"That's certainly a vital factor in the problem," he commented at length. "It changes our constant. I can see that this thing has got to be calculated from a new angle. The Bishop, it appears, is in our midst. But why should he come to haunt Lady Mae?"
"She is reported to have screamed at almost the exact moment of Robin's death."
"Aha!" Arnesson sat up. "I grasp your implication. She saw the Bishop from her window on the morning of Cock Robin's dissolution, and later he returned and perched on her door-knob as a warning for her to keep mum."
"Something like that, perhaps. . . . Have you enough integers now to work out your formula?"
"I'd like to cast an eye on this black bishop. Where is it?"
Vance reached in his pocket, and held out the chessman. Arnesson took it eagerly. His eyes glittered for a moment. He turned the piece over in his hand, and then gave it back.
"You seem to recognize this particular bishop," said Vance dulcetly. "You're quite correct. It was borrowed from your chess set in the library."
Arnesson nodded a slow affirmative.
"I believe it was." Suddenly he turned to Markham, and an ironic leer came over his lean features. "Was that why I was to be kept in the dark? Under suspicion, am I? Shades of Pythagoras! What penalty attaches to the heinous crime of distributing chessmen among one's neighbors?"
Markham got up and walked toward the hall.
"You are not under suspicion, Arnesson," he answered, with no attempt to conceal his ill-humor. "The bishop was left at Mrs. Drukker's at exactly midnight."
"And I was half an hour too late to qualify. Sorry to have disappointed you."
"Let us hear if your formula works out," said Vance, as we passed out of the front door. "We've a little visit to pay to Mr. Pardee now."
"Pardee? Oho! Calling in a chess expert on the subject of bishops, eh? I see your reasoning—it at least has the virtue of being simple and direct. . . ."
He stood on the little porch and watched us, like a japish gargoyle, as we crossed the street.
Pardee received us with his customary quiet courtesy. The tragic, frustrated look which was a part of his habitual expression was even more pronounced than usual; and when he drew up chairs for us in his study his manner was that of a man whose interest in life had died, and who was merely going through the mechanical motions of living.
"We have come here, Mr. Pardee," Vance began, "to learn what we can of Sprigg's murder in Riverside Park yesterday morning. We have excellent reasons for every question we are about to ask you."
Pardee nodded resignedly.
"I shall not be offended at any line of interrogation you take. After reading the papers I realize just how unusual a problem you are facing."
"First, then, please inform us where you were yesterday morning between seven and eight."
A faint flush overspread Pardee's face, but he answered in a low, even voice.
"I was in bed. I did not rise until nearly nine."
"Is it not your habit to take a walk in the park before breakfast?" (I knew this was sheer guesswork on Vance's part, for the subject of Pardee's habits had not come up during the investigation.)
"That is quite true," the man replied, without a moment's hesitation. "But yesterday I did not go,—I had worked rather late the night before."
"When did you first hear of Sprigg's death?"
"At breakfast. My cook repeated the gossip of the neighborhood. I read the official account of the tragedy in the early edition of the evening Sun."
"And you saw the reproduction of the Bishop note, of course, in this morning's paper.—What is your opinion of the affair, Mr. Pardee?"
"I hardly know." For the first time his lacklustre eyes showed signs of animation. "It's an incredible situation. The mathematical chances are utterly opposed to such a series of interrelated events being coincidental."
"Yes," Vance concurred. "And speaking of mathematics: are you at all familiar with the Riemann-Christoffel tensor?"
"I know of it," the man admitted. "Drukker uses it in his book on world lines. My mathematics, however, are not of the physicist's type. Had I not become enamored of chess"—he smiled sadly—"I would have been an astronomer. Next to manoeuvring the factors in a complicated chess combination, the greatest mental satisfaction one can get, I think, is plotting the heavens and discovering new planets. I even keep a five-inch equatorial telescope in a pent-house on my roof for amateur observations."
Vance listened to Pardee with close attention; and for several minutes discussed with him Professor Pickering's recent determination of the trans-Neptunean O,[21] much to Markham's bewilderment and to the Sergeant's annoyance. At length he brought the conversation back to the tensor formula.
"You were, I understand, at the Dillards' last Thursday when Mr. Arnesson was discussing this tensor with Drukker and Sprigg."
"Yes, I recall that the subject came up then."
"How well did you know Sprigg?"
"Only casually. I had met him with Arnesson once or twice."
"Sprigg, also, it seems, was in the habit of walking in Riverside Park before breakfast," observed Vance negligently. "Ever run into him there, Mr. Pardee?"
The man's eyelids quivered slightly, and he hesitated before answering.
"Never," he said finally.
Vance appeared indifferent to the denial. He rose and, going to the front window, looked out.
"I thought one might be able to see into the archery range from here. But I note that the angle cuts off the view entirely."
"Yes, the range is quite private. There's even a vacant lot opposite the wall, so that no one can see over it. . . . Were you thinking of a possible witness to Robin's death?"
"That, and other things." Vance returned to his chair. "You don't go in for archery, I take it."
"It's a trifle too strenuous for me. Miss Dillard once tried to interest me in the sport, but I was not a very promising acolyte. I've been to several tournaments with her, however."
An unusually soft note had crept into Pardee's voice, and for some reason which I could not exactly explain I got the feeling that he was fond of Belle Dillard. Vance, too, must have received the same impression, for after a brief pause he said:
"You will realize, I trust, that it is not our intention to pry unnecessarily into any one's private affairs; but the question of motive in the two murders we are investigating still remains obscure, and as Robin's death was at first superficially attributed to a rivalry for Miss Dillard's affections, it might help us to know, in a general way, what the true situation is concerning the young lady's preference. . . . As a friend of the family you probably know; and we'd appreciate your confidence in the matter."
Pardee's gaze travelled out of the window, and the suggestion of a sigh escaped him.
"I've always had the feeling that she and Arnesson would some day be married. But that is only conjecture. She once told me quite positively that she was not going to consider matrimony until she was thirty." (One could easily guess in what connection Belle Dillard had made this pronouncement to Pardee. His emotional, as well as his intellectual life, had apparently met with failure.)
"You do not believe then," pursued Vance, "that her heart is seriously concerned with young Sperling?"
Pardee shook his head. "However," he qualified, "martyrdom such as he is undergoing at present has a tremendous sentimental appeal for women."
"Miss Dillard tells me you called on her this morning."
"I generally drop over during the day." He was obviously uncomfortable and, I thought, a little embarrassed.
"Do you know Mrs. Drukker well?"
Pardee gave Vance a quick, inquisitive look.
"Not particularly," he said. "I've naturally met her several times."
"You've called at her house?"
"On many occasions, but always to see Drukker. I've been interested for years in the relation of mathematics to chess. . . ."
Vance nodded.
"How d
id your game with Rubinstein come out last night, by the by? I didn't see the papers this morning."
"I resigned on the forty-fourth move." The man spoke hopelessly. "Rubinstein found a weakness in my attack which I had entirely overlooked when I sealed my move at the adjournment."
"Drukker, Professor Dillard tells us, foresaw the outcome when you and he were discussing the situation last night."
I could not understand why Vance referred so pointedly to this episode, knowing as he did how sore a point it was with Pardee. Markham, also, frowned at what appeared to be an unforgivably tactless remark on Vance's part.
Pardee colored, and shifted in his chair.
"Drukker talked too much last night." The statement was not without venom. "Though he's not a tournament player, he should know that such discussions are taboo during unfinished games. Frankly, though, I put little stock in his prophecy. I thought my sealed move had taken care of the situation, but Drukker saw farther ahead than I did. His analysis was uncannily profound." There was the jealousy of self-pity in his tone, and I felt that he hated Drukker as bitterly as his seemingly mild nature would permit.
"How long did the game last?" Vance asked casually.
"It was over a little after one o'clock. There were only fourteen moves in last night's session."
"Were there many spectators?"
"An unusually large number, considering the late hour."
Vance put out his cigarette and got up. When we were in the lower hall on our way to the front door he halted suddenly and, fixing Pardee with a gaze of sardonic amusement, said:
"Y' know, the black bishop was at large again last night around midnight."
His words produced an astonishing effect. Pardee drew himself up as if he had been struck in the face; and his cheeks went chalky white. For a full half-minute he stared at Vance, his eyes like live coals. His lips moved with a slight tremor, but no word came from them. Then, as if with superhuman effort, he turned stiffly away and went to the door. Jerking it open he held it for us to pass out.
As we walked up Riverside Drive to the District Attorney's car, which had been left in front of the Drukker house in 76th Street, Markham questioned Vance sharply in regard to the final remark he had made to Pardee.
"I was in hopes," explained Vance, "of surprising some look of recognition or understanding from him. But, 'pon my soul, Markham, I didn't expect any effect like the one I produced. Astonishin' how he reacted. I don't grasp it—I don't at all grasp it. . . ."
He became engrossed in his thoughts. But as the car swung into Broadway at 72nd Street he roused himself and directed the chauffeur to the Sherman Square Hotel.
"I have a gaspin' desire to know more of that chess game between Pardee and Rubinstein. No reason for it—sheer vagary on my part. But the idea has been workin' in me ever since the professor mentioned it. . . . From eleven until past one—that's a deuced long time to play off an unfinished game of only forty-four moves."
We had drawn up to the curb at the corner of Amsterdam Avenue and 71st Street, and Vance disappeared into the Manhattan Chess Club. It was fully five minutes before he returned. In his hand he carried a sheet of paper filled with notations. There was, however, no sign of jubilance in his expression.
"My far-fetched but charmin' theory," he said, with a grimace, "has run aground on base prosaic facts. I just talked to the secret'ry of the club; and last night's session consumed two hours and nineteen minutes. It seems to have been a coruscatin' battle, full of esoteric quirks and strategical soul-searchin's. Along about half past eleven the onlooking genii had Pardee picked for the winner; but Rubinstein then staged a masterly piece of sustained analysis, and proceeded to tear Pardee's tactics to smithereens—just as Drukker had prognosticated. Astonishin' mind, Drukker's. . . ."
It was plain that even now he was not entirely satisfied with what he had learned; and his next words voiced his dissatisfaction.
"I thought while I was at it I'd take a page from the Sergeant's book, so to speak, and indulge in a bit of routine thoroughness. So I borrowed the score sheet of last night's game and copied down the moves. I may run over the game some day when time hangs heavy."
And, with what I thought unusual care, he folded the score and placed it in his wallet.
16. ACT THREE
(Tuesday, April 12—Saturday, April 16.)
After lunch at the Elysée Markham and Heath continued down-town. A hard afternoon lay before them. Markham's routine work had accumulated; and the Sergeant, having taken on the Sprigg case in addition to the Robin investigation, had to keep two separate machines working, co-ordinate all his reports, answer innumerable questions from his superiors, and attempt to satisfy the voraciousness of an army of reporters. Vance and I went to an exhibition of modern French art at Knoedler's, had tea at the St. Regis, and met Markham at the Stuyvesant Club for dinner. Heath and Inspector Moran joined us at half past eight for an informal conference; but though it lasted until nearly midnight nothing of a tangible nature came out of it.
Nor did the following day bring anything but discouragement. The report from Captain Dubois stated that the revolver given him by Heath contained no sign of a finger-print. Captain Hagedorn identified the weapon as the one used in the shooting of Sprigg; but this merely substantiated our already positive belief. The man set to guard the rear of the Drukker residence spent an uneventful night. No one had entered or departed from the house; and by eleven o'clock every window had been dark. Nor had a sound of any kind come from the house until the next morning when the cook set about her chores for the day. Mrs. Drukker had appeared in the garden a little after eight; and at half past nine Drukker went out the front door and sat for two hours in the park reading.
Two days went by. A watch was kept on the Dillard house; Pardee was put under strict surveillance; and a man was stationed each night under the willow trees behind the Drukker house. But nothing unusual happened; and, despite the Sergeant's tireless activities, all promising lines of investigation seemed to be automatically closed. Both Heath and Markham were deeply worried. The newspapers were outdoing themselves in gaudy rhetoric; and the inability of the Police Department and the District Attorney's office to make the slightest headway against the mystery of the two spectacular murders was rapidly growing into a political scandal.
Vance called on Professor Dillard and discussed the case along general lines. He also spent over an hour on Thursday afternoon with Arnesson in the hope that the working out of the proposed formula had brought to light some detail that could be used as a starting-point for speculation. But he was dissatisfied with the interview, and complained to me that Arnesson had not been wholly frank with him. Twice he dropped in at the Manhattan Chess Club and attempted to lead Pardee into conversation; but each time he was met with the reticence of cold courtesy. I noticed that he made no effort to communicate with either Drukker or Mrs. Drukker; and when I asked him his reason for ignoring them, he answered:
"The truth cannot be learned from them now. Each is playing a game; and both are thoroughly frightened. Until we have some definite evidence, more harm than good will result from any attempt to cross-examine them."
This definite evidence was to come the very next day from a most unexpected quarter; and it marked the beginning of the last phase of our investigation—a phase fraught with such sinister, soul-stirring tragedy and unspeakable horror, with such wanton cruelty and monstrous humor, that even now, years later, as I set down this reportorial record of it, I find it difficult to believe that the events were not, after all, a mere grotesque dream of fabulous wickedness.
Friday afternoon Markham, in a mood of desperation, called another conference. Arnesson asked permission to attend; and at four o'clock we all met, including Inspector Moran, in the District Attorney's private room in the old Criminal Courts Building. Arnesson was unwontedly silent during the discussion, and not once did he indulge in his usual flippancy. He listened with close attention to all that was said, and seemed pur
posely to avoid expressing an opinion, even when directly appealed to by Vance.
We had been in conference perhaps half an hour when Swacker entered quietly and placed a memorandum on the District Attorney's desk. Markham glanced at it and frowned. After a moment he initialed two printed forms and handed them to Swacker.
"Fill these in right away and give them to Ben,"[22] he ordered. Then when the man had gone out through the outer-hall door, he explained the interruption. "Sperling has just sent a request to speak to me. He says he has information that may be of importance. I thought, in the circumstances, it might be well to see him now."
Ten minutes later Sperling was brought in by a deputy sheriff from the Tombs. He greeted Markham with a friendly boyish smile, and nodded pleasantly to Vance. He bowed—a bit stiffly, I thought—to Arnesson, whose presence seemed both to surprise and disconcert him. Markham motioned him to a chair, and Vance offered him a cigarette.
"I wanted to speak to you, Mr. Markham," he began, a bit diffidently, "about a matter which may be of help to you. . . . You remember, when you were questioning me about my being in the archery-room with Robin, you wanted to know which way Mr. Drukker went when he left us. I told you I didn't notice, except that he went out by the basement door. . . . Well, sir, I've had a lot of time to think lately; and I've naturally gone over in my mind all that happened that morning. I don't know just how to explain it, but everything has become a lot clearer now. Certain—what you might call impressions—have come back to me. . . ."
He paused and looked down at the carpet. Then lifting his head, he went on:
"One of these impressions has to do with Mr. Drukker—and that's why I wanted to see you. Just this afternoon I was—well, sort of pretending I was in the archery-room again, talking to Robin; and all of a sudden the picture of the rear window flashed across my mind. And I remembered that when I had glanced out of the window that morning to see how the weather was for my trip, I had seen Mr. Drukker sitting in the arbor behind the house. . . ."
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