With the brilliant glare of the noonday sun shining full into his upturned eyes, a venerable man sat beside an open window. The gray-crowned head was a noble one, but strength and rugged manhood was gone; there was only the weakness of years and disaster, illumined and softened by a smile — the appealing, pathetic smile of helplessness. The window framed a vista of green landscape, broken by a dimpled splotch of blue where the sea ran in and lapped the shore, and, far away, a village sprinkled on the hills. But he looked upon it all with sightless eyes — eyes which turned instinctively toward the light as the blind ever seek a ray through their enshrouding gloom. A grateful tang of salt air drifted in, and he breathed deeply of its fragrance.

For a long time he sat thus, silently, then from a distant room came the trill of a song. His smile grew into an expression of infinite tenderness as he listened, and then the closing of a door broke the melody. He sat expectantly for a minute or so, and gradually his mind wandered back into the dreamy thoughtfulness which the voice had interrupted. After awhile he heard a light step in the hall, and then some other sound which he could not interpret. The steps approached the door of the room where he sat, and paused.

“Is that you, deary?” he asked gently.

There was no response, and he turned his sightless eyes expectantly toward the entrance.

“What is it, Mildred?” he inquired.

Again he heard the peculiar sound to which he had been unable to attach a meaning, but still there was no answer.

“Mildred!” he called sharply. He turned quickly in his chair, with a vague uneasiness in his manner, and gripped the arms as if to rise. “Mildred!” he repeated. “Why don’t you answer me?”

Suddenly there came an answer — a heart-racking, terrifying answer — shriek after shriek of agony, terror, helplessness. It was here, in this very room in which he stood, but the impenetrable pall of blindness veiled it all. There was a shuffling as of feet for an instant, a gurgling, despairing cry, then the old man tottered forward toward the door.

“Mildred, Mildred, Mildred!” he called despairingly. “What is it, child!”

There was a sound as of a soft body falling, then came utter silence. With straining heart and groping hands the old man kept on blindly seeking. Again he caught the meaningless sound, which he had heard before. One outstretched hand brushed against something which was instantly removed beyond reach. Intuitively he knew that something — somebody — menaced him, that Mildred his granddaughter was now or had been in peril — perhaps it was worse. There was some quick movement to his right, and the old man stretched out his quivering hands straight before him with a pitiful, helpless gesture.

“I am blind!” he said simply.

For a moment he stood there, with hands still outstretched, waiting. For what? He didn’t know. At last from the hall outside came a sliding, whispering sound, and the front door closed noiselessly. Instantly he started in that direction. Despite his blindness, he knew his way here in the little house where he had lived for years alone with his granddaughter.

In the hall another thought came to him. Whoever — whatever — it was, had come and gone. And Mildred? He turned and started back toward the room he had just left. One aged hand slipped along the wall to the door frame, and he turned in. For an instant he listened. He heard nothing.

“Mildred?” he called. “My God, child! where are you? What has happened?”

Still silence. He entered and began groping around pitifully. Mildred must be there, somewhere. And finally, as he groped on, he came upon her. One foot struck some yielding obstacle, and he dropped on his knees beside it. A touch of his fingers on the face told him it was Mildred. She was breathing faintly — a gurgle, which as he listened grew fainter.

His brain was instantly awakened to the full possibilities. She had been stabbed, or struck down, perhaps. There had been no shot, and yet, as his hands moved rapidly over the slender form, he found no wound on head, face, or body. The faint gasping breath grew fainter as he listened — she was dying under his hands, and he was helpless, unable to see even what was the matter.

“Mildred, Mildred, Mildred!” he repeated, and he shook the inert body in a frenzy of fear and anxiety.

And then came the end. There was a last faint gurgle, a spasmodic twitching of the body, and it lay rigid. And there crouching on the floor beside his dead, the aged grandfather was found a few minutes later. His sightless eyes were dry and staring, and his lip moved silently in prayer.

One of the first things to come under the observation of the police when they began their investigation of the strange murder of pretty little Mildred Barrett — she was hardly fourteen years old — was the fact that if her grandfather, Wendell Curtis Barrett, had not been blind, he could have saved her life. The girl had been strangled, garroted, with manila twine — a plain cord which is in every day use for the tying of heavy bundles. This twine had been drawn so tight about the child’s throat that it sank deep into the white soft flesh and slowly strangled her to death. Had her grandfather been able to see, had he not overlooked the possibility of such a thing, he could probably have saved her by cutting the twine. This, at least, was what the medical examiner said.

Outside attention had been attracted to the tragedy by two men who were driving past the little house overlooking the sea. They heard the child’s screams and stopped to investigate, entering by that front door through which, not more than a few seconds before, the slayer of the child had passed. But they had seen no one, nor had they heard anything except the child’s screams. They immediately notified the police. The strangler’s cord was not found until Detective Mallory arrived with a couple of his men and Hutchinson Hatch, a newspaper reporter.

The detective examined the garroter’s twine closely. There was one knot in it just where it pressed down upon the windpipe; and another at the back of the neck where powerful fingers had drawn it tight and fastened it with a knot similar to the running of a lasso.

“It’s a good job, all right,” commented Detective Mallory heartlessly enough as he scrutinized the two knots. “It was prepared for just such a purpose, and well prepared at that.”

“It isn’t unlike the garroting cord that the thugs of India use,” remarked Hatch.

“Is that so?” inquired the detective, as he turned quickly on the newspaper man. They had met before many times, and there was a professional friendship between them which amounted almost to enmity. “That may be useful to know.”

The reporter remained at the house and in the neighborhood for several hours while the detectives continued their investigations, and then summarized the entire affair, with every established fact, for the benefit of Professor Augustus S. F. X. Van Dusen — The Thinking Machine. They were well acquainted, these two, an acquaintance which had begun with the chess game incident which had given to the noted scientist the soubriquet by which he had since become known beyond the narrow pale of science. On a dozen or more occasions The Thinking Machine had interested himself in every day problems at the request of the newspaper man, and had invariably woven a woof from tangled, disconnected threads which the reporter brought to him.

“It’s absolutely astounding,” the reporter told the scientist now, “not only the method of the murder — right within reach, almost, of a man who was totally blind — but there is nothing to indicate any motive, so —”

“Begin at the beginning, Mr. Hatch,” interrupted The Thinking Machine crustily. “When you do a sum in arithmetic you put down all the figures, don’t you? Well, give me all the figures.”

“Well, here is every known fact in the case,” explained the reporter. “Mr. Barrett is about seventy-two years old; his granddaughter Mildred was a little less than fourteen. She was the only relative he had in the world, and had lived with him in the little house, which he owns, since the death of her father, who was killed in the Spanish–American War. They kept no servant, as the child, with a little assistance from the old man, was able to do practically all the simple housework. Occasionally they called in a woman who lived half a mile away to assist in house cleaning and the heavier work. It seems that Barrett has an income of about a thousand a year, and they were able to live comfortably on this.

“Very few persons ever called at the house, and preceding the tragedy there was no caller, at least that Barrett knows of. The child was somewhere in the rear of the house, and he was sitting in his own room. He heard no voices, no sound, nothing except the child singing, until she came along the hall, evidently to his room. The grim horror of the whole thing from that time on has unnerved the old man so that he is almost in a state of collapse.

“To me the mystery of the thing is intensified by the fact that the murdered girl is a mere child. Her extreme youth would indicate at least that there could have been no love affair, certainly from all I have been able to learn there was not. And her youth, too, would make it seem improbable that she could have had an enemy who would have gone to such an extreme. Besides, she seems to have been a sweet-tempered, sunny little girl, intelligent, bright, and lovable. Nothing whatever was stolen. There is positively no clue in the world, not even a vagrant footprint, or any small thing that might have been left to indicate who was there — that is, of course, except the cord with which she was strangled.”

“Would the old man have benefited by the child’s death?” inquired The Thinking Machine.

“In no way at all,” Hatch replied positively, “nor would anyone else. There is no property tied up, as far as anyone can find out, and the miserable little sum which it cost him to keep the child is not so much as he would have had to pay to employ a servant in her absence.”

The Thinking Machine sat for a long time with the squint blue eyes turned upward, and his white slender fingers pressed tip to tip. Minute wrinkles in his enormous brow grew momentarily deeper. “It’s a remarkable crime, Mr. Hatch,” he said at last, “perhaps the most remarkable that I have ever met. As you say, the youth of the child removes all the ordinary motives.” He was silent for a moment. “Our greatest criminals are never caught, and rarely ever heard of, Mr. Hatch,” he went on musingly. “The greatest crimes are never discovered, as a matter of fact. One might readily conceive of a brain so keen, so accurate, that in, say, a murder, there would be nothing to indicate one. I think perhaps in this case we have a difficult one. It would be best for me to see and talk with Mr. Barrett in person.”

They found the aged blind man, and he repeated for them in the minutest detail every fact as he remembered it. The Thinking Machine listened throughout with keen attention, and at the end asked some questions.

“You say, Mr. Barrett, that in addition to your granddaughter’s footsteps and voice you heard some other slight sound. Could you describe it?”

“I hardly think so,” was the reply. “It was strange — peculiar.”

“Was it the sound of a human voice, or of something being moved?” insisted the scientist.

“It could have been made by the human voice, I suppose; but it also could have been made by twanging a rubber band. It sounded guttural, unreal, uncanny.”

“And the thing you touched when you started toward your granddaughter, after she screamed?&rd............