The professor was plainly perturbed when we entered the library that noon. He sat in an easy chair with his back to the window, a glass of his precious port on the table beside him.

    "I've been expecting you, Markham," he said, before we had time to speak. "There's no need to dissemble. Drukker's death was no accident. I'll admit I felt inclined to discount the insane implications arising from the deaths of Robin and Sprigg; but the moment Pyne related the circumstances of Drukker's fall I realized that there was a definite design behind these deaths: the probabilities of their being accidental would be incalculable. You know it, as well as I; otherwise you wouldn't be here."

    "Very true." Markham had seated himself facing the professor. "We're confronted by a terrific problem. Moreover, Mrs. Drukker died of shock last night at almost the same time her son was killed."

    "That, at least," returned the old man after a pause, "may be regarded as a blessing. It's better she didn't survive him—her mind unquestionably would have collapsed." He looked up. "In what way can I help?"

    "You were probably the last person, with the exception of the actual murderer, to see Drukker alive; and we would like to know everything you can tell us of what took place last night."

    Professor Dillard nodded.

    "Drukker came here after dinner—about eight, I should say. Pardee had dined with us; and Drukker was annoyed at finding him here—in fact, he was openly hostile. Arnesson twitted him good-naturedly about his irascibility—which only made him more irritable; and, knowing that Drukker was anxious to thrash out a problem with me, I finally suggested that he and I stroll down to the park. . . ."

    "You were not gone very long," suggested Markham.

    "No. An unfortunate episode occurred. We walked up the bridle path to almost the exact spot where, I understand, the poor fellow was killed. We had been there for perhaps half an hour, leaning against the stone balustrade of the wall, when Pardee walked up. He stopped to speak to us, but Drukker was so antagonistic in his remarks that, after a few minutes, Pardee turned and walked away in the direction he had come. Drukker was very much upset, and I suggested we postpone the discussion. Furthermore, a damp mist had fallen, and I was beginning to get some twinges in my foot. Drukker straightway became morose, and said he didn't care to go indoors just yet. So I left him alone by the wall, and came home."

    "Did you mention the episode to Arnesson?"

    "I didn't see Sigurd after I got back. I imagine he'd gone to bed."

    Later as we rose to take our leave, Vance asked casually: "Can you tell us where the key to the alley door is kept?"

    "I know nothing about it, sir," the professor replied irritably, but added in a more equable tone: "However, as I remember, it used to hang on a nail by the archery-room door."

    From Professor Dillard we went straight to Pardee, and were received at once in his study. His manner was rigid and detached, and even after we had seated ourselves he remained standing by the window, staring at us with unfriendly eyes.

    "Do you know, Mr. Pardee," asked Markham, "that Mr. Drukker fell from the wall in the park at ten o'clock last night—shortly after you stopped and spoke to him?"

    "I heard of the accident this morning." The man's pallor became more noticeable, and he toyed nervously with his watch chain. "It's very unfortunate." His eyes rested vacantly for a while on Markham. "Have you asked Professor Dillard about it? He was with Drukker—"

    "Yes, yes; we've just come from him," interrupted Vance. "He said there was a ruffled atmosphere between you and Mr. Drukker last night."

    Pardee slowly walked to the desk and sat down stiffly.

    "Drukker was displeased for some reason to find me at the Dillards' when he came over after dinner. He hadn't the good taste to hide his displeasure, and created a somewhat embarrassing situation. But, knowing him as I did, I tried to pass the matter off. Soon, however, Professor Dillard took him out for a walk."

    "You didn't remain long afterward," observed Vance indolently.

    "No—about a quarter of an hour. Arnesson was tired and wanted to turn in, so I went for a walk myself. On my return I took the bridle path instead of the Drive, and came on Professor Dillard and Drukker standing by the wall talking. Not wishing to appear rude, I stopped for a moment. But Drukker was in a beastly mood and made several sneering remarks. I turned and walked back to 79th Street, crossed the Drive, and came home."

    "I say; didn't you loiter a bit by the wayside?"

    "I sat down near the 79th-Street entrance and smoked a cigarette."

    For nearly half an hour Markham and Vance interrogated Pardee, but nothing more could be learned from him. As we came out into the street Arnesson hailed us from the front porch of the Dillard house and stalked forward to meet us.

    "Just heard the sad news. Got home from the university a little while ago, and the professor told me you'd gone to rag Pardee. Learn anything?" Without waiting for an answer he ran on: "Frightful mess. I understand the entire Drukker family is wiped out. Well, well. And more story-book mumbo-jumbo to boot. . . . Any clews?"

    "Ariadne has not yet favored us," responded Vance. "Are you an ambassador from Crete?"

    "One never knows. Bring out your questionnaire." Vance had led the way toward the wall gate, and we now stepped down on the range.

    "We'll repair to the Drukker house first," he said. "There'll be a number of things to settle. I suppose you'll look after Drukker's affairs and the funeral arrangements."

    Arnesson made a grimace.

    "Elected! I refuse, however, to attend the funeral. Obscene spectacles, funerals. But Belle and I will see to everything. Lady Mae probably left a will. We'll have to find it. Now, where do women generally hide their wills? . . ."

    Vance halted by the Dillards' basement door and stepped into the archery-room. After glancing along the door's moulding he rejoined us on the range.

    "The alley key isn't there.—By the by, what do you know about it, Mr. Arnesson?"

    "You mean the key to yon wooden door in the fence? . . . Haven't an idea on the subject. Never use the alley myself—much simpler going out the front door. No one uses it, as far as I know. Belle locked it up years ago: thought some one might sneak in off the Drive and get an arrow in the eye. I told her, let 'em get popped—serve 'em right for being interested in archery."

    We entered the Drukker house by the rear door. Belle Dillard and Mrs. Menzel were busy in the kitchen.

    "Hallo, sis," Arnesson greeted the girl. His cynical manner had been dropped. "Hard lines for a young 'un like you. You'd better run home now. I'll assume command." And taking her arm in a jocularly paternal fashion, he led her to the door.

    She hesitated and looked back at Vance.

    "Mr. Arnesson is right," he nodded. "We'll carry on for the present.—But just one question before you go. Did you always keep the key to the alley door hanging in the archery-room?"

    "Yes—always. Why? Isn't it there now?"

    It was Arnesson who answered, with burlesque irony.

    "Gone! Disappeared!—Most tragic. Some eccentric key-collector has evidently been snooping around." When the girl had left us, he cocked an eye at Vance. "What, in the name of all that's unholy, has a rusty key to do with the case?"

    "Perhaps nothing," said Vance carelessly. "Let's go to the drawin'-room. It's more comfortable there." He led the way down the hall. "We want you to tell us what you can about last night."

    Arnesson took an easy chair by the front window, and drew out his pipe.

    "Last night, eh? . . . Well, Pardee came to dinner—it's a sort of habit with him on Fridays. Then Drukker, in the throes of quantum speculation, dropped in to pump the professor; and Pardee's presence galled him. Showed his feelings too, by Gad! No control. The professor broke up the contretemps by taking Drukker for an airing. Pardee moped for fifteen minutes or so, while I tried to keep awake. Then he had the goodness to depart. I looked over a few test papers . . . and so to bed." He lighted his pipe. "How does that thrilling recital explain the end of poor Drukker?"

    "It doesn't," said Vance. "But it's not without interest.—Did you hear Professor Dillard when he returned home?"

    "Hear him?" Arnesson chuckled. "When he hobbles about with his gouty foot, thumping his stick down and shaking the banisters, there's no mistaking his arrival on the scene. Fact is, he was unusually noisy last night."

    "Offhand, what do you make of these new developments?" asked Vance, after a short pause.

    "I'm somewhat foggy as to the details. The professor was not exactly phosphorescent. Sketchy, in fact. Drukker fell from the wall, like Humpty Dumpty, round ten o'clock, and was found this morning—that's all plain. But under what conditions did Lady Mae succumb to shock? Who, or what, shocked her? And how?"

    "The murderer took Drukker's key and came here immediately after the crime. Mrs. Drukker caught him in her son's room. There was a scene, according to the cook, who listened from the head of the stairs; and during it Mrs. Drukker died from dilatation of the heart."

    "Thereby relieving the gentleman of the bother of killing her."

    "That seems clear enough," agreed Vance. "But the reason for the murderer's visit here is not so lucid. Can you suggest an explanation?"

    Arnesson puffed thoughtfully on his pipe.

    "Incomprehensible," he muttered at length. "Drukker had no valuables, or no compromising documents. Straightforward sort of cuss—not the kind to mix in any dirty business. . . . No possible reason for any one prowling about his room."

    Vance lay back and appeared to relax.

    "What was this quantum theory Drukker was working on?"

    "Ha! Big thing!" Arnesson became animated. "He was on the path of reconciling the Einstein-Bohr theory of radiation with the facts of interference, and of overcoming the inconsistencies inherent in Einstein's hypothesis. His research had already led him to an abandonment of causal space-time coordination of atomic phenomena, and to its replacement by a statistical description.[27] . . . Would have revolutionized physics—made him famous. Shame he was told off before he'd put his data in shape."

    "Do you happen to know where Drukker kept the records of these computations?"

    "In a loose-leaf note-book—all tabulated and indexed. Methodical and neat about everything. Even his chirography was like copperplate."

    "You know, then, what the note-book looked like?"

    "I ought to. He showed it to me often enough. Red limp-leather cover—thin yellow pages—two or three clips on every sheet holding notations—his name gold-stamped in large letters on the binding. . . . Poor devil! Sic transit. . . ."

    "Where would this note-book be now?"

    "One of two places—either in the drawer of his desk in the study or else in the escritoire in his bedroom. In the daytime, of course, he worked in the study; but he fussed day and night when wrapped up in a problem. Kept an escritoire in his bedroom, where he put his current records when he retired, in case he got an inspiration to monkey with 'em during the night. Then, in the morning, back they'd go to the study. Regular machine for system."

    Vance had been gazing lazily out of the window as Arnesson rambled on. The impression he gave was that he had scarcely heard the description of Drukker's habits; but presently he turned and fixed Arnesson with a languid look.

    "I say," he drawled; "would you mind toddling up-stairs and fetching Drukker's note-book? Look in both the study and the bedroom."

    I thought I noticed an almost imperceptible hesitation on Arnesson's part; but straightway he rose.

    "Good idea. Too valuable a document to be left lying round." And he strode from the room.

    Markham began pacing the floor, and Heath revealed his uneasiness by puffing more energetically on his cigar. There was a tense atmosphere in the little drawing-room as we waited for Arnesson's return. Each of us was in a state of expectancy, though just what we hoped for or feared would have been difficult to define.

    In less than ten minutes Arnesson reappeared at the door. He shrugged his shoulders and held out empty hands.

    "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.