I attended a reception and wore the tiara. My daughter remained at home. At four o'clock this morning I returned. The maids had retired; Jeanette was sleeping soundly. I took off the tiara and placed it, with my other jewels, in the vault. I know that the small diamond now missing was in its setting at that time. I locked the vault, shot the bolt and turned the combination. Afterwards I tried the vault door to make certain it was fastened. It was then-then--"

For no apparent reason Mrs. Roswell suddenly burst into tears. The two men were silent and The Thinking Machine looked at her uneasily. He was not accustomed to women anyway, and women who wept were hopelessly beyond him.

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