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came abreast of the switchboard: “Dash it all! You forgot your lines, Sergeant. You should have told me that Miss Odell was out. But it doesn’t matter. . . . Mr. Skeel continues to the lady’s door . . . thus.”

      He walked past us, and we heard him ring the apartment bell. After a brief pause, he knocked on the door. Then he came back down the hall.

      “I guess you were right,” he said, quoting the words of Skeel as reported by Spively; and went on to the front door. Stepping out into the street, he turned toward Broadway.

      For exactly three minutes we waited. None of us spoke. Heath had become serious, and his accelerated puffing on his cigar bore evidence of his state of expectancy. Markham was frowning stoically. At the end of the three minutes Heath rose and hurried up the hall, with Markham and me at his heels. In answer to his knock, the apartment door was opened from the inside. Vance was standing in the little foyer.

      “The end of the first act,” he greeted us airily. “Thus did Mr. Skeel enter the lady’s boudoir Monday night after the side door had been bolted, without the operator’s seeing him.”

      Heath narrowed his eyes, but said nothing. Then he suddenly swung round and looked down the rear passageway to the oak door at the end. The handle of the bolt was in a vertical position, showing that the catch had been turned and that the door was unbolted. Heath regarded it for several moments; then he turned his eyes toward the switchboard. Presently he let out a gleeful whoop.

      “Very good, Mr. Vance—very good!” he proclaimed, nodding his head knowingly. “That was easy, though. And it don’t take psychology to explain it.—After you rang the apartment bell, you ran down this rear hallway and unbolted the door. Then you ran back and knocked. After that you went out the front entrance, turned toward Broadway, swung round across the street, came in the alley, walked in the side door, and quietly let yourself into the apartment behind our backs.”

      “Simple, wasn’t it?” agreed Vance.

      “Sure.” The Sergeant was almost contemptuous. “But that don’t get you nowhere. Anybody coulda figured it out if that had been the only problem connected with Monday night’s operations. But it’s the rebolting of that side door, after Skeel had gone, that’s been occupying my mind. Skeel might’ve—might’ve, mind you—got in the way you did. But he couldn’t have got out that way, because the door was bolted the next morning. And if there was some one here to bolt the door after him, then that same person could’ve unbolted the door for him earlier, without his doing the ten-foot dash down the rear hall to unbolt the door himself at half past nine. So I don’t see that your interesting little drama helps Jessup out any.”

      “Oh, but the drama isn’t over,” Vance replied. “The curtain is about to go up on the next act.”

      Heath lifted his eyes sharply.

      “Yeah?” His tone was one of almost jeering incredulity, but his expression was searching and dubious. “And you’re going to show us how Skeel got out and bolted the door on the inside without Jessup’s help?”

      “That is precisely what I intend to do, my Sergeant.”

      Heath opened his mouth to speak, but thought better of it. Instead, he merely shrugged his shoulders and gave Markham a sly look.

      “Let us repair to the public atrium,” proceeded Vance; and he led us into the little reception-room diagonally opposite to the switchboard. This room, as I have explained, was just beyond the staircase, and along its rear wall ran the little passageway to the side door. (A glance at the accompanying diagram will clarify the arrangement.)

      Vance shepherded us ceremoniously to chairs, and cocked his eye at the Sergeant.

      “You will be so good as to rest here until you hear me knock at the side door. Then come and open it for me.” He went toward the archway. “Once more I personate the departed Mr. Skeel; so picture me again en grande tenue—sartorially radiant. . . . The curtain ascends.”

      He bowed and, stepping from the reception-room into the main hall, disappeared round the corner into the rear passageway.

      Heath shifted his position restlessly and gave Markham a questioning, troubled look.

      “Will he pull it off, sir, do you think?” All jocularity had gone out of his tone.

      “I can’t see how.” Markham was scowling. “If he does, though, it will knock the chief underpinning from your theory of Jessup’s guilt.”

      “I’m not worrying,” declared Heath. “Mr. Vance knows a lot; he’s got ideas. But how in hell——?”

      He was interrupted by a loud knocking on the side door. The three of us sprang up simultaneously and hurried round the corner of the main hall. The rear passageway was empty. There was no door or aperture of any kind on either side of it. It consisted of two blank walls; and at the end, occupying almost its entire width, was the oak door which led to the court. Vance could have disappeared only through that oak door. And the thing we all noticed at once—for our eyes had immediately sought it—was the horizontal position of the bolt-handle. This meant that the door was bolted.

      Heath was not merely astonished—he was dumb-founded. Markham had halted abruptly, and stood staring down the empty passageway as if he saw a ghost. After a momentary hesitation Heath walked rapidly to the door. But he did not open it at once. He went down on his knees before the lock and scrutinized the bolt carefully. Then he took out his pocket-knife and inserted the blade into the crack between the door and the casing. The point halted against the inner moulding, and the edge of the blade scraped upon the circular bolt. There was no question that the heavy oak casings and mouldings of the door were solid and well fitted, and that the bolt had been securely thrown from the inside. Heath, however, was still suspicious, and, grasping the door-knob, he tugged at it violently. But the door held firmly. At length he threw the bolt-handle to a vertical position and opened the door. Vance was standing in the court, placidly smoking and inspecting the brickwork of the alley wall.

      “I say, Markham,” he remarked, “here’s a curious thing. This wall, d’ ye know, must be very old. It wasn’t built in these latter days of breathless efficiency. The beauty-loving mason who erected it laid the bricks in Flemish bond instead of the Running—or Stretcher—bond of our own restless age. And up there a bit”—he pointed toward the rear yard—“is a Rowlock and Checkerboard pattern. Very neat and very pretty—more pleasing even than the popular English Cross bond. And the mortar joints are all V-tooled. . . . Fancy!”

      Markham was fuming.

      “Damn it, Vance! I’m not building brick walls. What I want to know is how you got out here and left the door bolted on the inside.”

      “Oh, that!” Vance crushed out his cigarette and re-entered the building. “I merely made use of a bit of clever criminal mechanism. It’s very simple, like all truly effective appliances—oh, simple beyond words. I blush at its simplicity. . . . Observe!”

      He took from his pocket a tiny pair of tweezers to the end of which was tied a piece of purple twine about four feet long. Placing the tweezers over the vertical bolt-handle, he turned them at a very slight angle to the left and then ran the twine under the door so that about a foot of it projected over the sill. Stepping into the court, he closed the door. The tweezers still held the bolt-handle as in a vise, and the string extended straight to the floor and disappeared under the door into the court. The three of us stood watching the bolt with fascinated attention. Slowly the string became taut, as Vance gently pulled upon the loose end outside, and then the downward tug began slowly but surely to turn the bolt-handle. When the bolt had been thrown and the handle was in a horizontal position, there came a slight jerk on the string. The tweezers were disengaged from the bolt-handle, and fell noiselessly to the carpeted floor. Then as the string was pulled from without, the tweezers disappeared under the crack between the bottom of

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