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(Tuesday, November 30; noon)

Markham had considerable difficulty in persuading Ada to accompany us. The girl seemed almost in a panic of fright. Moreover, she held herself indirectly responsible for Rex’s death. But at last she permitted us to lead her down to the car.

Heath had already telephoned to the Homicide Bureau, and his arrangements for the investigation were complete when we started up Centre Street. At Police Headquarters Snitkin and another Central Office man named Burke were waiting for us, and crowded into the tonneau of Markham’s car. We made excellent time to the Greene mansion, arriving there in less than twenty minutes.

A plain-clothes man lounged against the iron railing at the end of the street a few yards beyond the gate of the Greene grounds, and at a sign from Heath came forward at once.

“What about it, Santos?” the Sergeant demanded gruffly. “Who’s been in and out of here this morning?”

“What’s the big idea?” the man retorted indignantly. “That old bimbo of a butler came out about nine and returned in less than half an hour with a package. Said he’d been to Third Avenue to get some dog-biscuits. The family sawbones drove up at quarter past ten—that’s his car across the street.” He pointed to Von Blon’s Daimler, which was parked diagonally opposite. “He’s still inside.—Then, about ten minutes after the doc arrived, this young lady”—he indicated Ada—“came out and walked toward Avenue A, where she hopped a taxi. And that’s every man, woman, or child that’s passed in or out of these gates since I relieved Cameron at eight o’clock this morning.”

“And Cameron’s report?”

“Nobody all night.”

“Well, some one got in some way,” growled Heath. “Run along the west wall there and tell Donnelly to come here pronto.”

Santos disappeared through the gate, and a moment later we could see him hurrying through the side yard toward the garage. In a few minutes Donnelly—the man set to watch the postern gate—came hurrying up.

“Who got in the back way this morning?” barked Heath.

“Nobody, Sergeant. The cook went marketing about ten o’clock, and two regular deliverymen left packages. That’s every one who’s been through the rear gate since yesterday.”

“Is that so!” Heath was viciously sarcastic.

“I’m telling you——”

“Oh, all right, all right.” The Sergeant turned to Burke. “You get up on this wall and make the rounds. See if you can find where any one has climbed over.—And you, Snitkin, look over the yard for footprints. When you guys finish, report to me. I’m going inside.”

We went up the front walk, which had been swept clean, and Sproot admitted us to the house. His face was as blank as ever, and he took our coats with his usual obsequious formality.

“You’d better go to your room now, Miss Greene,” said Markham, placing his hand kindly on Ada’s arm. “Lie down, and try to get a little rest. You look tired. I’ll be in to see you before I go.”

The girl obeyed submissively without a word.

“And you, Sproot,” he ordered; “come in the living-room.”

The old butler followed us and stood humbly before the centre-table, where Markham seated himself.

“Now, let’s hear your story.”

Sproot cleared his throat and stared out of the window.

“There’s very little to tell, sir. I was in the butler’s pantry, polishing the glassware, when I heard the shot——”

“Go back a little further,” interrupted Markham. “I understand you made a trip to Third Avenue at nine this morning.”

“Yes, sir. Miss Sibella bought a Pomeranian yesterday, and she asked me to get some dog-biscuits after breakfast.”

“Who called at the house this morning?”

“No one, sir—that is, no one but Doctor Von Blon.”

“All right. Now tell us everything that happened.”

“Nothing happened, sir—nothing unusual, that is—until poor Mr. Rex was shot. Miss Ada went out a few minutes after Doctor Von Blon arrived; and a little past eleven o’clock you telephoned to Mr. Rex. Then shortly afterward you telephoned a second time to Mr. Rex; and I returned to the pantry. I had only been there a few minutes when I heard the shot——”

“What time would you say that was?”

“About twenty minutes after eleven, sir.”

“Then what?”

“I dried my hands on my apron and stepped into the dining-room to listen. I was not quite sure that the shot had been fired inside the house, but I thought I’d better investigate. So I went up-stairs and, as Mr. Rex’s door was open, I looked in his room first. There I saw the poor young man lying on the floor with the blood running from a small wound in his forehead. I called Doctor Von Blon——”

“Where was the doctor?” Vance put the question.

Sproot hesitated, and appeared to think.

“He was up-stairs, sir; and he came at once——”

“Oh—up-stairs! Roaming about vaguely, I presume—a little here, a little there, what?” Vance’s eyes bored into the butler. “Come, come, Sproot. Where was the doctor?”

“I think, sir, he was in Miss Sibella’s room.”

“Cogito, cogito. . . . Well, drum your encephalon a bit and try to reach a conclusion. From what sector of space did the corporeal body of Doctor Von Blon emerge after you had called him?”

“The fact is, sir, he came out of Miss Sibella’s door.”

“Well, well. Fancy that! And, such being the case, one might conclude—without too great a curfuffling of one’s brains—that, preceding his issuing from that particular door, he was actually in Miss Sibella’s room?”

“I suppose so, sir.”

“Dash it all, Sproot! You know deuced well he was there.”

“Well—yes, sir.”

“And now suppose you continue with your odyssey.”

“It was more like the Iliad, if I may say so. More tragic-like, if you understand what I mean; although Mr. Rex was not exactly a Hector. However that may be, sir, Doctor Von Blon came immediately——”

“He had not heard the shot, then?”

“Apparently not, for he seemed very much startled when he saw Mr. Rex. And Miss Sibella, who followed him into Mr. Rex’s room, was startled, too.”

“Did they make any comment?”

“As to that I couldn’t say. I came down-stairs at once and telephoned to Mr. Markham.”

As he spoke Ada appeared at the archway, her eyes wide.

“Some one’s been in my room,” she announced, in a frightened voice. “The French doors to the balcony were partly open when I went up-stairs just now, and there were dirty snow-tracks across the floor. . . . Oh, what does it mean? Do you think——?”

Markham had jerked himself forward.

“You left the French doors shut when you went out?”

“Yes—of course,” she answered. “I rarely open them in winter.”

“And were they locked?”

“I’m not sure, but I think so. They must have been locked—though how could any one have got in unless I’d forgotten to turn the key?”

Heath had risen and stood listening to the girl’s story with grim bewilderment.

“Probably the bird with those galoshes again,” he mumbled. “I’ll get Jerym himself up here this time.”

Markham nodded and turned back to Ada.

“Thank you for telling us, Miss Greene. Suppose you go to some other room and wait for us. We want your room left just as you found it until we’ve had time to examine it.”

“I’ll go to the kitchen and stay with cook. I—I don’t want to be alone.” And with a catch of her breath she left us.

“Where’s Doctor Von Blon now?” Markham asked Sproot.

“With Mrs. Greene, sir.”

“Tell him we’re here and would like to see him at once.”

The butler bowed and went out.

Vance was pacing up and down, his eyes almost closed.

“It grows madder every minute,” he said. “It was insane enough without those foot-tracks and that open door. There’s something devilish going on here, Markham. There’s demonology and witchcraft afoot, or something strangely close to it. I say, is there anything in the Pandects or the Justinian Code relating to the proper legal procedure against diabolic possession or spiritism?”

Before Markham could rebuke him Von Blon entered. His usual suavity had disappeared. He bowed jerkily without speaking, and smoothed his moustache nervously with an unsteady hand.

“Sproot tells me, doctor,” said Markham, “that you did not hear the shot fired in Rex’s room.”

“No!” The fact seemed both to puzzle and disturb him. “I can’t make it out either, for Rex’s door into the hall was open.”

“You were in Miss Sibella’s room, were you not?” Vance had halted, and stood studying the doctor.

Von Blon lifted his eyebrows.

“I was. Sibella had been complaining about——”

“A sore throat or something of the kind, no doubt,” finished Vance. “But that’s immaterial. The fact is that neither you nor Miss Sibella heard the shot. Is that correct?”

The doctor inclined his head. “I knew nothing of it till Sproot knocked on the door and beckoned me across the hall.”

“And Miss Sibella accompanied you into Rex’s room?”

“She came in just behind me, I believe. But I told her not to touch anything, and sent her immediately back to her room. When I came out into the hall again I heard Sproot phoning the District Attorney’s office, and thought I’d better wait till the police arrived. After talking over the situation with Sibella I informed Mrs. Greene of the tragedy, and remained with her until Sproot told me of your arrival.”

“You saw no one else up-stairs, or heard no suspicious noise?”

“No one—nothing. The house, in fact, was unusually quiet.”

“Do you recall if Miss Ada’s door was open?”

The doctor pondered a moment. “I don’t recall—which means it was probably closed. Otherwise I would have noticed it.”

“And how is Mrs. Greene this morning?” Vance’s question, put negligently, sounded curiously irrelevant.

Von Blon gave a start.

“She seemed somewhat more comfortable when I first saw her, but the news of Rex’s death disturbed her considerably. When I left her just now she was complaining about the shooting pains in her spine.”

Markham had got up and now moved restlessly toward the archway.

“The Medical Examiner will be here any minute,” he said; “and I want to look over Rex’s room before he arrives. You might come with us, doctor.—And you, Sproot, had better remain at the front door.”

We went up-stairs quietly: I think it was in all our minds that we should not advertise our presence to Mrs. Greene. Rex’s room, like all those in the Greene mansion, was spacious. It had a large window at the front and another at the side. There were no draperies to shut out the light, and the slanting midday sun of winter poured in. The walls, as Chester had once told us, were lined with books; and pamphlets and papers were piled in every available nook. The chamber resembled a student’s workshop more than a bedroom.

In front of the Tudor fireplace in the centre of the left wall—a duplication of the fireplace in Ada’s room—sprawled the body of Rex Greene. His left arm was extended, but his right arm was crooked, and the fingers were tightened, as if holding some object. His domelike head was turned a little to one side; and a thin stream of blood ran down his temple to the floor from a tiny aperture over the right eye.

REX’S BEDROOM.

Heath studied the body for several minutes.

“He was shot standing still, Mr. Markham. He collapsed in a heap and then straightened out a little after he’d hit the floor.”

Vance was bending over the dead man with a puzzled expression.

“Markham, there’s something curious and inconsistent here,” he said. “It was broad daylight when this thing happened, and the lad was shot from the front—there are even powder marks on the face. But his expression is perfectly natural. No sign of fear or astonishment—rather peaceful and unconcerned, in fact. . . . It’s incredible. The murderer and the pistol certainly weren’t invisible.”

Heath nodded slowly.

“I noticed that too, sir. It’s damn peculiar.” He bent more closely over the body. “That wound looks to me like a thirty-two,” he commented, turning to the doctor for confirmation.

“Yes,” said Von Blon. “It appears to have been made with the same weapon that was used against the others.”

“It was the same weapon,” Vance pronounced sombrely, taking out his cigarette-case with thoughtful deliberation. “And it was the same killer who used it.” He smoked a moment, his troubled gaze resting on Rex’s face. “But why was it done at just this time—in the daylight, with the door open, and when there were people close at hand? Why didn’t the murderer wait until night? Why did he run such a needless risk?”

“Don’t forget,” Markham reminded him, “that Rex was on the point of coming to my office to tell me something.”

“But who knew he was about to indulge in revelations? He was shot within ten minutes of your call——” He broke off and turned quickly to the doctor. “What telephone extensions are there in the house?”

“There are three, I believe.” Von Blon spoke easily. “There’s one in Mrs. Greene’s room, one in Sibella’s room, and, I think, one in the kitchen. The main phone is, of course, in the lower front hall.”

“A regular central office,” growled Heath. “Almost anybody coulda listened in.” Suddenly he fell on his knees beside the body and unflexed the fingers of the right hand.

“I’m afraid you won’t find that cryptic drawing, Sergeant,” murmured Vance. “If the murderer shot Rex in order to seal his mouth the paper will surely be gone. Any one overhearing the phone calls, d’ye see, would have learned of the envelope he was to fetch along.”

“I guess you’re right, sir. But I’m going to have a look.”

He felt under the body and then systematically went through the dead man’s pockets. But he found nothing even resembling the blue envelope mentioned by Ada. At last he rose to his feet.

“It’s gone, all right.”

Then another idea occurred to him. Going hurriedly into the hall, he called down the stairs to Sproot. When the butler appeared Heath swung on him savagely.

“Where’s the private mail-box?”

“I don’t know that I exactly understand you.” Sproot’s answer was placid and unruffled. “There is a mail-box just outside the front door. Do you refer to that, sir?”

“No! You know damn well I don’t. I want to know where the private—get me?—private mail-box is, in the house.”

“Perhaps you are referring to the little silver pyx for outgoing mail on the table in the lower hall.”

“ ‘Pyx,’ is it!” The Sergeant’s sarcasm was stupendous. “Well, go down and bring me everything that’s in this here pyx.—No! Wait a minute—I’ll keep you company. . . . Pyx!” He took Sproot by the arm and fairly dragged him from the room.

A few moments later he returned, crestfallen.

“Empty!” was his laconic announcement.

“But don’t give up hope entirely just because your cabalistic diagram has disappeared,” Vance exhorted him. “I doubt if it would have helped you much. This case isn’t a rebus. It’s a complex mathematical formula, filled with moduli, infinitesimals, quantics, faciends, derivatives, and coefficients. Rex himself might have solved it if he hadn’t been shoved off the earth so soon.” His eyes wandered over the room. “And I’m not at all sure he hadn’t solved it.”

Markham was growing impatient.

“We’d better go down to the drawing-room and wait for Doctor Doremus and the men from Headquarters,” he suggested. “We can’t learn anything here.”

We went out into the hall, and as we passed Ada’s door Heath threw it open and stood on the threshold surveying the room. The French doors leading to the balcony were slightly ajar, and the wind from the west was flapping their green chintz curtains. On the light beige rug were several damp discolored tracks leading round the foot of the bed to the hall-door where we stood. Heath studied the marks for a moment, and then drew the door shut again.

“They’re footprints, all right,” he remarked. “Some one tracked in the dirty snow from the balcony and forgot to shut the glass doors.”

We were scarcely seated in the drawing-room when there came a knocking on the front door; and Sproot admitted Snitkin and Burke.

“You first, Burke,” ordered the Sergeant, as the two officers appeared. “Any signs of an entry over the wall?”

“Not a one.” The man’s overcoat and trousers were smudged from top to bottom. “I crawled all round the top of the wall, and I’m here to tell you that nobody left any traces anywheres. If any guy got over that wall, he vaulted.”

“Fair enough.—And now you, Snitkin.”

“I got news for you.” The detective spoke with overt triumph. “Somebody’s walked up those outside steps to the stone balcony on the west side of the house. And he walked up ’em this morning after the snowfall at nine o’clock, for the tracks are fresh. Furthermore, they’re the same size as the ones we found last time on the front walk.”

“Where do these new tracks come from?” Heath leaned forward eagerly.

“That’s the hell of it, Sergeant. They come from the front walk right below the steps to the front door; and there’s no tracing ’em farther back because the front walk’s been swept clean.”

“I mighta known it,” grumbled Heath. “And the tracks are only going one way?”

“That’s all. They leave the walk a few feet below the front door, swing round the corner of the house, and go up the steps to the balcony. The guy who made ’em didn’t come down that way.”

The Sergeant puffed disappointedly on his cigar.

“So he went up the balcony steps, entered the French doors, crossed Ada’s room to the hall, did his dirty work, and then—disappeared! A sweet case this is!” He clicked his tongue with disgust.

“The man may have gone out by the front door,” suggested Markham.

The Sergeant made a wry face and bellowed for Sproot, who entered immediately.

“Say, which way did you go up-stairs when you heard the shot?”

“I went up the servants’ stairs, sir.”

“Then some one mighta gone down the front stairs at the same time without your seeing him?”

“Yes, sir; it’s quite possible.”

“That’s all.”

Sproot bowed and again took up his post at the front door.

“Well, it looks like that’s what happened, sir,” Heath commented to Markham. “Only how did he get in and out of the grounds without being seen? That’s what I want to know.”

Vance was standing by the window gazing out upon the river.

“There’s something dashed unconvincing about those recurrent spoors in the snow. Our eccentric culprit is altogether too careless with his feet and too careful with his hands. He doesn’t leave a finger-print or any other sign of his presence except those foot-tracks—all nice and tidy and staring us in the face. But they don’t square with the rest of this fantastic business.”

Heath stared hopelessly at the floor. He was patently of Vance’s opinion; but the dogged thoroughness of his nature asserted itself, and presently he looked up with a forced show of energy.

“Go and phone Captain Jerym, Snitkin, and tell him I wish he’d hustle out here to look at some carpet-tracks. Then make measurements of those footprints on the balcony steps.—And you, Burke, take up a post in the upper hall, and don’t let any one go into the two front west rooms.”