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gambler whose paramount self-confidence would make him scorn, through sheer egotism, to bet on a sure-thing, could have committed such a crime.—Therefore, Cleaver was eliminated as a suspect.”

      Markham was now listening intently.

      “The test to which I put Spotswoode a little later,” Vance went on, “had originally been intended for Mannix, but he was out of the game. That didn’t matter, however, for, had I been able to eliminate both Cleaver and Spotswoode, then Mannix would undoubtedly have been the guilty man. Of course I would have planned something else to substantiate the fact; but, as it was, that wasn’t necess’ry. . . . The test I applied to Spotswoode was pretty well explained by the gentleman himself. As he said, not one player in a thousand would have wagered the limit against a pat hand, when he himself held nothing. It was tremendous—superb! It was probably the most remarkable bluff ever made in a game of poker. I couldn’t help admiring him when he calmly shoved forward all his chips, knowing, as I did, that he held nothing. He staked everything, d’ ye see, wholly on his conviction that he could follow my reasoning step by step and, in the last analysis, outwit me. It took courage and daring to do that. And it also took a degree of self-confidence which would never have permitted him to bet on a sure-thing. The psychological principles involved in that hand were identical with those of the Odell crime. I threatened Spotswoode with a powerful hand—a pat hand—just as the girl, no doubt, threatened him; and instead of compromising—instead of calling me or laying down—he outreached me; he resorted to one supreme coup, though it meant risking everything. . . . My word, Markham! Can’t you see how the man’s character, as revealed in that amazing gesture, dovetails with the psychology of the crime?”

      Markham was silent for a while; he appeared to be pondering the matter.

      “But you yourself, Vance, were not satisfied at the time,” he submitted at length. “In fact, you looked doubtful and worried.”

      “True, old dear. I was no end worried. The psychological proof of Spotswoode’s guilt came so dashed unexpectedly—I wasn’t looking for it, don’t y’ know. After eliminating Cleaver I had a parti pris, so to speak, in regard to Mannix; for all the material evidence in favor of Spotswoode’s innocence—that is, the seeming physical impossibility of his having strangled the lady—had, I admit, impressed me. I’m not perfect, don’t y’ know. Being unfortunately human, I’m still susceptible to the malicious animal magnetism about facts and appearances, which you lawyer chaps are continuously exuding over the earth like some vast asphyxiating effluvium. And even when I found that Spotswoode’s psychological nature fitted perfectly with all the factors of the crime, I still harbored a doubt in regard to Mannix. It was barely possible that he would have played the hand just as Spotswoode played it. That is why, after the game was over, I tackled him on the subject of gambling. I wanted to check his psychological reactions.”

      “Still, he staked everything on one turn of the wheel, as you put it.”

      “Ah! But not in the same sense that Spotswoode did. Mannix is a cautious and timid gambler as compared with Spotswoode. To begin with, he had an equal chance and an even bet, whereas Spotswoode had no chance at all—his hand was worthless. And yet Spotswoode wagered the limit on a pure bit of mental calculation. That was gambling in the higher ether. On the other hand, Mannix was merely tossing a coin, with an even chance of winning. Furthermore, no calculation of any kind entered into it; there was no planning, no figuring, no daring. And, as I have told you from the start, the Odell murder was premeditated and carefully worked out with shrewd calculation and supreme daring. . . . And what true gambler would ask an adversary to double a bet on the second flip of the coin, and then accept an offer to redouble on the third flip? I purposely tested Mannix in that way, so as to preclude any possibility of error. Thus I not only eliminated him—I expunged him, eradicated him, wiped him out utterly. It cost me a thousand dollars, but it purged my mind of any lingering doubt. I then knew, despite all the contr’ry material indications, that Spotswoode had done away with the lady.”

      “You make your case theoretically plausible. But, practically, I’m afraid I can’t accept it.” Markham was more impressed, I felt, than he cared to admit. “Damn it, man!” he exploded after a moment. “Your conclusion demolishes all the established landmarks of rationality and sane credibility.—Just consider the facts.” He had now reached the argumentative stage of his doubt. “You say Spotswoode is guilty. Yet we know, on irrefutable evidence, that five minutes after he came out of the apartment the girl screamed and called for help. He was standing by the switchboard, and, accompanied by Jessup, he went to the door and carried on a brief conversation with her. She was certainly alive then. Then he went out the front door, entered a taxicab, and drove away. Fifteen minutes later he was joined by Judge Redfern as he alighted from the taxicab in front of the club here—nearly forty blocks away from the apartment-house! It would have been impossible for him to have made the trip in less time; and, moreover, we have the chauffeur’s record. Spotswoode simply did not have either the opportunity or the time to commit the murder between half past eleven and ten minutes of twelve when Judge Redfern met him. And, remember, he played poker in the club here until three in the morning—hours after the murder took place.”

      Markham shook his head with emphasis.

      “Vance, there’s no human way to get round those facts. They’re firmly established; and they preclude Spotswoode’s guilt as effectively and finally as though he had been at the North Pole that night.”

      Vance was unmoved.

      “I admit everything you say,” he rejoined. “But as I have stated before, when material facts and psychological facts conflict, the material facts are wrong. In this case, they may not actually be wrong, but they’re deceptive.”

      “Very well, magnus Apollo!” The situation was too much for Markham’s exacerbated nerves. “Show me how Spotswoode could have strangled the girl and ransacked the apartment, and I’ll order Heath to arrest him.”

      “’Pon my word, I can’t do it,” expostulated Vance. “Omniscience was denied me. But—deuce take it!—I think I’ve done rather well in pointing out the culprit. I never agreed to expound his technic, don’t y’ know.”

      “So! Your vaunted penetration amounts only to that, does it? Well, well! Here and now I become a professor of the higher mental sciences, and I pronounce solemnly that Doctor Crippen murdered the Odell girl. To be sure, Crippen’s dead; but that fact doesn’t interfere with my newly adopted psychological means of deduction. Crippen’s nature, you see, fits perfectly with all the esoteric and recondite indications of the crime. To-morrow I’ll apply for an order of exhumation.”

      Vance looked at him with waggish reproachfulness, and sighed.

      “Recognition of my transcendent genius, I see, is destined to be posthumous. Omnia post obitum fingit majora vetustas. In the meantime I bear the taunts and jeers of the multitude with a stout heart. My head is bloody, but unbowed.”

      He looked at his watch, and then seemed to become absorbed with some line of thought.

      “Markham,” he said, after several minutes, “I’ve a concert at three o’clock, but there’s an hour to spare. I want to take another look at that apartment and its various approaches. Spotswoode’s trick—and I’m convinced it was nothing more than a trick—was enacted there; and if we are ever to find the explanation, we shall have to look for it on the scene.”

      I had got the impression that Markham, despite his emphatic denial of the possibility of Spotswoode’s guilt, was not entirely unconvinced. Therefore, I was not surprised when, with only a half-hearted protest, he assented to Vance’s proposal to revisit the Odell apartment.

      CHAPTER XXIX

       BEETHOVEN’S “ANDANTE”

       Table of Contents

      (Tuesday, September 18; 2 p. m.)

      Less than half an hour later we again entered the main hall of the little

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