As we walked slowly toward the Dillard house it was decided that immediate inquiries should be made regarding the whereabouts the night before of every person connected in any way with this gruesome drama.

    "We must be careful, however, to drop no hint of what befell Mrs. Drukker," warned Vance. "Our midnight bishop-bearer did not intend that we should learn of his call. He believed that the poor lady would be too frightened to tell us."

    "I'm inclined to think," objected Markham, "that you're attaching too much importance to the episode."

    "Oh, my dear fellow!" Vance stopped short and put both hands on the other's shoulders. "You're much too effete—that's your great shortcomin'. You don't feel—you are no child of nature. The poetry of your soul has run to prose. Now I, on the other hand, give my imagination full sway; and I tell you that the leaving of that bishop at Mrs. Drukker's door was no Hallowe'en prank, but the desperate act of a desperate man. It was meant as a warning."

    "You think she knows something?"

    "I think she saw Robin's body placed on the range. And I think she saw something else—something she would give her life not to have seen."

    In silence we moved on. It was our intention to pass through the wall gate into 75th Street and present ourselves at the Dillards' front door; but as we passed the archery-room the basement door opened, and Belle Dillard confronted us anxiously.

    "I saw you coming down the range," she said, with troubled eagerness, addressing her words to Markham. "For over an hour I've been waiting to get in touch with you—phoning your office. . . ." Her manner became agitated. "Something strange has happened. Oh, it may not mean anything . . . but when I came through the archery-room here this morning, intending to call on Lady Mae, some impulse made me go to the tool-chest again and look in the drawer,—it seemed so—so queer that the little revolver should have been stolen. . . . And there it lay—in plain sight—beside the other pistol!" She caught her breath. "Mr. Markham, some one returned it to the drawer last night!"

    This information acted electrically on Heath.

    "Did you touch it?" he asked excitedly.

    "Why—no. . . ."

    He brushed past her unceremoniously and, going to the tool-chest, yanked open the drawer. There, beside the larger automatic that we had seen the day before, lay a small pearl-handled .32. The Sergeant's eyes glistened as he ran his pencil through the trigger-guard and lifted it gingerly. He held it to the light and sniffed at the end of the barrel.

    "One empty chamber," he announced, with satisfaction. "And it's been shot off recently. . . . This oughta get us somewheres." He wrapped the revolver tenderly in a handkerchief and placed it in his coat pocket. "I'll get Dubois busy on this for finger-prints; and I'll have Cap Hagedorn[19] check up on the bullets."

    "Really now, Sergeant," said Vance banteringly; "do you imagine that the gentleman we're looking for would wipe a bow and arrow clean and then leave his digital monogram on a revolver?"

    "I haven't got your imagination, Mr. Vance," returned Heath surlily. "So I'm going ahead doing the things that oughta be done."

    "You're quite right." Vance smiled with good-natured admiration at the other's dogged thoroughness. "Forgive me for trying to damp your zeal."

    He turned to Belle Dillard.

    "We came here primarily to see the professor and Mr. Arnesson. But there's also a matter we'd like to speak about to you.—We understand you have a key to the rear door of the Drukker house."

    She gave him a puzzled nod.

    "Yes; I've had one for years. I run back and forth so much; and it saves Lady Mae a lot of bother. . . ."

    "Our only interest in the key is that it might have been used by some one who had no right to it."

    "But that's impossible. I've never lent it to any one. And I always keep it in my hand-bag."

    "Is it generally known you have a key to the Drukkers'?"

    "Why—I suppose so." She was obviously perplexed. "I've never made a secret of it. The family certainly know about it."

    "And you may perhaps have mentioned or revealed the fact when there were outsiders present?"

    "Yes—though I can't recall any specific instance."

    "Are you sure you have the key now?"

    She gave Vance a startled look, and without a word picked up a small lizard-skin hand-bag which lay on the wicker table. Opening it she felt swiftly in one of its inner compartments.

    "Yes!" she announced, with relief. "It's where I always keep it. . . . Why do you ask me about it?"

    "It's important that we know who had access to the Drukker house," Vance told her. Then, before she could question him further, he asked: "Could the key possibly have left your possession last night?—that is, could it have been extracted from your bag without your knowledge?"

    A look of fright came into her face.

    "Oh, what has happened?" she began; but Vance interrupted her.

    "Please, Miss Dillard! There's nothing for you to worry about. We're merely striving to eliminate certain remote possibilities in connection with our investigation.—Tell me: could any one have taken your key last night?"

    "No one," she answered uneasily. "I went to the theatre at eight o'clock, and had my bag with me the entire time."

    "When did you last make use of the key?"

    "After dinner last night. I ran over to see how Lady Mae was and to say good-night."

    Vance frowned slightly. I could see that this information did not square with some theory he had formed.

    "You made use of the key after dinner," he recapitulated, "and kept it with you in your hand-bag the rest of the evening, without letting it once go out of your sight.—Is that right, Miss Dillard?"

    The girl nodded.

    "I even held the bag in my lap during the play," she amplified.

    Vance regarded the hand-bag thoughtfully.

    "Well," he said lightly, "so ends the romance of the key.—And now we're going to bother your uncle again. Do you think you'd better act as our avant-courier; or shall we storm the citadel unannounced?"

    "Uncle is out," she informed us. "He went for a walk along the Drive."

    "And Mr. Arnesson, I suppose, has not yet returned from the university."

    "No; but he'll be here for lunch. He has no classes Tuesday afternoons."

    "In the meantime, then, we'll confer with Beedle and the admirable Pyne.—And I might suggest that it would do Mrs. Drukker no end of good if you'd pay her a visit."

    With a troubled smile and a little nod the girl passed out through the basement door.

    Heath at once went in search of Beedle and Pyne and brought them to the drawing-room, where Vance questioned them about the preceding night. No information, however, was obtained from them. They had both gone to bed at ten o'clock. Their rooms were on the fourth floor at the side of the house; and they had not even heard Miss Dillard when she returned from the theatre. Vance asked them about noises on the range, and intimated that the screen-porch door of the Drukkers might have slammed shut at about midnight. But apparently both of them had been asleep at that hour. Finally they were dismissed with a warning not to mention to any one the questions that had just been asked them.

    Five minutes later Professor Dillard came in. Though surprised to see us, he greeted us amiably.

    "For once, Markham, you've chosen an hour for your visit when I am not absorbed in work.—More questions, I suppose. Well, come along to the library for the inquisition. It'll be more comfortable there." He led the way up-stairs, and when we were seated he insisted that we join him in a glass of port which he himself served from the sideboard.

    "Drukker should be here," he remarked. "He has a fondness for my 'Ninety-six,' though he'll drink it only on rare occasions. I tell him he should take more port; but he imagines it's bad for him, and points to my gout. But there's no connection between gout and port—the notion is sheer superstition. Sound port is the most wholesome of wines. Gout is unknown in Oporto. A little physical stimulation of the right kind would be good for Drukker. . . . Poor fellow. His mind is like a furnace that's burning his body up. A brilliant man, Markham. If he had sufficient bodily energy to keep pace with his brain, he'd be one of the world's great physicists."

    "He tells me," commented Vance, "that you twitted him on his inability to work out a modification of the quantum theory in regard to light-interference."

    The old man smiled ruefully.

    "Yes. I knew that such a criticism would spur him to a maximum effort. The fact is, Drukker is on the track of something revolutionary. He has already worked out some very interesting theorems. . . . But I'm sure this isn't what you gentlemen came here to discuss. What can I do for you, Markham? Or, perhaps you came to give me news."

    "Unfortunately we have no news. We have come to solicit aid again. . . ." Markham hesitated as if uncertain how to proceed; and Vance assumed the rôle of questioner.

    "The situation has changed somewhat since we were here yesterday. One or two new matters have arisen, and there is a possibility that our investigation would be facilitated if we knew the exact movements of the members of your household last night. These movements, in fact, may have influenced certain factors in the case."

    The professor lifted his head in some surprise, but made no comment. He said merely: "That information is very easily given. To what members do you refer?"

    "To no member specifically," Vance hastened to assure him.

    "Well, let me see. . . ." He took out his old meerschaum pipe and began filling it. "Belle and Sigurd and I had dinner alone at six o'clock. At half past seven Drukker dropped in, and a few minutes later Pardee called. Then at eight Sigurd and Belle went to the theatre, and at half past ten Drukker and Pardee went away. I myself turned in shortly after eleven, after locking up the house—I'd let Pyne and Beedle go to bed early.—And that's about all I can tell you."

    "Do I understand that Miss Dillard and Mr. Arnesson went to the theatre together?"

    "Yes. Sigurd rarely patronizes the theatre, but whenever he does he takes Belle along. He attends Ibsen's plays, for the most part. He's a devout disciple of Ibsen's, by the way. His American upbringing hasn't in the least tempered his enthusiasm for things Norwegian. At heart he's quite loyal to his native country. He's as well grounded in Norwegian literature as any professor at the University of Oslo; and the only music he really cares for is Grieg's. When he goes to concerts or the theatre you're pretty sure to find that the programs are liberally Norwegian."

    "It was an Ibsen play, then, he attended last night?"

    "'Rosmersholm,' I believe. There's a revival of Ibsen's dramas at present in New York."

    Vance nodded. "Walter Hampden's doing them.—Did you see either Mr. Arnesson or Miss Dillard after they returned from the theatre?"

    "No; they came in rather late, I imagine. Belle told me this morning they went to the Plaza for supper after the play. However, Sigurd will be here at any minute, and you can learn the details from him." Though the professor spoke with patience, it was plain that he was annoyed by the apparently irrelevant nature of the interrogation.

    "Will you be good enough, sir," pursued Vance, "to tell us the circumstances connected with Mr. Drukker's and Mr. Pardee's visit here after dinner?"

    "There was nothing unusual about their call. They often drop in during the evening. The object of Drukker's visit was to discuss with me the work he had done on his modification of the quantum theory; but when Pardee appeared the discussion was dropped. Pardee is a good mathematician, but advanced physics is beyond his depth."

    "Did either Mr. Drukker or Mr. Pardee see Miss Dillard before she went to the theatre?"

    Professor Dillard took his pipe slowly from his mouth, and his expression became resentful.

    "I must say," he replied testily, "that I can see no valid object in my answering such questions.—However," he added, in a more indulgent tone, "if the domestic trivia of my household can be of any possible assistance to you, I will of course be glad to go into detail." He regarded Vance a moment. "Yes, both Drukker and Pardee saw Belle last night. All of us, including Sigurd, were together in this room for perhaps half an hour before theatre time. There was even a casual discussion about Ibsen's genius, in which Drukker annoyed Sigurd greatly by maintaining Hauptmann's superiority."

    "Then at eight o'clock, I gather, Mr. Arnesson and Miss Dillard departed, leaving you and Mr. Pardee and Mr. Drukker alone here."

    "That is correct."

    "And at half past ten, I think you said, Mr. Drukker and Mr. Pardee went away. Did they go together?"

    "They went down-stairs together," the professor answered, with more than a suggestion of tartness. "Drukker, I believe, went home; but Pardee had an appointment at the Manhattan Chess Club."

    "It seems a bit early for Mr. Drukker to have gone home," mused Vance, "especially as he had come to discuss an important matter with you and had had no adequate opportunity to do so up to the time of his departure."

    "Drukker is not well." The professor's voice was again studiously patient. "As I've told you, he tires easily. And last night he was unusually played out. In fact, he complained to me of his fatigue and said he was going immediately to bed."

    "Yes . . . quite in keeping," murmured Vance. "He told us a little while ago that he was up working at six yesterday morning."

    "I'm not surprised. Once a problem has posed itself in his mind he works on it incessantly. Unfortunately he has no normal reactions to counterbalance his consuming passion for mathematics. There have been times when I've feared for his mental stability."

    Vance, for some reason, steered clear of this point.

    "You spoke of Mr. Pardee's engagement at the Chess Club last night," he said, when he had carefully lighted a fresh cigarette. "Did he mention the nature of it to you?"

    Professor Dillard smiled with patronizing lenity.

    "He talked about it for fully an hour. It appears that a gentleman named Rubinstein—a genius of the chess world, I understand, who is now visiting this country—had taken him on for three exhibition games. The last one was yesterday. It began at two o'clock, and was postponed at six. It should have been played off at eight, but Rubinstein was the lion of some dinner down-town; so the hour set for the play-off was eleven, Pardee was on tenter-hooks, for he had lost the first game and drawn the second; and if he could have won last night's game he would have broken even with Rubinstein. He seemed to think he had an excellent chance according to the way the game stood at six o'clock; although Drukker disagreed with him. . . . He must have gone directly from here to the club, for it was fully half past ten when he and Drukker went out."

    "Rubinstein's a strong player," observed Vance. A new note of interest, which he strove to conceal, had come into his voice. "He's one of the grand masters of the game. He defeated Capablanca at San Sebastian in 1911, and between 1907 and 1912 was considered the logical contender for the world's title held by Doctor Lasker.[20] . . . Yes, it would have been a great feather in Pardee's cap to have beaten him. Indeed, it was no small compliment to him that he should have been matched with Rubinstein. Pardee, despite the fame of his gambit, has never been ranked as a master.—Have you heard the result of last night's game, by the by?"

    Again I noted a faint tolerant smile at the corners of the professor's mouth. He gave the impression of looking down benevolently on the foolish capers of children from some great intellectual height.

    "No," he answered; "I didn't inquire. But my surmise is that Pardee lost; for when Drukker pointed out the weakness of his adjourned position, he was more positive than usual. Drukker by nature is cautious, and he rarely expresses a definite opinion on a problem without having excellent grounds for so doing."

    Vance raised his eyebrows in some astonishment.

    "Do you mean to tell me that Pardee analyzed his unfinished game with Drukker and discussed the possibilities of its ending? Not only is such a course unethical, but any player would be disqualified for doing such a thing."

    "I'm unfamiliar with the punctilio of chess," Professor Dillard returned acidly; "but I am sure Pardee would not be guilty of a breach of ethics in that regard. And, as a matter of fact, I recall that when he was engaged with the chessmen at the table over there and Drukker stepped up to look on, Pardee requested him to offer no advice. The discussion of the position took place some time later, and was kept entirely to generalities. I don't believe there was a mention of any specific line of play."

    Vance leaned slowly forward and crushed out his cigarette with that taut deliberation which I had long since come to recognize as a sign of repressed excitement. Then he rose carelessly and moved to the chess table in the corner. He stood there, one hand resting on the exquisite marquetry of the alternating squares.

    "You say that Mr. Pardee was analyzing his position on this board when Mr. Drukker came over to him?"

    "Yes, that is right." Professor Dillard spoke with forced politeness. "Drukker sat down facing him and studied the layout. He started to make some remark, and Pardee requested him to say nothing. A quarter of an hour or so later Pardee put the men away; and it was then that Drukker told him that his game was lost—that he had worked himself into a position which, though it looked favorable, was fundamentally weak."

    Vance had been running his fingers aimlessly over the board; and he had taken two or three of the men from the box and tossed them back, as if toying with them.

    "Do you remember just what Mr. Drukker said?" he asked without looking up.

    "I didn't pay very close attention—the subject was not exactly one of burning moment to me." There was an unescapable note of irony in the answer. "But, as nearly as I can recall, Drukker said that Pardee could have won provided it had been a rapid-transit game, but that Rubinstein was a notoriously slow and careful player and would inevitably find the weak spot in Pardee's position."

    "Did Pardee resent this criticism?" Vance now strolled back to his chair and selected another cigarette from his case; but he did not sit down again.

    "He did—very much. Drukker has an unfortunately antagonistic manner. And Pardee is hypersensitive on the subject of his chess. The fact is, he went white with anger at Drukker's strictures. But I personally changed the subject; and when they went away the incident had apparently been forgotten."

    We remained but a few minutes longer. Markham was profuse in his apologies to the professor and sought to make amends for the patent annoyance our visit had caused him. He was not pleased with Vance for his seemingly garrulous insistence on the details of Pardee's chess game, and when we had descended to the drawing-room he expressed his displeasure.

    "I could understand your questions relating to the whereabouts of the various occupants of this house last night, but I could see no excuse for your harping on Pardee's and Drukker's disagreement over a game of chess. We have other things to do besides gossip."

    "A hate of gossip parlance also crown'd Tennyson's Isabel thro' all her placid life," Vance returned puckishly. "But—my word, Markham!—our life is not like Isabel's. Speakin' seriously, there was method in my gossip. I prattled—and I learned."

    "You learned what?" Markham demanded sharply.

    With a cautious glance into the hall Vance leaned forward and lowered his voice.

    "I learned, my dear Lycurgus, that a black bishop is missing from that set in the library, and that the chessman left at Mrs. Drukker's door matches the other pieces up-stairs!"