Ruby Reagan, expert cracksman, was busily, albeit quietly, engaged in the practice of his profession. His rubber soles fell silently upon the deep carpet as he stepped into the utter gloom of the study and closed the door noiselessly behind him. For a long time he stood perfectly still, listening, feeling with that vague single sense for the presence of some one else; then he flashed his electric light. A flat topped library table was directly in front of him, littered over with books, and to his left were the bulky outlines of a roll top desk. There were some chairs, a cabinet or so, and rows of bookcases.

His scrutiny, brief but comprehensive, seemed to satisfy Reagan; for the light went out suddenly, and, turning in his tracks, he slid the bolt of the door into its socket slowly, to avoid even a click. Next he released the grips on one of the windows, for it might be necessary to leave the room that way in the event of some one entering by the single door. Then he settled down to work. First was the desk, and after a long, minute inspection of the lock he dropped on his knees before it and began trying his skeleton keys. The electric flash, with the light fixed, was on the left leaf of the desk, brightly illuminating the lock and lending a deeper glow of ruby red to his hair. On the right leaf of the desk, within instant reach, was his revolver.

It was nearly half an hour before the lock yielded, and then, with a sigh of relief, Reagan carefully pushed up the roll top. Inside he found a metal box. From a score of pigeonholes he dragged forth papers of all descriptions, ruthlessly scattering them about him after a quick examination of each in turn. Then he went through drawer after drawer, carefully scrutinizing each article before he laid it down.

“Guess it’s in the box,” he mused at length.

Sitting flat upon the floor, with the box between his knees, he lavished his talents upon it. After a few minutes the lock clicked, and the metal lid lifted. Again Reagan smiled, for here were packages and packages of banknotes. But after a moment they too were spilled out on the floor. It was something else he sought.

“Now, that’s funny,” he told himself finally. “It isn’t here.” He paused thoughtfully, while his eyes rested lovingly upon the packages of money. “Of course, if I can’t get what I want I’ll take what I can get,” he went on at last. And he proceeded to stuff the money away in his pockets.

Several times he ran his fingers slowly through his red hair. It was plain that he was deeply puzzled. He was on the point of rising to continue his investigations in other directions, when he heard something. It was a voice — a quiet, soothing, pleasant voice — about fourteen inches behind his right ear.

“Don’t try to get your revolver, please!” the voice advised. “If you do, I’ll shoot!”

Involuntarily Reagan’s hand darted out toward the weapon on the leaf of the desk; but it was drawn back as suddenly when he heard a sharp click behind him. Nonplussed for the moment, he sat down again on the floor, half expecting a shot. It didn’t come, and he screwed his head around to see why.

What he saw astounded him. It was a diaphanous, floating, lacy, white something — the figure of a girl. Or was it a girl? The head was sheathed in white, the features covered by a misty, hazy, veily thing, and in the dim reflected light the whole figure seemed ridiculously unsubstantial. It was a girl’s voice, though.

“Sit perfectly still, please, and don’t make any noise!” the voice advised again. Yes, it was a girl’s voice.

Reagan noted the small, gold mounted revolver in her right hand, with the barrel, at just that moment, on a direct line with his head and only a foot or so away; and he noted that it remained steadily where it was without one tremor or quiver.

“Yes’m,” he said at last.

The white figure walked around him — or did it float? — and picked up his revolver from the desk.

“This is Mr. Reagan, isn’t it?” she inquired.

“Yes’m,” responded Reagan. The admission was surprised out of him.

“Did you find it?”

“No’m.”

Was this thing real? Reagan rubbed his eyes doubtfully. He was dreaming, of course. He would wake up in a minute. He opened his eyes again. Yes, there she was. But she wasn’t real — she couldn’t be real — she was a ghost. She was certainly not in the room when he entered, and she could not have come in since, because he had bolted the door on the inside.

“I shall trouble you now, Mr. Reagan,” the ghost woman went on, “to take all that money from your pocket and put it back in the box.”

Reagan stared at the end of the revolver a moment, and the ghost woman wriggled it. That was real enough, anyway. Promptly and without a word he began to disgorge packages of banknotes. Then at last looked up again.

“You put back only eight packages,” said the ghost woman calmly. “You took out nine.”

“Yes’m,” said Reagan.

He fished through his pockets again, in a semi-hypnotic condition, produced more money, and deposited it with the other. He closed the metal lid and snapped the lock.

“That will do very nicely,” she said approvingly. “Now I shall trouble you, please, to go on about your business.”

Reagan started to rise, awkwardly enough, on hands and knees. The ghost woman stepped back a little; but still she was not far enough away, for when Reagan suddenly came to his feet his outstretched arms struck her violently beneath the wrists and sent the two revolvers flying upward. With another quick movement he swept the electric light from the desk, extinguishing it. There was a sound of scuffling feet in the darkness, as of persons struggling, a little despairing cry, then finally a pistol shot.

Reagan stumbled blindly about the room, seeking the door. He found it at last, still bolted on the inside, and tugged at it frantically. Then came the sound of heavy feet running along the hall outside toward the study, and Reagan stopped. The window! It was the only way now! The shot had aroused the household. He rushed toward the window; but it refused to move.

The clamor was at the door. Desperately Reagan sought for the side grips on the window; but they seemed to have disappeared. The door trembled as some heavy body was hurled against it. The bolt would yield — it was yielding — Reagan heard the woodwork crack. Then deliberately he drove his clenched fist through the glass, took one step on a chair and hurled himself straight through. The door crashed under the onslaught and swung inward.

On the following morning Chester Mills, a wealthy merchant, called on Detective Mallory, chief of the bureau of criminal investigation.

“I own a large country estate forty miles out of town,” Mills began abruptly. “Yesterday was the last day of the month. I went to the bank and drew nine hundred dollars, and placed it in a metal box in my desk at home and locked both the box and desk.

“I went to bed at eleven o’clock. About two o’clock this morning I heard a pistol shot in the study. I jumped out of bed and rushed into the hall toward the study, meeting on the way one of my servants, O’Brien. We found the study locked, and started to smash the door in. As we did so we heard a great crash of glass inside.

“Then we did smash the door, and O’Brien turned on the electric lights. One of the two windows was smashed out as if somebody had jumped or been thrown through it; my desk had been ransacked, and my papers scattered all over the floor. The desk was standing open, and I picked up the box. It had a bullet hole in it. The ball went in the top and came out the side. I found it sticking in the desk. It was thirty-two caliber. Here it is.”

Mills tossed the misshapen leaden missile on the table, and Detective Mallory examined it.

“Then I found the first real puzzle,” Mills went on. “I opened the box and counted the money. Instead of any of it being missing, there was more there than there was when I put the box in the desk. Where there had been only nine hundred dollars, verified by the paying teller and myself, there was now nine hundred and ten dollars — an extra ten-dollar bill.”

Detective Mallory chewed his cigar frantically.

“O’Brien found a soft black hat in the room, near the door,” continued Mills, “a revolver, thirty-eight caliber, with every chamber loaded, an overcoat, an electric flashlight which had been thrown to the floor and broken, and a very complete kit of burglar’s tools. I straightened the women folk all out, had the house searched, and went back to bed. So far as I have been able to find out, nothing was stolen — nothing is missing.”

“Well, in that case —” began the detective.

“I haven’t started yet,” interrupted Mills tersely. “The window was out, as I said; so when we went to bed again we left O’Brien in the study on watch. About halfpast three o’clock I was awakened again by a scream — a woman. Again I jumped out and ran along toward the study. The lights were going, but there was no sign of O’Brien. I presumed then that his attention had been attracted by the scream and he had gone to investigate. But — Well, O’Brien has disappeared. No one has seen or heard of him since — there’s not a trace.”

Detective Mallory sat for a long time silently smoking, and staring into the eyes of his caller.

At this point the problem came under the observation of that eminent logician, Professor Augustus S. F. X. Van Dusen — The Thinking Machine. As Hutchinson Hatch, reporter, related the known facts, the distinguished man of science permitted his eyes to narrow down to mere slits of watery blue, and the tall, domelike forehead was deeply furrowed.

“Why was any shot fired?” Hatch demanded of the scientist in perplexity. “And who fired it? Were there two burglars? Did they fight? Was one wounded? There were bloodstains on the ground outside the window; but we can see that whoever jumped out might have cut himself on the glass. And why was the hole shot in the tin box? Not to break the lock, obviously; for it could have been taken along. Where does the odd ten-dollar bill in the box figure? Where is O’Brien? Who was the woman who screamed that second time? Why did she scream? Why wasn’t something stolen?”

Having relieved himself of this torrent of questions, Hatch dropped back into his chair expectantly and lighted a cigarette. The Thinking Machine permitted two disapproving eyes to settle on the young man for a moment.

“And still you haven’t asked the one vital question,” he remarked tartly. “That is, What particular object in that study, or supposed to be in that study, is of such great importance to some one unknown that two bold, daring I might say, attempts were made to get it in the same night?”

“It seems to me it would be impossible to learn that, until —”

“Nothing is impossible, Mr. Hatch. It is merely a little sum in arithmetic. Two and two make four; not sometimes but all the time. This problem, at the moment, seems remarkably disjointed, particularly when we consider the disappearance of O’Brien. First, then, is Mr. Mills positive nothing was stolen?”

“Absolutely so,” replied Hatch. “He has checked off every paper, and accounted for every article.”

The furrows in the tall brow deepened perceptibly, and for a long time the crabbed little scientist sat silent. “How much blood was found outside?” he asked suddenly.

“Quite a good deal of it,” Hatch responded. “It looks as if some one, whoever jumped or was thrown out, received some nasty cuts. The edges of the glass are stained.”

The Thinking Machine nodded. “It is established beyond all question that the woman who screamed that second time was not one of those in the house?” he asked.

“Oh, yes,” returned Hatch confidently. “They had all retired after the first fright, and the second didn’t even arouse them. They didn’t know of O’Brien’s disappearance until morning.”

“The police have found nothing yet?”

“Not yet. The articles left in the room, of course — the hat and coat and burglar’s tools — are clues that they are working on. They might establish identity by their aid.”

“Well, we’ll have to find the man who jumped,” remarked the scientist placidly. “When we do that, we can go somewhere with this affair.”

“Yes, when we do that,” Hatch agreed, with a grin.

“Of course we can do it!” snapped The Thinking Machine. “Here we seek a man with neither hat nor overcoat, who is cut up with glass, possibly badly wounded.”

“But he’s the sort of man who would scuttle to cover like a scared rabbit,” Hatch protested.

“Wouldn’t matter how badly hurt he was, if he could walk he would hide.”

“You seem to think, Mr. Hatch, that leaping through a window, taking all the glass with ............