LITMIR.BIZ

       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

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