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 which he and hatch were driven back to police headquarters.

after some wire pulling and a good deal of red tape the thinking machine and his companion were permitted to see knight. they found him standing at the barred cell door, staring out with weary eyes and pallid face.

the thinking machine was introduced to the prisoner by hatch who had previously tried vainly to induce the young man to talk.

“i have nothing to say,” knight declared belligerently. “see my attorney.”

“i would like to ask three or four questions to which you can have no possible objection,” said the thinking machine. “if you do object of course don’t answer.”

“well?” demanded the prisoner.

“have you ever travelled in europe?”

“i was there for nearly a year. i only returned to this country three months ago.”

“have you ever been interested in any other woman? or has any other woman ever been interested in you?”

the prisoner stared at his questioner coldly.

“no,” he responded, emphatically.

“your answer to that question may mean your freedom within a few hours,” said the thinking machine quite calmly. “tell me the truth.”

“that is the truth — on my honour.”

the answer came frankly, and there came a quick gleam of hope in the prisoner’s face.

“just where in italy did you buy that stiletto cane?” was the next question.

“in rome.”

“rather expensive?”

“five hundred lira — that is about one hundred dollars.”

“i suppose they are very common in italy?”

“yes, rather.”

knight pressed eagerly against the bars of his cell and gazed deeply but uncomprehendingly into the quiet squinting blue eyes.

“there has never been any sort of a quarrel — serious or otherwise between you and miss oliver?”

“never,” was the quick response.

“now, only one more question,” said the thinking machine. “i shall not ask it to hurt you.” there was a little pause and hatch waited expectantly. “does it happen that you know whether or not miss oliver ever had any other love affair?”

“certainly not,” exclaimed the young man, hotly. “she was just a girl — only twenty, out of vassar just a few months ago and — and —”

“you needn’t say any more,” interrupted the thinking machine. “it isn’t necessary. make your plans to leave here tonight, not later than midnight. it is now four o’clock. tomorrow the newspapers will exonerate you.”

the prisoner seemed almost overcome by his emotions. he started to speak, but only extended an open hand through the bars. the thinking machine laid his slender fingers in it with a slight look of annoyance, said “good day” mechanically and he and hatch went out.

the reporter was in a sort of a trance, not an unusual condition in him when in the company of his scientific friend. they climbed into the cab again and were driven away. hatch was thinking too deeply to note the destination when the scientist gave it to the cabby.

“do you actually anticipate that you will be able to get knight out of this thing so easily?” he asked incredulously.

“certainly,” was the response. “the problem is solved except for one or two minor points. now i am proving it.”

“but — but —”

“i will make it all clear to you in due time,” interrupted the other.

they were both silent until the cab stopped. hatch glanced out and recognized the oliver home. he followed the thinking machine up the steps and into the reception hall. there the scientist handed a card to the servant.

“tell mr. oliver, please, that i will only take a moment,” he explained.

the servant bowed and left them. a short wait and mr. oliver entered.

“i am sorry to disturb you at such a time, mr. oliver,” said the scientist, “but if you can give me just a little information i think perhaps we may get a full light on this unfortunate affair.”

mr. oliver bowed.

“first, let me ask you to confirm what i may say is my knowledge that your daughter, eleanor, knew this man. i will ask, too, that you do not mention his name now.”

he scribbled hastily on a piece of paper and handed it to mr. oliver. an expression of deep surprise came into the latter’s face and he shook his head.

“i can answer that question positively,” he said. “she does not know him. she had never been abroad and he has never been in this country until now.”

the thinking machine arose with something nearly akin to agitation in his face, and his slender fingers worked nervously.

“what?” he demand abruptly. “what?” then, after a pause: “i beg your pardon, sir. it startled me a little. but are you sure?”

“perfectly sure,” replied mr. oliver firmly. “they could not have met in any way.”

for a long time the thinking machine stood squinting aggressively at his host with bewilderment plainly apparent in his manner. hatch looked on with absorbed interest. something had gone wrong; a cog had slipped; the wheels of logic had been thrown out of gear.

“i have made a mistake, mr. oliver,” said the thinking machine at last. “i am sorry to have disturbed you.”

mr. oliver bowed courteously and they were ushered out.

“what is it?” asked hatch anxiously as they once more took their seats in the cab.

the thinking machine shook his head in frank annoyance.

“what happened?” hatch insisted.

“i’ve made a mistake,” was the petulant response. “i’m going home and start all over again. it may be that i shall send for you later.”

hatch accepted that as a dismissal and went his way wonderingly. that evening the thinking machine called him to the ‘phone.

“mr. hatch?”

“yes.”

“did miss oliver have any sisters?”

“yes, one. her name is florence. there’s something about her in the afternoon papers in connection with the murder story.”

“how old is she?”

“i don’t know — twenty-two or three.”

“ah!” came a long, aspirated sigh of relief over the wire. “run by and bring detective mallory up to my place.”

“all right. but what was the matter?”

“i was a fool, that’s all. good bye.”

detective mallory was still delighted with himself when hatch entered his office.

“what particular line is your friend van dusen working?” he asked a little curiously.

the reporter shrugged his shoulders.

“he asked me to come by and bring you up,” he replied. “he has evidently reached some conclusion.”

“if it’s anything that doesn’t count knight in it’s all wind,” he said loftily. for once in his life he was confident that he could deliver a blow which would obliterate any theory but his own. in this mood, therefore, he went with hatch. they found the thinking machine pacing back and forth across his small laboratory with his slender hands clasped behind his back. hatch noted that the perplexed wrinkles had gone.

“in adding up a column of figures,” began the scientist abruptly as he sat down, “the oversight of even so trivial a unit as one will make a glaring error in the result. you, mr. mallory, have overlooked a figure one, therefore your conclusion is wrong. in my first consideration of this affair i also overlooked a figure one and my conclusion toppled over just at the moment when it seemed to be corroborated. so i had to start over; i found the one.”

“but this thing against knight is conclusive,” said the detective explosively.

“except for the figure one,” added the scientist.

detective mallory snorted politely.

“now here is the logic of the thing,” resumed the thinking machine. “it will show how i overlooked the figure one — that is a vital fact — and how i found it.”

he dropped back into the reflective attitude which was so familiar to his hearers, squint eyes turned upward and with his fingers pressed tip to tip. for several minutes he was silent while detective mallory vented his impatience by chewing his moustache.

“in the beginning,” began the thinking machine at last, “we have a girl, pretty, young and wealthy in a box at the opera with her parents and her fiance. it would seem, at first glance, to be as safe a place as her home would be, yet she is murdered mysteriously. a stiletto is thrust into her heart. we will assume that her death occurred in the box; that the knife thrust came while she was in a dead faint. this temporary unconsciousness would account for the fact that she did not scream, as the heart would have been pierced by a sudden thrust before consciousness of pain was awakened.

“now the three persons who were with her. there seemed no reason to suspect either the father or mother, so we come to sylvester knight, her intended husband. there is always to be found a motive, either real or imaginary, for a man to kill his sweetheart. in this case knight had the opportunity, but not the exclusive opportunity. therefore, an unlimited field of speculation was opened up.”

detective mallory raised his hand impressively and started to say something, then thought better of it.

“after mr. knight’s arrest,” the thinking machine continued, “your investigation, mr. mallory, drew a net about him. that’s what you wanted to say, i believe. there was the stiletto, the other end of the cane and the alleged threats. i admit all these things. on this statement of the case it looked black for mr. knight.”

“that’s what,” remarked the detective.

“now a stiletto naturally suggests italy. the blade with which miss oliver was killed bore an italian manufacturer’s mark. i presume you noticed it?”

“oh, that!” exclaimed the detective.

“means nothing conclusively,” added the thinking machine. “i agree with you. still it was a suggestion. then i saw the thing that did mean something. this was the fact that the handle of the stiletto was not of the same wood as the part of the cane you found in mr. knight’s room. this difference is so slight that you would hardly notice it even now, but it was there and showed a possible clue leading away from mr. knight.”

detective mallory could not readily place his tongue on words to fittingly express his disgust, so he remained silent.

“when i considered what manner of man mr. knight is and the singular nature of the crime,” resumed the scientist, “i had no hesitancy in assuring mr. hatch that you had the wrong man. after we first saw you we examined the opera box. it was on the left of the theatre and separated from the next box by a latticed partition. it was against this partition that miss oliver was leaning.

“remember, i saw the box after i examined the stiletto and while i was seeking a method by which another person might have stabbed her without entering the box. i found it. by using a stiletto without a guard it would have been perfectly possible for a person in the next box to have killed her by thrusting the blade through the lattice partition. that is exactly what happened.”

detective mallory arose with a mouth full of words. they tumbled out in incoherent surprise and protest, then he sat down again. the thinking machine was still staring upward.

“i then took steps to learn who was in the adjoining box at the time of her death,” he continued quietly. “the manager of the theatre told me it was occupied by mr. and mrs. franklin dupree, and their guest an italian nobleman. italian nobleman! italian stiletto! you see the connection?

“then we saw mr. knight. he assured me, and i believed him, that he had never had any other love affair, therefore no woman would have had a motive in killing miss oliver because of him. he was positive, too, that miss oliver had never had any other love affair, yet i saw the possibility of some connecting link between her and the nobleman. it was perfectly possible, indeed probable, that he would not know of it. at the moment i was convinced that there had been such an affair.

“mr. knight also told me that he bought his stiletto cane in rome; and he paid a price that would seem to guarantee that it would be a perfect one, with the same wood in the handle and lower part, and that he and miss oliver had never had any sort of a quarrel.”

there was a little pause and the thinking machine shifted his position slightly.

“here i had a motive — jealousy of one man who was thrown over for another; the method of death, through the lattice; a clue to the murderer in the stiletto, and the name of the man. it seemed conclusive but i had overlooked a figure one. i saw that when mr. oliver assured me that miss eleanor oliver did not know the nobleman whose name i wrote for him; that she could not have known him. the entire structure tumbled. i was nonplussed and a little rude, i fear, in my surprise. then i had to reconsider the matter from the beginning. the most important of all the connecting links was missing, yet the logic was right. it is always right.

“there are times when imagination has to bridge gaps caused by the absence of demonstrable facts. i considered the matter carefully, then saw where i had dropped the figure one. i ‘phoned to mr. hatch to know if miss oliver had a sister. she had. the newspapers to which mr. hatch referred me told me the rest of it. it was eleanor oliver’s sister who had the affair with the nobleman. that cleared it. there is the name of the murderer.”

he laid down a card on which was scribbled this name and address: “count leo tortino, hotel teutonic.” hatch and the detective read it simultaneously, then looked at the thinking machine inquiringly.

“but i don’t see it yet,” expostulated the detective. “this man knight —”

“briefly it is this,” declared the other impatiently. “the newspapers carried a story of florence oliver’s love affair with count tortino at the time she was travelling in europe with her mother. according to what i read she jilted him and returned to this country where her engagement to another man was rumoured. that was several months ago. now it doesn’t follow that because the count knew florence oliver that he knew or even knew of eleanor oliver.

“suppose he came here maddened by disappointment and seeking revenge, suppose further he reached the theatre, as he did, while the anvil chorus was on, the party started into the wrong box and the usher mentioned casually that the olivers were in there. we presume he knew mrs. oliver by sight, and saw her. he might reasonably have surmised, perhaps he was told, that the other woman was miss oliver — and miss oliver meant to him the woman who had jilted him. the lattice work offered a way, the din of the music covered the act — and that’s all. it doesn’t really appear — it isn’t necessary to know — how he carried the stiletto about him, or why.”

the detective was gnawing his moustache. he was silent for several minutes trying to see the tragedy in this new light.

“but the threats knight made?” he inquired finally.

“has he explained them?”

“oh, he said something about the girl being ill and wanting to go home, and he urged her not to. he told her, he says, that she mustn’t go, because he would have to do something desperate. silly explanation i call it.”

“but i dare say it’s perfectly correct,” commented the thinking machine. “men of your profession, mr. mallory, never believe the simple things. if you would take the word of an accused man at face value occasionally you would have less trouble.” there was a pause, then: “i promised mr. knight that he would be free by midnight. it is now ten. suppose you run down to the teutonic and see count tortino. he will hardly deny anything.”

detective mallory and hatch found the count in his room. he was lying face down across a bed with a bullet hole in his temple. a note of explanation confessed the singular error which had led to the murder of eleanor oliver.

it was three minutes of midnight when sylvester knight walked out of his cell a heartbroken man, but free.