"Yes, Markham, quite mad," Vance summarized, as we were finishing breakfast in his apartment the next morning. "Quite. A poisonous madman, like some foul, crawling creature. His end is rapidly approaching, and a hideous fear has wrecked his brain. The sudden anticipation of death has severed his cord of sanity. He's seeking a hole in which to hide from the unescapable. But he has nowhere to take cover—only the mephitic charnel house which his warped brain has erected. That is his one remaining reality...A vile creature that should be stamped out as one would destroy a deadly germ. A mental, moral and spiritual leper. Unclean. Polluted. And I—I—am to save him from the horrors infinity holds for him!"

    "You must have had a pleasant evening with him," commented Markham with distaste.

    Sergeant Heath, having arrived in answer to an earlier telephone summons from Vance, had listened attentively to the conversation. But he seemed to withdraw into himself when, a few moments later, Gracie Allen came tripping gaily into the library.

    She carried a small wooden box, held tightly to her. Behind her was George Burns, diffident and hesitant. Miss Allen explained things buoyantly.

    "I just had to come, Mr. Vance, to show you my clues. And George had just come to see me; so I brought him along, too. I think he should know how we're getting along. Don't you, Mr. Vance? And mother, she's coming over too in a little while. She said she wants to see you, though I can't even imagine why."

    The girl paused long enough for Vance to present Markham. She accepted him without the suspicion she had previously accorded Heath; and Markham was both fascinated and amused by her lively and irrelevant chatter.

    "And now, Mr. Vance," the girl continued, going to the desk and taking the tight cover from the little box she had brought, "I've simply got to show you my clues. But I really don't think they're any good, because I didn't know exactly where to look for them. Anyhow..."

    She began to display her treasures. Vance humoured her and pretended to be greatly interested. Markham, puzzled but smiling, came forward a few steps; and Burns stood, ill at ease, at the other side of the desk. Heath, annoyed by the frivolous interruption, disgustedly lighted a cigar and walked to the window.

    "Now here, Mr. Vance, is the exact size of a footprint." Gracie Allen took out a slip of paper with some figures written on it. "It measures just eleven inches long, and the man at the shoe store said that was the length of a number nine-and-a-half shoe—unless it was an English shoe, and then it might be only a number nine. But I don't think he was English—I mean the man with the foot. I think he was a Greek, because he was one of the waiters up at the Domdaniel. You see, I went up there because that's where you said the dead man was found. And I waited a long time for someone to come out of the kitchen to make a footprint; and then, when no one was looking, I measured it..."

    She put the paper to one side.

    "And now, here's a piece of blotter that I took from the desk in Mr. Puttie's office at lunch-time yesterday, when he wasn't there. And I held it to a mirror, but all it says is '4 dz Sw So,' just like I wrote it out again here. All that means is, 'four dozen boxes of sandalwood soap.'..."

    She brought out two or three other useless odds and ends which she explained in amusing detail, as she placed them beside the others.

    Vance did not interrupt her during this diverting, but pathetic, display. But Burns, who was growing nervous and exasperated at the girl's unnecessary wasting of time, finally seemed to lose his patience and burst out: "Why don't you show the gentlemen the almonds you have there, and get this silly business over with?"

    "I haven't any almonds, George. There's only one thing left in the box, and that hasn't anything to do with it. I was just sort of practising when I got that due—"

    "But something smells like bitter almond to me."

    Vance suddenly became seriously interested.

    "What else have you in the box, Miss Allen?" he asked.

    She giggled as she took out the last item—a slightly bulging and neatly sealed envelope.

    "It's only an old cigarette," she said. "And that's a good joke on George. He's always smelling the funniest smells. I guess he can't help it."

    She tore away the corner of the envelope and let a flattened and partly broken cigarette slip into her hand. At first glimpse, I would have said that it had not been lighted, but then I noticed its charred end, as if a few inhalations had been taken of it. Vance took the cigarette and held it gingerly near his nose.

    "Here's your smell of bitter almond, Mr. Burns." His eyes were focused somewhere far in space. Then he sealed the cigarette again in one of his own envelopes, and placed it on the mantelpiece.

    "Where did you find that cigarette, Miss Allen?" he asked.

    The girl giggled again musically.

    "Why, that's the one that burned a hole in my dress last Saturday out in Riverdale. You remember...And then when you told me all about how important cigarettes are, I thought I'd go out there right away. I wanted to see if I could find the cigarette and maybe tell if it was a man or a woman that had thrown it at me. You see, I didn't really believe it was you that did it...I had a terrible time finding the cigarette, because I had stepped on it and it was half covered up. Anyhow, I couldn't tell anything from it, and I was awfully mad all over again. I started to throw it away. But I thought I'd just better keep it, because it was the first clue I had gotten—although it really didn't have anything to do with the case I was helping you with."

    "My dear child," said Vance slowly, "it may not have anything to do with our case, but it may have something to do with some other case."

    "Oh, wouldn't that be wonderful!" the girl exclaimed delightedly. "Then we'd have two cases, and I'd really be a detective, wouldn't I?"

    Markham had come forward.

    "What did you mean by that last remark, Vance?"

    "Cyanide may have been on this cigarette." He looked at Markham significantly. "For the possible action of this drug, as well as the possible means of its administration, I have only to refer you to Doremus's remarks Sunday night."

    Markham made a gesture of impatience. "For Heaven's sake, Vance! Your attitude toward this case is becoming more insane every minute."

    Vance ignored the other's comment, and continued. "Assuming my fantastic, and probably fleeting, notion that this cigarette is the actual lethal weapon we have been yearning for, many other equally fantastic things in the case become rational. We could then connect several of our unknown, nightmarish quantities and thus build up a theory which—within its own limitations, at least—would glimmer with sense. Perpend: We could account for Hennessey's failure to see the chap enter the office Saturday evening. We could limit the knowledge of the secret door to Mirche and his immediate circle—which, you must admit, would be logical. We could assume that the crime took place elsewhere than in Mirche's office—in Riverdale, to be specific—and that the body was brought to the office for some definite reason. Such an assumption might offer an explanation of the peculiar manner in which the police were notified; and it might account for the difficulty Doctor Mendel had in determining the time of death. For if the killing took place in the office, it could not have been earlier than ten o'clock, since Miss Allen was in there at about that hour; whereas if the killing took place elsewhere, it could have been at any time within ten hours prior to the finding of the body."

    Vance moved to the mantelpiece and thoughtfully tapped the envelope containing the cigarette.

    "Should that cigarette prove to have been impregnated with the poison, and should it have been used as Doremus indicated such an item could be used, then we're up against an utterly implausible coincidence. To wit, we'd have two people, in separate parts of the city, murdered by the same obscure agent, on the some day. And, added to that, we have only one body."

    Markham nodded slowly without enthusiasm. "Remotely specious. But——"

    "I know your objections, Markham," Vance interrupted. "And they are mine, too. My whole capricious supposition may be less than gossamer—but it's mine own and, at the moment, I adore it."

    Markham started to speak, but Vance ran on.

    "Let me rave a moment longer ere you encase me in a strait-jacket...I behold, as in a dream, the most comforting pastures into which my quaint assumption might lead. It might even tie together the annoyin' factors that have robbed me of sweet sleep—Mirche's ready admission concerning his secret door; the hatred I glimpsed in the eyes of the Lorelei; the mystic lore of the Tofanas; and the presence of the 'Owl' at the Domdaniel Saturday night. It might explain the subtle implications in the name of the cafe. It might even justify the Sergeant's haunting hypothesis of a criminal ring. It might, conceivably, elucidate Mr. Burns' migrat'ry cigarette-case with its scent of jonquille. And there are other things now baffling me that might be assembled into a consistent whole...My word, Markham! it has the most amazin' possibilities. Let me have my hasheesh dream. A pattern is forming at last in my whirling brain; and it is the first coherent design that has invaded my en-fevered imagination since Sabbath eve. With the droll premise that the cigarette was adequately poisoned, I can force a score of hitherto recalcitrant elements into line—or, rather, they tumble into line themselves, like the tiny coloured particles in a kaleidoscope."

    "Vance, for the love of Heaven! You're simply creating a new and more preposterous fantasy to explain away your first fantasy." Markham's severe tone quickly sobered Vance.

    "Yes, you're quite right," he said. "I shall, of course, send the cigarette at once to Doremus for analysis. And it will probably reveal nothing. As you say. Frankly, I don't understand how the smell could have remained on the cigarette so long, unless one of the combining poisons acted as a fixator and retarded volatilization...But, Markham, I do want—I need—a dead man who was killed in Riverdale last Saturday."

    Gracie Allen had been looking from one to the other in a bewildered daze. "Oh, now I bet I understand!" she exclaimed exultantly. "You really think the cigarette could have killed somebody...But I never heard of anyone dying from smoking just one cigarette."

    "Not an ordin'ry cigarette, my dear," Vance explained patiently. "It is only possible if the cigarette has been dipped in some terrible poison."

    "Why, that's awful, if it's really true," she mused. "And up in Riverdale, of all places! It's so pretty and quiet up there..."

    Her eyes began to grow wide, and finally she exclaimed: "But I bet I know who the dead man was! I bet I know!"

    "What in the world are you talking about?" Vance laughed and looked at her with puzzled eyes. "Who do you think it was?"

    She looked back at him searchingly for a few moments, and then said: "Why, it was Benny the Buzzard!"

    Sergeant Heath stiffened suddenly, his mouth agape.

    "Where did you ever hear that name, Miss?" he almost shouted.

    "Why—why——" She stammered, taken aback by his vehemence. "Mr. Vance told me all about him."

    "Mr. Vance told you——?"

    "Of course he did!" the girl said defiantly. "That's how I know that Benny the Buzzard was killed in Riverdale."

    "Killed in Riverdale?" The Sergeant looked dazed. "And maybe you know who killed him, too?"

    "I should say I do know...It was Mr. Vance himself!"