Sergeant Heath appeared at the door.

    "The young doc's just coming downstairs. Want to see him, sir?"

    Vance hesitated; then nodded.

    "Yes, ask him to come in here, Sergeant."

    Heath disappeared and a moment later Doctor Kane entered the drawing-room. His face was drawn and haggard as if from insufficient rest, but the look of strain and apprehension had gone from his eyes. His manner was almost cheerful as he greeted us.

    "How is your patient this morning?" Vance asked him.

    "Practically normal, sir. I remained here a couple of hours after you gentlemen went last night, and Miss Llewellyn was resting quietly when I left. Naturally she feels weak this morning and is highly nervous; but her pulse and respiration and blood-pressure are normal."

    "Have you any suggestion, doctor," Vance asked, "as to what drug it was that brought about her condition last night?"

    Doctor Kane pursed his lips and looked into space.

    "No," he returned at length, "—though I've naturally thought about the matter a good deal. Her symptoms were the usual ones of collapse—nothing distinctive about them—and, of course, there are a number of drugs that, therapeutically speaking, could have produced them. An overdose of any one of the various proprietary sleeping powders containing the barbiturates might have done it. But, you can understand, I shouldn't care to express an opinion offhand. I had intended to do a little research on the subject as soon as I return to my office."

    Vance did not push the subject. He let the doctor go and then sent for the butler.

    Smith was as imperturbable as ever, and his face was still pale.

    "Please tell Miss Llewellyn," Vance said, "that we should like to have a few words with her, either in her own quarters or here in the drawing-room—whichever is more convenient for her."

    The butler bowed and went out. On returning he informed Vance that Miss Llewellyn would see us in her room, and we went upstairs.

    The girl was reclining on a chaise-longue, dressed in elaborately embroidered Japanese pyjamas. At her side stood a small red-lacquered tabouret on which were a complete cigarette service, a few art magazines, and a silver statuette of abstract design in imitation of Archipenko. Her greeting to us was a curt nod and a cynical attempt at a smile.

    "Your visit, I understand from Doctor Kane, just missed coming under the head of 'viewing the remains.'"

    "We are delighted," Vance returned seriously, "to find you so much better."

    "But some one," she said bitterly, "surely will not take my recovery in so charitable a light." She shrugged slightly and made a grimace. "I'm beginning to feel like a visitor at the Borgias' palace. I was positively afraid to take my toast and coffee this morning."

    Vance nodded understandingly.

    "I doubt, though, that you need have any further fear. Something went radically wrong last night. The poisoner must have lost his way among unforeseen coincidences. And by the time he has reassembled his lines and planned another campaign of action, we hope to have the situation well in hand. We at least know now where we must look for indicat'ry activities."

    Amelia Llewellyn glanced up quizzically and all cynicism faded from her face.

    "That sounds," she remarked, "as if you knew more than you are divulging."

    "Yes—quite. Considerably more. But not enough. Still, we're forrader, and always hoping. . . . You've seen your brother? He's quite recovered. And he got an uglier jolt than you did."

    "Yes," the girl mused. "We're the two failures. It's quite like us, you know. We're always disappointing somebody."

    "I trust," said Vance, "I sha'n't disappoint you in this case. In the meanwhile would you mind if I took a peep in your clothes closet and made a little experiment there?"

    "Peep and experiment, by all means. I'd be delighted." She waved her arm almost gayly toward a door at her left.

    Vance went to it and opened it. The space beyond was, as she had explained to us the night before, an old-fashioned passageway which had connected the two main rooms in the south wing of the house. There was a shoe-rack and a small cupboard on the right, and on the left hung a long row of dresses and gowns. Halfway down the passage there still remained the old marble-topped washbasin with its two high swan-necked spigots. At the opposite end of the improvised closet another door was visible. Vance walked to it and opened it, and we could see through into the large bedroom where Virginia Llewellyn had met her tragic end.

    Vance came back to us and, turning to me, said:

    "Van, go into the other room, close both doors and stand beside the bed. Then call to me in a fairly loud voice. When you hear me knock on the farther door, call again in the same tone of voice."

    I went through the clothes closet into the farther room and, standing beside the bed on which Virginia Llewellyn had died, called out. After a few moments I heard Vance's knock on the door, and I called again. Then Vance opened the door.

    "That's all, Van. Many thanks."

    When we were again in Amelia Llewellyn's room, the girl gave Vance a satirical look.

    "And what, Monsieur Lecoq," she asked, "did you learn?"

    "Merely that you told us the truth regarding the acoustic possibilities between the two rooms," Vance returned lightly. "I could not hear Mr. Van Dine with both doors shut, but I did hear him distinctly while standing in the clothes closet."

    The girl drew a deep dramatic sigh.

    "I'm so glad to have my veracity proved for once. Mother's favorite criticism of me is that I would always rather lie than tell the truth."

    "Speaking of your mother"—Vance sat down and regarded the girl with serious eyes—"I want you to tell us just how you came to drink the glass of water in your mother's room last night."

    Amelia Llewellyn sobered quickly under Vance's grave tone.

    "How does one ever come to take a drink of water?—I only know that I felt thirsty and instinctively reached for the water that stood at my side. I was going to wait there until mother came back. I was naturally upset and wanted to talk to some one—"

    "Did you taste anything peculiar about the water?"

    "No. It seemed perfectly all right."

    "How much water was in the jug?"

    "Barely a glassful. I vaguely remember wishing there had been more. But I was too lazy to get up. When mother returned I had a raging headache and my ears were pounding, and I felt terribly weak. My mind was confused, and I started for my own room. That's all I recall."

    "You distinctly remember your mother's return to the room?"

    "Oh, yes. We said something to each other—I don't recall just what it was. I probably complained about my headache—but everything was spinning around by that time."

    "When you first felt thirsty—that is, before you took the drink of water—did you mention the fact to your mother?"

    The girl thought a moment. Then she answered:

    "No. Mother was at the dressing-table, beautifying herself for the interview with you. I don't think we spoke to each other then. I merely reached over and helped myself to what water there was in the jug, and mother swept grandly and haughtily from the room."

    "What of the water in your own carafe last night?" Vance asked. "The maid said she filled it. But while you were unconscious in your mother's room, your carafe was inspected and found to be empty."

    "Yes, I know it was empty. I drank all the water it contained while I was sketching earlier in the night." Her eyes opened a little wider. "Was my water poisoned too?"

    Vance shook his head.

    "No, it couldn't have been. Too much time elapsed after you had taken it. You would have felt the effects of the poison within half an hour, at the most. . . ."

    Vance turned suddenly and went softly to the hall door. He turned the knob carefully and then swiftly drew the door inward. In the corridor, facing us, stood Richard Kinkaid.

    Not a muscle of his face moved to show that Vance's sudden action had disconcerted him. He took his cigarette slowly from his mouth and bowed with curt formality.

    "Good morning, Mr. Vance," he said in a cold steady voice. "I came down to inquire about my niece. But when I heard voices in the room I thought you and Mr. Markham might be here, and I didn't care to disturb you. But you evidently heard me. . . ."

    "Yes, yes. I heard some one moving outside the door." Vance stood to one side. "We were just asking Miss Llewellyn a few questions. But we're through now. . . . She is much better this morning."

    Kinkaid stepped into the room, and, after greeting his niece with a conventional phrase or two, he sat down.

    "Any further developments?" he asked, lifting his head to Vance with a shrewd, calculating look.

    "Oh, any number," Vance returned non-committally. "We're bringin' in the sheaves, as it were. But we're not rejoicin' just yet. . . . However, I'm glad you dropped in. I wanted to ask you, before we went, for Bloodgood's address. We're particularly anxious to have a little chat with the gentleman."

    Kinkaid's jaw tightened, and the look in his eyes became harder. But there was no other indication that he was surprised by Vance's remarks.

    "Bloodgood lives at the Astoria Hotel in 22nd Street," he said, and slowly broke the ashes of his cigarette in a tray at his side. "However," he added, with a slight note of contempt in his voice, "you're barking up the wrong tree there. But go ahead and question him, by all means. He'll be at his hotel all day—I just talked to him on the phone. But you'll be wasting your time—Bloodgood's as straight as a die."

    "I really don't know the chap very well," Vance murmured. "But in view of the fact that it was he who ordered the plain water for Lynn Llewellyn last night at the Casino, it might be interestin' to have his views on the subject, don't y' know."

    Amelia Llewellyn, who had perceptibly stiffened at the mention of Bloodgood's name, now stood up and stared at Vance defiantly, with blazing eyes.

    "What do you mean by that?" she demanded. "Are you accusing Mr. Bloodgood of giving the poison to Lynn?"

    "My dear young lady!"

    "For if you are," the girl went on in a cold angry tone, "I can tell you exactly who's responsible for everything that happened to this family last night."

    Vance gazed at her calmly, and the chill of his tone matched hers.

    "When the truth becomes known, Miss Llewellyn," he said, "your testimony will not, I fear, be needed." He bowed formally to her and to Kinkaid, and we took our departure.

    When we were about to descend to the main floor Vance hesitated and then went down the hall toward Mrs. Llewellyn's room.

    "There's one little matter I should like to mention to the lady of the house before we go," he explained to Markham, as he tapped on the door.

    Mrs. Llewellyn received us with ill grace, and her manner was one of marked antagonism.

    Vance apologized for disturbing her.

    "I merely wished to tell you, as a matter of possible interest to you, that your son seemed greatly perturbed when I informed him of the volumes on toxicology in the library downstairs. He appeared to have been unaware of their existence."

    "And how should that be of interest to me?" the woman retorted with frigid disdain. "My son does not read much—his literary needs are entirely satisfied by the theatre. I doubt if he is familiar with the titles of any of the books his father left. Nothing could be more alien to his interests than scientific research. And his perturbation over the existence of books on poisons in this house is, I assure you, perfectly natural in view of the experience through which he went last night."

    Vance nodded as if satisfied with the explanation.

    "That's quite plausible," he murmured. "And perhaps you can give us as colorable an explanation as to why you yourself spent part of this morning in the library."

    "So my movements are being spied upon!" This was said with scathing and vindictive indignation; but a change quickly came over the woman's attitude. Her eyes contracted and a shrewd smile appeared on her lips. "The intimation beneath your words is, I suppose, that I myself was consulting these particular books on poisons."

    Vance waited, and the woman went on.

    "Well, that's exactly what I was doing. If it will help your inquiries: I was looking for some common drug that might account for the condition of my son and daughter last night."

    "And did you find any reference to such a drug, madam?"

    "No! I did not."

    Vance left the matter there. He made his adieux and added:

    "There will be no more spying—for the time being, at least. The police will be removed from your house, and you and your family are free to come and go as you please."

    When we were again downstairs Markham drew Vance into the drawing-room.

    "See here, Vance," he asked with deep concern, "aren't you being a bit hasty?"

    "My dear Markham," Vance chided him, "I'm never hasty. Slow and ploddin' and cautious. The human tortoise. I must have reasons for everything I do. And I now have excellent reasons for temporarily removing all supervision from the Llewellyn domicile."

    "Still," demurred Markham, "I don't like the situation here, and I think it should be watched."

    "A virtuous idea. But not helpful." Vance contemplated Markham plaintively. "Watching won't help us. I was invited to watch Lynn's passing out. And we were all in the house watching last night when Amelia was smitten. Really, y' know, we can't be expected to supply every member of the Llewellyn family with a bodyguard indefinitely."

    Markham studied Vance closely, as if trying to read the other's thoughts.

    "That was a peculiar remark of the girl's about her knowing who's responsible for this affair. Do you believe her, perhaps?"

    "Oh, my dear Markham!" Vance sighed dolefully. "It's too early to begin believing anybody. Our only hope lies in complete skepticism. Honest doubtin'—not thought highly of, but most efficacious at times. It gives the mind a chance for free functioning."

    "Nevertheless," pursued Markham irritably, "you have something definite in mind when you want the police withdrawn."

    "No, no; nothing definite," Vance returned, and smiled. "Just gropin'. Strainin' for illumination. . . . And I do want to see the post-mortem report. That, at least, will be definite. It may even prove revealin'."

    Markham gave in reluctantly.

    "Very well. I'll give Heath orders to withdraw temporarily and send the boys home."

    "And tell him to pick up our croupier at the Astoria and bring him along to your office," said Vance. "I'm eager to grill him, as you public prosecutors would say. And I think the judicial and depressin' surroundings of the Criminal Courts Building might have the right psychological effect."

    "What do you expect to find out from him?"

    "Nothing—positively nothing," Vance replied, and then added: "But even negation might be of help. I have a psychic feelin' this case will eventually be solved by minus signs."

    Markham grunted, and we went out into the hall where the Sergeant was waiting despondently.

    Ten minutes later Vance and Markham and I were on our way downtown, Heath having been duly instructed as to the procedure Vance had requested.

    As soon as we entered the District Attorney's dingy but spacious old office overlooking the drab gray walls of the Tombs, Markham rang for Swacker and inquired about the statement from Doctor Doremus and also about the report on the specimens of typing which had been sent to the scientific laboratory.

    "The lab report has come in," Swacker told him, pointing to a sealed envelop on the desk; "but Doctor Doremus phoned at eleven to say that the autopsy report is delayed. I called back ten minutes ago, and one of the assistants told me the report was on the way. I'll bring it in as soon as it arrives."

    Markham jerked his head curtly, and Swacker went out.

    "Delayed—eh, what?" drawled Vance. "There shouldn't have been any trouble. Belladonna poisoning indicated. The toxicologist knew just what to look for. I wonder. . . . In the meantime, let's see what the bright boy with the magnifying glass has to offer."

    Markham had already opened the envelop to which Swacker had referred. He laid the three specimens of typing to one side and perused the accompanying report. After a few moments he put that down too.

    "Just what you suspected," he said to Vance without enthusiasm. "All the typing was done on the same machine, and within a reasonable period of time—that is, the ink on the ribbon was at the same stage of usage in all three, and it can't be stated with certainty which of the three was typed first. Also, the suicide note and the letter you received were probably typed by the same person. Peculiarities of pressure and punctuation, and consistencies in the errors when the wrong letters were struck, are the same in both. There's a lot of technical detail, but that's the gist of it." He picked up the report and held it out to Vance. "Do you care to see it?"

    Vance made a negative gesture with his hand.

    "No, I merely craved verification."

    Markham leant forward.

    "See here, Vance, what's the point about these two typewritten documents? Granting the possibility that the girl did not commit suicide, what would have been the object of the person who poisoned her in sending you that letter?"

    Vance became serious.

    "Really, Markham, I don't know." He walked slowly up and down the room as he spoke. "If only that letter to me and the suicide note had been typed by two different people, the thing would be comparatively simple. It would merely mean that some one had planned to poison the girl in such a way as to make it appear as suicide, and that some one else, with an inkling that murder was afoot, had sent me a dramatic call for help. In such an event two conclusions might have been tenable: first, that the anonymous letter-writer feared that Lynn was to be the victim; and, second, that the writer suspected Lynn himself of having murderous designs on his wife and wanted me to keep an eye on him. . . ."

    "And they were both victims," Markham interpolated glumly. "So that hypothesis doesn't get us anywhere. In any event, it's merely a speculation based on the false premise that two different people prepared the two documents. Why not come to the point?"

    "Oh, my dear chap!" Vance moaned. "I'm strivin' desperately to come to the point—but, dash it all! I don't know what the point is. As the case stands now, the poisoner deliberately called my attention to the situation and even intimated strongly that Lynn's wife was not going to commit suicide, but would actually be murdered."

    "That doesn't make sense."

    "And yet, Markham, you have the substantiation of my apparently insane conclusion lying on your desk. There's the suicide note; there's the letter to me, filled with innuendoes and suspicions of foul play; and there's your report that the same hand typed them both."

    He paused.

    "And what of the next inevitable step in our ratiocination? As I have whispered into your reluctant ear, I think the murderer wishes us to look in the wrong direction for our culprit. He is, as it were, attempting the impossible feat of taking two tricks of the same suit with a singleton. And that's what makes the thing so subtle and fiendish."

    "But it wasn't a singleton," Markham objected. "You overlook the fact that three people were poisoned. If your theory is correct, why couldn't the murderer merely have poisoned the girl and then poisoned the victim we were supposed to fix on? Why make us a party to his plan when he's apparently in the wholesale poisoning business?"

    "A reasonable question," Vance nodded; "and one that has tortured me since last night. Such a procedure would have been the rational one. But, Markham, there's nothing rational about this crime. There isn't merely one straw-man confronting us, but a series of straw-men. And I have a horrible suspicion that they are arranged in a circle, with the actual murderer beyond the circumference. Our only hope lies in the fact that something has gone wrong. In any delicate and intricate mechanism, one little failure—one trifling slip in functioning—undermines the entire structure and renders the machine incapable of operating. This is not a plastic crime. Despite all its hyper-subtleties and divagations and convolutions, it's static and fixed in its conception. And therein lies both its strength and its weakness. . . ."

    At this point Swacker tapped on the leather swinging door and pushed it open. In his hand was a thick envelop.

    "The autopsy report," he said, placing it on Markham's desk and going out again.

    Markham opened the envelop at once and glanced over the typewritten pages which were bound together in a blue folder. As he read, his face clouded and a puzzled look came into his eyes; and when he had reached the end of the last page there was a deep scowl on his forehead.

    He raised his head slowly and fixed on Vance, who had seated himself before the desk, a look of baffled calculation.

    "My dear Markham," Vance complained; "what dark secret are you hoarding?"

    "There was no belladonna whatever found in the girl's stomach! And no quinin or camphor—which entirely eliminates the rhinitis tablets."

    Vance lighted a cigarette with slow deliberation.

    "Any details?"

    Markham referred to the report.

    "The exact findings are: Congestion of the lungs; considerable serum in the pleural cavities; blood mostly in the veinous side of the circulation; right heart engorged, left heart comparatively empty; brain tissues and meninges congested; and the throat, trachea and œsophagus hyperemic. . . ."

    "All symptoms of death from asphyxia." Vance looked out unhappily through the high windows to the south. "And no poison! . . . Does Doremus offer any opinion?"

    "Nothing specific," Markham informed him. "He's professionally non-committal here. He merely states that the cause of asphyxia is as yet unknown."

    "Yes, yes. Pending analysis of the liver, kidneys, intestines, and blood. That will take a couple of days. But some of the poison should be in the stomach, if it was taken orally."

    "But Doremus states here that the history he received of the case and his findings on the immediate examination of the body, indicated an overdose of belladonna or atropin."

    "We knew that last night." Vance reached over and, taking the report, went through it carefully. "Yes. As you say."

    He settled down in his chair, brought his eyes slowly back to Markham's troubled gaze, and took a deep inhalation on his cigarette. Then he tossed the report back on Markham's desk with a despondent gesture.

    "That tears it, old dear. A lady is given poison, presumably orally; but no traces of it are found. Two other persons are poisoned and recover. We are supposed to tag some innocent bystander for the heinous crime. . . . Oh, my aunt! What an astonishin' situation! . . ."