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Then for a time The Thinking Machine sat with fingertips pressed idly together, squinting blankly at the ceiling.

"While a motive is never absolutely essential to the solution of any criminal problem," he observed after awhile, "it will frequently indicate a line of investigation. Now, in the usual case when a motive appears the solution is inevitable. But this case differs from the usual case in that we have too many motives-three excellent ones that we know-a jealous woman, a suitor discarded on the eve of his wedding, and perhaps a vengeful father or brother. And beyond those there are other possibilities."

Hatch went about his business with turbulent, troubled thoughts-a vague sense of treading on dangerous ground-while The Thinking Machine turned to the telephone. Five minutes later he picked up his hat and went to the Hotel Bellevoir.

"Did Dr. Curtis telephone you?" he inquired of the clerk.

"Yes. Is this Mr. Van Dusen?"

The Thinking Machine bobbed his head, and was ushered into Miss Langham's apartments.

Pallid as the sheets, resistlessly inert, the girl lay staring upward as if fascinated by the brilliant scintillating point which floated backward and forward rhythmically before her eyes as The Thinking Machine slowly waved his arm. It was like some weird exorcism, some uncanny incantation, but it compelled attention.

"Watch it closely, please!"

The scientist's tone was low, almost a whisper, yet it carried a command. The swing of his arm shortened gradually, almost imperceptibly, and slowly the bright spot passed upward in little erratic circles until it was directly before her eyes. And there it stopped for a moment. After awhile it moved on again, still farther upward, in a straight line, until the girl was aware of a queerly strained feeling in her eyes. It paused again, then very, very slowly began to move round and round.

After awhile the fascination in the girl's eyes gave way to a vacant staring, and the pupils distended, as a mist crept over them. Slowly, slowly, the swing of the bright spot decreased, until at last it hung motionless, suspended in air, between the slim fingers of the scientist. Thus for a time, and the vacant staring became glassy-dead. Then the bright spot was withdrawn, materializing as the lower part of the bowl of a silver spoon which The Thinking Machine laid on the table beside him. One hand passed over the girl's white face once. The long fingers lingered caressingly on the lids, and pressed them together.

The Thinking Machine passed round from the head of the couch where the girl lay and took a seat, with his hand on her wrist. The pulse fluttered a little, but he nodded his head as if satisfied.

"You are on a train-in a private compartment," he said, still in a voice that was almost a whisper.

"Yes," breathed the girl. It was nearly inaudible.

"A young woman is sleeping there."

"Yes," came the sigh again.

"You hate her."

"No."

It was a flat, unequivocal denial, and the dreamy, sighing tone hardened suddenly. Again The Thinking Machine pressed his fingers down on her eyelids, and sat silent for a time.

"You dislike her," he suggested.

"No," the girl denied once more dreamily. "She and I were--" and the phrase drifted off into intangible incoherency.

"You have a revolver in your traveling bag."

"Yes."

The petulant, crabbed face of The Thinking Machine lighted suddenly, exultantly. But when he spoke again it was in the same whispering monotone. "You always carry a revolver when traveling."

"No."

"Your revolver is thirty-two caliber."

"I don't know."

"The sleeping woman loves the man you love."

"Yes."

"She is at your mercy; therefore you will kill her."

"No, no, no!"

There was a sudden horror in the voice, a strange, convulsive working of the face, and the eyelids fluttered. Thrice The Thinking Machine passed his hands over her face, and she became calm again.

"You are back in your own apartments at the Hotel Bellevoir," he continued after a minute.

"Yes," she answered readily.

"Your revolver is in the traveling bag."

"No."

The Thinking Machine glanced quickly round the room, and again his eyes settled on the pallid face.

"It is in the dressing table."

"Yes."

With set, inscrutable face, the scientist arose and went to the table. In the drawer lay a handsomely mounted weapon. He picked it up, examined it closely as he whirled the barrel in his fingers, and then replaced it, after which he returned to the girl.

"You have fainted," he said. "You will return to consciousness in a moment."

He leaned forward and blew gently into the closed eyes, and the girl sighed. Thrice he did this, then a trace of color appeared in the face, and she raised her eyelids. For an instant she stared into the drawn face of the scientist.

"Why, I must have fainted," she said.

Hutchinson Hatch burst into the laboratory, where The Thinking Machine was at work, with an air of excitement which caused the eminent scientist to turn and squint at him in disapproval.

"That man Devore lied about where--" he began.

"Just a moment, Mr. Hatch," interrupted The Thinking Machine curtly. "Did you see the sleeping car in which Miss Farrar was killed?"

"Yes," replied the reporter, and, somewhat abashed, sat down.

"I suppose the windows were all screened, as is usually the case?"

"Why, I suppose so," was the reply.

"Was there any hole of any sort in the screen of the window in the private compartment?"

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