Gradually the lights dimmed and the great audience became an impalpable, shadowy mass broken here and there by the vagrant glint of a jewel or the gleam of white shoulders. There was a preliminary blare of horns, then the crashing anvil chorus of “Il Trovatore” began. Sparks spattered and flashed as the sledges rose and fell in exquisite rhythm while the clangorous music roared through the big theatre.

Eleanor Oliver arose, and moving from the front of the box into the gloom at the rear, leaned her head wearily against the latticed partition. Her mother, beside whom she had been sitting, glanced up inquiringly as did her father and their guest Sylvester Knight.

“What’s the matter, my dear?” asked Mrs. Oliver.

“Those sparks and that noise give me a headache,” she explained. “Father, sit in front there if you wish. I’ll stay here in the dark until I feel better.”

Mr. Oliver took the seat near his wife and Knight immediately lost interest in the stage, turning his chair to face Eleanor. She seemed a little pale and mingled eagerness and anxiety in his face showed his concern. They chatted together for a minute or so and under cover of darkness his hand caught hers and held it a fluttering prisoner.

As they talked the drone of their voices interfered with Mrs. Oliver’s enjoyment of the music and she glanced back warningly. Neither noticed it for Knight was gazing deeply into the girl’s eyes with adoration in his own. She made some remark to him and he protested quickly.

“Please don’t,” Mrs. Oliver heard him say pleadingly as his voice was raised. “It won’t be long.”

“I’m afraid I’ll have to,” the girl replied.

“You mustn’t,” Knight commanded earnestly. “If you insist on it I shall have to do something desperate.”

Mrs. Oliver turned and looked back at them reprovingly.

“You children chatter too much,” she said good naturedly. “You make more noise than the anvils.”

She turned again to the stage and Knight was silent for a moment. Finally the girl said something else that the mother didn’t catch.

“Certainly,” he replied.

He arose quietly and left the box. The swish and fall of the curtain behind him were smothered in the heavy volume of music. The girl sat white and inert. Knight found her in just that position when he returned with a glass of water. He had been out only a minute or so, and the encore to the chorus was just ending.

He offered the glass to Eleanor but she made no move to take it and he touched her lightly on the arm. Still she did not move and he leaned over and looked at her closely. Then he turned quickly to Mrs. Oliver.

“Eleanor has fainted, I think,” he whispered uneasily.

“Fainted?” exclaimed Mrs. Oliver as she arose. “Fainted?”

She pushed her chair back and in a moment was beside her daughter chafing her hands. Mr. Oliver turned and glanced at them with languid interest.

“What’s the matter now?” he inquired.

“We’ll have to go,” replied Mrs. Oliver. “Eleanor has fainted.”

“Again?” he asked impatiently.

Knight hovered about anxiously, helplessly as the father and mother worked with the girl. Finally in some way he never understood Eleanor was lifted out, still unconscious and white as death, and removed in a waiting carriage to her home. Two physicians were summoned and disappeared into her boudoir while Knight paced back and forth restlessly between the smoking room and the hall. Mrs. Oliver was with her daughter; Mr. Oliver sat quietly smoking.

“I wouldn’t worry,” he advised the young man after a few minutes. “She has a trick of fainting like that. You will know more about her after awhile — when she is Mrs. Knight.”

From somewhere upstairs came a scream and Knight started nervously. It was a shrill, penetrating cry that tore straight through him. Mr. Oliver took it phlegmatically, even smiled at his nervousness.

“That’s my wife fainting,” he explained. “She always does it that way. You know,” he added confidentially, “my wife and two daughters are so exhausted with this everlasting social game that they go off like that at any minute. I’ve talked to them about it but they won’t listen.”

Heedless of the idle, even heartless, comments of the father Knight stopped in the hall and stood at the foot of the stairs looking up. After a minute a man came down; it was Dr. Brander, one of the two physicians who had been called. On his face was an expression of troubled perplexity.

“How is she?” demanded Knight abruptly.

“Where is Mr. Oliver?” asked Dr. Brander.

“In the smoking room,” replied the young man. “What’s the matter?”

Without answering the physician went on to the father. Mr. Oliver looked up.

“Bring her around all right?” he asked.

“She’s dead,” replied the physician.

“Dead?” gasped Knight.

Mr. Oliver rose suddenly and gripped the physician fiercely by a shoulder. For an instant he gazed and then his face grew deathly pale. With a distinct effort he recovered himself.

“Her heart?’ he asked at last.

“No. She was stabbed.”

Dr. Brander looked from one to the other of the two white faces with troubled lines about his eyes.

“Why it can’t be,” burst out Knight suddenly. “Where is she? I’ll go to her.”

Dr. Brander laid a detaining hand on his shoulder.

“You can do no good,” he said quietly.

For a time Mr. Oliver was dumb and the physician curiously watched the struggle in his face. The hand that clung to his shoulder was trembling horribly. At last the father found voice.

“What happened?” he asked.

“She was stabbed,” said Dr. Brander again. “When we examined her we found the knife — a long, keen, short-handled stiletto. It was driven in with great force directly under her left arm and penetrated the heart. She must have been dead when she was lifted from the box at the opera. The stiletto remained in the wound and prevented any flow of blood while its position and the short handle caused it to be overlooked when she was lifted into the carriage. We did not find the knife for several minutes after we arrived. It was covered by her arm.”

“Did you tell my wife?” asked Mr. Oliver quickly.

“She was present,” the physician went on. “She screamed and fainted. Dr. Seaver is attending her. Her condition is — is not very good. Where is your ‘phone? I must notify the police.”

Mr. Oliver started to ask something else, paused and dropped back in his chair only to rise instantly and rush up the stairs. Knight into whose face there had come a deadly calm stood stone-like while Dr. Brander used the telephone. At last the physician finished.

“The calling of the police means that Eleanor did not kill herself?” asked the young man.

“It was murder,” was the positive reply. “She could not have stabbed herself. The knife went straight in, entering here,” and he indicated a spot about four inches below his left arm. “You see,” he explained, “it took a very long blade to penetrate the heart.”

There was dull despair in Knight’s eyes. He dropped down at a table with his head on his arms and sat motionless for a long time. He looked up once and asked a question.

“Where is the knife?”

“I have it,” replied Dr. Brander. “I shall turn it over to the authorities.”

“Now,” began The Thinking Machine in his small, irritated voice as Hutchinson Hatch, reporter, stopped talking and leaned back to listen, “all problems are merely sums in addition, when reduced to their primary parts. Therefore this one is simply a matter of putting facts together in order to prove that two and two do not sometimes but always make four.”

Professor Augustus S. F. X. Van Dusen, scientist and logician, paused to adjust his head comfortably on the cushion in the big chair, then resumed:

“Your statement of the case, Mr. Hatch, gives me these absolute facts: Eleanor Oliver is dead; she died of a stab wound; a stiletto made this wound; it was in such a position that she could hardly have inflicted it herself; and Sylvester Knight, her fiance, is under arrest. That’s all we know isn’t it?”

“You forget that she was stabbed while in a box at the opera,” the reporter put in, “in the hearing of three or four thousand persons.”

“I forget nothing,” snapped the scientist. “It does not appear at all that she was stabbed while in that box. It appears merely that she was ill and might have fainted. She might have been stabbed while in the carriage, or even after she was in her room.”

Hatch’s eyes opened wide at the bare mention of these possibilities.

“The presumption is of course,” The Thinking Machine went on a little less aggressively, “that she was stabbed while in the box, but we can’t put that down as an absolute fact to work on until we know it. Remember the stiletto was not found until she was in her room.”

This gave the reporter something new to think about and he was silent as he considered it. He saw that either of the possibilities suggested by the scientist was tenable, but on the other hand — on the other hand, and there his mind refused to work.

“You have told me that Knight was arrested at the suggestion of Mr. Oliver last night shortly after the police learned of the affair,” The Thinking Machine went on, musingly. “Now just what have you or the police learned as to him? How do they connect him with the affair?”

“First the police acted on the general ground of exclusive opportunity,” the reporter explained. “Then Knight was arrested. The stiletto used was not an ordinary one. It had a blade of about seven inches and was very slender, but instead of a guard on it there was only a gold band. The handle is a straight, highly polished piece of wood. Around it, below the gold band where the guard should have been, there were threads as if it had been screwed into something.”

“Yes, yes, I see,” the other interrupted impatiently. “It was intended to be carried hidden in a walking cane, perhaps, and was screwed down with the blade in the stick. Go on.”

“Detective Mallory surmised that when he saw the stiletto,” the reporter continued, “so after Knight was locked up he searched his rooms for the other part — the lower end — of the cane.”

“And he found it, without the stiletto?”

“Yes, that’s the chain against. Knight. First, exclusive opportunity, then the stiletto and the finding of the lower end of the cane in his possession.”

“Exclusive fiddlesticks!” exclaimed the scientist irritably. “I presume Knight denies that he killed Miss Oliver?”

“Naturally.”

“And where is the stiletto that belongs to his cane? Does he attempt to account for it?”

“He doesn’t seem to know where it is — in fact he doesn’t deny that the stiletto might be his. He merely says he doesn’t know.”

The Thinking Machine was silent for several minutes.

“Looks bad for him,” he remarked at last.

“Thank you,” remarked Hatch dryly. It was one of those rare occasions when the scientist saw a problem exactly as he saw it.

“Miss Oliver and Mr. Knight were to be married — when?”

“Three weeks from next Wednesday.”

“I suppose Detective Mallory has the stiletto and cane?”

“Yes.”

The Thinking Machine arose and found his hat.

“Let’s run over to police headquarters,” he suggested.

They found Detective Mallory snugly ensconced behind a fat cigar with beatific satisfaction on his face.

“Ah, gentlemen,” he remarked graciously — the graciousness of conscious superiority. “We’ve nailed it to our friend Knight all right.”

“How?” inquired The Thinking Machine.

The detective gloated a little — twisted his tongue around the dainty morsel — before he answered.

“I suppose Hatch has told you the grounds of the arrest?” he asked. “Exclusive opportunity and all that? Then you know, too, how I searched Knight’s rooms and found the other part of the stiletto cane. Of course that was enough to convict, but early this evening the last link in the chain against him was supplied when Mrs. Oliver made a statement to me.”

The detective paused in enjoyment of the curiosity he had aroused.

“Well?” asked The Thinking Machine, at last.

“Mrs. Oliver heard — understand me — heard Knight threaten her daughter only a few minutes before she was found dead.”

“Threaten her?” exclaimed Hatch, as he glanced at The Thinking Machine. “By George!”

Detective Mallory tugged at his moustache complacently.

“Mrs. Oliver heard Knight first say something like, ‘Please don’t. It won’t be very long.’ Her daughter answered something she couldn’t catch after which she heard Knight say positively, ‘You mustn’t. If you do I shall do something desperate’ or something like that. Now as she remembers it the tone was threatening — it must have been raised in anger to be heard above the anvils. Thus the case is complete.”

The Thinking Machine and Hatch silently considered this new point.

“Remember this was only three or four minutes before she was found stabbed,” the detective went on with conviction. “It all connects up straight from exclusive opportunity to the ownership of the stiletto; from that to the threat and there you are.”

“No motive of course?” asked The Thinking Machine.

“Well, the question of motive isn’t exactly clear but our further investigations will bring it out all right,” the detective admitted. “I should imagine the motive to be jealousy. Of course the story of Knight not knowing where his stiletto is has no weight.”

Detective Mallory was so charmed with himself that he offered cigars to his visitors — an unusual burst of generosity — and Hatch was so deeply thoughtful that he accepted. The Thinking Machine never smoked.

“May I see the stiletto and cane?” he asked instead.

The detective was delighted to oblige. He watched the scientist with keen satisfaction as that astute gentleman squinted at the slender blade, still stained with blood, and then as he examined the lower part of the cane. Finally the scientist thrust the long blade into the hollow stick and screwed the handle in. It fitted perfectly. Detective Mallory smiled.

“I don’t suppose you’ll try to put a crimp in me this time?” he asked jovially.

“Very clever, Mr. Mallory, very clever,” replied The Thinking Machine, and with Hatch trailing he left headquarters.

“Mallory will swell like a balloon after that,” Hatch commented grimly.

“Well, he might save himself that trouble,” replied the scientist crustily. “He has the wrong man.”

The reporter glanced quickly into the inscrutable face of his companion.

“Didn’t Knight do it?” he asked.

“Certainly not,” was the impatient answer.

“Who did?”

“I don’t know.”

Together they went on to the theatre from which Miss Oliver had been removed the night before. There a few words with the manager gained permission to look at the Oliver box — a box which the Olivers held only on alternate nights during the opera season. It was on the first balcony level, to the left as they entered the house.

The first three rows of seats in the balcony ran around to and stopped at the box, one of four on that level and the furthest from the stage. The Thinking Machine pottered around aimlessly for ten minutes while Hatch looked on. He entered the box two or three times, examined the curtains, the partitions, the floor and the chairs after which he led the way into the lobby.

There he excused himself to Hatch and stopped in the manager’s office. He remained only a few minutes, afterwards climbing into a cab in w............