The very next morning his prognostication was verified. We went to Markham's office at eleven o'clock to hear Heath's report and to discuss further lines of action. Though nine days had passed since Robin had been found murdered, no progress had been made in the case, and the newspapers had grown bitter in their criticisms of the police and the District Attorney's office. It was therefore with considerable depression that Markham greeted us that Monday morning. Heath had not yet arrived; but when he came a few minutes later it was obvious that he, too, was discouraged.
"We run up against a brick wall, sir, every way we turn," he repined, when he had outlined the results of his men's activities. "There ain't a sign of a motive, and outside of Sperling there's nobody on the landscape that we can hang anything on. I'm coming to the conclusion that it was some stick-up man who ambled into the archery-room that morning and messed things up."
"'Stick-up' men, Sergeant," countered Vance, "are deuced unimaginative, and they're without a sense of humor; whereas the johnny who sent Robin on the long, long trail had both imagination and humor. He wasn't content merely to kill Robin: he had to turn the act into an insane joke. Then, lest the public wouldn't see the point, he wrote explanat'ry letters to the press.—Does that sound like the procedure of an itinerant thug?"
Heath smoked unhappily for several minutes without speaking, and at length turned a gaze of exasperated dismay upon Markham.
"There's no sense in anything that's breaking round this town lately," he complained. "Just this morning a guy named Sprigg was shot in Riverside Park, up near 84th Street. Money in his pocket—nothing taken. Just shot. Young fella—student at Columbia. Lived with his parents; no enemies. Went out to take his usual walk before going to class. Found dead half an hour later by a bricklayer." The Sergeant chewed viciously on his cigar. "Now we got that homicide to worry about; and we'll probably get hell from the newspapers if we don't clear it up pronto. And there's nothing—absolutely nothing—to go on."
"Still, Sergeant," said Vance consolingly, "shooting a man is an ordin'ry event. There are numerous commonplace reasons for that sort of crime. It's the scenic and dramatic appurtenances of Robin's murder that play havoc with all our processes of deduction. If only it wasn't a nursery affair—"
Suddenly he stopped speaking, and his eyelids drooped slightly. Leaning forward he very deliberately crushed out his cigarette.
"Did you say, Sergeant, that this chap's name was Sprigg?"
Heath nodded gloomily.
"And I say,"—despite Vance's effort, there was a note of eagerness in his tone—"what was his first name?"
Heath gave Vance a look of puzzled surprise; but after a brief pause he drew forth his battered notebook and riffled the pages.
"John Sprigg," he answered. "John E. Sprigg."
Vance took out another cigarette, and lighted it with great care.
"And tell me: was he shot with a .32?"
"Huh?" Heath's eyes rounded, and his chin shot forward. "Yes, a .32. . . ."
"And was he shot through the top of his head?"
The Sergeant sprang to his feet, and stared at Vance with ludicrous bewilderment. Slowly his head moved up and down.
"That's right.—But how in hell, sir?"
Vance held up a silencing hand. It was, however, the look on his face, rather than his gesture, that cut short the query.
"Oh, my precious aunt!" He rose like a man in a daze and gazed fixedly before him. Had I not known him so well I would have sworn he was frightened. Then going to the tall window behind Markham's desk he stood looking down on the gray stone walls of the Tombs.
"I can't credit it," he murmured. "It's too ghastly. . . . But of course it's so! . . ."
Markham's impatient voice sounded.
"What's all this mumbling about, Vance? Don't be so damned mysterious! How did you happen to know that Sprigg was shot through the crown with a .32? And what's the point, anyway?"
Vance turned and met Markham's eyes.
"Don't you see?" he asked softly. "It's the second act of this devilish parody! . . . Have you forgotten your 'Mother-Goose'?" And in a hushed voice that brought a sense of unutterable horror into that dingy old office he recited:
"'There was a little man,
And he had a little gun,
And his bullets were made of lead, lead, lead;
He shot Johnny Sprig
Through the middle of his wig,
And knocked it right off of his head, head, head.'"
9. THE TENSOR FORMULA
(Monday, April 11; 11.30 a.m.)
Markham sat staring at Vance like a man hypnotized. Heath stood rigid, his mouth partly open, his cigar held a few inches from his lips. There was something almost comic in the Sergeant's attitude, and I had a nervous inclination to laugh; but for the moment my blood seemed frozen, and all muscular movement was impossible.
Markham was the first to speak. Jerking his head backward, he brought his hand down violently on the desk-top.
"What new lunacy of yours is this?" He was fighting desperately against Vance's dumbfounding suggestion. "I'm beginning to think the Robin case has affected your mind. Can't a man with the commonplace name of Sprigg be shot without your trying to turn it into some grotesque hocus-pocus?"
"Still, you must admit, Markham old dear," returned Vance mildly, "this particular Johnny Sprigg was shot with 'a little gun', through 'the middle of his wig', so to speak."
"What if he was?" A dull flush had crept into Markham's face. "Is that any reason for your going about babbling Mother-Goose rhymes?"
"Oh, I say! I never babble, don't y' know."
Vance had dropped into a chair facing the District Attorney's desk. "I may not be a thrillin' elocutionist; but really, now, I don't babble." He gave Heath an ingratiating smile. "Do I, Sergeant?"
But Heath had no opinion to express. He still held his astonished pose, though his eyes had now become mere slits in his broad, pugnacious face.
"Are you seriously suggesting—?" began Markham; but Vance interrupted him.
"Yes! I'm seriously suggesting that the person who killed Cock Robin with an arrow has vented his grim humor upon the hapless Sprigg. Coincidence is out of the question. Such repetitive parallels would knock the entire foundation out from all sanity and reason. 'Pon my soul, the world is mad enough; but such madness would dissipate all science and rational thinking. Sprigg's death is rather hideous; but it must be faced. And however much you may force yourself to protest against its incredible implications you'll eventually have to accept them."
Markham had risen, and was pacing nervously up and down.
"I'll grant there are inexplicable elements in this new crime." His combativeness had gone, and his tone had moderated. "But if we assume, even tentatively, that some maniac is at large reconstructing the rhymes of his nursery days, I can't see how it will help us. It would practically close all routine lines of investigation."
"I shouldn't say that, don't y' know." Vance was smoking meditatively. "I'm inclined to think that such an assumption would supply us with a definite basis of inquiry."
"Sure!" snapped Heath with ponderous sarcasm. All we gotta do is to go out and find one bug among six million people. A cinch!"
"Don't let the fumes of discouragement overcome you, Sergeant. Our elusive jester is a rather distinctive entomological specimen. Moreover, we have certain clews as to his exact habitat. . . ."
Markham swung round. "What do you mean by that?"
"Merely that this second crime is related to the first not only psychologically, but geographically. Both murders were committed within a few blocks of each other,—our destructive demon at least has a weakness for the neighborhood in which the Dillard house is situated. Furthermore, the very factors of the two murders preclude the possibility of his having come from afar to give rein to his distorted humor in unfamiliar surroundings. As I learnedly pointed out to you, Robin was translated into the Beyond by some one who knew all the conditions obtaining at
the Dillard house at the exact hour the grisly drama was performed; and surely it's obvious that this second crime could not have been so tidily staged had not the impresario been acquainted with Sprigg's ambulat'ry intentions this morning. Indeed, the entire mechanism of these weird playlets proves that the operator was intimately cognizant of all the circumstances surrounding his victims."
The heavy silence that followed was broken by Heath.
"If you're right, Mr. Vance, then that lets Sperling out." The Sergeant made even this qualified admission reluctantly; but it showed that Vance's argument had not been without its effect on him. He turned desperately to the District Attorney. "What do you think we'd better do, sir?"
Markham was still battling against the acceptance of Vance's theory, and he did not answer. Presently, however, he reseated himself at his desk and drummed with his fingers upon the blotter. Then, without looking up, he asked:
"Who's in charge of the Sprigg case, Sergeant?"
"Captain Pitts. The local men at the 68th-Street Station grabbed it first; but when the news was relayed to the Bureau, Pitts and a couple of our boys went up to look into it. Pitts got back just before I came over here. Says it's a washout. But Inspector Moran[15] told him to stay with it."
Markham pressed the buzzer beneath the edge of his desk, and Swacker, his youthful secretary, appeared at the swinging door that led to the clerical room between the District Attorney's private office and the main waiting-room.
"Get Inspector Moran on the wire," he ordered.
When the connection had been made he drew the telephone toward him and spoke for several minutes.
When he had replaced the receiver, he gave Heath a weary smile.
"You're now officially handling the Sprigg case, Sergeant. Captain Pitts will be here presently, and then we'll know where we stand." He began looking through a pile of papers before him. "I've got to be convinced," he added half-heartedly, "that Sprigg and Robin are tied up in the same sack."
Pitts, a short, stocky man, with a lean, hard face and a black tooth-brush moustache, arrived ten minutes later. He was, I learned afterwards, one of the most competent men in the Detective Division. His specialty was "white-collar" gangsters. He shook hands with Markham and gave Heath a companionable leer. When introduced to Vance and me he focussed suspicious eyes on us and bowed grudgingly. But as he was about to turn away his expression suddenly changed.
"Mr. Philo Vance, is it?" he asked.
"Alas! So it seems, Captain," Vance sighed.
Pitts grinned and, stepping forward, held out his hand.
"Glad to meet you, sir. Heard the Sergeant speak of you often."
"Mr. Vance is helping us unofficially with the Robin case, Captain," explained Markham; "and since this man Sprigg was killed in the same neighborhood we thought we'd like to hear your preliminary report on the affair." He took out a box of Corona Perfectos, and pushed it across the desk.
"You needn't put the request that way, sir." The Captain smiled, and selecting a cigar held it to his nose with a kind of voluptuous satisfaction. "The Inspector told me you had some ideas about this new case, and wanted to take it on. To tell you the truth, I'm glad to get rid of it." He sat down leisurely, and lighted his cigar. "What would you like to know, sir?"
"Let us have the whole story," said Markham.
Pitts settled himself comfortably.
"Well, I happened to be on hand when the case came through—a little after eight this morning—and I took a couple of the boys and beat it up-town. The local men were on the job, and an assistant Medical Examiner arrived the same time I did. . . ."
"Did you hear his report, Captain?" asked Vance.
"Sure. Sprigg was shot through the top of the head with a .32. No signs of a struggle—no bruises or anything. Nothing fancy. Just a straight shooting."
"Was he lying on his back when found?"
"That's right. Stretched out nice and pretty, right in the middle of the walk."
"And wasn't his skull fractured where he'd fallen on the asphalt?" The question was put negligently.
Pitts took his cigar from his mouth and gave Vance a sly look.
"I guess maybe you fellows over here do know something about this case." He nodded his head sagaciously. "Yes, the back of the guy's skull was all bashed in. He sure had a tough fall. But I guess he didn't feel it—not with that bullet in his brain. . . ."
"Speaking of the shot, Captain, didn't anything about it strike you as peculiar?"
"Well . . . yes," Pitts admitted, rolling his cigar meditatively between his thumb and forefinger. "The top of a guy's head isn't where I'd ordinarily look for a bullet-hole. And his hat wasn't touched,—it must have fallen off before he was potted. You might call those facts peculiar, Mr. Vance."
"Yes, Captain, they're dashed peculiar. . . . And I take it the pistol was held at close range."
"Not more'n a couple of inches away. The hair was singed round the hole." He made a broad gesture of inconsequence. "Still and all, the guy might have seen the other fellow draw the gun, and ducked forward, spilling his hat. That would account for his getting the shot at close range in the top of the head."
"Quite, quite. Except that, in that case, he wouldn't have fallen over back, but would have pitched forward on his face. . . . But go on with the story, Captain."
Pitts gave Vance a look of crafty agreement, and continued.
"The first thing I did was to go through the fellow's pockets. He had a good gold watch on him and about fifteen dollars in bills and silver. So it didn't look like a robbery—unless the guy that shot him got panicky and beat it. But that didn't seem likely, for there's never any one round that part of the park early in the morning; and the walk there dips under a stone bluff, so that the view is cut off. The bird that did the job certainly picked a swell place for it. . . . Anyhow, I left a couple of men to guard the body till the wagon came for it, and went up to Sprigg's house in 93rd Street,—I'd got his name and address from a couple of letters in his pocket. I found out he was a student at Columbia, living with his parents, and that it was his habit to take a walk in the park after breakfast. He left home this morning about half past seven. . . ."
"Ah! It was his habit to promenade in the park each morning," murmured Vance. "Most interestin'."
"Even so, that don't get us anywheres," returned Pitts. "Plenty of fellows take an early constitutional. And there was nothing unusual about Sprigg this morning. He wasn't worried about anything, his folks told me; and was cheerful enough when he said good-bye to 'em.—After that I hopped up to the university and made inquiries; talked to a couple of the students that knew him, and also to one of the instructors. Sprigg was a quiet sort of chap. Didn't make friends and kept pretty much to himself. Serious bird—always working at his studies. Stood high in his classes, and was never seen going around with Janes. Didn't like women, in fact. Wasn't what you'd call sociable. From all reports he was the last man to get in a mess of any kind. That's why I can't see anything special in his getting shot. It must have been an accident of some kind. Might have been taken for somebody else."
"And he was found at what time?"
"About quarter of eight. A bricklayer on the new 79th-Street dock was cutting across the embankment toward the railway tracks, and saw him. He notified one of the post officers on the Drive, who phoned in to the local station."
"And Sprigg left his home in 93rd Street at half past seven." Vance gazed at the ceiling meditatively. "Therefore he would have had just enough time to reach this point in the park before being killed. It looks as if some one who knew his habits was waiting for him. Neatness and dispatch, what? . . . It doesn't appear exactly fortuitous, does it, Markham?"
Ignoring the jibe Markham addressed Pitts.
"Was there nothing found that could possibly be used as a lead?"
"No, sir. My men combed the spot pretty thoroughly, but nothing showed up."
"And in Sprigg's pockets—among his papers. . . ?"
"Not
a thing. I've got all the stuff at the Bureau—a couple of ordinary letters, a few odds and ends of the usual kind. . . ." He paused as if suddenly remembering something, and pulled out a dog-eared note-book. "There was this," he said unenthusiastically, handing a torn, triangular scrap of paper to Markham. "It was found under the fellow's body. It don't mean anything, but I stuck it in my pocket—force of habit."
The paper was not more than four inches long, and appeared to have been torn from the corner of an ordinary sheet of unruled stationery. It contained part of a typewritten mathematical formula, with the lambda, the equals and the infinity sign marked in with pencil. I reproduce the paper here, for, despite its seeming irrelevancy, it was to play a sinister and amazing part in the investigation of Sprigg's death.
Vance glanced only casually at the exhibit, but Markham held it in his hand frowning at it for several moments. He was about to make some comment when he caught Vance's eye; and, instead, he tossed the paper to the desk carelessly with a slight shrug.
"Is this everything you found?"
"That's all, sir."
Markham rose.
"We're very grateful to you, Captain. I don't know what we'll be able to make out of this Sprigg case, but we'll look into it." He pointed to the box of Perfectos. "Put a couple in your pocket before you go."
"Much obliged, sir." Pitts selected the cigars, and placing them tenderly in his waistcoat pocket, shook hands with all of us.
When he had gone Vance got up with alacrity, and bent over the scrap of paper on Markham's desk.
"My word!" He took out his monocle and studied the symbols for several moments. "Most allurin'. Now where have I seen that formula recently? . . . Ah! The Riemann-Christoffel tensor—of course! Drukker uses it in his book for determining the Gaussian curvature of spherical and homaloidal space. . . . But what was Sprigg doing with it? The formula is considerably beyond the college curricula. . . ." He held the paper up to the light. "It's the same stock as that on which the Bishop notes are written. And you probably observed that the typing is also similar."
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