The Philo Vance Megapack

by S. S. Van Dine

  “Gone!” he announced. “Looked in every likely place—couldn’t find it.” He threw himself into a chair and relighted his pipe. “Can’t understand it.… Perhaps he hid it.”

  “Perhaps,” murmured Vance.

  CHAPTER XX

  THE NEMESIS

  (Saturday, April 16; 1 P.M.)

  It was past one o’clock, and Markham, Vance and I rode to the Stuyvesant Club. Heath remained at the Drukker house to carry on the routine work, to draw up his report, and to deal with the reporters who would be swarming there shortly.

  Markham was booked for a conference with the Police Commissioner at three o’clock; and after lunch Vance and I walked to Stieglitz’s Intimate Gallery and spent an hour at an exhibition of Georgia O’Keeffe’s floral abstractions. Later we dropped in at Aeolian Hall and sat through Debussy’s G-minor quartette. There were some Cézanne water-colors at the Montross Galleries; but by the time we had pushed our way through the late-afternoon traffic of Fifth Avenue the light had begun to fail, and Vance ordered the chauffeur to the Stuyvesant Club, where we joined Markham for tea.

  “I feel so youthful, so simple, so innocent,” Vance complained lugubriously. “So many things are happenin’, and they’re bein’ manipulated so ingeniously that I can’t grasp ’em. It’s very disconcertin’, very confusin’. I don’t like it—I don’t at all like it. Most wearin’.” He sighed drearily and sipped his tea.

  “Your sorrows leave me cold,” retorted Markham.

  “You’ve probably spent the afternoon inspecting arquebuses and petronels at the Metropolitan Museum. If you’d had to go through what I’ve suffered—”

  “Now, don’t be cross,” Vance rebuked him. “There’s far too much emotion in the world. Passion is not going to solve this case. Cerebration is our only hope. Let us be calm and thoughtful.” His mood became serious. “Markham, this comes very near being the perfect crime. Like one of Morphy’s great chess combinations, it has been calculated a score of moves ahead. There are no clews; and even if there were, they’d probably point in the wrong direction. And yet…and yet there’s something that’s trying to break through. I feel it: sheer intuition—that is to say, nerves. There’s an inarticulate voice that wants to speak, and can’t. A dozen times I’ve sensed the presence of some struggling force, like an invisible ghost trying to make contact without revealing its identity.”

  Markham gave an exasperated sigh.

  “Very helpful. Do you advise calling in a medium?”

  “There’s something we’ve overlooked,” Vance went on, disregarding the sarcasm. “The case is a cipher, and the key-word is somewhere before us, but we don’t recognize it. ’Pon my soul, it’s dashed annoyin’.… Let’s be orderly. Neatness—that’s our desideratum. First, Robin is killed. Next, Sprigg is shot. Then Mrs. Drukker is frightened with a black bishop. After that, Drukker is shoved over a wall. Makin’ four distinct episodes in the murderer’s extravaganza. Three of ’em were carefully planned. One—the leaving of the bishop at Mrs. Drukker’s door—was forced on the murderer, and was therefore decided on without preparation.…”

  “Clarify your reasoning on that point.”

  “Oh, my dear fellow! The conveyor of the black bishop was obviously acting in self-defence. An unexpected danger developed along his line of campaign, and he took this means of averting it. Just before Robin’s death Drukker departed from the archery-room and installed himself in the arbor of the yard, where he could look into the archery-room through the rear window. A little later he saw some one in the room talking to Robin. He returned to his house, and at that moment Robin’s body was thrown on the range. Mrs. Drukker saw it, and at the same time she probably saw Drukker. She screamed—very natural, what? Drukker heard the scream, and told us of it later in an effort to establish an alibi for himself after we’d informed him that Robin had been killed. Thus the murderer learned that Mrs. Drukker had seen something—how much, he didn’t know. But he wasn’t taking any chances. He went to her room at midnight to silence her, and took the bishop to leave beside her body as a signature. But he found the door locked, and left the bishop outside, by way of warning her to say nothing on pain of death. He didn’t know that the poor woman suspected her own son.”

  “But why didn’t Drukker tell us whom he saw in the archery-room with Robin?”

  “We can only assume that the person was some one whom he couldn’t conceive of as being guilty. And I’m inclined to believe he mentioned the fact to this person and thus sealed his own doom.”

  “Assuming the correctness of your theory, where does it lead us?”

  “To the one episode that wasn’t elaborately prepared in advance. And when there has been no preparation for a covert act there is pretty sure to be a weakness in one or more of the details.—Now, please note that at the time of each of the three murders any one of the various persons in the drama could have been present. No one had an alibi. That, of course, was cleverly calculated: the murderer chose an hour when all of the actors were, so to speak, waiting in the wings. But that midnight visit! Ah! That was a different matter. There was no time to work out a perfect set of circumstances,—the menace was too immediate. And what was the result? Drukker and Professor Dillard were, apparently, the only persons on hand at midnight. Arnesson and Belle Dillard were supping at the Plaza and didn’t return home until half past twelve. Pardee was hornlocked with Rubinstein over a chess-board from eleven to one. Drukker is now of course eliminated.… What’s the answer?”

  “I could remind you,” returned Markham irritably, “that the alibis of the others have not been thoroughly checked.”

  “Well, well, so you could.” Vance lay back indolently and sent a long regular series of smoke-rings toward the ceiling. Suddenly his body tensed, and with meticulous care he leaned over and put out his cigarette. Then he glanced at his watch and got to his feet. He fixed Markham with a quizzical look.

  “Allons, mon vieux. It’s not yet six. Here’s where Arnesson makes himself useful.”

  “What now?” expostulated Markham.

  “Your own suggestion,” Vance replied, taking him by the arm and leading him toward the door. “We’re going to check Pardee’s alibi.”

  Half an hour later we were seated with the professor and Arnesson in the Dillard Library.

  “We’ve come on a somewhat unusual errand,” explained Vance; “but it may have a vital bearing on our investigation.” He took out his wallet, and unfolded a sheet of paper. “Here’s a document, Mr. Arnesson, I wish you’d glance over. It’s a copy of the official scoresheet of the chess game between Pardee and Rubinstein. Very interestin’. I’ve toyed with it a bit, but I’d like your expert analysis of it. The first part of the game is usual enough, but the play after the adjournment rather appeals to me.”

  Arnesson took the paper and studied it with cynical amusement.

  “Aha! The inglorious record of Pardee’s Waterloo, eh?”

  “What’s the meaning of this, Markham?” asked professor Dillard contemptuously. “Do you hope to run a murderer to earth by dilly-dallying over a chess game?”

  “Mr. Vance hoped something could be learned from it.”

  “Fiddlesticks!” The professor poured himself another glass of port and, opening a book, ignored us completely.

  Arnesson was absorbed in the notations of the chess score.

  “Something a bit queer here,” he muttered. “The time’s askew. Let’s see.… The scoresheet shows that, up to the time of adjournment, White—that is, Pardee—had played one hour and forty-five minutes, and Black, or Rubinstein, one hour and fifty-eight minutes. So far, so good. Thirty moves. Quite in order. But the time at the end of the game, when Pardee resigned, totals two hours and thirty minutes for White, and three hours and thirty-two minutes for Black—which means that, during the second session of the game, White consumed only forty-five minutes whereas Black used up one hour and thirty-four minutes.”

  Vance nodded.

  “Exactly. Th
ere were two hours and nineteen minutes of play beginning at 11 p. m., which carried the game to 1.19 a. m. And Rubinstein’ s moves during that time took forty-nine minutes longer than Pardee’s.—Can you make out what happened?”

  Arnesson pursed his lips and squinted at the notations.

  “It’s not clear. I’d need time.”

  “Suppose,” Vance suggested, “we set up the game in the adjourned position and play it through. I’d like your opinion on the tactics.”

  Arnesson rose jerkily and went to the little chess table in the corner.

  “Good idea.” He emptied the men from the box. “Let’s see now.… Oho! A black bishop is missing. When do I get it back, by the way?” He gave Vance a plaintive leer. “Never mind. We don’t need it here. One black bishop was swapped.” And he proceeded to arrange the men to accord with the position of the game at the time of adjournment. Then he sat down and studied the set-up.

  “It doesn’t strike me as a particularly unfavorable position for Pardee,” ventured Vance.

  “Me either. Can’t see why he lost the game. Looks drawish to me.” After a moment Arnesson referred to the scoresheet. “We’ll run through the play and find out where the trouble lay.” He made half a dozen moves; then, after several minutes’ study, gave a grunt. “Ha! This is rather deep stuff of Rubinstein’s. Amazing combination he began working up here. Subtle, by Gad! As I know Rubinstein, it took him a long time to figure it out. Slow, plodding chap.”

  “It’s possible, isn’t it,” suggested Vance, “that the working out of that combination explains the discrepancy in time between Black and White?”

  “Oh, undoubtedly. Rubinstein must have been in good form not to have made the discrepancy greater. Planning the combination took him all of forty-five minutes—or I’m a duffer.”

  “At what hour, would you say,” asked Vance carelessly, “did Rubinstein use up that forty-five minutes?”

  “Well, let’s see. The play began at eleven: six moves before the combination started.… Oh, say, somewhere between half past eleven and half past twelve.… Yes, just about. Thirty moves before the adjournment: six moves beginning at eleven—that makes thirty-six: then on the forty-fourth move Rubinstein moved his pawn to Bishop-7-check, and Pardee resigned.… Yes—the working out of the combination was between eleven-thirty and twelve-thirty.”

  Vance regarded the men on the board, which were now in the position they had occupied at the time of Pardee’s resignation.101

  “Out of curiosity,” he said quietly, “I played the game through to the checkmate the other night.—I say, Mr. Arnesson; would you mind doin’ the same. I could bear to hear your comment on it.”

  Arnesson studied the position closely for a few minutes. Then he turned his head slowly and lifted his eyes to Vance. A sardonic grin overspread his face.

  “I grasp the point. Gad! What a situation! Five moves for Black to win through. And an almost unheard-of finale in chess. Can’t recall a similar instance. The last move would be Bishop to Knight-7, mating. In other words, Pardee was beaten by the black bishop! Incredible!”102

  Professor Dillard put down his book.

  “What’s this?” he exclaimed, joining us at the chess table. “Pardee was defeated by the bishop?” He gave Vance a shrewd, admiring look. “You evidently had good reason, sir, for investigating that chess game. Pray overlook an old man’s temper.” He stood gazing down at the board with a sad, puzzled expression.

  Markham was frowning with deep perplexity.

  “You say it’s unusual for a bishop alone to mate?” he asked Arnesson.

  “Never happens—almost unique situation. And that it should happen to Pardee of all people! Incomprehensible!” He gave a short ironic laugh. “Inclines one to believe in a nemesis. You know, the bishop has been Pardee’s bête noir for twenty years—it’s ruined his life. Poor beggar! The black bishop is the symbol of his sorrow. Fate, by Gad! It’s the one chessman that defeated the Pardee gambit. Bishop-to-Knight-5 always broke up his calculations—disqualified his pet theory—made a hissing and a mocking of his life’s work. And now, with a chance to break even with the great Rubinstein, the bishop crops up again and drives him back into obscurity.”

  A few minutes later we took our departure and walked to West End Avenue, where we hailed a taxicab.

  “It’s no wonder, Vance,” commented Markham, as we rode downtown, “that Pardee went white the other afternoon when you mentioned the black bishop’s being at large at midnight. He probably thought you were deliberately insulting him—throwing his life’s failure in his face.”

  “Perhaps.…” Vance gazed dreamily out into the gathering shadows. “Dashed queer about the bishop being his incubus all these years. Such recurring discouragements affect the strongest minds sometimes; create a desire for revenge on the world, with the cause of one’s failure exalted to an Astraean symbol.”

  “It’s difficult to picture Pardee in a vindictive rôle,” objected Markham. Then, after a moment: “What was your point about the discrepancy in time between Pardee’s and Rubinstein’s playing? Suppose Rubinstein did take forty-five minutes or so to work out his combination. The game wasn’t over until after one. I don’t see that your visit to Arnesson put us ahead in any way.”

  “That’s because you’re unacquainted with the habits of chess players. In a clock game of that kind no player sits at the table all the time his opponent is figuring out moves. He walks about, stretches his muscles, takes the air, ogles the ladies, imbibes ice-water, and even indulges in food. At the Manhattan Square Masters Tournament last year there were four tables, and it was a common sight to see as many as three empty chairs at one time. Pardee’s a nervous type. He wouldn’t sit through Rubinstein’s protracted mental speculations.”

  Vance lighted a cigarette slowly.

  “Markham, Arnesson’s analysis of that game reveals the fact that Pardee had three-quarters of an hour to himself around midnight.”

  CHAPTER XXI

  MATHEMATICS AND MURDER

  (Saturday, April 16; 8.30 p. m.)

  Little was said about the case during dinner, but when we had settled ourselves in a secluded corner of the club lounge-room Markham again broached the subject.

  “I can’t see,” he said, “that finding a loophole in Pardee’s alibi helps us very much. It merely complicates an already intolerable situation.”

  “Yes,” sighed Vance. “A sad and depressin’ world. Each step appears to tangle us a little more. And the amazin’ part of it is, the truth is staring us in the face; only, we can’t see it.”

  “There’s no evidence pointing to any one. There’s not even a suspect against whose possible culpability reason doesn’t revolt.”

  “I wouldn’t say that, don’t y’ know. It’s a mathematician’s crime; and the landscape has been fairly cluttered with mathematicians.”

  Throughout the entire investigation no one had been indicated by name as the possible murderer. Yet each of us realized in his own heart that one of the persons with whom we had talked was guilty; and so hideous was this knowledge that we instinctively shrank from admitting it. From the first we had cloaked our true thoughts and fears with generalities.

  “A mathematician’s crime?” repeated Markham. “The case strikes me as a series of senseless acts committed by a maniac running amuck.”

  Vance shook his head.

  “Our criminal is supersane, Markham. And his acts are not senseless: they’re hideously logical and precise. True, they have been conceived with a grim and terrible humor, with a tremendously cynical attitude; but within themselves they are exact and rational.”

  Markham regarded Vance thoughtfully.

  “How can you reconcile these Mother-Goose crimes with the mathematical mind?” he asked. “In what way can they be regarded as logical? To me they’re nightmares, unrelated to sanity.”

  Vance settled himself deeper in his chair, and smoked for several minutes. Then he began an analysis of the case, which not on
ly clarified the seeming madness of the crimes themselves, but brought all the events and the characters into a uniform focus. The accuracy of this analysis was brought home to us with tragic and overwhelming force before many days had passed.103

  “In order to understand these crimes,” he began, “we must consider the stock-in-trade of the mathematician, for all his speculations and computations tend to emphasize the relative insignificance of this planet and the unimportance of human life.—Regard, first, the mere scope of the mathematician’s field. On the one hand he attempts to measure infinite space in terms of parsecs and light-years, and, on the other, to measure the electron which is so infinitely small that he has to invent the Rutherford unit—a millionth of a millimicron. His vision is one of transcendental perspectives, in which this earth and its people sink almost to the vanishing point. Some of the stars—such as Arcturus, Canopus and Betelgeuse—which he regards merely as minute and insignificant units, are many times more massive than our entire solar system. Shapleigh’s estimate of the diameter of the Milky Way is 300,000 light-years; yet we must place 10,000 Milky Ways together to get the diameter of the universe—which gives us a cubical content a thousand milliard times greater than the scope of astronomical observation. Or, to put it relatively in terms of mass:—the sun’s weight is 324,000 times greater than the weight of the earth; and the weight of the universe is postulated as that of a trillion104—a milliard times a milliard—suns.… Is it any wonder that workers in such stupendous magnitudes should sometimes lose all sense of earthly proportions?”

  Vance made an insignificant gesture.

  “But these are element’ry figures—the every-day facts of journeyman calculators. The higher mathematician goes vastly further. He deals in abstruse and apparently contradict’ry speculations which the average mind can not even grasp. He lives in a realm where time, as we know it, is without meaning save as a fiction of the brain, and becomes a fourth co-ordinate of three-dimnensional space; where distance also is meaningless except for neighboring points, since there are an infinite number of shortest routes between any two given points; where the language of cause and effect becomes merely a convenient shorthand for explanat’ry purposes; where straight lines are non-existent and insusceptible of definition; where mass grows infinitely great when it reaches the velocity of light; where space itself is characterized by curvatures; where there are lower and higher orders of infinities; where the law of gravitation is abolished as an acting force and replaced by a characteristic of space—a conception that says, in effect, that the apple does not fall because it is attracted by the earth, but because it follows a geodesic, or world-line.…