A Project Gutenberg of Australia eBook

Title:      The Bishop Murder Case (A Philo Vance Story)(1928)
Author:     S. S. Van Dine
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Date first posted:          March 2002
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A Project Gutenberg of Australia eBook

Title:      The Bishop Murder Case (A Philo Vance Story)(1928)
Author:     S. S. Van Dine



The Earth is a Temple where there is going on a Mystery Play,
childish and poignant, ridiculous and awful enough in all
conscience.--Conrad.



CONTENTS


CHAPTER

I.  "WHO KILLED COCK ROBIN?"

II.  ON THE ARCHERY RANGE

III.  A PROPHECY RECALLED

IV.  A MYSTERIOUS NOTE

V.  A WOMAN'S SCREAM

VI.  "'I,' SAID THE SPARROW"

VII.  VANCE REACHES A CONCLUSION

VIII.  ACT TWO

IX.  THE TENSOR FORMULA

X.  A REFUSAL OF AID

XI.  THE STOLEN REVOLVER

XII.  A MIDNIGHT CALL

XIII.  IN THE BISHOP'S SHADOW

XIV.  A GAME OF CHESS

XV.  AN INTERVIEW WITH PARDEE

XVI.  ACT THREE

XVII.  AN ALL-NIGHT LIGHT

XVIII.  THE WALL IN THE PARK

XIX.  THE RED NOTE-BOOK

XX.  THE NEMESIS

XXI.  MATHEMATICS AND MURDER

XXII.  THE HOUSE OF CARDS

XXIII.  A STARTLING DISCOVERY

XXIV.  THE LAST ACT

XXV.  THE CURTAIN FALLS

XXVI.  HEATH ASKS A QUESTION




CHARACTERS OF THE BOOK


PHILO VANCE

JOHN F.-X. MARKHAM
District Attorney of New York County.

ERNEST HEATH
Sergeant of the Homicide Bureau.

PROFESSOR BERTRAND DILLARD
A famous physicist.

BELLE DILLARD
His niece.

SIGURD ARNESSON
His adopted son: an associate professor of mathematics.

PYNE
The Dillard butler.

BEEDLE
The Dillard cook.

ADOLPH DRUKKER
Scientist and author.

MRS. OTTO DRUKKER
His mother.

GRETE MENZEL
The Drukker cook.

JOHN PARDEE
Mathematician and chess expert: inventor of the Pardee gambit.

J. C. ROBIN
Sportsman and champion archer.

RAYMOND SPERLING
Civil Engineer.

JOHN E. SPRIGG
Senior at Columbia University.

DR. WHITNEY BARSTEAD
An eminent neurologist.

QUINAN
Police Reporter of the World.

MADELEINE MOFFAT

CHIEF INSPECTOR O'BRIEN
Of the Police Department of New York City.

WILLIAM M. MORAN
Commanding Officer of the Detective Bureau.

CAPTAIN PITTS
Of the Homicide Bureau.

GUILFOYLE
Detective of the Homicide Bureau.

SNITKIN
Detective of the Homicide Bureau.

HENNESSEY
Detective of the Homicide Bureau.

EMERY
Detective of the Homicide Bureau.

BURKE
Detective of the Homicide Bureau.

CAPTAIN DUBOIS
Finger-print expert.

DR. EMANUEL DOREMUS
Medical Examiner.

SWACKER
Secretary to the District Attorney.

CURRIE
Vance's valet.




THE BISHOP MURDER CASE



CHAPTER I

"WHO KILLED COCK ROBIN?"


(Saturday, April 2; noon)


Of all the criminal cases in which Philo Vance participated as an
unofficial investigator, the most sinister, the most bizarre, the
seemingly most incomprehensible, and certainly the most terrifying,
was the one that followed the famous Greene murders.*  The orgy of
horror at the old Greene mansion had been brought to its astounding
close in December; and after the Christmas holidays Vance had gone
to Switzerland for the winter sports.  Returning to New York at the
end of February he had thrown himself into some literary work he
had long had in mind--the uniform translation of the principal
fragments of Menander found in the Egyptian papyri during the early
years of the present century; and for over a month he had devoted
himself sedulously to this thankless task.


* "The Greene Murder Case"  (Scribner's 1928)


Whether or not he would have completed the translations, even had
his labors not been interrupted, I do not know; for Vance was a man
of cultural ardencies, in whom the spirit of research and
intellectual adventure was constantly at odds with the drudgery
necessary to scholastic creation.  I remember that only the
preceding year he had begun writing a life of Xenophon--the result
of an enthusiasm inherited from his university days when he had
first read the Anabasis and the Memorabilia--and had lost interest
in it at the point where Xenophon's historic march led the Ten
Thousand back to the sea.  However, the fact remains that Vance's
translation of Menander was rudely interrupted in early April; and
for weeks he became absorbed in a criminal mystery which threw the
entire country into a state of gruesome excitement.

This new criminal investigation, in which he acted as a kind of
amicus curiae for John F.-X. Markham, the District Attorney of New
York, at once became known as the Bishop murder case.  The
designation--the result of our journalistic instinct to attach
labels to every cause célèbre--was, in a sense, a misnomer.  There
was nothing ecclesiastical about that ghoulish saturnalia of crime
which set an entire community to reading the "Mother Goose
Melodies" with fearful apprehension;* and no one of the name of
Bishop was, as far as I know, even remotely connected with the
monstrous events which bore that appellation.  But, withal, the
word "Bishop" was appropriate, for it was an alias used by the
murderer for the grimmest of purposes.  Incidentally it was this
name that eventually led Vance to the almost incredible truth, and
ended one of the most ghastly multiple crimes in police history.


* Mr. Joseph A. Margolies of Brentano's told me that for a period
of several weeks during the Bishop murder case more copies of
"Mother Goose Melodies" were sold than of any current novel.  And
one of the smaller publishing houses reprinted and completely sold
out an entire edition of those famous old nursery rhymes.


The series of uncanny and apparently unrelated events which
constituted the Bishop murder case and drove all thought of
Menander and Greek monostichs from Vance's mind, began on the
morning of April 2, less than five months after the double shooting
of Julia and Ada Greene.  It was one of those warm luxurious spring
days which sometimes bless New York in early April; and Vance was
breakfasting in his little roof garden atop his apartment in East
38th Street.  It was nearly noon--for Vance worked or read until
all hours, and was a late riser--and the sun, beating down from a
clear blue sky, cast a mantle of introspective lethargy over the
city.  Vance sprawled in an easy chair, his breakfast on a low
table beside him, gazing with cynical, regretful eyes down at the
treetops in the rear yard.

I knew what was in his mind.  It was his custom each spring to go
to France; and it had long since come to him to think, as it came
to George Moore, that Paris and May were one.  But the great trek
of the post-war American nouveaux riches to Paris had spoiled his
pleasure in this annual pilgrimage; and, only the day before, he
had informed me that we were to remain in New York for the summer.

For years I had been Vance's friend and legal adviser--a kind of
monetary steward and agent-companion.  I had quitted my father's
law firm of Van Dine, Davis & Van Dine to devote myself wholly to
his interests--a post I found far more congenial than that of
general attorney in a stuffy office--and though my own bachelor
quarters were in a hotel on the West Side, I spent most of my time
at Vance's apartment.

I had arrived early that morning, long before Vance was up, and,
having gone over the first-of-the-month accounts, now sat smoking
my pipe idly as he breakfasted.

"Y' know, Van," he said to me, in his emotionless drawl; "the
prospect of spring and summer in New York is neither excitin' nor
romantic.  It's going to be a beastly bore.  But it'll be less
annoyin' than travelin' in Europe with the vulgar hordes of
tourists jostlin' one at every turn. . . .  It's very distressin'."

Little did he suspect what the next few weeks held in store for
him.  Had he known I doubt if even the prospect of an old pre-war
spring in Paris would have taken him away; for his insatiable mind
liked nothing better than a complicated problem; and even as he
spoke to me that morning the gods that presided over his destiny
were preparing for him a strange and fascinating enigma--one which
was to stir the nation deeply and add a new and terrible chapter to
the annals of crime.

Vance had scarcely poured his second cup of coffee when Currie, his
old English butler and general factotum, appeared at the French
doors bearing a portable telephone.

"It's Mr. Markham, sir," the old man said apologetically.  "As he
seemed rather urgent, I took the liberty of informing him you were
in."  He plugged the telephone into a baseboard switch, and set the
instrument on the breakfast table.

"Quite right, Currie," Vance murmured, taking off the receiver.
"Anything to break this deuced monotony."  Then he spoke to
Markham.  "I say, old man, don't you ever sleep?  I'm in the midst
of an omelette aux fines herbes.  Will you join me?  Or do you
merely crave the music of my voice--?"

He broke off abruptly, and the bantering look on his lean features
disappeared.  Vance was a marked Nordic type, with a long, sharply
chiselled face; gray, wide-set eyes; a narrow aquiline nose; and a
straight oval chin.  His mouth, too, was firm and clean-cut, but it
held a look of cynical cruelty which was more Mediterranean than
Nordic.  His face was strong and attractive, though not exactly
handsome.  It was the face of a thinker and recluse; and its very
severity--at once studious and introspective--acted as a barrier
between him and his fellows.

Though he was immobile by nature and sedulously schooled in the
repression of his emotions, I noticed that, as he listened to
Markham on the phone that morning, he could not entirely disguise
his eager interest in what was being told him.  A slight frown
ruffled his brow; and his eyes reflected his inner amazement.  From
time to time he gave vent to a murmured "Amazin'!" or "My word!" or
"Most extr'ordin'ry!"--his favorite expletives--and when at the end
of several minutes he spoke to Markham, a curious excitement marked
his manner.

"Oh, by all means!" he said.  "I shouldn't miss it for all the lost
comedies of Menander. . . .  It sounds mad. . . .  I'll don fitting
raiment immediately. . . .  Au revoir."

Replacing the receiver, he rang for Currie.

"My gray tweeds," he ordered.  "A sombre tie, and my black Homburg
hat."  Then he returned to his omelet with a preoccupied air.

After a few moments he looked at me quizzically.

"What might you know of archery, Van?" he asked.

I knew nothing of archery, save that it consisted of shooting
arrows at targets, and I confessed as much.

"You're not exactly revealin', don't y' know."  He lighted one of
his Régie cigarettes indolently.  "However, we're in for a little
flutter of toxophily, it seems.  I'm no leading authority on the
subject myself, but I did a bit of potting with the bow at Oxford.
It's not a passionately excitin' pastime--much duller than golf and
fully as complicated."  He smoked a while dreamily.  "I say, Van;
fetch me Doctor Elmer's tome on archery from the library--there's a
good chap."*


* The book Vance referred to was that excellent and comprehensive
treatise, "Archery," by Robert P. Elmer, M.D.


I brought the book, and for nearly half an hour he dipped into it,
tarrying over the chapters on archery associations, tournaments and
matches, and scanning the long tabulation of the best American
scores.  At length he settled back in his chair.  It was obvious he
had found something that caused him troubled concern and set his
sensitive mind to work.

"It's quite mad, Van," he remarked, his eyes in space.  "A
mediaeval tragedy in modern New York!  We don't wear buskins and
leathern doublets, and yet--BY JOVE!"  He suddenly sat upright.
"No--no!  It's absurd.  I'm letting the insanity of Markham's news
affect me. . . ."  He drank some more coffee, but his expression
told me that he could not rid himself of the idea that had taken
possession of him.

"One more favor, Van," he said at length.  "Fetch me my German
diction'ry and Burton E. Stevenson's 'Home Book of Verse.'"

When I had brought the volumes, he glanced at one word in the
dictionary, and pushed the book from him.

"That's that, unfortunately--though I knew it all the time."

Then he turned to the section in Stevenson's gigantic anthology
which included the rhymes of the nursery and of childhood.  After
several minutes he closed that book, too, and, stretching himself
out in his chair, blew a long ribbon of smoke toward the awning
overhead.

"It can't be true," he protested, as if to himself.  "It's too
fantastic, too fiendish, too utterly distorted.  A fairy tale in
terms of blood--a world in anamorphosis--a perversion of all
rationality. . . .  It's unthinkable, senseless, like black magic
and sorcery and thaumaturgy.  It's downright demented."

He glanced at his watch and, rising, went indoors, leaving me to
speculate vaguely on the cause of his unwonted perturbation.  A
treatise on archery, a German dictionary, a collection of
children's verses, and Vance's incomprehensible utterances
regarding insanity and fantasy--what possible connection could
these things have?  I attempted to find a least common denominator,
but without the slightest success.  And it was no wonder I failed.
Even the truth, when it came out weeks later bolstered up by an
array of incontestable evidence, seemed too incredible and too
wicked for acceptance by the normal mind of man.

Vance shortly broke in on my futile speculations.  He was dressed
for the street, and seemed impatient at Markham's delay in
arriving.

"Y' know, I wanted something to interest me--a nice fascinatin'
crime, for instance," he remarked; "but--my word!--I wasn't exactly
longin' for a nightmare.  If I didn't know Markham so well I'd
suspect him of spoofing."

When Markham stepped into the roof garden a few minutes later it
was only too plain that he had been in deadly earnest.  His
expression was sombre and troubled, and his usual cordial greeting
he reduced to the merest curt formality.  Markham and Vance had
been intimate friends for fifteen years.  Though of antipodal
natures--the one sternly aggressive, brusque, forthright, and
almost ponderously serious; the other whimsical, cynical, debonair,
and aloof from the transient concerns of life--they found in each
other that attraction of complementaries which so often forms the
basis of an inseparable and enduring companionship.

During Markham's year and four months as District Attorney of New
York he had often called Vance into conference on matters of grave
importance, and in every instance Vance had justified the
confidence placed in his judgments.  Indeed, to Vance almost
entirely belongs the credit for solving the large number of major
crimes which occurred during Markham's four years' incumbency.
His knowledge of human nature, his wide reading and cultural
attainments, his shrewd sense of logic, and his FLAIR for the
hidden truth beneath misleading exteriors, all fitted him for the
task of criminal investigator--a task which he fulfilled
unofficially in connection with the cases which came under
Markham's jurisdiction.

Vance's first case, it will be remembered, had to do with the
murder of Alvin Benson;* and had it not been for his participation
in that affair I doubt if the truth concerning it would ever have
come to light.  Then followed the notorious strangling of Margaret
Odell#--a murder mystery in which the ordinary methods of police
detection would inevitably have failed.  And last year the
astounding Greene murders (to which I have already referred) would
undoubtedly have succeeded had not Vance been able to frustrate
their final intent.


* "The Benson Murder Case"  (Scribners 1926)
# "The 'Canary' Murder Case"  (Scribners 1927)


It was not surprising, therefore, that Markham should have turned
to Vance at the very beginning of the Bishop murder case.  More and
more, I had noticed, he had come to rely on the other's help in his
criminal investigations; and in the present instance it was
particularly fortunate that he appealed to Vance, for only through
an intimate knowledge of the abnormal psychological manifestations
of the human mind, such as Vance possessed, could that black,
insensate plot have been contravened and the perpetrator unearthed.

"This whole thing may be a mare's-nest," said Markham, without
conviction.  "But I thought you might want to come along. . . ."

"Oh, quite!" Vance gave Markham a sardonic smile.  "Sit down a
moment and tell me the tale coherently.  The corpse won't run away.
And it's best to get our facts in some kind of order before we view
the remains.--Who are the parties of the first part, for instance?
And why the projection of the District Attorney's office into a
murder case within an hour of the deceased's passing?  All that
you've told me so far resolves itself into the utterest nonsense."

Markham sat down gloomily on the edge of a chair and inspected the
end of his cigar.

"Damn it, Vance!  Don't start in with a mysteries-of-Udolpho
attitude.  The crime--if it is a crime--seems clear-cut enough.
It's an unusual method of murder, I'll admit; but it's certainly
not senseless.  Archery has become quite a fad of late.  Bows and
arrows are in use to-day in practically every city and college in
America."

"Granted.  But it's been a long time since they were used to kill
persons named Robin."

Markham's eyes narrowed, and he looked at Vance searchingly.

"That idea occurred to you, too, did it?"

"Occurred to me?  It leapt to my brain the moment you mentioned the
victim's name."  Vance puffed a moment on his cigarette.  "'Who
Killed Cock Robin?'  And with a bow and arrow! . . .  Queer how the
doggerel learned in childhood clings to the memory.--By the by,
what was the unfortunate Mr. Robin's first name?"

"Joseph, I believe."

"Neither edifyin' nor suggestive. . . .  Any middle name?"

"See here, Vance!" Markham rose irritably.  "What has the murdered
man's middle name to do with the case?"

"I haven't the groggiest.  Only, as long as we're going insane we
may as well go the whole way.  A mere shred of sanity is of no
value."

He rang for Currie and sent him for the telephone directory.
Markham protested, but Vance pretended not to hear; and when the
directory arrived he thumbed its pages for several moments.

"Did the departed live on Riverside Drive?" he asked finally,
holding his finger on a name he had found.

"I think he did."

"Well, well."  Vance closed the book, and fixed a quizzically
triumphant gaze on the District Attorney.  "Markham," he said
slowly, "there's only one Joseph Robin listed in the telephone
direct'ry.  He lives on Riverside Drive, and his middle name is--
Cochrane!"

"What rot is this?"  Markham's tone was almost ferocious.  "Suppose
his name WAS Cochrane: are you seriously suggesting that the fact
had anything to do with his being murdered?"

"'Pon my word, old man, I'm suggesting nothing."  Vance shrugged
his shoulders slightly.  "I'm merely jotting down, so to speak, a
few facts in connection with the case.  As the matter stands now: a
Mr. Joseph Cochrane Robin--to wit: Cock Robin--has been killed by a
bow and arrow.--Doesn't that strike even your legal mind as deuced
queer?"

"No!"  Markham fairly spat the negative.  "The name of the dead man
is certainly common enough; and it's a wonder more people haven't
been killed or injured with all this revival of archery throughout
the country.  Moreover, it's wholly possible that Robin's death was
the result of an accident."

"Oh, my aunt!" Vance wagged his head reprovingly.  "That fact, even
were it true, wouldn't help the situation any.  It would only make
it queerer.  Of the thousands of archery enthusiasts in these fair
states, the one with the name of Cock Robin should be accidentally
killed with an arrow!  Such a supposition would lead us into
spiritism and demonology and whatnot.  Do you, by any chance,
believe in Eblises and Azazels and jinn who go about playing
Satanic jokes on mankind?"

"Must I be a Mohammedan mythologist to admit coincidences?"
returned Markham tartly.

"My dear fellow!  The proverbial long arm of coincidence doesn't
extend to infinity.  There are, after all, laws of probability,
based on quite definite mathematical formulas.  It would make me
sad to think that such men as Laplace* and Czuber and von Kries had
lived in vain.--The present situation, however, is even more
complicated than you suspect.  For instance, you mentioned over the
phone that the last person known to have been with Robin before his
death is named Sperling."


* Though Laplace is best known for his "Méchanique Céleste," Vance
was here referring to his masterly work, "Théorie Analytique des
Probabilités," which Herschel called "the ne plus ultra of
mathematical skill and power."


"And what esoteric significance lies in that fact?"

"Perhaps you know what Sperling means in German," suggested Vance
dulcetly.

"I've been to High School," retorted Markham.  Then his eyes opened
slightly, and his body became tense.

Vance pushed the German dictionary toward him.  "Well, anyway, look
up the word.  We might as well be thorough.  I looked it up myself.
I was afraid my imagination was playing tricks on me, and I had a
yearnin' to see the word in black and white."

Markham opened the book in silence, and let his eye run down the
page.  After staring at the word for several moments he drew
himself up resolutely, as if fighting off a spell.  When he spoke
his voice was defiantly belligerent.

"Sperling means 'sparrow.'  Any school boy knows that.  What of
it?"

"Oh, to be sure."  Vance lit another cigarette languidly.  "And any
school boy knows the old nursery rhyme entitled 'The Death and
Burial of Cock Robin,' what?"  He glanced tantalizingly at Markham,
who stood immobile, staring out into the spring sunshine.  "Since
you pretend to be unfamiliar with that childhood classic, permit me
to recite the first stanza."

A chill, as of some unseen spectral presence, passed over me as
Vance repeated those old familiar lines:


     "Who killed Cock Robin?
     'I,' said the sparrow,
     'With my bow and arrow.
      I killed Cock Robin.'"



CHAPTER II

ON THE ARCHERY RANGE


(Saturday, April 2; 12.30 p.m.)


Slowly Markham brought his eyes back to Vance.

"It's mad," he remarked, like a man confronted with something at
once inexplicable and terrifying.

"Tut, tut!"  Vance waved his hand airily.  "That's plagiarism.  I
said it first."  (He was striving to overcome his own sense of
perplexity by a lightness of attitude.)  "And now there really
should be an inamorata to bewail Mr. Robin's passing.  You recall,
perhaps, the stanza:


     "Who'll be chief mourner?
     'I,' said the dove,
     'I mourn my lost love;
      I'll be chief mourner.'"


Markham's head jerked slightly, and his fingers beat a nervous
tattoo on the table.

"Good God, Vance!  There IS a girl in the case.  And there's a
possibility that jealousy lies at the bottom of this thing."

"Fancy that, now!  I'm afraid the affair is going to develop into a
kind of tableau-vivant for grownup kindergartners, what?  But
that'll make our task easier.  All we'll have to do is to find the
fly."

"The fly?"

"The Musca domestica, to speak pedantically. . . .  My dear
Markham, have you forgotten?--


     "Who saw him die?
     'I,' said the fly,
     'With my little eye;
      I saw him die.'"


"Come down to earth!" Markham spoke with acerbity.  "This isn't a
child's game.  It's damned serious business."

Vance nodded abstractedly.

"A child's game is sometimes the most serious business in life."
His words held a curious, far-away tone.  "I don't like this thing--
I don't at all like it.  There's too much of the child in it--the
child born old and with a diseased mind.  It's like some hideous
perversion."  He took a deep inhalation on his cigarette, and made
a slight gesture of repugnance.  "Give me the details.  Let's find
out where we stand in this topsy-turvy land."

Markham again seated himself.

"I haven't many details.  I told you practically everything I know
of the case over the phone.  Old Professor Dillard called me
shortly before I communicated with you--"

"Dillard?  By any chance, Professor Bertrand Dillard?"

"Yes.  The tragedy took place at his house.--You know him?"

"Not personally.  I know him only as the world of science knows
him--as one of the greatest living mathematical physicists.  I have
most of his books.--How did he happen to call you?"

"I've known him for nearly twenty years.  I had mathematics under
him at Columbia, and later did some legal work for him.  When
Robin's body was found he phoned me at once--about half past
eleven.  I called up Sergeant Heath at the Homicide Bureau and
turned the case over to him--although I told him I'd come along
personally later on.  Then I phoned you.  The Sergeant and his men
are waiting for me now at the Dillard home."

"What's the domestic situation there?"

"The professor, as you probably know, resigned his chair some ten
years ago.  Since then he's been living in West 75th Street, near
the Drive.  He took his brother's child--a girl of fifteen--to live
with him.  She's around twenty-five now.  Then there's his protégé,
Sigurd Arnesson, who was a classmate of mine at college.  The
professor adopted him during his junior year.  Arnesson is now
about forty, an instructor in mathematics at Columbia.  He came to
this country from Norway when he was three, and was left an orphan
five years later.  He's something of a mathematical genius, and
Dillard evidently saw the makings of a great physicist in him and
adopted him."

"I've heard of Arnesson," nodded Vance.  "He recently published
some modifications of Mie's theory on the electrodynamics of moving
bodies. . . .  And do these three--Dillard, Arnesson and the girl--
live alone?"

"With two servants.  Dillard appears to have a very comfortable
income.  They're not very much alone, however.  The house is a kind
of shrine for mathematicians, and quite a cénacle has developed.
Moreover, the girl, who has always gone in for outdoor sports, has
her own little social set.  I've been at the house several times,
and there have always been visitors about--either a serious student
or two of the abstract sciences up-stairs in the library, or some
noisy young people in the drawing-room below."

"And Robin?"

"He belonged to Belle Dillard's set--an oldish young society man
who held several archery records. . . ."

"Yes, I know.  I just looked up the name in this book on archery.
A Mr. J. C. Robin seems to have made the high scores in several
recent championship meets.  And I noted, too, that a Mr. Sperling
has been the runner-up in several large archery tournaments.--Is
Miss Dillard an archer as well?"

"Yes, quite an enthusiast.  In fact, she organized the Riverside
Archery Club.  Its permanent ranges are at Sperling's home in
Scarsdale; but Miss Dillard has rigged up a practice range in the
side yard of the professor's 75th-Street house.  It was on this
range that Robin was killed."

"Ah!  And, as you say, the last person known to have been with him
was Sperling.  Where is our sparrow now?"

"I don't know.  He was with Robin shortly before the tragedy; but
when the body was found he had disappeared.  I imagine Heath will
have news on that point."

"And wherein lies the possible motive of jealousy you referred to?"
Vance's eyelids had drooped lazily, and he smoked with leisurely
but precise deliberation--a sign of his intense interest in what
was being told him.

"Professor Dillard mentioned an attachment between his niece and
Robin; and when I asked him who Sperling was and what his status
was at the Dillard house, he intimated that Sperling was also a
suitor for the girl's hand.  I didn't go into the situation over
the phone, but the impression I got was that Robin and Sperling
were rivals, and that Robin had the better of it."

"And so the sparrow killed Cock Robin."  Vance shook his head
dubiously.  "It won't do.  It's too dashed simple; and it doesn't
account for the fiendishly perfect reconstruction of the Cock-Robin
rhyme.  There's something deeper--something darker and more
horrible-in this grotesque business.--Who, by the by, found Robin?"

"Dillard himself.  He had stepped out on the little balcony at the
rear of the house, and saw Robin lying below on the practice range,
with an arrow through his heart.  He went down-stairs immediately--
with considerable difficulty, for the old man suffers abominably
from gout--and, seeing that the man was dead, phoned me.--That's
all the advance information I have."

"Not what you'd call a blindin' illumination, but still a bit
suggestive."  Vance got up.  "Markham old dear, prepare for
something rather bizarre--and damnable.  We can rule out accidents
and coincidence.  While it's true that ordin'ry target arrows--
which are made of soft wood and fitted with little bevelled piles--
could easily penetrate a person's clothing and chest wall, even
when driven with a medium weight bow, the fact that a man named
'Sparrow' should kill a man named Cochrane Robin, WITH A BOW AND
ARROW, precludes any haphazard concatenation of circumstances.
Indeed, this incredible set of events proves conclusively that
there has been a subtle, diabolical intent beneath the whole
affair."  He moved toward the door.  "Come, let us find out
something more about it at what the Austrian police officials
eruditely call the situs criminis."

We left the house at once and drove up-town in Markham's car.
Entering Central Park at Fifth Avenue we emerged through the 72nd-
Street gate, and a few minutes later were turning off of West End
Avenue into 75th Street.  The Dillard house--number 391--was on our
right, far down the block toward the river.  Between it and the
Drive, occupying the entire corner, was a large fifteen-story
apartment house.  The professor's home seemed to nestle, as if for
protection, in the shadow of this huge structure.

The Dillard house was of gray, weather-darkened limestone, and
belonged to the days when homes were built for permanency and
comfort.  The lot on which it stood had a thirty-five-foot
frontage, and the house itself was fully twenty-five feet across.
The other ten feet of the lot, which formed an areaway separating
the house from the apartment structure, was shut off from the
street by a ten-foot stone wall with a large iron door in the
centre.

The house was of modified Colonial architecture.  A short flight of
shallow steps led from the street to a narrow brick-lined porch
adorned with four white Corinthian pillars.  On the second floor a
series of casement windows, paned with rectangular laded glass,
extended across the entire width of the house.  (These, I learned
later, were the windows of the library.)  There was something
restful and distinctly old-fashioned about the place: it appeared
like anything but the scene of a gruesome murder.

Two police cars were parked near the entrance when we drove up, and
a dozen or so curious onlookers had gathered in the street.  A
patrolman lounged against one of the fluted columns of the porch,
gazing at the crowd before him with bored disdain.

An old butler admitted us and led us into the drawing-room on the
left of the entrance hall, where we found Sergeant Ernest Heath and
two other men from the Homicide Bureau.  The Sergeant, who was
standing beside the centre-table smoking, his thumbs hooked in the
armholes of his waistcoat, came forward and extended his hand in a
friendly greeting to Markham.

"I'm glad you got here, sir," he said; and the worried look in his
cold blue eyes seemed to relax a bit.  "I've been waiting for you.
There's something damn fishy about this case."

He caught sight of Vance, who had paused in the background, and his
broad pugnacious features crinkled in a good-natured grin.

"Howdy, Mr. Vance.  I had a sneaking idea you'd be lured into this
case.  What you been up to these many moons?"  I could not help
comparing this genuine friendliness of the Sergeant's attitude with
the hostility of his first meeting with Vance at the time of the
Benson case.  But much water had run under the bridge since that
first encounter in the murdered Alvin's garish living-room; and
between Heath and Vance there had grown up a warm attachment, based
on a mutual respect and a frank admiration for each other's
capabilities.

Vance held out his hand, and a smile played about the corners of
his mouth.

"The truth is, Sergeant, I've been endeavorin' to discover the
lost glories of an Athenian named Menander, a dramatic rival of
Philemon's.  Silly, what?"

Heath grunted disdainfully.

"Well, anyhow, if you're as good at it as you are at discovering
crooks, you'll probably get a conviction."  It was the first
compliment I had ever heard pass his lips, and it attested not
only to his deep-seated admiration for Vance, but also to his own
troubled and uncertain state of mind.

Markham sensed the Sergeant's mental insecurity, and asked somewhat
abruptly:  "Just what seems to be the difficulty in the present
case?"

"I didn't say there was any difficulty, sir," Heath replied.  "It
looks as though we had the bird who did it dead to rights.  But I
ain't satisfied, and--oh, hell!  Mr. Markham . . . it ain't
natural; it don't make sense."

"I think I understand what you mean."  Markham regarded the
Sergeant appraisingly.  "You're inclined to think that Sperling's
guilty?"

"Sure, he's guilty," declared Heath with overemphasis.  "But that's
not what's worrying me.  To tell you the truth, I don't like the
name of this guy who was croaked--especially as he was croaked with
a bow and arrow. . . ."  He hesitated, a bit shamefaced.  "Don't it
strike you as peculiar, sir?"

Markham nodded perplexedly.

"I see that you, too, remember your nursery rhymes," he said, and
turned away.

Vance fixed a waggish look on Heath.

"You referred to Mr. Sperling just now as a 'bird,' Sergeant.  The
designation was most apt.  Sperling, d' ye see, means 'sparrow' in
German.  And it was a sparrow, you recall, who killed Cock Robin
with an arrow. . . .  A fascinatin' situation--eh, what?"

The Sergeant's eyes bulged slightly, and his lips fell apart.  He
stared at Vance with almost ludicrous bewilderment.

"I said this here business was fishy!"

"I'd say, rather, it was avian, don't y' know."

"You WOULD call it something nobody'd understand," Heath retorted
truculently.  It was his wont to become bellicose when confronted
with the inexplicable.

Markham intervened diplomatically.

"Let's have the details of the case, Sergeant.  I take it you've
questioned the occupants of the house."

"Only in a general way, sir."  Heath flung one leg over the corner
of the centre-table and relit his dead cigar.  "I've been waiting
for you to show up.  I knew you were acquainted with the old
gentleman up-stairs; so I just did the routine things.  I put a man
out in the alley to see that nobody touches the body till Doc
Doremus arrives,* he'll be here when he finishes lunch.--I phoned
the finger-print men before I left the office, and they oughta be
on the job any minute now; though I don't see what good they can
do. . . ."


* Heath was referring to Doctor Emanuel Doremus, the Chief Medical
Examiner of New York.


"What about the bow that fired the arrow?" put in Vance.

"That was our one best bet; but old Mr. Dillard said he picked it
up from the alley and brought it in the house.  He probably gummed
up any prints it mighta had."

"What have you done about Sperling?" asked Markham.

"I got his address--he lives in a country house up Westchester way--
and sent a coupla men to bring him here as soon as they could lay
hands on him.  Then I talked to the two servants--the old fellow
that let you in, and his daughter, a middle-aged woman who does the
cooking.  But neither of 'em seemed to know anything, or else
they're acting dumb.--After that I tried to question the young lady
of the house."  The Sergeant raised his hands in a gesture of
irritated despair.  "But she was all broke up and crying; so I
thought I'd let YOU have the pleasure of interviewing her.--Snitkin
and Burke"--he jerked his thumb toward the two detectives by the
front window--"went over the basement and the alley and back yard
trying to pick up something; but drew a blank.--And that's all I
know so far.  As soon as Doremus and the finger-print men get here,
and after I've had a heart-to-heart talk with Sperling, then I'll
get the ball to rolling and clean up the works."

Vance heaved an audible sigh.

"You're so sanguine, Sergeant!  Don't be disappointed if your ball
turns out to be a parallelopiped that won't roll.  There's
something deuced oddish about this nursery extravaganza; and,
unless all the omens deceive me, you'll be playing blind-man's-buff
for a long time to come."

"Yeh?"  Heath gave Vance a look of despondent shrewdness.  It was
evident he was more or less of the same opinion.

"Don't let Mr. Vance dishearten you, Sergeant," Markham rallied
him.  "He's permitting his imagination to run away with him."  Then
with an impatient gesture he turned toward the door.  "Let's look
over the ground before the others arrive.  Later I'll have a talk
with Professor Dillard and the other members of the household.
And, by the way, Sergeant, you didn't mention Mr. Arnesson.  Isn't
he at home?"

"He's at the university; but he's expected to return soon."

Markham nodded and followed the Sergeant into the main hall.  As we
passed down the heavily-carpeted passage to the rear, there was a
sound on the staircase, and a clear but somewhat tremulous woman's
voice spoke from the semi-darkness above.

"Is that you, Mr. Markham?  Uncle thought he recognized your voice.
He's waiting for you in the library."

"I'll join your uncle in a very few minutes, Miss Dillard."
Markham's tone was paternal and sympathetic.  "And please wait with
him, for I want to see you, too."

With a murmured acquiescence, the girl disappeared round the head
of the stairs.

We moved on to the rear door of the lower hall.  Beyond was a
narrow passageway terminating in a flight of wooden steps which led
to the basement.  At the foot of these steps we came into a large,
low-ceilinged room with a door giving directly upon the areaway at
the west side of the house.  This door was slightly ajar, and in
the opening stood the man from the Homicide Bureau whom Heath had
set to guard the body.

The room had obviously once been a basement storage; but it had
been altered and redecorated, and now served as a sort of club-
room.  The cement floor was covered with fibre rugs, and one entire
wall was painted with a panorama of archers throughout the ages.
In an oblong panel on the left was a huge illustrated reproduction
of an archery range labelled "Ayme for Finsburie Archers--London
1594," showing Bloody House Ridge in one corner, Westminster Hall
in the centre, and Welsh Hall in the foreground.  There were a
piano and a phonograph in the room; numerous comfortable wicker
chairs; a varicolored divan; an enormous wicker centre-table
littered with all manner of sports magazines; and a small bookcase
filled with works on archery.  Several targets rested in one
corner, their gold discs and concentric chromatic rings making
brilliant splashes of color in the sunlight which flooded in from
the two rear windows.  One wall space near the door was hung with
long bows of varying sizes and weights; and near them was a large
old-fashioned tool-chest.  Above it was suspended a small cupboard,
or ascham, strewn with various odds and ends of tackle, such as
bracers, shooting-gloves, piles, points of aim, and bow strings.
A large oak panel between the door and the west window contained a
display of one of the most interesting and varied collections of
arrows I had ever seen.

This panel attracted Vance particularly, and adjusting his monocle
carefully, he strolled over to it.

"Hunting and war arrows," he remarked.  "Most inveiglin'. . . .
AH!  One of the trophies seems to have disappeared.  Taken down
with considerable haste, too.  The little brass brad that held it
in place is shockingly bent."

On the floor stood several quivers filled with target arrows.  He
leaned over and, withdrawing one, extended it to Markham.

"This frail shaft may not look as if it would penetrate the human
breast; but target arrows will drive entirely through a deer at
eighty yards. . . .  Why, then, the missing hunting arrow from the
panel?  An interestin' point."

Markham frowned and compressed his lips; and I realized that he had
been clinging to the forlorn hope that the tragedy might have been
an accident.  He tossed the arrow hopelessly on a chair, and walked
toward the outer door.

"Let's take a look at the body and the lie of the land," he said
gruffly.

As we emerged into the warm spring sunlight a sense of isolation
came over me.  The narrow paved areaway in which we stood seemed
like a canyon between steep stone walls.  It was four or five feet
below the street level, which was reached by a short flight of
steps leading to the gate in the wall.  The blank, windowless rear
wall of the apartment house opposite extended upwards for 150 feet;
and the Dillard house itself, though only four stories high, was
the equivalent of six stories gauged by the architectural
measurements of to-day.  Though we were standing out of doors in
the heart of New York, no one could see us except from the few side
windows of the Dillard house and from a single bay window of the
house on 76th Street, whose rear yard adjoined that of the Dillard
grounds.

This other house, we were soon to learn, was owned by a Mrs.
Drukker; and it was destined to play a vital and tragic part in the
solution of Robin's murder.  Several tall willow trees acted as a
mask to its rear windows; and only the bay window at the side of
the house had an unobstructed view of that part of the areaway in
which we stood.

I noticed that Vance had his eye on this bay window, and as he
studied it I saw a flicker of interest cross his face.  It was not
until much later that afternoon that I was able to guess what had
caught and held his attention.

The archery range extended from the wall of the Dillard lot on 75th
Street all the way to a similar street wall of the Drukker lot on
76th Street, where a butt of hay bales had been erected on a
shallow bed of sand.  The distance between the two walls was 200
feet, which, as I learned later, made possible a sixty-yard range,
thus permitting target practice for all the standard archery
events, with the one exception of the York Round for men.

The Dillard lot was 135 feet deep, the depth of the Drukker lot
therefore being sixty-five feet.  A section of the tall ironwork
fence that separated the two rear yards had been removed where it
had once transected the space now used for the archery range.  At
the further end of the range, backing against the western line of
the Drukker property, was another tall apartment house occupying
the corner of 76th Street and Riverside Drive.  Between these two
gigantic buildings ran a narrow alleyway, the range end of which
was closed with a high board fence in which had been set a small
door with a lock.

For purposes of clarity I am incorporating in this record a
diagram of the entire scene; for the arrangement of the various
topographical and architectural details had a very important
bearing on the solution of the crime.  I would call attention
particularly to the following points:--first, to the little second-
story balcony at the rear of the Dillard house, which projects
slightly over the archery range; secondly, to the bay window (on
the second floor) of the Drukker house, whose southern angle has a
view of the entire archery range toward 75th Street; and thirdly,
to the alleyway between the two apartment houses, which leads from
Riverside Drive into the Dillard rear yard.


[Diagram--Diagram.gif]


The body of Robin lay almost directly outside of the archery-room
door.  It was on its back, the arms extended, the legs slightly
drawn up, the head pointing toward the 76th-Street end of the
range.  Robin had been a man of perhaps thirty-five, of medium
height, and with an incipient corpulency.  There was a rotund
puffiness to his face, which was smooth-shaven except for a narrow
blond moustache.  He was clothed in a two-piece sport suit of light
gray flannel, a pale-blue silk shirt, and tan Oxfords with thick
rubber soles.  His hat--a pearl-colored felt fedora--was lying near
his feet.

Beside the body was a large pool of coagulated blood which had
formed in the shape of a huge pointing hand.  But the thing which
held us all in a spell of fascinated horror was the slender shaft
that extended vertically from the left side of the dead man's
breast.  The arrow protruded perhaps twenty inches, and where it
had entered the body there was the large dark stain of the
hemorrhage.  What made this strange murder seem even more
incongruous were the beautifully fletched feathers on the arrow.
They had been dyed a bright red; and about the shaftment were two
stripes of turquoise blue--giving the arrow a gala appearance.  I
had a feeling of unreality about the tragedy, as though I were
witnessing a scene in a sylvan play for children.

Vance stood looking down at the body with half-closed eyes, his
hands in his coat pockets.  Despite the apparent indolence of his
attitude I could tell that he was keenly alert, and that his mind
was busy co-ordinating the factors of the scene before him.

"Dashed queer, that arrow," he commented.  "Designed for big game;
. . . undoubtedly belongs to that ethnological exhibit we just saw.
And a clean hit--directly into the vital spot, between the ribs and
without the slightest deflection.  Extr'ordin'ry! . . . I say,
Markham; such marksmanship isn't human.  A chance shot might have
done it; but the slayer of this johnny wasn't leaving anything to
chance.  That powerful hunting arrow, which was obviously wrenched
from the panel inside, shows premeditation and design--"  Suddenly
he bent over the body.  "Ah!  Very interestin'.  The nock of the
arrow is broken down,--I doubt if it would even hold a taut
string."  He turned to Heath.  "Tell me, Sergeant: where did
Professor Dillard find the bow?--not far from that club-room
window, what?"

Heath gave a start.

"Right outside the window, in fact, Mr. Vance.  It's in on the
piano now, waiting for the finger-print men."

"The professor's sign-manual is all they'll find, I'm afraid."
Vance opened his case and selected another cigarette.  "And I'm
rather inclined to believe that the arrow itself is innocent of
prints."

Heath was scrutinizing Vance inquisitively.

"What made you think the bow was found near the window, Mr. Vance?"
he asked.

"It seemed the logical place for it, in view of the position of Mr.
Robin's body, don't y' know."

"Shot from close range, you mean?"

Vance shook his head.

"No, Sergeant.  I was referring to the fact that the deceased's
feet are pointing toward the basement door, and that, though his
arms are extended, his legs are drawn up.  Is that the way you'd
say a man would fall who'd been shot through the heart?"

Heath considered the point.

"No-o," he admitted.  "He'd likely be more crumpled up; or, if he
did fall over back, his legs would be straight out and his arms
drawn in."

"Quite.--And regard his hat.  If he had fallen backwards it would
be behind him, not at his feet."

"See here, Vance," Markham demanded sharply; "what's in your mind?"

"Oh, numberless things.  But they all boil down to the wholly
irrational notion that this defunct gentleman wasn't shot with a
bow and arrow at all."

"Then why, in God's name--"

"Exactly!  Why the utter insanity of the elaborate stage-setting?--
My word, Markham!  This business is ghastly."

As Vance spoke the basement door opened, and Doctor Doremus,
shepherded by Detective Burke, stepped jauntily into the areaway.
He greeted us breezily and shook hands all round.  Then he fixed a
fretful eye on Heath.

"By Gad, Sergeant!" he complained, pulling his hat down to an even
more rakish angle.  "I only spend three hours out of the twenty-
four eating my meals; and you invariably choose those three hours
to worry me with your confounded bodies.  You're ruining my
digestion."  He looked about him petulantly and, on seeing Robin,
whistled softly.  "For Gad's sake!  A nice fancy murder you picked
out for me this time!"

He knelt down and began running his practised fingers over the
body.

Markham stood for a moment looking on, but presently he turned to
Heath.

"While the doctor's busy with his examination, Sergeant, I'll go
up-stairs and have a chat with Professor Dillard."  Then he
addressed himself to Doremus.  "Let me see you before you go,
doctor."

"Oh, sure."  Doremus did not so much as look up.  He had turned the
body on one side, and was feeling the base of the skull.



CHAPTER III

A PROPHECY RECALLED


(Saturday, April 2; 1.30 p.m.)


When we reached the main hall Captain Dubois and Detective Bellamy,
the finger-print experts from Headquarters, were just arriving.
Detective Snitkin, who had evidently been watching for them, led
them at once toward the basement stairs, and Markham, Vance and I
went up to the second floor.

The library was a large, luxurious room at least twenty feet deep,
occupying the entire width of the building.  Two sides of it were
lined to the ceiling with great embayed bookcases; and in the
centre of the west wall rose a massive bronze Empire fireplace.  By
the door stood an elaborate Jacobean side-board, and opposite, near
the windows which faced on 75th Street, was an enormous carved
table-desk, strewn with papers and pamphlets.  There were many
interesting objets-d'art in the room; and two diagrammatic Dürers
looked down on us from the tapestried panels beside the mantel.
All the chairs were spacious and covered with dark leather.

Professor Dillard sat before the desk, one foot resting on a small
tufted ottoman; and in a corner near the windows, huddled in a
sprawling armchair, was his niece, a vigorous, severely tailored
girl with strong, chiselled features of classic cast.  The old
professor did not rise to greet us, and made no apology for the
omission.  He appeared to take it for granted that we were aware of
his disability.  The introductions were perfunctory, though Markham
gave a brief explanation of Vance's and my presence there.

"I regret, Markham," the professor said, when we had settled
ourselves, "that a tragedy should be the reason for this meeting;
but it's always good to see you.--I suppose you will want to cross-
examine Belle and me.  Well, ask anything you care to."

Professor Bertrand Dillard was a man in his sixties, slightly
stooped from a sedentary studious life: clean-shaven, and with a
marked brachycephalic head surmounted with thick white hair combed
pompadour.  His eyes, though small, were remarkably intense and
penetrating; and the wrinkles about his mouth held that grim pursed
expression which often comes with years of concentration on
difficult problems.  His features were those of the dreamer and
scientist; and, as the world knows, this man's wild dreams of space
and time and motion had been actualized into a new foundation of
scientific fact.  Even now his face reflected an introspective
abstraction, as if the death of Robin were but an intrusion upon
the inner drama of his thoughts.

Markham hesitated a moment before answering.  Then he said with
marked deference:

"Suppose, sir, you tell me just what you know of the tragedy.  Then
I'll put whatever questions I deem essential."

Professor Dillard reached for an old meerschaum pipe on the stand
beside him.  When he had filled and lighted it he shifted himself
more comfortably in his chair.

"I told you practically everything I know over the telephone.
Robin and Sperling called this morning about ten o'clock to see
Belle.  But she had gone to the courts to play tennis, so they
waited in the drawing-room down-stairs.  I heard them talking there
together for half an hour or so before they went to the basement
club-room.  I remained here reading for perhaps an hour, and then,
as the sunshine looked so pleasant, I decided to step out on the
balcony at the rear of the house.  I had been there about five
minutes, I should say, when I chanced to look down on the archery
range; and to my horrified amazement I saw Robin lying on his back
with an arrow-shaft protruding from his breast.  I hastened down as
quickly as my gout would permit, but I could see at once that the
poor fellow was dead; so I immediately telephoned to you.  There
was no one in the house at the time but old Pyne--the butler--and
myself.  The cook had gone marketing; Arnesson had left for the
university at nine o'clock; and Belle was still out playing tennis.
I sent Pyne to look for Sperling, but he was nowhere about; and I
came back to the library here to wait for you.  Belle returned
shortly before your men arrived, and the cook came in a little
later.  Arnesson won't be back until after two."

"There was no one else here this morning--no strangers or
visitors?"

The professor shook his head.

"Only Drukker,--I believe you met him here once.  He lives in the
house at our rear.  He often drops in--mostly, however, to see
Arnesson: they have much in common.  He's written a book on 'World
Lines in Multidimensional Continua.'  The man's quite a genius in
his way; has the true scientific mind. . . .  But when he found
that Arnesson was out he sat for a while with me discussing the
Brazilian expedition of the Royal Astronomical Society.  Then he
went home."

"What time was this?"

"About half past nine.  Drukker had already gone when Robin and
Sperling called."

"Was it unusual, Professor Dillard," asked Vance, "for Mr. Arnesson
to be away on Saturday mornings?"

The old professor looked up sharply, and there was a brief
hesitation before he answered.

"Not unusual exactly; although he's generally here on Saturdays.
But this morning he had some important research work to do for me
in the faculty library. . . .  Arnesson," he added, "is working
with me on my next book."*



* The book referred to by Professor Dillard was the great work
which appeared two years later, "The Atomic Structure of Radiant
Energy," a mathematical emendation of Planck's quantum theory
refuting the classical axiom of the continuity of all physical
processes, as contained in Maximus Tyrius' [Greek text--Greek.gif].


There was a short silence; then Markham spoke.

"You said this morning that both Robin and Sperling were suitors
for Miss Dillard's hand. . . ."

"Uncle!"  The girl sat upright in her chair and turned angry,
reproachful eyes upon the old professor.  "That wasn't fair."

"But it was true, my dear."  His voice was noticeably tender.

"It was true--in a way," she admitted.  "But there was no need of
mentioning it.  You know, as well as they did, how I regarded them.
We were good friends--that was all.  Only last night, when they
were here together, I told them--quite plainly--that I wouldn't
listen to any more silly talk of marriage from either of them.
They were only boys . . . and now one of them's gone. . . .  Poor
Cock Robin!"  She strove bravely to stifle her emotion.

Vance raised his eyebrows and leaned forward.

"'Cock Robin'?"

"Oh, we all called him that.  We did it to tease him, because he
didn't like the nickname."

"The sobriquet was inevitable," Vance observed sympathetically.
"And it was rather a nice nickname, don't y' know.  The original
Cock Robin was loved by 'all the birds of the air,' and they all
mourned his passing."  He watched the girl closely as he spoke.

"I know," she nodded.  "I told him that once.--And every one liked
Joseph, too.  You couldn't help liking him.  He was so--so
goodhearted and kind."

Vance again settled back in his chair; and Markham continued his
questioning.

"You mentioned, professor, that you heard Robin and Sperling
talking in the drawing-room.  Could you hear any of their
conversation?"

The old man shot a sidelong glance at his niece.

"Does that question really matter, Markham?" he asked, after a
moment's hesitation.

"It may have some very vital bearing on the situation."

"Perhaps."  The professor drew on his pipe thoughtfully.  "On the
other hand, if I answer it I may give an erroneous impression, and
do a grave injustice to the living."

"Can you not trust me to judge that point?"  Markham's voice had
become at once grave and urgent.

There was another short silence, broken by the girl.

"Why don't you tell Mr. Markham what you heard, uncle?  What harm
can it do?"

"I was thinking of you, Belle," the professor answered softly.
"But perhaps you are right."  He looked up reluctantly.  "The fact
is, Markham, Robin and Sperling were having some angry words over
Belle.  I heard only a little, but I gathered that each regarded
the other as being guilty of playing unfair--of standing in each
other's way. . . ."

"Oh!  They didn't mean it," Miss Dillard interpolated vehemently.
"They were always ragging each other.  There WAS a little jealousy
between them; but I wasn't the real cause of it.  It was their
archery records.  You see, Raymond--Mr. Sperling--used to be the
better shot; but this last year Joseph beat him at several meets,
and at our last annual tournament he became the club's Champion
Archer."

"And Sperling thought, perhaps," added Markham, "that he had
correspondingly fallen in your estimation."

"That's absurd!" the girl retorted hotly.

"I think, my dear, we can leave the matter safely in Mr. Markham's
hands," Professor Dillard said mollifyingly.  Then to Markham:
"Were there any other questions you cared to ask?"

"I'd like to know anything you can tell me about Robin and
Sperling--who they are; their associations; and how long you have
known them."

"I think that Belle can enlighten you better than I.  Both boys
belonged to her set.  I saw them only occasionally."

Markham turned inquiringly to the girl.

"I've known both of them for years," she said promptly.  "Joseph
was eight or ten years older than Raymond, and lived in England up
to five years ago, when his father and mother both died.  He came
to America, and took bachelor quarters on the Drive.  He had
considerable money, and lived idly, devoting himself to fishing and
hunting and other outdoor sports.  He went about in society a
little, and was a nice, comfortable friend who'd always fill in at
a dinner or make a fourth hand at bridge.  There was nothing really
much to him--in an intellectual way, you understand. . . ."

She paused, as if her remarks were in some way disloyal to the
dead, and Markham, sensing her feelings, asked simply:

"And Sperling?"

"He's the son of a wealthy manufacturer of something or other--
retired now.  They live in Scarsdale in a beautiful country home,--
our archery club has its regular ranges there,--and Raymond is a
consulting engineer for some firm down-town; though I imagine he
works merely to placate his father, for he only goes to the office
two or three days a week.  He's a graduate of Boston Tech, and I
met him when he was a sophomore, home on vacation.  Raymond will
never set the world afire, Mr. Markham; but he's really an awfully
fine type of American young man--sincere, jolly, a little bashful,
and perfectly straight."

It was easy to picture both Robin and Sperling from the girl's
brief descriptions; and it was correspondingly difficult to connect
either of them with the sinister tragedy that had brought us to the
house.

Markham sat frowning for a while.  Finally he lifted his head and
looked straight at the girl.

"Tell me, Miss Dillard: have you any theory or explanation that
might, in any way, account for the death of Mr. Robin?"

"No!"  The word fairly burst from her.  "Who could want to kill
Cock Robin?  He hadn't an enemy in the world.  The whole thing is
incredible.  I couldn't believe it had happened until I went and--
and saw for myself.  Even then it didn't seem real."

"Still, my dear child," put in Professor Dillard, "the man was
killed; so there must have been something in his life that you
didn't know or suspect.  We're constantly finding new stars that
the old-time astronomers didn't believe existed."

"I can't believe Joseph had an enemy," she retorted.  "I won't
believe it.  It's too utterly absurd."

"You think then," asked Markham, "that it's unlikely Sperling was
in any way responsible for Robin's death?"

"Unlikely?"  The girl's eyes flashed.  "It's impossible!"

"And yet, y' know, Miss Dillard,"--it was Vance who now spoke in
his lazy casual tone--"Sperling means 'sparrow'."

The girl sat immobile.  Her face had gone deathly pale, and her
hands tightened over the arms of the chair.  Then slowly, and as if
with great difficulty, she nodded, and her breast began to rise and
fall with her labored breathing.  Suddenly she shuddered and
pressed her handkerchief to her face.

"I'm afraid!" she whispered.

Vance rose and, going to her, touched her comfortingly on the
shoulder.

"Why are you afraid?"

She looked up and met his eyes.  They seemed to reassure her, for
she forced a pitiful smile.

"Only the other day," she said, in a strained voice, "we were all
on the archery range down-stairs; and Raymond was just preparing to
shoot a single American Round, when Joseph opened the basement door
and stepped out on the range.  There really wasn't any danger, but
Sigurd--Mr. Arnesson, you know--was sitting on the little rear
balcony watching us; and when I cried 'He! He!' jokingly to Joseph,
Sigurd leaned over and said:  'You don't know what a chance you're
running, young man.  You're a Cock Robin, and that archer's a
sparrow; and you remember what happened to your namesake when a Mr.
Sparrow wielded the bow and arrow'--or something like that.  No one
paid much attention to it at the time.  But now! . . ."  Her
voice trailed off into an awed murmur.

"Come, Belle; don't be morbid."  Professor Dillard spoke
consolingly, but not without impatience.  "It was merely one of
Sigurd's ill-timed witticisms.  You know he's continually sneering
and jesting at realities: it's about the only outlet he has from
his constant application to abstractions."

"I suppose so," the girl answered.  "Of course, it was only a joke.
But now it seems like some terrible prophecy.--Only," she hastened
to add, "Raymond COULDN'T have done it."

As she spoke the library door opened suddenly, and a tall gaunt
figure appeared on the threshold.

"Sigurd!"  Belle Dillard's startled exclamation held an undeniable
note of relief.

Sigurd Arnesson, Professor Dillard's protégé and adopted son, was a
man of striking appearance--over six feet tall, wiry and erect,
with a head which, at first view, appeared too large for his body.
His almost yellow hair was unkempt, like a schoolboy's; his nose
was aquiline; and his jowls were lean and muscular.  Though he
could not have been over forty, there was a net-work of lines in
his face.  His expression was sardonically puckish; but the intense
intellectual passion that lighted his blue-gray eyes belied any
superficiality of nature.  My initial reaction to his personality
was one of liking and respect.  There were depths in the man--
powerful potentialities and high capabilities.

As he entered the room that afternoon, his searching eyes took us
all in with a swift, inquisitive glance.  He nodded jerkily to Miss
Dillard, and then fixed the old professor with a look of dry
amusement.

"What, pray, has happened in this three-dimensional house?  Wagons
and populace without: a guardian at the portals . . . and when I
finally overcame the Cerberus and was admitted by Pyne, two
plainclothes men hustled me up here without ceremony or explanation.
Very amusing, but disconcerting. . . .  Ah!  I seem to recognize
the District Attorney.  Good morning--or rather, afternoon--Mr.
Markham."

Before Markham could return this belated greeting Belle Dillard
spoke.

"Sigurd, please be serious.--Mr. Robin has been killed."

"'Cock Robin,' you mean.  Well, well!  With such a name what could
the beggar expect?"  He appeared wholly unmoved by the news.  "Who,
or what, returned him to the elements?"

"As to who it was, we don't know."  It was Markham who answered,
in a tone of reproach for the other's levity.  "But Mr. Robin was
killed with an arrow through the heart."

"Most fitting."  Arnesson sat down on the arm of a chair and
extended his long legs.  "What could be more appropriate than that
Cock Robin should die from an arrow shot from the bow of--"

"Sigurd!"  Belle Dillard cut him short.  "Haven't you joked enough
about that?  You KNOW that Raymond didn't do it."

"Of course, sis."  The man looked at her somewhat wistfully.  "I
was thinking of Mr. Robin's ornithological progenitor."  He turned
slowly to Markham.  "So it's a real murder mystery, is it--with a
corpse, and clews, and all the trappings?  May I be entrusted with
the tale?"

Markham gave him a brief outline of the situation, to which he
listened with rapt interest.  When the account was ended he asked:

"Was there no bow found on the range?"

"Ah!"  Vance, for the first time since the man's arrival, roused
himself from seeming lethargy, and answered for Markham.  "A most
pertinent question, Mr. Arnesson.--Yes, a bow was found just
outside of the basement window, barely ten feet from the body."

"That of course simplifies matters," said Arnesson, with a note of
disappointment.  "It's only a question now of taking the finger-
prints."

"Unfortunately the bow has been handled," explained Markham.
"Professor Dillard picked it up and brought it into the house."

Arnesson turned to the older man curiously.

"What impulse, sir, directed you to do that?"

"Impulse?  My dear Sigurd, I didn't analyze my emotions.  But it
struck me that the bow was a vital piece of evidence, and I placed
it in the basement as a precautionary measure until the police
arrived."

Arnesson made a wry face and cocked one eye humorously.

"That sounds like what our psychoanalytic friends would call a
suppression-censor explanation.  I wonder what submerged idea was
actually in your mind. . . ."

There was a knock at the door, and Burke put his head inside.

"Doc Doremus is waiting for you down-stairs, Chief.  He's finished
his examination."

Markham rose and excused himself.

"I sha'n't bother you people any more just at present.  There's
considerable preliminary routine work to be done.  But I must ask
you to remain upstairs for the time being.  I'll see you again
before I go."

Doremus was teetering impatiently on his toes when we joined him in
the drawing-room.

"Nothing complicated about it," he began, before Markham had a
chance to speak.  "Our sporty friend was killed by an arrow with a
mighty sharp point entering his heart through the fourth
intercostal space.  Lot of force behind it.  Plenty of hemorrhage
inside and out.  He's been dead about two hours, I should say,
making the time of his death around half past eleven.  That's only
guesswork, however.  No signs of a struggle--no marks on his
clothes or abrasions on his hands.  Death supervened most likely
without his knowing what it was all about.  He got a nasty bump,
though, where his head hit the rough cement when he fell. . . ."

"Now, that's very interestin'."  Vance's drawling voice cut in on
the Medical Examiner's staccato report.  "How serious a 'bump' was
it, Doctor?"

Doremus blinked and eyed Vance with some astonishment.

"Bad enough to fracture the skull.  I couldn't feel it, of course;
but there was a large haematoma over the occipital region, dried
blood in the nostrils and the ears, and unequal pupils, indicating
a fracture of the vault.  I'll know more about it after the
autopsy."  He turned back to the District Attorney.  "Anything
else?"

"I think not, Doctor.  Only let us have your postmortem report as
soon as possible."

"You'll have it to-night.  The Sergeant's already phoned for the
wagon."  And shaking hands with all of us, he hurried away.

Heath had stood glowering in the background.

"Well, that don't get us anywheres, sir," he complained, chewing
viciously on his cigar.

"Don't be downhearted, Sergeant," Vance chided him.  "That blow on
the back of the head is worthy of your profoundest consideration.
I'm of the opinion it wasn't entirely due to the fall, don't y'
know."

The Sergeant was unimpressed by this observation.

"What's more, Mr. Markham," he went on, "there wasn't any finger-
prints on either the bow or the arrow.  Dubois says they looked as
though they'd both been wiped clean.  There were a few smears on
the end of the bow where the old gentleman picked it up; but not
another sign of a print."

Markham smoked a while in gloomy silence.

"What about the handle on the gate leading to the street?  And the
knob on the door to the alley between the apartment houses?"

"Nothing!"  Heath snorted his disgust.  "Both of rough, rusty iron
that wouldn't take a print."

"I say, Markham," observed Vance; "you're going at this thing the
wrong way.  Naturally there'd be no finger-prints.  Really, y'
know, one doesn't carefully produce a playlet and then leave all
the stage props in full view of the audience.  What we've got to
learn is why this particular impresario decided to indulge in silly
theatricals."

"It ain't as easy as all that, Mr. Vance," submitted Heath
bitterly.

"Did I intimate it was easy?  No, Sergeant; it's deucedly difficult.
And it's worse than difficult: it's subtle and obscure and . . .
fiendish."



CHAPTER IV

A MYSTERIOUS NOTE


(Saturday, April 2; 2 p.m.)


Markham sat down resolutely before the centre-table.

"Suppose, Sergeant, we overhaul the two servants now."

Heath stepped into the hall and gave an order to one of his men.  A
few moments later a tall, sombre, disjointed man entered and stood
at respectful attention.

"This is the butler, sir," explained the Sergeant.  "Named Pyne."

Markham studied the man appraisingly.  He was perhaps sixty years
old.  His features were markedly acromegalic; and this distortion
extended to his entire figure.  His hands were large, and his feet
broad and misshapen.  His clothes, though neatly pressed, fitted
him badly; and his high clerical collar was several sizes too large
for him.  His eyes, beneath gray, bushy eyebrows, were pale and
watery, and his mouth was a mere slit in an unhealthily puffy face.
Despite his utter lack of physical prepossession, however, he gave
one the impression of shrewd competency.

"So you are the Dillard butler," mused Markham.  "How long have you
been with the family, Pyne?"

"Going on ten years, sir."

"You came, then, just after Professor Dillard resigned his chair at
the university?"

"I believe so, sir."  The man's voice was deep and rumbling.

"What do you know of the tragedy that occurred here this morning?"
Though Markham put the question suddenly, in the hope, I imagine,
of surprising some admission, Pyne received it with the utmost
stoicism.

"Nothing whatever, sir.  I was unaware that anything had happened
until Professor Dillard called to me from the library and asked me
to look for Mr. Sperling."

"He told you of the tragedy then?"

"He said:  'Mr. Robin has been murdered, and I wish you'd find Mr.
Sperling for me.'--That was all, sir."

"You're sure he said 'murdered,' Pyne?" interjected Vance.

For the first time the butler hesitated, and an added astuteness
crept into his look.

"Yes, sir--I'm sure he did.  'Murdered' is what he said."

"And did you see the body of Mr. Robin when you pushed your
search?" pursued Vance, his eyes idly tracing a design on the wall.

Again there was a brief hesitation.

"Yes, sir.  I opened the basement door to look out on the archery
range, and there I saw the poor young gentleman. . . ."

"A great shock it must have given you, Pyne," Vance observed drily.
"Did you, by any hap, touch the poor young gentleman's body?--or
the arrow, perhaps?--or the bow?"

Pyne's watery eyes glistened for a moment.  "No--of course not,
sir. . . .  Why should I, sir?"

"Why, indeed?" Vance sighed wearily.  "But you saw the bow?"

The man squinted, as if for purposes of mental visualization.

"I couldn't say, sir.  Perhaps, yes; perhaps, no.  I don't recall."

Vance seemed to lose all interest in him; and Markham resumed the
interrogation.

"I understand, Pyne, that Mr. Drukker called here this morning
about half past nine.  Did you see him?"

"Yes, sir.  He always uses the basement door; and he said good-
morning to me as he passed the butler's pantry at the head of the
steps."

"He returned the same way he came?"

"I suppose so, sir--though I was up-stairs when he went.  He lives
in the house at the rear--"

"I know."  Markham leaned forward.  "I presume it was you who
admitted Mr. Robin and Mr. Sperling this morning."

"Yes, sir.  At about ten o'clock."

"Did you see them again, or overhear any of their remarks while
they waited here in the drawing-room?"

"No, sir.  I was busy in Mr. Arnesson's quarters most of the
morning."

"Ah!"  Vance turned his eyes on the man.  "That would be on the
second floor rear, wouldn't it?--the room with the balcony?"

"Yes, sir."

"Most interestin'. . . .  And it was from that balcony that
Professor Dillard first saw Mr. Robin's body.--How could he have
entered the room without your knowing it?  You said, I believe,
that your first intimation of the tragedy was when the professor
called you from the library and told you to seek Mr. Sperling."

The butler's face turned a pasty white, and I noticed that his
fingers twitched nervously.

"I might have stepped out of Mr. Arnesson's room for a moment," he
explained, with effort.  "Yes--it's quite likely.  In fact, sir, I
recall going to the linen-closet. . . ."

"Oh, to be sure."  Vance lapsed into lethargy.

Markham smoked a while, his gaze concentrated on the table-top.

"Did any one else call at the house this morning, Pyne?" he asked
presently.

"No one, sir."

"And you can suggest no explanation for what happened here?"

The man shook his head heavily, his watery eyes in space.

"No, sir.  Mr. Robin seemed a pleasant, well-liked young man.  He
wasn't the kind to inspire murder--if you understand what I mean."

Vance looked up.

"I can't say that I, personally, understand exactly what you mean,
Pyne.  How do you know it wasn't an accident?"

"I don't, sir," was the unperturbed answer.  "But I know a bit
about archery--if you'll pardon my saying so--and I saw right away
that Mr. Robin had been killed by a hunting arrow."

"You're very observin', Pyne," nodded Vance.  "And quite correct."

It was plain that no direct information was to be got from the
butler, and Markham dismissed him abruptly, at the same time
ordering Heath to send in the cook.

When she entered I noticed at once a resemblance between father and
daughter.  She was a slatternly woman of about forty, also tall and
angular, with a thin, elongated face and large hands and feet.
Hyperpituitarism evidently ran in the Pyne family.

A few preliminary questions brought out the information that she
was a widow, named Beedle, and had, at the death of her husband
five years before, come to Professor Dillard as the result of
Pyne's recommendation.

"What time did you leave the house this morning, Beedle?" Markham
asked her.

"Right after half past ten."  She seemed uneasy and on the alert,
and her voice was defensively belligerent.

"And what time did you return?"

"About half past twelve.  That man let me in"--she looked viciously
at Heath--"and treated me like I'd been a criminal."

Heath grinned.  "The time's O. K., Mr. Markham.  She got sore
because I wouldn't let her go down-stairs."

Markham nodded non-committally.

"Do you know anything of what took place here this morning?" he
went on, studying the woman closely.

"How should I know?  I was at Jefferson market."

"Did you see either Mr. Robin or Mr. Sperling?"

"They went down-stairs to the archery-room past the kitchen a
little while before I went out."

"Did you overhear anything they said?"

"I don't listen at keyholes."

Markham set his jaw angrily and was about to speak when Vance
addressed the woman suavely.

"The District Attorney thought that perhaps the door was open, and
that you might have overheard some of their conversation despite
your commendable effort not to listen."

"The door might've been open, but I didn't hear anything," she
answered sullenly.

"Then you couldn't tell us if there was any one else in the
archery-room."

Beedle narrowed her eyes and gave Vance a calculating look.

"Maybe there was some one else," she said slowly.  "In fact, I
thought I heard Mr. Drukker."  A note of venom came into her voice,
and the shadow of a hard smile passed over her thin lips.  "He was
here to call on Mr. Arnesson early this morning."

"Oh, was he, now?"  Vance appeared surprised at this news.  "You
saw him perhaps?"

"I saw him come in, but I didn't see him go out--anyway, I didn't
notice.  He sneaks in and out at all hours."

"Sneaks, eh?  Fancy that! . . .  By the by, which door did you use
when you went a-marketing?"

"The front door.  Since Miss Belle made a clubroom out of the
basement, I always use the front door."

"Then you didn't enter the archery-room this morning?"

"No."

Vance raised himself in his chair.

"Thanks for your help, Beedle.  We won't need you any more now."

When the woman had left us Vance rose and walked to the window.

"We're expending too much zeal in irrelevant channels, Markham,"
he said.  "We'll never get anywhere by ballyragging servants and
questioning members of the household.  There's a psychological wall
to be battered down before we can begin storming the enemy's
trenches.  Everybody in this ménage has some pet privacy that he's
afraid will leak out.  Each person so far has told us either less
or more than he knows.  Disheartenin', but true.  Nothing that
we've learned dovetails with anything else; and when chronological
events don't fit together, you may rest assured that the serrated
points of contact have been deliberately distorted.  I haven't
found one clean joinder in all the tales that have been poured into
our ears."

"It's more likely the connections are missing," Markham argued;
"and we'll never find them if we don't pursue our questionings."

"You're much too trustin'."  Vance walked back to the centre-table.
"The more questions we ask the farther afield we'll be taken.  Even
Professor Dillard didn't give us a wholly honest account.  There's
something he's keeping back--some suspicion he won't voice.  Why
did he bring that bow indoors?  Arnesson put his finger on a vital
spot when he asked the same question.  Shrewd fella, Arnesson.--
Then there's our athletic young lady with the muscular calves.
She's entangled in various amat'ry meshes, and is endeavoring to
extricate herself and her whole coterie without leaving a blemish
on any one.  A praiseworthy aim, but not one conducive to the
unadulterated truth.--Pyne has ideas, too.  That flabby facial mask
of his curtains many an entrancin' thought.  But we'll never probe
his cortex by chivyin' him with questions.  Somethin' rum, too,
about his matutinal labors.  He says he was in Arnesson's room all
morning; but he obviously didn't know that the professor took a
sunnin' on Arnesson's verandah.  And that linen-closet alibi--
much too specious.--Also, Markham, let your mind flutter about the
widowed Beedle's tale.  She doesn't like the over-sociable Mr.
Drukker; and when she saw a chance to involve him, she did so.
She 'thought' she heard his voice in the archery-room.  But did
she?  Who knows?  True, he might have tarried among the slings
and javelins on his way home and been joined later by Robin and
Sperling. . . .  Yes, it's a point we must investigate.  In
fact, a bit of polite converse with Mr. Drukker is strongly
indicated. . . ."

Footsteps were heard descending the front stairs, and Arnesson
appeared in the archway of the living-room.

"Well, who killed Cock Robin?" he asked, with a satyr-like grin.

Markham rose, annoyed, and was about to protest at the intrusion;
but Arnesson held up his hand.

"One moment, please.  I'm here to offer my exalted services in the
noble cause of justice--mundane justice, I would have you
understand.  Philosophically, of course, there's no such thing as
justice.  If there really were justice we'd all be in for a
shingling in the cosmic wood-shed."  He sat down facing Markham and
chuckled cynically.  "The fact is, the sad and precipitate
departure of Mr. Robin appeals to my scientific nature.  It makes a
nice, orderly problem.  It has a decidedly mathematical flavor--no
undistributed terms, you understand; clear-cut integers with
certain unknown quantities to be determined.--Well, I'm the genius
to solve it."

"What would be your solution, Arnesson?"  Markham knew and
respected the man's intelligence, and seemed at once to sense a
serious purpose beneath his attitude of sneering flippancy.

"Ah!  As yet I haven't tackled the equation."  Arnesson drew out an
old briar pipe and fingered it affectionately.  "But I've always
wanted to do a little detective work on a purely earthly plane--the
insatiable curiosity and natural inquisitiveness of the physicist,
you understand.  And I've long had a theory that the science of
mathematics can be advantageously applied to the trivialities of
our life on this unimportant planet.  There's nothing but law in
the universe--unless Eddington is right and there's no law at all--
and I see no sufficient reason why the identity and position of a
criminal can't be determined just as Leverrier calculated the mass
and ephemeris of Neptune from the observed deviations in the orbit
of Uranus.  You remember how, after his computations, he told
Galle, the Berlin astronomer, to look for the planet in a specified
longitude of the ecliptic."

Arnesson paused and filled his pipe.

"Now, Mr. Markham," he went on; and I tried to decide whether or
not the man was in earnest, "I'd like the opportunity of applying
to this absurd muddle the purely rational means used by Leverrier
in discovering Neptune.  But I've got to have the data on the
perturbations of Uranus's orbit, so to speak--that is, I must know
all the varying factors in the equation.  The favor I've come here
to ask is that you take me into your confidence and tell me all the
facts.  A sort of intellectual partnership.  I'll figure out this
problem for you along scientific lines.  It'll be bully sport; and
incidentally I'd like to prove my theory that mathematics is the
basis of all truth however far removed from scholastic abstractions."
He at last got his pipe going, and sank back in his chair.  "Is
it a bargain?"

"I'll be glad to tell you whatever we know, Arnesson," Markham
replied after a brief pause.  "But I can't promise to reveal
everything that may arise from now on.  It might work against the
ends of justice and embarrass our investigation."

Vance had sat with half-closed eyes, apparently bored by Arnesson's
astonishing request; but now he turned to Markham with a
considerable show of animation.

"I say, y' know; there's really no reason why we shouldn't give Mr.
Arnesson a chance to translate this crime into the realm of applied
mathematics.  I'm sure he'd be discreet and use our information
only for scientific purposes.  And--one never knows, does one?--we
may need his highly trained assistance before we're through with
this fascinatin' affair."

Markham knew Vance well enough to realize that his suggestion had
not been made thoughtlessly; and I was in no wise astonished when
he faced Arnesson and said:

"Very well, then.  We'll give you whatever data you need to work
out your mathematical formula.  Anything special you want to know
now?"

"Oh, no.  I know the details thus far as well as you; and I'll
strip Beedle and old Pyne of their contributions when you're gone.
But if I solve this problem and determine the exact position of the
criminal, don't pigeon-hole my findings as Sir George Airy did
those of poor Adams when he submitted his Neptunean calculations
prior to Leverrier's. . . ."

At this moment the front door opened, and the uniformed officer
stationed on the porch came in, followed by a stranger.

"This gent here says he wants to see the professor," he announced
with radiating suspicion; and turning to the man he indicated
Markham with a gesture of the head.  "That's the District Attorney.
Tell him your troubles."

The newcomer seemed somewhat embarrassed.  He was a slender, well-
groomed man with an unmistakable air of refinement.  His age, I
should say, was fifty, though his face held a perennially youthful
look.  His hair was thin and graying, his nose a trifle sharp, and
his chin small but in no way weak.  His eyes, surmounted by a high
broad forehead, were his most striking characteristic.  They were
the eyes of a disappointed and disillusioned dreamer--half sad,
half resentful, as if life had tricked him and left him unhappy and
bitter.

He was about to address Markham when he caught sight of Arnesson.

"Oh, good-morning, Arnesson," he said, in a quiet, well-modulated
voice.  "I hope there's nothing seriously wrong."

"A mere death, Pardee," the other replied carelessly.  "The
proverbial tempest in a teapot."

Markham was annoyed at the interruption.

"What can I do for you, sir?" he asked.

"I trust I am not intruding," the man apologized.  "I am a friend
of the family,--I live just across the street; and I perceived that
something unusual had happened here.  It occurred to me I might be
of some service."

Arnesson chuckled.  "My dear Pardee!  Why clothe your natural
curiosity in the habiliments of rhetoric?"

Pardee blushed.

"I assure you, Arnesson--" he began; but Vance interrupted him.

"You say you live opposite, Mr. Pardee.  You have perhaps been
observing this house during the forenoon?"

"Hardly that, sir.  My study, however, overlooks 75th Street, and
it's true I was sitting at the window most of the morning.  But I
was busy writing.  When I returned to my work from lunch I noticed
the crowd and the police cars and also the officer in uniform at
the door."

Vance had been studying him from the corner of his eye.

"Did you happen to see any one enter or leave this house this
morning, Mr. Pardee?" he asked.

The man shook his head slowly.

"No one in particular.  I noticed two young men--friends of Miss
Dillard--call at about ten o'clock; and I saw Beedle go out with
her market basket.  But that's all I recall."

"Did you see either of these young men depart?"

"I don't remember."  Pardee knit his brows.  "And yet it seems to
me one of them left by the range gate.  But it's only an
impression."

"What time would that have been?"

"Really, I couldn't say.  Perhaps an hour or so after his arrival.
I wouldn't care to be more specific."

"You recall no other person whatever either coming or going from
the house this morning?"

"I saw Miss Dillard return from the tennis courts about half past
twelve, just as I was called to lunch.  In fact, she waved her
racket to me."

"And no one else?"

"I'm afraid not."  There was unmistakable regret in his quiet
response.

"One of the young men you saw enter here has been killed," Vance
told him.

"Mr. Robin--alias Cock Robin," supplemented Arnesson, with a comic
grimace which affected me unpleasantly.

"Good Heavens!  How unfortunate!"  Pardee appeared genuinely
shocked.  "Robin?  Wasn't he the Champion Archer of Belle's club?"

"His one claim to immortality.--That's the chap."

"Poor Belle!"  Something in the man's manner caused Vance to regard
him sharply.  "I hope she's not too greatly upset by the tragedy."

"She's dramatizing it, naturally," Arnesson returned.  "So are the
police, for that matter.  Awful pother about nothing in particular.
The earth is covered with 'small crawling masses of impure
carbohydrates' like Robin--referred to in the aggregate as
humanity."

Pardee smiled with tolerant sadness,--he was obviously familiar
with Arnesson's cynicisms.  Then he appealed to Markham.

"May I be permitted to see Miss Dillard and her uncle?"

"Oh, by all means."  It was Vance who answered before Markham could
reach a decision.  "You'll find them in the library, Mr. Pardee."

The man left the room with a polite murmur of thanks.

"Queer fellow," commented Arnesson, when Pardee was out of hearing.
"Cursed with money.  Leads an indolent life.  His one passion is
solving chess problems. . . ."

"Chess?"  Vance looked up with interest.  "Is he, by any chance,
John Pardee, the inventor of the famous Pardee gambit?"

"The same."  Arnesson's face crinkled humorously.  "Spent twenty
years developing a cast-iron offensive that was to add new decimal
points to the game.  Wrote a book about it.  Then went forth
proselytizing like a crusader before the gates of Damascus.  He's
always been a great patron of chess, contributing to tournaments,
and scurrying round the world to attend the various chess jousting-
bouts.  Consequently was able to get his gambit tested.  It made a
great stir among the infra-champions of the Manhattan Chess Club.
Then poor Pardee organized a series of Masters Tournaments.  Paid
all the expenses himself.  Cost him a fortune, by the way.  And of
course he stipulated that the Pardee gambit be played exclusively.
Well, well, it was very sad.  When men like Doctor Lasker and
Capablanca and Rubinstein and Finn got to combating it, it went to
pieces.  Almost every player who used it lost.  It was disqualified--
even worse than the ill-fated Rice gambit.  Terrible blow for
Pardee.  It put snow in his hair, and took all the rubber out of his
muscles.  Aged him, in short.  He's a broken man."

"I know the history of the gambit," murmured Vance, his eyes
resting pensively on the ceiling.  "I've used it myself.  Edward
Lasker* taught it to me. . . ."


* The American chess master--sometimes confused with Doctor Emanuel
Lasker, the former world champion.


The uniformed officer again appeared in the archway and beckoned to
Heath.  The Sergeant rose with alacrity--the ramifications of chess
obviously bored him--and went into the hall.  A moment later he
returned bearing a small sheet of paper.

"Here's a funny one, sir," he said, handing it to Markham.  "The
officer outside happened to see it sticking outa the mail-box just
now, and thought he'd take a peep at it.--What do you make of it,
sir?"

Markham studied it with puzzled amazement, and then without a word
handed it to Vance.  I rose and looked over his shoulder.  The
paper was of the conventional typewriter size, and had been folded
to fit into the mail-box.  It contained several lines of typing
done on a machine with élite characters and a faded blue ribbon.

The first line read:


     Joseph Cochrane Robin is dead.


The second line asked:


     Who Killed Cock Robin?


Underneath was typed:


     Sperling means sparrow.


And in the lower right-hand corner--the place of the signature--
were the two words, in capitals:


     THE BISHOP.



CHAPTER V

A WOMAN'S SCREAM


(Saturday, April 2; 2.30 p.m.)


Vance, after glancing at the strange message with its even stranger
signature, reached for his monocle with that slow deliberation
which I knew indicated a keen suppressed interest.  Having adjusted
the glass he studied the paper intently.  Then he handed it to
Arnesson.

"Here's a valuable factor for your equation."  His eyes were fixed
banteringly on the man.

Arnesson regarded the note superciliously, and with a wry grimace
laid it on the table.

"I trust the clergy are not involved in this problem.  They're
notoriously unscientific.  One can't attack them with mathematics.
'The Bishop'. . . ," he mused.  "I'm unacquainted with any
gentlemen of the cloth.---I think I'll rule out this abracadabra
when making my calculations."

"If you do, Mr. Arnesson," replied Vance seriously, "your equation,
I fear, will fall to pieces.  That cryptic epistle strikes me as
rather significant.  Indeed--if you will pardon a mere lay opinion--
I believe it is the most mathematical thing that has appeared thus
far in the case.  It relieves the situation of all haphazardness or
accident.  It's the g, so to speak--the gravitational constant
which will govern all our equations."

Heath had stood looking down on the typewritten paper with solemn
disgust.

"Some crank wrote this, Mr. Vance," he declared.

"Undoubtedly a crank, Sergeant," agreed Vance.  "But don't overlook
the fact that this particular crank must have known many
interestin' and intimate details--to wit, that Mr. Robin's middle
name was Cochrane; that the gentleman had been killed with a bow
and arrow; and that Mr. Sperling was in the vicinity at the time of
the Robin's passing.  Moreover, this well-informed crank must have
had what amounted to foreknowledge regarding the murder; for the
note was obviously typed and inserted in the letter-box before you
and your men arrived on the scene."

"Unless," countered Heath doggedly, "he's one of those bimboes out
in the street, who got wise to what had happened and then stuck
this paper in the box when the officer's back was turned."

"Having first run home and carefully typewritten his communication--
eh, what?"  Vance shook his head with a rueful smile.  "No,
Sergeant, I'm afraid your theory won't do."

"Then what in hell does it mean?" Heath demanded truculently.

"I haven't the foggiest idea."  Vance yawned and rose.  "Come,
Markham, let's while away a few brief moments with this Mr. Drukker
whom Beedle abhors."

"Drukker!" exclaimed Arnesson, with considerable surprise.  "Where
does he fit in?"

"Mr. Drukker," explained Markham, "called here this morning to see
you; and it's barely possible he met Robin and Sperling before he
returned home."  He hesitated.  "Would you care to accompany us?"

"No, thanks."  Arnesson knocked out his pipe and got up.  "I've a
pile of class papers to look over.--It might be as well, however,
to take Belle along.  Lady Mae's a bit peculiar. . . ."

"Lady Mae?"

"My mistake.  Forgot you didn't know her.  We all call her Lady
Mae.  Courtesy title.  Pleases the poor old soul.  I'm referring
to Drukker's mother.  Odd character."  He tapped his forehead
significantly.  "Bit touched.  Oh, perfectly harmless.  Bright
as a whistle, but monominded, as it were.  Thinks the sun rises
and sets in Drukker.  Mothers him as if he were an infant.  Sad
situation. . . .  Yes, you'd better take Belle along.  Lady Mae
likes Belle."

"A good suggestion, Mr. Arnesson," said Vance.  "Will you ask Miss
Dillard if she'll be good enough to accompany us?"

"Oh, certainly."  Arnesson gave us an inclusive smile of farewell--
a smile which seemed at once patronizing and satirical--and went
up-stairs.  A few moments later Miss Dillard joined us.

"Sigurd tells me you want to see Adolph.  He, of course, won't
mind; but poor Lady Mae gets so upset over even the littlest
things. . . ."

"We sha'n't upset her, I hope."  Vance spoke reassuringly.  "But
Mr. Drukker was here this morning, d' ye see; and the cook says she
thought she heard him speaking to Mr. Robin and Mr. Sperling in the
archery-room.  He may be able to help us."

"I'm sure he will if he can," the girl answered with emphasis.
"But be very careful with Lady Mae, won't you?"

There was a pleading, protective note in her voice, and Vance
regarded her curiously.

"Tell us something of Mrs. Drukker--or Lady Mae--before we visit
her.  Why should we be so careful?"

"She's had such a tragic life," the girl explained.  "She was once
a great singer--oh, not just a second-rate artist, but a prima
donna with a marvelous career before her.*  She married a leading
critic of Vienna--Otto Drucker#--and four years later Adolph was
born.  Then one day in the Wiener Prater, when the baby was two
years old, she let him fall; and from that moment on her entire
life was changed.  Adolph's spine was injured, and he became a
cripple.  Lady Mae was heartbroken.  She held herself to blame for
his injury, and gave up her career to devote herself to his care.
When her husband died a year later she brought Adolph to America,
where she had spent some of her girlhood, and bought the house
where she now lives.  Her whole life has been centred on Adolph,
who grew up a hunchback.  She has sacrificed everything for him,
and cares for him as though he were a baby. . . ."


* Mae Brenner will still be remembered by Continental music lovers.
Her début was made at the unprecedented age of twenty-three as
Sulamith in "Die Königin von Saba" at the Imperial Opera House in
Vienna; although her greatest success was perhaps her Desdemona in
"Otello"--the last rôle she sang before her retirement.

# The name was, of course, originally spelled Drucker.  The change--
possibly some vague attempt at Americanization--was made by Mrs.
Drukker when she settled in this country.


A shadow crossed her face.  "Sometimes I think--we all think--that
she still imagines he's only a child.  She has become--well, morbid
about it.  But it's the sweet, terrible morbidity of a tremendous
motherlove--a sort of insanity of tenderness, uncle calls it.
During the past few months she has grown very strange--and peculiar.
I've often found her crooning old German lullabies and kindergarten
songs, with her arms crossed on her breast, as if--oh, it seems so
sacred and so terrible!--as if she were holding a baby. . . .  And
she has become frightfully jealous of Adolph.  She's resentful of
all other men.  Only last week I took Mr. Sperling to see her--we
often drop in to call on her: she seems so lonely and unhappy--and
she looked at him almost fiercely, and said:  'Why weren't you a
cripple, too?' . . ."

The girl paused and searched our faces.

"Now don't you understand why I asked you to be careful? . . .
Lady Mae may think we have come to harm Adolph."

"We sha'n't add unnecessarily to her suffering," Vance assured her
sympathetically.  Then, as we moved toward the hall, he asked her a
question which recalled to my mind his brief intent scrutiny of the
Drukker house earlier that afternoon.  "Where is Mrs. Drukker's
room situated?"

The girl shot him a startled look, but answered promptly:

"On the west side of the house--its bay window overlooks the
archery range."

"Ah!"  Vance took out his cigarette case, and carefully selected a
Régie.  "Does she sit much at this window?"

"A great deal.  Lady Mae always watches us at archery practice--why
I don't know.  I'm sure it pains her to see us, for Adolph isn't
strong enough to shoot.  He's tried it several times, but it tired
him so he had to give it up."

"She may watch you practising for the very reason that it does
torture her--a kind of self-immolation, y' know.  Those situations
are very distressing."  Vance spoke almost with tenderness--which,
to one who did not know his real nature, would have sounded
strange.  "Perhaps," he added, as we emerged into the archery range
through the basement door, "it would be best if we saw Mrs. Drukker
first for a moment.  It might tend to allay any apprehensions our
visit might cause her.  Could we reach her room without Mr.
Drukker's knowledge?"

"Oh, yes."  The girl was pleased at the idea.  "We can go in the
rear way.  Adolph's study, where he does his writing, is at the
front of the house."

We found Mrs. Drukker sitting in the great bay window on a
sprawling old-fashioned chaise-longue, propped up with pillows.
Miss Dillard greeted her filially and, bending over her with tender
concern, kissed her forehead.

"Something rather awful has happened at our house this morning,
Lady Mae," she said; "and these gentlemen wanted to see you.  I
offered to bring them over.  You don't mind, do you?"

Mrs. Drukker's pale, tragic face had been turned away from the door
as we entered, but now she stared at us with fixed horror.  She was
a tall woman, slender to the point of emaciation; and her hands,
which lay slightly flexed on the arms of the chair, were sinewy and
wrinkled like the talons of fabulous bird-women.  Her face, too,
was thin and deeply seamed; but it was not an unattractive face.
The eyes were clear and alive, and the nose was straight and
dominant.  Though she must have been well past sixty, her hair was
luxuriant and brown.

For several minutes she neither moved nor spoke.  Then her hands
closed slowly, and her lips parted.

"What do you want?" she asked in a low resonant voice.

"Mrs. Drukker,"--it was Vance who answered--"as Miss Dillard has
told you, a tragedy occurred next door this morning, and since your
window is the only one directly overlooking the archery range, we
thought that you might have seen something that would aid us in our
investigation."

The woman's vigilance relaxed perceptibly, but it was a moment or
two before she spoke.

"And what did take place?"

"A Mr. Robin was killed.--You knew him perhaps?"

"The archer--Belle's Champion Archer? . . .  Yes, I knew him.
A strong healthy child who could pull a heavy bow and not get
tired.--Who killed him?"

"We don't know."  Vance, despite his negligent air, was watching
her astutely.  "But inasmuch as he was killed on the range, within
sight of your window, we hoped you might be able to help us."

Mrs. Drukker's eyelids drooped craftily, and she clasped her hands
with a kind of deliberate satisfaction.

"You are sure he was killed on the range?"

"We found him on the range," Vance returned non-committally.

"I see. . . .  But what can I do to help you?"  She lay back
relaxed.

"Did you notice any one on the range this morning?" asked Vance.

"No!"  The denial was swift and emphatic.  "I saw no one.  I
haven't looked out on the range all day."

Vance met the woman's gaze steadily, and sighed.

"It's most unfortunate," he murmured.  "Had you been looking out of
the window this morning, it's wholly possible you might have seen
the tragedy. . . .  Mr. Robin was killed with a bow and arrow, and
there seems to have been no motive whatever for the act."

"You know he was killed with a bow and arrow?" she asked, a tinge
of color coming into her ashen cheeks.

"That was the Medical Examiner's report.  There was an arrow
through his heart when we found him."

"Of course.  That seems perfectly natural, doesn't it? . . .  An
arrow through the Robin's heart!"  She spoke with vague aloofness,
a distant, fascinated look in her eyes.

There was a strained silence, and Vance moved toward the window.

"Do you mind if I look out?"

With difficulty the woman brought herself back from some far train
of thought.

"Oh, no.  It isn't much of a view, though.  I can see the trees of
76th Street toward the north, and a part of the Dillard yard to the
south.  But that brick wall opposite is very depressing.  Before
the apartment house was built I had a beautiful view of the river."

Vance looked for a while down into the archery range.

"Yes," he observed; "if only you had been at the window this
morning you might have seen what happened.  Your view of the range
and the basement door of the Dillards' is very clear. . . .  Too
bad."  He glanced at his watch.  "Is your son in, Mrs. Drukker?"

"My son!  My baby!  What do you want with him?"  Her voice rose
pitifully, and her eyes fastened on Vance with venomous hatred.

"Nothing important," he said pacifying.  "Only, he may have seen
some one on the range--"

"He saw no one!  He couldn't have seen any one, for he wasn't here.
He went out early this morning, and hasn't returned."

Vance looked with pity at the woman.

"He was away all morning?--Do you know where he was?"

"I always know where he is," Mrs. Drukker answered proudly.  "He
tells me everything."

"And he told you where he was going this morning?" persisted Vance
gently.

"Certainly.  But I forget for the moment.  Let me think. . . ."
Her long fingers tapped on the arm of the chair, and her eyes
shifted uneasily.  "I can't recall.  But I'll ask him the moment he
returns."

Miss Dillard had stood watching the woman with growing perplexity.

"But, Lady Mae, Adolph was at our house this morning.  He came to
see Sigurd--"

Mrs. Drukker drew herself up.

"Nothing of the kind!" she snapped, eyeing the girl almost
viciously.  "Adolph had to go--down-town somewhere.  He wasn't near
your house--I KNOW he wasn't."  Her eyes flashed, and she turned a
defiant glare on Vance.

It was an embarrassing moment; but what followed was even more
painful.

The door opened softly, and suddenly Mrs. Drukker's arms went out.

"My little boy--my baby!" she cried.  "Come here, dear."

But the man at the door did not come forward.  He stood blinking
his beady little eyes at us, like a person waking in strange
surroundings.  Adolph Drukker was scarcely five feet tall.  He had
the typical congested appearance of the hunchback.  His legs were
spindling, and the size of his bulging, distorted torso seemed
exaggerated by his huge, dome-like head.  But there was
intellectuality in the man's face--a terrific passionate power
which held one's attention.  Professor Dillard had called him a
mathematical genius; and one could have no doubts as to his
erudition.*


* He gave me very much the same impression as did General Homer Lee
when I visited him at Santa Monica shortly before his death.


"What does all this mean?" he demanded in a high-pitched, tremulous
voice, looking toward Miss Dillard.  "Are these friends of yours,
Belle?"

The girl started to speak, but Vance halted her with a gesture.

"The truth is, Mr. Drukker," he explained sombrely, "there has been
a tragedy next door.  This is Mr. Markham, the District Attorney,
and Sergeant Heath of the Police Department; and at our request
Miss Dillard brought us here that we might ask your mother whether
or not she had noticed anything unusual on the archery range this
morning.  The tragedy occurred just outside the basement door of
the Dillard house."

Drukker thrust his chin forward and squinted.

"A tragedy, eh?  What kind of tragedy?"

"A Mr. Robin was killed--with a bow and arrow."

The man's face began to twitch spasmodically.

"Robin killed?  KILLED? . . .  What time?"

"Some time between eleven and twelve probably."

"Between eleven and twelve?"  Quickly Drukker's gaze shifted to his
mother.  He seemed to grow excited, and his huge splay fingers
worried the hem of his smoking-jacket.  "What did you see?"  His
eyes glinted as he focussed them on the woman.

"What do you mean, son?"  The retort was a panic-stricken whisper.

Drukker's face became hard, and the suggestion of a sneer twisted
his lips.

"I mean that it was about that time when I heard a scream in this
room."

"You didn't!  No--no!"  She caught her breath, and wagged her head
jerkily.  "You're mistaken, son.  I didn't scream this morning."

"Well, some one did."  There was a cold relentlessness in the man's
tone.  Then, after a pause, he added:  "The fact is, I came up-
stairs after I heard the scream, and listened at the door here.
But you were walking about humming 'Eia Popeia,' so I went back to
my work."

Mrs. Drukker pressed a handkerchief to her face, and her eyes
closed momentarily.

"You were at your work between eleven and twelve?"  Her voice now
rang with subdued eagerness.  "But I called you several times--"

"I heard you.  But I didn't answer.  I was too busy."

"So that was it."  She turned slowly toward the window.  "I thought
you were out.  Didn't you tell me?"

"I told you I was going to the Dillards'.  But Sigurd wasn't there,
and I came back a little before eleven."

"I didn't see you come in."  The woman's energy was spent, and she
lay back listlessly, her eyes on the brick wall opposite.  "And
when I called and you didn't answer I naturally thought you were
still out."

"I left the Dillards' by the street gate, and took a walk in the
park."  Drukker's voice was irritable.  "Then I let myself in by
the front door."

"And you say you heard me scream. . . .  But why should I scream,
son?  I've had no pains in my back this morning."

Drukker frowned, and his little eyes moved swiftly from Vance to
Markham.

"I heard some one scream--a woman--in this room," he iterated
stubbornly.  "About half past eleven."  Then he sank into a chair
and gazed moodily at the floor.

This perplexing verbal intercourse between mother and son had held
us all spellbound.  Though Vance had stood before an old
eighteenth-century print near the door, regarding it with apparent
absorption, I knew that no word or inflection had escaped him.  Now
he swung about and, giving Markham a signal not to interfere,
approached Mrs. Drukker.

"We're very sorry, madam, that we've had to trouble you.  Forgive
us, if you can."

He bowed and turned to Miss Dillard.

"Do you care to pilot us back?  Or shall we find our own way down?"

"I'll come with you," the girl said; and going to Mrs. Drukker she
put her arm about her.  "I'm so sorry, Lady Mae."

As we were passing out into the hall Vance, as if on second
thought, paused and looked back at Drukker.

"You'd better come with us, sir," he said, in a casual yet urgent
tone.  "You knew Mr. Robin, and you may be able to suggest
something."

"Don't go with them, son!" cried Mrs. Drukker.  She was sitting
upright now, her face contorted with anguish and fear.  "Don't go!
They're the enemy.  They want to hurt you. . . ."

Drukker had risen.

"Why shouldn't I go with them?" he retorted petulantly.  "I want to
find out about this affair.  Maybe--as they say--I can help them."
And with a gesture of impatience he joined us.



CHAPTER VI

"'I,' SAID THE SPARROW"


(Saturday, April 2; 3 p.m.)


When we were again in the Dillard drawing-room and Miss Dillard
had left us to rejoin her uncle in the library, Vance, without
preliminaries, proceeded to the business in hand.

"I didn't care to worry your mother, Mr. Drukker, by questioning
you in front of her, but inasmuch as you called here this morning
shortly before Mr. Robin's death, it is necessary--as a mere
routine procedure--that we seek whatever information you can give
us."

Drukker had seated himself near the fireplace.  He now drew in his
head cautiously, but made no answer.

"You came here," continued Vance, "about half past nine, I believe,
to call on Mr. Arnesson."

"Yes."

"By way of the archery range and the basement door?"

"I always come that way.  Why walk around the block?"

"But Mr. Arnesson was out this morning."

Drukker nodded.  "At the university."

"And, finding Mr. Arnesson away, you sat for a while in the library
with Professor Dillard, I understand, discussing an astronomical
expedition to South America."

"The expedition of the Royal Astronomical Society to Sobral to test
the Einsteinian deflection," amplified Drukker.

"How long were you in the library?"

"Less than half an hour."

"And then?"

"I went down to the archery-room, and glanced at one of the
magazines.  There was a chess problem in it--a Zugszwang end-game
that came up recently between Shapiro and Marshall--and I sat down
and worked it out. . . ."

"Just a moment, Mr. Drukker."  A note of suppressed interest came
into Vance's voice.  "You're interested in chess?"

"To a certain extent.  I don't spend much time at it, however.
The game is not purely mathematical; and it's insufficiently
speculative to appeal to a wholly scientific mind."

"Did you find the Shapiro-Marshall position difficult?"

"Not so difficult as tricky."  Drukker was watching Vance shrewdly.
"As soon as I discovered that an apparently useless pawn move was
the key to the impasse, the solution was simple."

"How long did it take you?"

"Half an hour or so."

"Until about half past ten, shall we say?"

"That would be about right."  Drukker settled deeper into his
chair, but his covert alertness did not relax.

"Then you must have been in the archery-room when Mr. Robin and Mr.
Sperling came there."

The man did not answer at once, and Vance, pretending not to notice
his hesitancy, added:  "Professor Dillard said they called at the
house about ten and, and after waiting a while in the drawing-room
here, went down to the basement."

"Where's Sperling now, by the way?"  Drukker's eyes darted
suspiciously from one to the other of us.

"We expect him here any minute," Vance replied.  "Sergeant Heath
has sent two of his men to fetch him."

The hunchback's eyebrows lifted.  "Ah!  So Sperling is being
forcibly brought back."  He pyramided his spatulate fingers and
inspected them musingly.  Then he slowly lifted his eyes to Vance.
"You asked me if I saw Robin and Sperling in the archery-room.--
Yes; they came down-stairs just as I was going."

Vance leaned back and stretched his legs before him.

"Did you get the impression, Mr. Drukker, that they had--as we
euphemistically say--been having words?"

The man considered this question for several moments.

"Now that you mention it," he said at length, "I do recall that
there seemed to be a coolness between them.  I wouldn't, however,
care to be too categorical on that point.  You see, I left the room
almost immediately after they entered."

"You went out the basement door, I think you said, and thence
through the wall gate into 75th Street.  Is that correct?"

For a moment Drukker seemed loath to answer; but he replied with an
effort at unconcern.

"Quite.  I thought I'd take a stroll along the river before going
back to work.  I went to the Drive, then up the bridle path, and
turned into the park at 79th Street."

Heath, with his habitual suspicion of all statements made to the
police, put the next question.

"Did you meet any one you knew?"

Drukker turned angrily, but Vance quickly stepped into the breach.

"It really doesn't matter, Sergeant.  If it's necess'ry later on to
ascertain that point, we can take the matter up again."  Then to
Drukker:  "You returned from your walk a little before eleven, I
think you said, and entered your house by the front door."

"That's right."

"You saw nothing, by the by, that was in the least extr'ordin'ry
when you were here this morning?"

"I saw nothing except what I've told you."

"And you're quite sure you heard your mother scream at about half
past eleven?"

Vance did not move as he asked this question; but a slightly
different note had crept into his voice, and it acted on Drukker in
a startling manner.  He heaved his squat body out of his chair, and
stood glaring down on Vance with menacing fury.  His tiny round
eyes flashed, and his lips worked convulsively.  His hands,
dangling before him, flexed and unflexed like those of a man in a
paroxysm.

"What are you driving at?" he demanded, his voice a shrill
falsetto.  "I tell you I heard her scream.  I don't care a damn
whether she admits it or not.  Moreover, I heard her walking in her
room.  SHE WAS IN HER ROOM, understand, AND I WAS IN MY ROOM,
between eleven and twelve.  And you can't prove anything different.
Furthermore, I'm not going to be cross-examined by you or any one
else as to what I was doing or where I was.  It's none of your
damned business--do you hear me? . . ."

So insensate was his wrath that I expected any minute to see him
hurl himself on Vance.  Heath had risen and stepped forward,
sensing the potential danger of the man.  Vance, however, did not
move.  He continued to smoke languidly, and when the other's fury
had been spent, he said quietly and without a trace of emotion:

"There's nothing more we have to ask you, Mr. Drukker.  And really,
y' know, there's no need to work yourself up.  It merely occurred
to me that your mother's scream might help to establish the exact
time of the murder."

"What could her scream have to do with the time of Robin's death?
Didn't she tell you she saw nothing?"  Drukker appeared exhausted,
and leaned heavily against the table.

At this moment Professor Dillard appeared in the archway.  Behind
him stood Arnesson.

"What seems to be the matter?" the professor asked.  "I heard the
noise here, and came down."  He regarded Drukker coldly.  "Hasn't
Belle been through enough to-day without your frightening her this
way?"

Vance had risen, but before he could speak Arnesson came forward
and shook his finger in mock reprimand at Drukker.

"You really should learn control, Adolph.  You take life with such
abominable seriousness.  You've worked in interstellar spatial
magnitudes long enough to have some sense of proportion.  Why
attach so much importance to this pin-point of life on earth?"

Drukker was breathing stertorously.

"These swine--" he began.

"Oh, my dear Adolph!"  Arnesson cut him short.  "The entire human
race are swine.  Why particularize? . . .  Come along.  I'll see
you home."  And he took Drukker's arm firmly and led him
downstairs.

"We're very sorry we disturbed you, sir," Markham apologized to
Professor Dillard.  "The man flew off the handle for some unknown
reason.  These investigations are not the pleasantest things in the
world; but we hope to be through before long."

"Well, make it as brief as you can, Markham.  And do try to spare
Belle as much as possible.--Let me see you before you go."

When Professor Dillard had returned up-stairs, Markham took a turn
up and down the room, his brows knit, his hands clasped behind him.

"What do you make of Drukker?" he asked, halting before Vance.

"Decidedly not a pleasant character.  Diseased physically and
mentally.  A congenital liar.  But canny--oh, deuced canny.  An
abnormal brain--you often find it in cripples of his type.
Sometimes it runs to real constructive genius, as with Steinmetz;
but too often it takes to abstruse speculation along impractical
lines, as with Drukker.  Still, our little verbal give-and-take has
not been without fruit.  He's hiding something that he'd like to
tell but doesn't dare."

"That's possible, of course," returned Markham doubtfully.  "He's
touchy on the subject of that hour between eleven and noon.  And he
was watching you all the time like a cat."

"A weasel," Vance corrected him.  "Yes, I was aware of his
flatterin' scrutiny."

"Anyway, I can't see that he's helped us very much."

"No," agreed Vance.  "We're not exactly forrader.  But we're at
least getting some luggage aboard.  Our excitable mathematical
wizard has opened up some very interestin' lines of speculation.
And Mrs. Drukker is fairly teemin' with possibilities.  If we knew
what both of 'em together know we might find the key to this silly
business."

Heath had been sullen for the past hour, and had looked on at the
proceedings with bored disdain.  But now he drew himself up
combatively.

"I'm here to tell you, Mr. Markham, that we're wasting our time.
What's the good of all these parleys?  Sperling's the boy we want,
and when my men bring him in and put him through a little sweating,
we'll have enough material for an indictment.  He was in love with
the Dillard girl and was jealous of Robin--not only on account of
the girl, but because Robin could shoot those red sticks straighter
than he could.  He had a scrap with Robin in this here room--the
professor heard 'em at it; and he was down-stairs with Robin,
according to the evidence, a few minutes before the murder. . . ."

"And," added Vance ironically, "his name means 'sparrow.'  Quod
erat demonstrandum.--No, Sergeant; it's much too easy.  It works
out like a game of Canfield with the cards stacked; whereas this
thing was planned much too carefully for suspicion to fall directly
on the guilty person."

"I can't see any careful planning about it," persisted Heath.
"This Sperling gets sore, picks up a bow, grabs an arrow off of the
wall, follows Robin outside, shoots him through the heart, and
beats it."

Vance sighed.

"You're far too forthright for this wicked world, Sergeant.  If
only things happened with such naïve dispatch, life would be very
simple--and depressin'.  But such was not the modus operandi of the
Robin's murder.  First, no archer could shoot at a moving human
target and strike just between the ribs over the vital spot of the
heart.  Secondly, there's that fracture of Robin's skull.  He may
have acquired it in falling, but it's not likely.  Thirdly, his hat
was at his feet, where it wouldn't have been if he had fallen
naturally.  Fourthly, the nock on the arrow is so bruised that I
doubt if it would hold a string.  Fifthly, Robin was facing the
arrow, and during the drawing and aiming of the bow he would have
had time to call out and cover himself.  Sixthly. . . ."

Vance paused in the act of lighting a cigarette.

"BY JOVE, Sergeant!  I've overlooked something.  When a man's
stabbed in the heart there's sure to be an immediate flow of blood,
especially when the end of the weapon is larger than the shaft and
there's no adequate plug for the hole.  I say!  It's quite possible
that you'll find some blood spots on the floor of the archery-room--
somewhere near the door most likely."

Heath hesitated, but only momentarily.  Experience had long since
taught him that Vance's suggestions were not to be treated
cavalierly; and with a good-natured grunt he got up and disappeared
toward the rear of the house.

"I think, Vance, I begin to see what you mean," observed Markham,
with a troubled look.  "But, good God!  If Robin's apparent death
with a bow and arrow was merely an ex-post-facto stage-setting,
then we're confronted by something almost too diabolical to
contemplate."

"It was the work of a maniac," declared Vance, with unwonted
sobriety.  "Oh, not the conventional maniac who imagines he's
Napoleon, but a madman with a brain so colossal that he has carried
sanity to a, humanly speaking, reductio ad absurdum--to a point,
that is, where humor itself becomes a formula in four dimensions."

Markham smoked vigorously, lost in speculation.

"I hope Heath doesn't find anything," he said at length.

"Why--in Heaven's name?" returned Vance.  "If there's no material
evidence that Robin met his end in the archery-room, it'll only
make the problem more difficult legally."

But the material evidence was forthcoming.  The Sergeant returned a
few minutes later, crestfallen but excited.

"Damn it, Mr. Vance!" he blurted.  "You had the dope all right."
He made no attempt to keep the admiration out of his look.  "There
isn't any actual blood on the floor; but there's a dark place on
the cement where somebody's scrubbed it with a wet rag to-day some
time.  It ain't dry yet; and the place is right near the door,
where you said.  And what makes it more suspicious is that one of
those rugs has been pulled over it.--But that don't let Sperling
out altogether," he added pugnaciously.  "He mighta shot Robin
indoors."

"And then cleaned up the blood, wiped off the bow and arrow, and
placed the body and the bow on the range, before making his
departure? . . .  Why? . . .  Archery, to begin with, isn't an
indoor sport, Sergeant.  And Sperling knows too much about it to
attempt murder with a bow and arrow.  A hit such as the one that
ended Robin's uneventful career would have been a pure fluke.
Teucer himself couldn't have achieved it with any degree of
certainty--and, according to Homer, Teucer was the champion archer
of the Greeks."

As he spoke Pardee passed down the hall on his way out.  He had
nearly reached the front door when Vance rose suddenly and went to
the archway.

"Oh, I say, Mr. Pardee.  Just a moment, please."  The man turned
with an air of gracious compliance.

"There is one other question we'd like to ask you," said Vance.
"You mentioned seeing Mr. Sperling and Beedle leave here this
morning by the wall gate.  Are you sure you saw no one else use the
gate?"

"Quite sure.  That is, I don't recall any one else."

"I was thinking particularly of Mr. Drukker."

"Oh, Drukker?"  Pardee shook his head with mild emphasis.  "No, I
would have remembered him.  But you realize a dozen people might
have entered and left this house without my noticing them."

"Quite--quite," Vance murmured indifferently.  "How good a chess
player, by the by, is Mr. Drukker?"

Pardee showed a flicker of surprise.

"He's not a player in the practical sense at all," he explained
with careful precision.  "He's an excellent analyst, however, and
understands the theory of the game amazingly well.  But he's had
little practice at actual over-the-board play."

When Pardee had gone Heath cocked a triumphant eye at Vance.

"I notice, sir," he remarked good-naturedly, "that I'm not the only
one who'd like to check the hunchback's alibi."

"Ah, but there's a difference between checking an alibi, and
demanding that the person himself prove it."

At this moment the front door was thrown open.  There were heavy
footsteps in the hall, and three men appeared in the archway.  Two
were obviously detectives, and between them stood a tall, clean-cut
youth of about thirty.

"We got him, Sergeant," announced one of the detectives, with a
grin of vicious satisfaction.  "He beat it straight home from here,
and was packing up when we walked in on him."

Sperling's eyes swept the room with angry apprehension.  Heath had
planted himself before the man, and stood looking him up and down
triumphantly.

"Well, young fella, you thought you'd get away, did you?"  The
Sergeant's cigar bobbed up and down between his lips as he spoke.

The color mounted to Sperling's cheeks, and he set his mouth
stubbornly.

"So!  You've got nothing to say?"  Heath went on, squaring his jaw
ferociously.  "You're one of these silent lads, are you?  Well,
we'll make you talk."  He turned to Markham.  "How about it, sir?
Shall I take him to Headquarters?"

"Perhaps Mr. Sperling will not object to answering a few questions
here," said Markham quietly.

Sperling studied the District Attorney a moment; then his gaze
moved to Vance, who nodded to him encouragingly.

"Answer questions about what?" he asked, with an obvious effort at
self-control.  "I was preparing to go away for the week-end when
these ruffians forced their way into my room; and I was brought
here without a word of explanation or even an opportunity to
communicate with my family.  Now you talk of taking me to Police
Headquarters."  He gave Heath a defiant glare.  "All right, take me
to Police Headquarters--and be damned to you!"

"What time did you leave here this morning, Mr. Sperling?"  Vance's
tone was soft and ingratiating, and his manner reassuring.

"About a quarter past eleven," the man answered.  "In time to catch
the 11.40 Scarsdale train from Grand Central."

"And Mr. Robin?"

"I don't know what time Robin went.  He said he was going to wait
for Belle--Miss Dillard.  I left him in the archery-room."

"You saw Mr. Drukker?"

"For a minute--yes.  He was in the archery-room when Robin and I
went down-stairs; but he left immediately."

"Through the wall gate?  Or did he walk down the range?"

"I don't remember--in fact, I didn't notice. . . .  Say, look here:
what's all this about anyway?"

"Mr. Robin was killed this morning," said Vance, "--at some time
near eleven o'clock."

Sperling's eyes seemed to start from his head.

"Robin killed?  My God! . . .  Who--who killed him?"  The man's
lips were dry, and he wetted them with his tongue.

"We don't know yet," Vance answered.  "He was shot through the
heart with an arrow."

This news left Sperling stunned.  His eyes traveled vaguely from
side to side, and he fumbled in his pocket for a cigarette.

Heath stepped nearer to him, and thrust out his chin.

"Maybe YOU can tell us who killed him--WITH A BOW AND ARROW!"

"Why--why do you--think I know?" Sperling managed to stammer.

"Well," returned the Sergeant relentlessly, "you were jealous of
Robin, weren't you?  You had a hot argument with him about the
girl, right in this room, didn't you?  And you were alone with him
just before he was croaked, weren't you?  And you're a pretty good
shot with the bow and arrow, aren't you?--That's why I think that
maybe you know something."  He narrowed his eyes and drew his upper
lip over his teeth.  "Say!  Come clean.  Nobody else but you coulda
done it.  You had a fight with him over the girl, and you were the
last person seen with him--ONLY A FEW MINUTES BEFORE HE WAS KILLED.
And who else woulda shot him with a bow and arrow except a champeen
archer--huh? . . .  Make it easy for yourself, and spill the story.
We've got you."

A strange light had gathered in Sperling's eyes, and his body
became rigid.

"Tell me,"--he spoke in a strained, unnatural voice--"did you find
the bow?"

"Sure we found it."  Heath laughed unpleasantly.  "Right where you
left it--in the alley."

"What kind of a bow was it?"  Sperling's gaze had not moved from
some distant point.

"What kind of a bow?" repeated Heath.  "A regular bow--"

Vance, who had been watching the youth closely, interrupted.

"I think I understand the question, Sergeant.--It was a woman's
bow, Mr. Sperling.  About five-feet-six, and rather light--under
thirty pounds, I should say."

Sperling drew a slow, deep breath, like a man steeling himself for
some bitter resolution.  Then his lips parted in a faint, grim
smile.

"What's the use?" he asked listlessly.  "I thought I'd have time to
get away. . . .  Yes, I killed him."

Heath grunted with satisfaction, and his belligerent manner at once
disappeared.

"You got more sense than I thought you had," he said, in an almost
paternal tone, nodding in a businesslike manner to the two
detectives.  "Take him along, boys.  Use my buggy--it's outside.
And lock him up without booking him.  I'll prefer the charge when I
get to the office."

"Come along, bo," ordered one of the detectives, turning toward the
hall.

But Sperling did not at once obey.  Instead he looked appealingly
at Vance.

"Could I--might I--" he began.

Vance shook his head.

"No, Mr. Sperling.  It would be best if you didn't see Miss
Dillard.  No use of harrowin' her feelings just now. . . .
Ch