Markham, walking up and down earnestly, continued: "The features of the situation revolving round these inferable facts are as follows:, There was no one hiding in the apartment at seven o'clock, the hour the maid went home. Therefore, the murderer entered the apartment later. First, then, let us consider the side door. At six o'clock, an hour before the maid's departure, the janitor bolted it on the inside, and both operators disavow emphatically that they went near it. Moreover, you, Sergeant, found it bolted this morning. Hence, we may a.s.sume that the door was bolted on the inside all night, and that n.o.body could have entered that way. Consequently, we are driven to the inevitable alternative that the murderer entered by the front door. Now, let us consider this other means of entry.

The phone operator who was on duty until ten o'clock last night a.s.serts positively that the only person who entered the front door and pa.s.sed down the main hall to this apartment was a man who rang the bell and, getting no answer, immediately walked out again. The other operator, who was on duty from ten o'clock until this morning, a.s.serts with equal positiveness that no one entered the front door and pa.s.sed the switchboard coming to this apartment. Add to all this the fact that every window on this floor is barred, and that no one from upstairs can descend into the main hall without coming face to face with the operator, and we are, for the moment, confronted with an impa.s.se."

Heath scratched his head and laughed mirthlessly. "It don't make sense, does it, sir?"

"What about the next apartment?" asked Vance, "the one with the door facing the rear pa.s.sageway, No. 2, I think?"

Heath turned to him patronizingly. "I looked into that the first thing this morning. Apartment No. 2 is occupied by a single woman; and I woke her up at eight o'clock and searched the place. Nothing there. Anyway, you have to walk past the switchboard to reach her apartment the same as you do to reach this one; and n.o.body called on her or left her apartment last night. What's more, Jessup, who's a shrewd sound lad, told me this woman is a quiet, ladylike sort, and that she and Odell didn't even know each other."

"You're so thorough, Sergeant!" murmured Vance.

"Of course," put in Markham, "it would have been possible for someone from the other apartment to have slipped in here behind the operator's back between seven and eleven, and then to have slipped back after the murder. But as Sergeant Heath's search this morning failed to uncover anyone, we can eliminate the possibility of our man having operated from that quarter."

"I dare say you're right," Vance indifferently admitted. "But it strikes me, Markham old dear, that your own affectin' recapitulation of the situation jolly well eliminates the possibility of your man's having operated from any quarter. . . . And yet he came in, garroted the unfortunate damsel, and departed, eh, what? . . . It's a charmin' little problem. I wouldn't have missed it for worlds."

"It's uncanny," p.r.o.nounced Markham gloomily.

"It's positively spiritualistic," amended Vance. "It has the caressin' odor of a seance. Really, y' know, I'm beginning to suspect that some medium was hovering in the vicinage last night doing some rather tip-top materializations. . . . I say, Markham, could you get an indictment against an ectoplasmic emanation?"

"It wasn't no spook that made those fingerprints," growled Heath, with surly truculence.

Markham halted his nervous pacing and regarded Vance irritably.

"d.a.m.n it! This is rank nonsense. The man got in some way, and he got out, too. There's something wrong somewhere. Either the maid is mistaken about someone being here when she left, or else one of those phone operators went to sleep and won't admit it."

"Or else one of 'em's lying," supplemented Heath.

Vance shook his head. "The dusky fille de chambre, I'd say, is eminently trustworthy. And if there was any doubt about anyone's having come in the front door unnoticed, the lads on the switchboard would, in the present circ.u.mstances, be only too eager to admit it. . . . No, Markham, you'll simply have to approach this affair from the astral plane, so to speak."

Markham grunted his distaste of Vance's jocularity. "That line of investigation I leave to you with your metaphysical theories and esoteric hypotheses."

"But, consider," protested Vance banteringly. "You've proved conclusively, or, rather, you've demonstrated legally, that no one could have entered or departed from this apartment last night; and, as you've often told me, a court of law must decide all matters, not in accord with the known or suspected facts, but according to the evidence; and the evidence in this case would prove a sound alibi for every corporeal being extant. And yet, it's not exactly tenable, d' ye see, that the lady strangled herself. If only it had been poison, what an exquisite and satisfyin' suicide case you'd have! . . . Most inconsiderate of her homicidal visitor not to have used a.r.s.enic instead of his hands!"

"Well, he strangled her," p.r.o.nounced Heath. "Furthermore, I'll lay my money on the fellow who called here last night at half past nine and couldn't get in. He's the bird I want to talk to."

"Indeed?" Vance produced another cigarette. "I shouldn't say, to judge from our description of him, that his conversation would prove particularly fascinatin'."

An ugly light came into Heath's eyes. "We've got ways," he said through his teeth, "of getting d.a.m.n interesting conversation outta people who haven't no great reputation for repartee."

Vance sighed. "How the Four Hundred needs you, my Sergeant!"

Markham looked at his watch.

"I've got pressing work at the office," he said, "and all this talk isn't getting us anywhere." He put his hand on Heath's shoulder.

"I leave you to go ahead. This afternoon I'll have these people brought down to my office for another questioning, maybe I can jog their memories a bit. . . . You've got some line of investigation planned?"

"The usual routine," replied Heath drearily. "I'll go through Odell's papers, and I'll have three or four of my men check up on her."

"You'd better get after the Yellow Taxicab Company right away Markham suggested. "Find out, if you can, who the man was who left here at half past eleven last night, and where he went."

"Do you imagine for one moment," asked Vance, "that if this man knew anything about the murder, he would have stopped in the hall and asked the operator to call a taxi for him?"

"Oh, I don't look for much in that direction." Markham's tone was almost listless. "But the girl may have said something to him that'll give us a lead."

Vance shook his head facetiously. "O welcome pure-ey'd Faith, white-handed Hope, thou hovering angel, girt with golden wings!"

Markham was in no mood for chaffing. He turned to Heath, and spoke with forced cheeriness. "Call me up later this afternoon. I may get some new evidence out of the outfit we've just interviewed. . ..

And," he added, "be sure to put a man on guard here. I want this apartment kept just as it is until we see a little more light."

"I'll attend to that," Heath a.s.sured him.

Markham and Vance and I went out and entered the car. A few minutes later we were winding rapidly across town through Central Park.

"Recall our recent conversazione about footprints in the snow? asked Vance, as we emerged into Fifth Avenue and headed south.

Markham nodded abstractedly.

"As I remember," mused Vance, "in the hypothetical case you presented there were not only footprints but a dozen or more witnesses, including a youthful prodigy, who saw a figure of some kind cross the hibernal landscape. . . . Grau, teurer Freund, ist alle Theorie! Here you are in a most beastly pother because of the disheartenin' fact that there are neither footprints in the snow nor witnesses who saw a fleeing figure. In short, you are bereft of both direct and circ.u.mstantial evidence. . . . Sad, sad."

He wagged his head dolefully.

"Y' know, Markham, it appears to me that the testimony in this case const.i.tutes conclusive legal proof that no one could have been with the deceased at the hour of her pa.s.sing, and that, ergo, she is presumably alive. The strangled body of the lady is, I take it, simply an irrelevant circ.u.mstance from the standpoint of legal procedure. I know that you learned lawyers won't admit a murder without a body; but how, in sweet Heaven's name, do you get around a corpus delicti without a murder?"

"You're talking nonsense," Markham rebuked him, with a show of anger.

"Oh, quite," agreed Vance. "And yet, it's a distressin' thing for a lawyer not to have footprints of some kind, isn't it, old dear? It leaves one so up in the air."

Suddenly Markham swung round. "YOU, of course, don't need footprints, or any other kind of material clues," he flung at Vance tauntingly. "YOU have powers of divination such as are denied ordinary mortals. If I remember correctly, you informed me, somewhat grandiloquently, that, knowing the nature and conditions of a crime, you could lead me infallibly to the culprit, whether he left footprints or not. You recall that boast? . . . Well, here's a crime, and the perpetrator left no footprints coming or going. Be so kind as to end my suspense by confiding in me who killed the Odell girl."

Vance's serenity was not ruffled by Markham's ill-humored challenge.

He sat smoking lazily for several minutes; then he leaned over and flicked his cigarette ash out of the window.

"'Pon my word, Markham," he rejoined evenly, "I'm half inclined to look into this silly murder. I think I'll wait, though, and see whom the nonplussed Heath turns up with his inquiries."

Markham grunted scoffingly and sank back on the cushions. "Your generosity wrings me," he said.

THE PACK IN FULL CRY (Tuesday, September 11; afternoon) On our way downtown that morning we were delayed for a considerable time in the traffic congestion just north of Madison Square, and Markham anxiously looked at his watch.

"It's past noon," he said. "I think I'll stop at the club and have a bite of lunch. . . . I presume that eating at this early hour would be too plebeian for so exquisite a hothouse flower as you."

Vance considered the invitation.

"Since you deprived me of my breakfast," he decided, "I'll permit you to buy me some eggs Benedictine."

A few minutes later we entered the almost empty grill of the Stuyvesant Club and took a table near one of the windows looking southward over the treetops of Madison Square.

Shortly after we had given our order a uniformed attendant entered and, bowing deferentially at the district attorney's elbow, held out an unaddressed communication sealed in one of the club's envelopes.

Markham read it with an expression of growing curiosity, and as he studied the signature a look of mild surprise came into his eyes.

At length he looked up and nodded to the waiting attendant. Then, excusing himself, he left us abruptly. It was fully twenty minutes before he returned.

"Funny thing," he said. "That note was from the man who took the Odell woman to dinner and the theater last night. . . . A small world," he mused. "He's staying here at the club, he's a nonresident member and makes it his headquarters when he's in town."

"You know him?" Vance put the question disinterestedly.

"I've met him several times, chap named Spotswoode." Markham seemed perplexed. "He's a man of family, lives in a country house on Long Island, and is regarded generally as a highly respectable member of society, one of the last persons I'd suspect of being mixed up with the Odell girl. But, according to his own confession, he played around a good deal with her during his visits to New York, 'sowing a few belated wild oats,' as he expressed it, and last night took her to Francelle's for dinner and to the Winter Garden afterwards."

"Not my idea of an intellectual, or even edifyin', evening commented Vance. "And he selected a deuced unlucky day for it I say, imagine opening the morning paper and learning that your pet.i.te dame of the preceding evening had been strangled! Disconcertin', what?"

"He's certainly disconcerted," said Markham. "The early afternoon papers were out about an hour ago, and he'd been phoning my office every ten minutes, when I suddenly walked in here. He's afraid his connection with the girl will leak out and disgrace him."

"And won't it?"

"I hardly see the necessity. No one knows who her escort was last evening; and since he obviously had nothing to do with the crime, what's to be gained by dragging him into it? He told me the whole story, and offered to stay in the city as long as I wanted him to."

"I infer, from the cloud of disappointment that enveloped you when you returned just now, that his story held nothing hopeful for you in the way of clues."

"No," Markham admitted. "The girl apparently never spoke to him of her intimate affairs; and he couldn't give me a single helpful suggestion. His account of what happened last night agreed perfectly with Jessup's. He called for the girl at seven, brought her home at about eleven, stayed with her half an hour or so, and then left her. When he heard her call for help, he was frightened, but on being a.s.sured by her there was nothing wrong, he concluded she had dozed off into a nightmare, and thought no more of it. He drove direct to the club here, arriving about ten minutes to twelve.

Judge Redfern, who saw him descend from the taxi, insisted on his coming upstairs and playing poker with some men who were waiting in the judge's rooms for him. They played until three o'clock this morning."

"Your Long Island Don Juan has certainly not supplied you with any footprints in the snow."

"Anyway, his coming forward at this time closes one line of inquiry over which we might have wasted considerable time."

"If many more lines of inquiry are closed," remarked Vance dryly, "you'll be in a distressin' dilemma, don't y' know."

"There are enough still open to keep me busy," said Markham, pushing back his plate and calling for the check. He rose; then pausing, regarded Vance meditatingly. "Are you sufficiently interested to want to come along?"

"Eh, what? My word! . . . Charmed, I'm sure. But, I say, sit down just a moment, there's a good fellow!, till I finish my coffee."

I was considerably astonished at Vance's ready acceptance, careless and bantering though it was, for there was an exhibition of old Chinese prints at the Montross Galleries that afternoon, which he had planned to attend. A Riokai and a Moyeki, said to be very fine examples of Sung painting, were to be shown; and Vance was particularly eager to acquire them for his collection.

We rode with Markham to the Criminal Courts building and, entering by the Franklin Street door, took the private elevator to the district attorney's s.p.a.cious but dingy private office, which overlooked the gray-stone ramparts of the Tombs. Vance seated himself in one of the heavy leather-upholstered chairs near the carved oak table on the right of the desk and lighted a cigarette with an air of cynical amus.e.m.e.nt.

"I await with antic.i.p.at'ry delight the grinding of the wheels of justice," he confided, leaning back lazily.