isn’t simple. Lord, no!—I say, how would the equation work out if we used algebra, or spherical trigonometry, or differential calculus? Let’s cast it in the fourth dimension—or the fifth, or the sixth.…” He held his temples in both hands. “Oh, promise, Markham—promise me that you’ll hire a kind, gentle keeper for me.”
“I know how you feel. I’ve been in the same mental state for a week.”
“It’s the quartet idea that’s driving me mad,” moaned Vance. “It wrings me to have my tetrad lopped off in such brutal fashion. I’d set my young trustin’ heart on that quartet, and now it’s only a pair. My sense of order and proportion has been outraged.… I want my quartet.”
“I’m afraid you’ll have to be satisfied with two of them,” Markham returned wearily. “One of them can’t qualify, and one is in bed. You might send some flowers to the hospital if it would cheer you any.”
“One is in bed—one is in bed,” repeated Vance. “Well, well—to be sure! And one from four leaves three. More arithmetic. Three!… On the other hand, there is no such thing as a straight line. All lines are curved; they transcribe circles in space. They look straight, but they’re not. Appearances, y know—so deceptive!… Let’s enter the silence, and substitute mentation for sight.”
He gazed up out of the great windows into Fifth Avenue. For several moments he sat smoking thoughtfully. When he spoke again, it was in an even, deliberate voice.
“Markham, would it be difficult for you to invite Mannix and Cleaver and Spotswoode to spend an evening—this evening, let us say—in your apartment?”
Markham set down his cup with a clatter and regarded Vance narrowly. “What new harlequinade is this?”
“Fie on you! Answer my question.”
“Well, of course, I might arrange it,” replied Markham hesitantly. “They’re all more or less under my jurisdiction at present.”
“So that such an invitation would be rather in line with the situation—eh, what? And they wouldn’t be likely to refuse you, old dear—would they?”
“No, I hardly think so.…”
“And if, when they had assembled in your quarters, you should propose a few hands of poker, they’d probably accept, without thinking the suggestion strange?”
“Probably,” said Markham, nonplussed at Vance’s amazing request. “Cleaver and Spotswoode both play, I know; and Mannix doubtless knows the game. But why poker? Are you serious, or has your threatened dementia already overtaken you?”
“Oh, I’m deuced serious.” Vance’s tone left no doubt as to the fact. “The game of poker, d’ ye see, is the crux of the matter. I knew Cleaver was an old hand at the game; and Spotswoode, of course, played with Judge Redfern last Monday night. So that gave me a basis for my plan. Mannix, we’ll assume, also plays.”
He leaned forward, speaking earnestly.
“Nine-tenths of poker, Markham, is psychology; and if one understands the game, one can learn more of a man’s inner nature at a poker table in an hour than during a year’s casual association with him. You rallied me once when I said I could lead you to the perpetrator of any crime by examining the factors of the crime itself. But naturally I must know the man to whom I am to lead you; otherwise I cannot relate the psychological indications of the crime to the culprit’s nature. In the present case, I know the kind of man who committed the crime; but I am not sufficiently acquainted with the suspects to point out the guilty one. However, after our game of poker I hope to be able to tell you who planned and carried out the Canary’s murder.”37
Markham gazed at him in blank astonishment. He knew that Vance played poker with amazing skill and that he possessed an uncanny knowledge of the psychological elements in the game; but he was unprepared for the latter’s statement that he might be able to solve the Odell murder by means of it. Yet Vance had spoken with such undoubted earnestness that Markham was impressed. I knew what was passing in his mind almost as well as if he had voiced his thoughts. He was recalling the way in which Vance had, in a former murder case, put his finger unerringly on the guilty man by a similar process of psychological deduction. And he was also telling himself that, however incomprehensible and seemingly extravagant Vance’s requests were, there was always a fundamentally sound reason behind them.
“Damn it!” he muttered at last. “The whole scheme seems idiotic.… And yet, if you really want a game of poker with these men, I’ve no special objection. It’ll get you nowhere—I’ll tell you that beforehand. It’s stark nonsense to suppose that you can find the guilty man by such fantastic means.”
“Ah, well,” sighed Vance, “a little futile recreation will do us no harm.”
“But why do you include Spotswoode?”
“Really, y’ know, I haven’t the slightest notion—except, of course, that he’s one of my quartet. And we’ll need an extra hand.”
“Well, don’t tell me afterwards that I’m to lock him up for murder. I’d have to draw the line. Strange as it may seem to your layman’s mind, I wouldn’t care to prosecute a man, knowing that it was physically impossible for him to have committed the crime.”
“As to that,” drawled Vance, “the only obstacles that stand in the way of physical impossibilities are material facts. And material facts are notoriously deceivin’. Really, y’ know, you lawyers would do better if you ignored them entirely.”
Markham did not deign to answer such heresy, but the look he gave Vance was most expressive.
CHAPTER 27
A GAME OF POKER
(Monday, September 17; 9 P.M.)
Vance and I went home after lunch, and at about four o’clock Markham telephoned to say that he had made the necessary arrangements for the evening with Spotswoode, Mannix, and Cleaver. Immediately following this confirmation Vance left the house and did not return until nearly eight o’clock. Though I was filled with curiosity at so unusual a proceeding, he refused to enlighten me. But when, at a quarter to nine, we went downstairs to the waiting car, there was a man I did not know in the tonneau; and I at once connected him with Vance’s mysterious absence.
“I’ve asked Mr. Allen to join us tonight,” Vance vouchsafed, when he had introduced us. “You don’t play poker, and we really need another hand to make the game interestin’, y’ know. Mr. Allen, by the bye, is an old antagonist of mine.”
The fact that Vance would, apparently without permission, bring an uninvited guest to Markham’s apartment amazed me but little more than the appearance of the man himself. He was rather short, with sharp, shrewd features; and what I saw of his hair beneath his jauntily tipped hat was black and sleek, like the painted hair on Japanese dolls. I noted, too, that his evening tie was enlivened by a design of tiny white forget-me-nots, and that his shirtfront was adorned with diamond studs.
The contrast between him and the immaculately stylish and meticulously correct Vance was aggressively evident. I wondered what could be the relationship between them. Obviously it was neither social nor intellectual.
Cleaver and Mannix were already on hand when we were ushered into Markham’s drawing room, and a few minutes later Spotswoode
