Vance ran past the covered body of Swift on the settee, and crossed to the garden gate. As he reached it he was confronted by the haughty and majestic figure of Madge Weatherby. Evidently her intention was to step into the garden, but she drew back abruptly when she saw us. Our presence, however, seemed neither to surprise nor to embarrass her.

    "Charmin' of you to come up, Miss Weatherby," said Vance. "But I gave orders that every one was to remain downstairs."

    "I had a right to come here!" she returned, drawing herself up with almost regal dignity.

    "Ah!" murmured Vance. "Yes, of course. It might be, don't y' know. But would you mind explainin'?"

    "Not at all." Her expression remained unchanged, and her voice was hollow and artificial. "I wished to ascertain if he could have done it."

    "And who," asked Vance, "is this mysterious 'he'?"

    "Who?" she repeated, throwing her head back sarcastically. "Why, Cecil Kroon!"

    Vance's eyelids drooped, and he studied the woman narrowly for a brief moment. Then he said lightly:

    "Most interestin'. But let that wait a moment. How did you get up here?"

    "That was very simple." She tossed her head negligently. "I pretended to be faint and told your minion I was going into the butler's pantry to get a drink of water. I went out through the pantry door into the public hallway, came up the main stairs, and out on this terrace."

    "But how did you know that you could reach the garden by this route?"

    "I didn't know." She smiled enigmatically. "I was merely reconnoitring. I was anxious to prove to myself that Cecil Kroon could have shot poor Woody."

    "And are you satisfied that he could have?" asked Vance quietly.

    "Oh, yes," the woman replied with bitterness. "Beyond a doubt. I've known for a long time that Cecil would kill him sooner or later. And I was quite certain when you said that Woody had been murdered that Cecil had done it. But I did not understand how he could have gotten up here, after leaving us this afternoon. So I endeavored to find out."

    "And why, may I ask," said Vance, "would Mr. Kroon desire to dispose of Swift?"

    The woman clasped her hands theatrically against her breast. Taking a step forward, she said in a histrionically sepulchral voice:

    "Cecil was jealous—frightfully jealous. He's madly in love with me. He has tortured me with his attentions..." One of her hands went to her forehead in a gesture of desperation. "There has been nothing I could do. And when he learned that I cared for Woody, he became desperate. He threatened me. I was horribly frightened. I didn't dare break everything off with him—I didn't know what he might do. So I humored him: I went about with him, hoping, hoping that this madness of his would subside. For a time I thought he was becoming more normal and rational. And then—today—this terrible crime!..." Her voice trailed off in an exaggerated sigh.

    Vance's keen regard showed neither the sympathy her pompous recital called for, nor the cynicism which I knew he felt. There was only a studied interest in his gaze.

    "Sad—very sad," he mumbled.

    Miss Weatherby jerked her head up and her eyes flashed.

    "I came up here to see if it were possible that Cecil could have done this thing. I came up in the cause of justice!"

    "Very accommodatin'." Vance's manner had suddenly changed. "We're most appreciative, and all that sort of thing. But I must insist, don't y' know, that you return downstairs and wait there with the others. And you will be so good as to come through the garden and go down the apartment stairs."

    He was brutally matter-of-fact as he drew the gate shut and directed the woman to the passageway door. She hesitated a moment and then followed his indicating finger. As she passed the wicker settee she stopped suddenly and sank to her knees.

    "Oh, Woody, Woody!" she wailed dramatically. "It was all my fault!" She covered her face with her hands and bent her head far forward in an attitude of abject misery.

    Vance heaved a deep sigh, threw away his cigarette and, taking her firmly by one arm, lifted her to her feet.

    "Really, y' know, Miss Weatherby," he said brusquely, leading her toward the door, "this is not a melodrama."

    She straightened up with a stifled sob and went down the passageway toward the stairs.

    Vance turned to the detective and nodded toward the entrance.

    "Snitkin," he said wearily, "go downstairs and tell Hennessey to keep an eye on Sarah Bernhardt till we need her."

    Snitkin grinned and followed Miss Weatherby below.

    When we were back in the study Vance sank into a chair and yawned.

    "My word!" he complained. "The case is difficult enough without these amateur theatricals."

    Markham, I could see, had been both impressed and puzzled by the incident.

    "Maybe it's not all dramatics," he suggested. "The woman made some very definite statements."

    "Oh, yes. She would. She's the type." Vance took out his cigarette case. "Definite statements, yes. And misleadin'. Really, y' know, I don't for a moment believe she regards Kroon as the culprit."

    "Well, what then?" snapped Markham.

    "Nothing—really nothing." Vance sighed. "Vanity and futility. The lady is vanity—we're futility. Neither leads anywhere."

    "But she certainly has something on her mind," protested Markham.

    "So have we all. I wonder...But if we could read one person's mind completely, we'd probably understand the universe. Akin to omniscience, and that sort of thing."

    "God Almighty!" Markham stood up and planted himself belligerently in front of Vance. "Can't you be rational?"

    "Oh, Markham—my dear Markham!" Vance shook his head sadly. "What is rationality? However...As you say. There is something back of the lady's histrionics. She has ideas. But she's circuitous. And she wants us to be like those Chinese gods who can't proceed except in a straight line. Sad. But let's try makin' a turn. The situation is something like this: An unhappy lady slips out through the butler's pantry and presents herself on the roof-garden, hopin' to attract our attention. Having succeeded, she informs us that she has proved conclusively that a certain Mr. Kroon has done away with Swift because of amorous jealousy. That's the straight line—the longest distance between two points.—Now for the curve. The lady herself, let us assume, is the spurned and not the spurner. She resents it. She has a temper and is vengeful—and she comes to the roof here for the sole purpose of convincing us that Kroon is guilty. She's not beyond that sort of thing. She'd be jolly well glad to see Kroon suffer, guilty or not."

    "But her story is plausible enough," said Markham aggressively. "Why try to find hidden meanings in obvious facts? Kroon could have done it. And your psychological theory regarding the woman's motives eliminates him entirely."

    "My dear Markham—oh, my dear Markham! It doesn't eliminate him at all. It merely tends to involve the lady in a rather unpleasant bit of chicanery. The fact is, her little drama here on the roof may prove most illuminatin'."

    Vance stretched his legs out before him and sank deeper into his chair.

    "Curious situation. Y' know, Markham, Kroon deserted the party about fifteen or twenty minutes before the big race—legal matters to attend to for a maiden aunt, he explained—and he didn't appear again until after I had phoned you. Assumed immediately that Swift had shot himself. Also mentioned a couple of accurate details. All of which could have been either the result of actual knowledge or mere guesswork. Doubt inspired me to converse with the elevator boy. I learned that Kroon had not gone down or up in the elevator since his arrival here early in the afternoon..."

    "What's that!" Markham exclaimed. "That's more than suspicious—taken with what we have just heard from this Miss Weatherby."

    "I dare say." Vance was unimpressed. "The legal mind at work. But from my gropin' amateur point of view, I'd want more—oh, much more. However,"—Vance rose and meditated a moment—"I'll admit that a bit of lovin' communion with Mr. Kroon is definitely indicated." He turned to Heath. "Send the chappie up, will you, Sergeant? And be sweet to him. Don't annoy him. La politesse. No need to put him on his guard."

    Heath nodded and started toward the door. "I get you, Mr. Vance."

    "And Sergeant," Vance halted him; "you might question the elevator boy and find out if there is any one else in the building whom Kroon is in the habit of calling on. If so, follow it up with a few discreet inquiries."

    Heath vanished down the stairs, and a minute or so later Kroon sauntered into the study with the air of a man who is bored and not a little annoyed.

    "I suppose I'm in for some more tricky questions," he commented, giving Markham and Snitkin a fleeting contemptuous glance and letting his eyes come to rest on Vance with a look of resentment. "Do I take the third-degree standing or sitting?"

    "Just as you wish," Vance returned mildly; and Kroon, after glancing about him, sat down leisurely at one end of the davenport. The man's manner, I could see, infuriated Markham, who leaned forward and asked in cold anger:

    "Have you any urgent reasons for objecting to give us what assistance you can in our investigation of this murder?"

    Kroon raised his eyebrows and smoothed the waxed ends of his mustache:

    "None whatever," he said with calm superiority. "I might even be able to tell you who shot Woody."

    "That's most interestin'," murmured Vance, studying the man indifferently. "But we'd much rather find out for ourselves, don't y' know. Much more sportin', what? And there's always the possibility that our own findin's might prove more accurate than the guesses of others."

    Kroon shrugged maliciously and said nothing.

    "When you deserted the party this afternoon, Mr. Kroon," Vance went on in an almost lackadaisical manner, "you gratuitously informed us that you were headed for a legal conference of some kind with a maiden aunt. I know we've been over this before, but I ask again: would you object to giving us, merely as a matter of record, the name and address of your aunt, and the nature of the legal documents which lured you so abruptly away from the Rivermont Handicap, after you had wagered five hundred dollars on the outcome?"

    "I most certainly would object," returned Kroon coolly. "I thought you were investigating a murder; and I assure you my aunt had nothing to do with it. I fail to see why you should be interested in my family affairs."

    "Life is full of surprises, don't y' know," murmured Vance. "One never knows where family affairs and murder overlap."

    Kroon chuckled mirthlessly, but checked himself with a cough.

    "In the present instance, I am happy to inform you that, so far as I am concerned, they do not overlap at all."

    Markham swung round toward the man.

    "That's for us to decide," he snapped. "Do you intend to answer Mr. Vance's question?"

    Kroon shook his head.

    "I do not! I regard that question as incompetent, irrelevant, and immaterial. Also frivolous."

    "Yes, yes." Vance smiled at Markham. "It could be, don't y' know. However, let it pass, Markham. Present status: Name and address of maiden aunt, unknown; nature of legal documents, unknown; reason for the gentleman's reticence, also unknown."

    Markham resentfully mumbled a few unintelligible words and resumed smoking his cigar while Vance continued the interrogation.

    "I say, Mr. Kroon, would you also consider it irrelevant—and the rest of the legal verbiage—if I asked you by what means you departed and returned to the Garden apartment?"

    Kroon appeared highly amused.

    "I'd consider it irrelevant, yes; but since there is only one sane way I could have gone and come back, I'm perfectly willing to confess to you that I took a taxicab to and from my aunt's."

    Vance gazed up at the ceiling as he smoked. "Suppose," he said, "that the elevator boy should deny that he took you either down or up in the car since your first arrival here this afternoon. What would you say?"

    Kroon jerked himself up to attention.

    "I'd say that he had lost his memory—or was lying."

    "Yes, of course. The obvious retort. Quite." Vance's eyes moved slowly to the man on the davenport. "You will probably have the opportunity of saying just that on the witness stand."

    Kroon's eyes narrowed and his face reddened. Before he could speak, Vance went on.

    "And you may also have the opportunity of officially giving or withholding your aunt's name and address. The fact is, you may find yourself in the most distressin' need of an alibi."

    Kroon sank back on the davenport with a supercilious smile.

    "You're very amusing," he commented lightly. "What next? If you'll ask me a reasonable question, I'll be only too happy to answer. I'm a highly esteemed citizen of these States—always willing, not to say anxious, to assist the authorities—to aid in the cause of justice, and all that sort of rot." There was an undercurrent of venom in his contumelious tone.

    "Well, let's see where we stand." Vance suppressed an amused smile. "You left the apartment at approximately a quarter to four, took the elevator downstairs and then a taxi, went to your aunt's to fuss a bit with legal documents, drove back in a taxi, and took the elevator upstairs. Bein' gone a little over half an hour. During your absence Swift was shot. Is that correct?"

    "Yes." Kroon was curt.

    "But how do you account for the fact that when I met you in the hall on your return, you seemed miraculously cognizant of the details of Swift's passing?"

    "We've been over that, too. I knew nothing about it. You told me Swift was dead, and I merely surmised the rest."

    "Yes—quite. No crime in accurate surmisals. Deuced queer coincidence, however. Taken with other facts. As likely as a five-horse win parlay. Extr'ordin'ry."

    "I'm listening with great interest." Kroon had again assumed his air of superiority. "Why don't you stop beating about the bush?"

    "Worth-while suggestion." Vance crushed out his cigarette and, drawing himself up in his chair, leaned forward and rested his elbows on his knees. "What I was leadin' up to was the fact that some one has definitely accused you of murdering Swift."

    Kroon started, and his face went pale. After a few moments he forced a harsh guttural noise intended for a laugh. "And who, may I ask, has accused me?"

    "Miss Madge Weatherby."

    One corner of Kroon's mouth went up in a sneer of hatred.

    "She would! And she probably told you that it was a crime of passion— caused by an uncontrollable jealousy."

    "Just that," nodded Vance. "It seems you have been forcing your unwelcome attentions upon her, with dire threats; whereas, all the time, she was madly enamored of Mr. Swift. And so, when the strain became too great, you eliminated your rival. Incidentally, she has a very pretty theory which fits the known facts, and which your own refusal to answer my questions bolsters up considerably."

    "Well, I'll be damned!" Kroon got to his feet slowly and thrust his hands deep into his pockets. "I see what you're driving at. Why didn't you tell me this in the first place?"

    "Waitin' for the final odds," Vance returned. "You hadn't laid your bet. But now that I've told you, do you care to give us the name and address of your maiden aunt and the nature of the legal documents you had to sign?"

    "That's all damned nonsense," Kroon spluttered. "I don't need an alibi. When the time comes—" At this moment Heath appeared at the door, and walking directly to Vance, handed him a page torn from his note-book, on which were several lines of handwriting.

    Vance read the note rapidly as Kroon looked on with malignant resentment. Then he folded the paper and slipped it into his pocket.

    "When the time comes...," he murmured. "Yes—quite." He raised his eyes lazily to Kroon. "As you say. When the time comes. The time has now come, Mr. Kroon."

    The man stiffened, but did not speak. I could see that he was aggressively on his guard.

    "Do you, by any chance," Vance continued, "know a lady named Stella Fruemon? Has a snug little apartment on the seventeenth floor of this building—only two floors below. Says you were visitin' her around four o'clock today. Left her at exactly four-fifteen. Which might account for your not using the elevator. Also for your reluctance to give us your aunt's name and address. Might account for other things as well...Do you care to revise your story?"

    Kroon appeared to be thinking fast. He walked nervously up and down the study floor.

    "Puzzlin' and interestin' situation," Vance went on. "Gentleman leaves this apartment at—let's say—ten minutes to four. Family documents to sign. Doesn't enter the elevator. Appears in apartment two floors below within a few minutes—been a regular visitor there. Remains till four-fifteen. Then departs. Shows up again in this apartment at half-past four. In the meantime, Swift is shot through the head—exact time unknown. Gentleman is apparently familiar with various details of the shooting. Refuses to give information regarding his whereabouts during his absence. A lady accuses him of the murder, and demonstrates how he could have accomplished it. Also kindly supplies the motive. Fifteen minutes of gentleman's absence—namely, from four-fifteen to four-thirty—unaccounted for."

    Vance drew on his cigarette.

    "Fascinatin' assortment of facts. Add them up. Mathematically speakin', they make a total...I say, Mr. Kroon, any suggestions?"

    Kroon came to a sudden halt and swung about.

    "No!" he blurted. "Damn your mathematics! And you people hang men on such evidence!" He sucked in a deep noisy breath and made a despairing gesture. "All right, here's the story. Take it or leave it. I've been mixed up with Stella Fruemon for the past year. She's nothing but a gold-digger and blackmailer. Madge Weatherby got on to it. She's the jealous member of this combination—not me. And she cared about as much for Woode Swift as I did. Anyway, I got involved with Stella Fruemon. It came to a show-down, and I had to pay through the nose. To avoid scandal for my family, of course. Otherwise, I'd have thrown her through the window and called it my boy scout's good deed for the day. At any rate, we each got our lawyers, and a settlement was reached. She finally named a stiff figure and agreed to sign a general release from all claims. In the circumstances, I had no alternative. Four o'clock today was the time set for the completion of the transaction. My lawyer and hers were to be at her apartment. The certified check and the papers were ready. So I went down there a little before four to clean up the whole dirty business. And I cleaned it up and got out. I had walked down the two flights of stairs to her apartment, and at four-fifteen, when the hold-up was over, I told the lady she could go to hell, and I walked back up the stairs."

    Kroon took a deep breath and frowned.

    "I was so furious—and relieved—that I kept on walking without realizing where I was going. When I opened the door which I thought led into the public hallway outside the Garden apartment, I found I was out on the terrace of the roof." He cocked an angry eye at Vance. "I suppose that fact is suspicious too—walking up three flights of stairs instead of two—after what I'd been through?"

    "No. Oh, no." Vance shook his head. "Quite natural. Exuberant spirits. Weight off the shoulders, and all that. Three flights of stairs seemin' like two. Light impost, so to speak. Horses run better that way. Don't feel the extra furlong, as it were. Quite comprehensible...But please proceed."

    "Maybe you mean that—and maybe you don't." Kroon spoke truculently. "Anyway; it's the truth...When I saw where I was I thought I'd come through the garden and go down the stairway there. It was really the natural thing to do..."

    "You knew about the gate leading into the garden, then?"

    "I've known about it for years. Everybody who's been up here knows about it. On summer nights Floyd used to leave the gate open and we'd walk up and down the terrace. Anything wrong with my knowing about the gate?"

    "No. Quite natural. And so, you opened the gate and entered the garden?"

    "Yes."

    "And that would be between a quarter after four and twenty minutes after four?"

    "I wasn't holding a stop-watch on myself, but I guess that's close enough...When I entered the garden I saw Swift slumped down in his chair. His position struck me as funny, but I paid no attention to it until I spoke to him and got no answer. Then I approached and saw the revolver lying on the tiles, and the hole in his head. It gave me a hell of a shock, I can tell you, and I started to run downstairs to give the alarm. But I realized it would look bad for me. There I was, alone on the roof with a dead man..."

    "Ah, yes. Discretion. So you played safe. Can't say that I blame you entirely—if your chronology is accurate. So, I take it, you re-entered the public stairway and came down to the front door of the Garden apartment."

    "That's just what I did." Kroon's tone was as vigorous as it was resentful.

    "By the by, during the brief time you were on the roof, or even after you returned to the stairway, did you hear a shot?"

    Kroon looked at Vance in obvious surprise.

    "A shot? I've told you the fellow was already dead when I first saw him."

    "Nevertheless," said Vance, "there was a shot. Not the one that killed him, but the one that summoned us to the roof. There were two shots, don't y' know—although no one seems to have heard the first."

    Kroon thought a moment.

    "By George! I did hear something, now that you put it that way. I thought nothing of it at the time, since Woody was already dead. But just as I re-entered the stairway there was an explosion of some kind outside. I thought it was a car back-firing down in the street, and paid no attention to it."

    Vance nodded with a puzzled frown.

    "That's very interestin'..." His eyes drifted off into space. "I wonder..." After a moment he returned his gaze to Kroon. "But to continue your tale. You say you left the roof immediately and came downstairs. But there were at least ten minutes from the time you left the garden to the time I encountered you entering the apartment at the front door. How and where did you spend these ten intervening minutes?"

    "I stayed on the landing of the stairs and smoked a couple of cigarettes. I was trying to pull myself together. After what I had been through, and then finding Woody shot, I was in a hell of a mental state."

    Heath stood up quickly, one hand in his outside coat pocket, and thrust out his jaw belligerently toward the agitated Kroon.

    "What kind of cigarettes do you smoke?" he barked.

    The man looked at the Sergeant in bewilderment, and then said: "I smoke gold-tipped Turkish cigarettes. What about it?"

    Heath drew his hand from his pocket and looked at something which he held on his palm.

    "All right," he muttered. Then he addressed Vance. "I got the stubs here. Picked 'em up on the landing when I came up from the dame's apartment. Thought maybe they might have some connection."

    "Well, well," sneered Kroon. "So the police actually found something!...What more do you want?" he demanded of Vance.

    "Nothing for the moment, thank you," Vance, returned with exaggerated courtesy. "You have done very well by yourself this afternoon, Mr. Kroon. We won't need you any more...Sergeant, give instructions to Hennessey that Mr. Kroon may leave the apartment."

    Kroon went to the door without a word.

    "Oh, I say." Vance delayed him at the threshold. "Do you, by any chance, possess a maiden aunt?"

    Kroon looked back over his shoulder with a vicious grin.

    "No, thank God!" And he slammed the door noisily behind him.