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

The man turned without another word and went out between his
captors.



CHAPTER VII

VANCE REACHES A CONCLUSION


(Saturday, April 2; 3.30 p.m.)


When we were again alone in the drawing-room Vance rose and,
stretching himself, went to the window.  The scene that had just
been enacted, with its startling climax, had left us all somewhat
dazed.  Our minds were busy, I think, with the same idea; and when
Vance spoke it was as if he were voicing our thoughts.

"We're back in the nursery, it seems. . . .


     "'I,' said the Sparrow,
      'With my bow and arrow,
       I killed Cock Robin.' . . .


I say, Markham; this is getting a bit thick."

He came slowly back to the centre-table and crushed out his
cigarette.  From the corner of his eye he looked at Heath.

"Why so pensive, Sergeant?  You should be singing roundelays and
doing a joyous tarantella.  Has not your villain confessed to the
dark deed?  Does it not fill you with gladness to know that the
culprit will soon be languishin' in an oubliette?"

"To tell you the truth, Mr. Vance," Heath admitted sullenly, "I'm
not satisfied.  That confession came too easy, and--well, I've seen
a lot of guys come across, but this one somehow didn't act like he
was guilty.  And that's a fact, sir."

"At any rate," submitted Markham hopefully, "his preposterous
confession will damp the newspapers' curiosity and give us a free
field to push our investigation.  This case is going to make an
ungodly noise; but as long as the reporters think the guilty person
is jailed, they won't be bothering us for news of 'developments.'"

"I'm not saying he ain't guilty," asserted Heath pugnaciously,
obviously arguing against his own convictions.  "We certainly had
the goods on him, and he mighta realized it and spilled the works,
thinking it would go easier with him at the trial.  Maybe he's not
so dumb, after all."

"It won't do, Sergeant," said Vance.  "The lad's mental workin's
were deucedly simple.  He knew Robin was waiting to see Miss
Dillard, and he also knew she'd non-suited him, so to speak, last
night.  Sperling evidently didn't have a high opinion of Robin; and
when he heard of the gentleman's death at the hands of some one who
wielded a short, light bow, he jumped to the conclusion that Robin
had overstepped the bounds of propriety in his wooing, and received
a righteous shaft through the heart.  There was then nothing for
our noble, mid-Victorian sparrow to do but slap his own manly bosom
and proclaim:  'Ecce homo!' . . .  It's most distressin'."

"Well, anyhow," grumbled Heath, "I'm not going to turn him loose.
If Mr. Markham don't want to prosecute, that's up to him."

Markham looked at the Sergeant tolerantly.  He realized the strain
the man was under, and it was in keeping with his bigness of nature
that he took no offence at the other's words.

"Perhaps, however, Sergeant," he said kindly, "you'll not object to
continuing the investigation with me, even if I don't decide to
prosecute Sperling."

Heath was at once contrite.  He got up briskly and, going to
Markham, held out his hand.

"You know it, sir!"

Markham took the offered hand, and rose with a gracious smile.

"I'll leave things with you, then, for the time being.  I've some
work to do at the office, and I told Swacker to wait for me."*  He
moved dispiritedly toward the hall.  "I'll explain the situation to
Miss Dillard and the professor before I go.--Anything special in
mind, Sergeant?"


* Saturday was a "half day" at the District Attorney's office.
Swacker was Markham's secretary.


"Well, sir, I think I'll take a good look for that rag that was
used to wipe up the floor down-stairs.  And while I'm at it I'll
go over the archery-room with a fine-tooth comb.  Also, I'll put
the screws to the cook and the butler again--especially the cook.
She musta been mighty close at hand when the dirty work was going
on. . . .  Then the regular routine stuff--inquiries in the
neighborhood and that sorta thing."

"Let me know the results.  I'll be at the Stuyvesant Club later
to-day and to-morrow afternoon."

Vance had joined Markham in the archway.

"I say, old man," he remarked, as we went toward the stairs; "don't
minimize the importance of that cryptic note left in the mail-box.
I've a strong psychic suspicion that it may be the key to the
nursery.  You'd better ask Professor Dillard and his niece if
'Bishop' has any provocative significance for them.  That diocesan
signature has a meaning."

"I'm not so sure," returned Markham dubiously.  "It appears utterly
meaningless to me.  But I'll follow your suggestion."

Neither the professor nor Miss Dillard, however, could recall any
personal association with the word Bishop; and the professor was
inclined to agree with Markham that the note was without any
significant bearing on the case.

"It strikes me," he said, "as a piece of juvenile melodrama.  It
isn't likely that the person who killed Robin would adopt a vague
pseudonym and write notes about his crime.  I'm not acquainted with
criminals, but such conduct doesn't impress me as logical."

"But the crime itself was illogical," ventured Vance pleasantly.

"One can't speak of a thing being illogical, sir," returned the
professor tartly, "when one is ignorant of the very premises of a
syllogism."

"Exactly." Vance's tone was studiously courteous.  "Therefore, the
note itself may not be without logic."

Markham tactfully changed the subject.

"What I came particularly to tell you, professor, is that Mr.
Sperling called a short time ago and, when informed of Mr. Robin's
death, confessed to having done it himself. . . ."

"Raymond confessed!" gasped Miss Dillard.

Markham looked at the girl sympathetically.

"To be quite frank, I didn't believe Mr. Sperling.  Some mistaken
idea of chivalry undoubtedly led him to admit the crime."

"'Chivalry'?" she repeated, leaning forward tensely.  "What exactly
do you mean by that, Mr. Markham?"

It was Vance who answered.

"The bow that was found on the range was a woman's bow."

"Oh!"  The girl covered her face with her hands, and her body shook
with sobs.

Professor Dillard regarded her helplessly; and his impotency took
the form of irritation.

"What flummery is this, Markham?" he demanded.  "Any archer can
shoot with a woman's bow. . . .  That unutterable young idiot!
Why should he make Belle miserable by his preposterous confession!
. . .  Markham, my friend, do what you can for the boy."

Markham gave his assurances, and we rose to go.

"By the by, Professor Dillard," said Vance, pausing at the door;
"I trust you won't misunderstand me, but there's a bare possibility
that it was some one with access to this house who indulged in the
practical joke of typing that note.  Is there, by any chance, a
typewriter on the premises?"

It was patent that the professor resented Vance's question, but he
answered civilly enough.

"No,--nor has there ever been one to my knowledge.  I threw my own
machine away ten years ago when I left the university.  An agency
does whatever typing I need."

"And Mr. Arnesson?"

"He never uses a typewriter."

As we descended the stairs we met Arnesson returning from Drukker's.

"I've placated our local Leipnitz," he announced, with an
exaggerated sigh.  "Poor old Adolph!  The world is too much with
him.  When he's wallowing in the relativist formulas of Lorentz and
Einstein he's serene.  But when he's dragged down to actuality he
disintegrates."

"It may interest you to know," said Vance casually, "that Sperling
has just confessed to the murder."

"Ha!"  Arnesson chuckled.  "Quite in keeping.  'I,' said the
Sparrow. . . .  Very neat.  Still, I don't know how it'll work out
mathematically."

"And, since we agreed to keep you posted," continued Vance, "it may
help your calculations to know that we have reason to believe that
Robin was killed in the archery-room and placed on the range
afterwards."

"Glad to know it."  Arnesson became momentarily serious.  "Yes,
that may affect my problem."  He walked with us to the front door.
"If there's any way I can be of service to you, call on me."

Vance had paused to light a cigarette, but I knew, by the languid
look in his eyes, that he was making a decision.  Slowly he turned
to Arnesson.

"Do you know if Mr. Drukker or Mr. Pardee has a typewriter?"

Arnesson gave a slight start, and his eyes twinkled shrewdly.

"Aha!  That Bishop note. . . .  I see.  Merely a matter of being
thorough.  Quite right."  He nodded with satisfaction.  "Yes; both
have typewriters.  Drukker types incessantly--thinks to the
keyboard, so he says.  And Pardee's chess correspondence is as
voluminous as a movie hero's.  Types it all himself, too."

"Would it be any great trouble to you," asked Vance, "to secure a
specimen of the typing of each machine, and also a sample of the
paper these two gentlemen use?"

"None whatever."  Arnesson appeared delighted with the commission.
"Have them for you this afternoon.  Where'll you be?"

"Mr. Markham will be at the Stuyvesant Club.  You might phone him
there, and he can arrange--"

"Why bother to arrange anything?  I'll bring my findings to Mr.
Markham personally.  Only too glad.  Fascinating game, being a
sleuth."

Vance and I returned home in the District Attorney's car, and
Markham continued to the office.  At seven o'clock that night the
three of us met at the Stuyvesant Club for dinner; and at half past
eight we were sitting in Markham's favorite corner of the lounge-
room smoking and having our coffee.

During the meal no mention of the case had been made.  The late
editions of the afternoon papers had carried brief accounts of
Robin's death.  Heath had evidently succeeded in curbing the
reporters' curiosity and clipping the wings of their imagination.
The District Attorney's office being closed, the newspaper men were
unable to bombard Markham with questions, and so the late press was
inadequately supplied with information.  The Sergeant had guarded
the Dillard house well, for the reporters had not succeeded in
reaching any member of the household.

Markham had picked up a late Sun on his way from the dining-room,
and glanced through it carefully as he sipped his coffee.

"This is the first faint echo," he commented ruefully.  "I shudder
to think what the morning papers will contain."

"There's nothing to do but bear it," smiled Vance unfeelingly.
"The moment some bright journalistic lad awakes to the robin-
sparrow-arrow combination the city editors will go mad with joy,
and every front page in the country will look like a Mother-Goose
hoarding."

Markham lapsed into despondency.  Finally he struck the arm of his
chair angrily with his fist.

"Damn it, Vance!  I won't let you inflame my imagination with this
idiocy about nursery rhymes."  Then he added, with the ferocity of
uncertainty:  "It's a sheer coincidence, I tell you.  There simply
couldn't be anything in it."

Vance sighed.  "Convince yourself against your will; you're of the
same opinion still--to paraphrase Butler."  He reached into his
pocket and took out a sheet of paper.  "Putting all juvenilia to
one side pro tempore, here's an edifyin' chronology I drew up
before dinner. . . .  Edifyin'?  Well, it might be if we knew how
to interpret it."

Markham studied the paper for several minutes.  What Vance had
written down was this:



9.00 a.m.  Arnesson left house to go to university library.

9.15 a.m.  Belle Dillard left house for the tennis courts.

9.30 a.m.  Drukker called at house to see Arnesson.

9.50 a.m.  Drukker went down-stairs to archery-room.

10.00 a.m.  Robin and Sperling called at house and remained in
drawing-room for half an hour.

10.30 a.m.  Robin and Sperling went down to archery-room.

10.32 a.m.  Drukker says he went out for a walk, by the wall gate.

10.35 a.m.  Beedle went marketing.

10.55 a.m.  Drukker says he returned to his own house.

11.15 a.m.  Sperling went away by wall gate.

11.30 a.m.  Drukker says he heard a scream in his mother's room.

11.35 a.m.  Professor Dillard went on balcony of Arnesson's room.

11.40 a.m.  Professor Dillard saw Robin's body on archery range.

11.45 a.m.  Professor Dillard telephoned to District Attorney's
office.

12.25 p.m.  Belle Dillard returned from tennis.

12.30 p.m.  Police arrived at Dillard house.

12.35 p.m.  Beedle returned from market.

2.00 p.m.  Arnesson returned from university.


Ergo:  Robin was killed at some time between 11.15 (when Sperling
departed) and 11.40 (when Professor Dillard discovered body).


The only other persons known to have been in the house during this
time were Pyne and Professor Dillard.


The disposition of all other persons connected in any way with the
murder was as follows (according to statements and evidence now in
hand):

1.  Arnesson was at the university library between 9 a.m. and 2 p.m.

2.  Belle Dillard was at the tennis courts between 9.15 a.m. and
12.25 p.m.

3.  Drukker was walking in the park between 10.32 a.m. and 10.55
a.m.; and was in his study from 10.55 a.m. on.

4.  Pardee was in his house the entire morning.

5.  Mrs. Drukker was in her room the entire morning.

6.  Beedle was marketing between 10.35 a.m. and 12.35 p.m.

7.  Sperling was on his way to the Grand Central Station between
11.15 a.m. and 11.40 a.m., at which hour he took a train for
Scarsdale.


Conclusion:  Unless at least one of these seven alibis is shaken,
the whole weight of suspicion, and indeed the actual culpability,
must rest upon either Pyne or Professor Dillard.


When Markham finished reading the paper, he made a gesture of
exasperation.

"Your entire implication is preposterous," he said irritably; "and
your conclusion is a non-sequitur.  The chronology helps set the
time of Robin's death, but your assumption that one of the persons
we've seen to-day is necessarily guilty is arrant nonsense.  You
completely ignore the possibility that any outsider could have
committed the crime.  There were three ways of reaching the range
and the archery-room without entering the house--the wall gate on
75th Street, the other wall gate on 76th Street, and the alleyway
between the two apartment houses, leading to Riverside Drive."

"Oh, it's highly probable that one of these three entrances was
used," returned Vance.  "But don't overlook the fact that the most
secluded, and therefore the most likely, of these three means of
entry--to wit, the alleyway--is guarded by a locked door to which
no one would be apt to have a key except some member of the Dillard
household.  I can't picture a murderer walking into the range from
either of the street gates: he would be taking too many chances of
being seen."

Vance leaned forward seriously.

"And, Markham, there are other reasons why we may eliminate
strangers or casual prowlers.  The person who sent Robin to his
Maker must have been privy to the exact state of affairs in the
Dillard house this morning between a quarter past eleven and twenty
minutes to twelve.  He knew that Pyne and the old professor were
alone there.  He knew that Belle Dillard was not roaming about the
premises.  He knew that Beedle was away and could neither hear him
nor surprise him.  He knew that Robin--his victim--was there, and
that Sperling had departed.  Moreover, he knew something of the lie
of the land--the situation of the archery-room, for instance; for
it's only too plain that Robin was killed in that room.  No one who
wasn't familiar with all these details would have dared enter the
grounds and staged a spectacular murder.  I tell you, Markham, it
was some one very close to the Dillard ménage--some one who was
able to find out just what conditions obtained in that household
this morning."

"What about that scream of Mrs. Drukker's?"

"Ah, what about it, indeed?  Mrs. Drukker's window may have been a
factor that the murderer overlooked.  Or perhaps he knew about it
and decided to take that one chance of being seen.  On the other
hand, we don't know whether the lady screamed or not.  She says No;
Drukker says Yes.  They both have an ulterior motive for what they
poured into our trustin' ears.  Drukker may have told of the scream
by way of proving he was at home between eleven and twelve; and
Mrs. Drukker may have denied it for fear he wasn't home.  It's very
much of an olla podrida.  But it doesn't matter.  The main point
I'm trying to make is that only an intimate of the Dillard house
could have done this devilish business."

"We have too few facts to warrant that conclusion," asserted
Markham.  "Chance may have played a part--"

"Oh, I say, old man!  Chance may work out to a few permutations,
but not to twenty.--And there is that note left in the mail-box.
The murderer even knew Robin's middle name."

"Assuming, of course, that the murderer wrote the note."

"Do you prefer to assume that some balmy joker found out about the
crime through telepathy or crystal-gazing, hied to a typewriter,
composed a dithyramb, returned hot-footed to the house, and, for no
good reason, took the terrific risk of being seen putting the paper
in the mail-box?"

Before Markham could answer Heath entered the lounge room and
hurried to our corner.  That he was worried and uneasy was obvious.
With scarcely a word of greeting he handed a typewritten envelope
to Markham.

"That was received by the World in the late afternoon mail.
Quinan, the police reporter of the World, brought it to me a little
while ago; and he says that the Times and the Herald also got
copies of it.  The letters were stamped at one o'clock to-day, so
they were probably posted between eleven and twelve.  What's more,
Mr. Markham, they were mailed in the neighborhood of the Dillard
house, for they went through Post Office Station 'N' on West 69th
Street."

Markham withdrew the enclosure from the envelope.  Suddenly his
eyes opened wide, and the muscles about his mouth tightened.
Without looking up he handed the letter to Vance.  It consisted of
a single sheet of typewriting paper, and the words printed on it
were identical to those on the note left in the Dillard mail-box.
Indeed, the communication was an exact duplicate of the other:--
"Joseph Cochrane Robin is dead.  Who Killed Cock Robin?  Sperling
means sparrow.--THE BISHOP."

Vance scarcely glanced at the paper.

"Quite in keeping, don't y' know," he said indifferently.  "The
Bishop was afraid the public might miss the point of his joke; so
he explained it to the press."

"Joke, did you say, Mr. Vance?" asked Heath bitterly.  "It ain't
the kind of joke I'm used to.  This case gets crazier--"

"Exactly, Sergeant.  A crazy joke."

A uniformed boy stepped up to the District Attorney and, bending
over his shoulder discreetly, whispered something.

"Bring him here right away," ordered Markham.  Then to us:  "It's
Arnesson.  He'll probably have those specimens of typing."  A
shadow had settled on his face; and he glanced again at the note
Heath had brought him.  "Vance," he said in a low voice, "I'm
beginning to believe that this case may turn out to be as terrible
as you think.  I wonder if the typing will correspond. . . ."

But when the note was compared with the specimens Arnesson brought,
no similarity whatever could be discerned.  Not only were the
typing and the ink different from those of either Pardee's or
Drukker's machine, but the paper did not match any one of the
samples that Arnesson had secured.



CHAPTER VIII

ACT TWO


(Monday, April 11; 11.30 a.m.)


There is no need to recall here the nation-wide sensation caused by
Robin's murder.  Every one remembers how that startling tragedy was
featured in the country's press.  It was referred to by various
designations.  Some newspapers called it the Cock Robin murder.
Others, more alliterative but less accurate,* termed it the Mother
Goose murder.  But the signature of the typewritten notes appealed
strongly to the journalistic sense of mystery; and in time the
killing of Robin came to be known as the Bishop murder case.  Its
strange and fearful combination of horror and nursery jargon
inflamed the public's imagination; and the sinister and insane
implications of its details affected the entire country like some
grotesque nightmare whose atmosphere could not be shaken off.


* The old anonymous nursery rhyme, "The Death and Burial of Cock
Robin," is not, as is commonly supposed, one of the original
"Mother Goose Melodies," although it has often been included in
modern editions of that famous work.


During the week following the discovery of Robin's body, the
detectives of the Homicide Bureau, as well as the detectives
connected with the District Attorney's office, were busy night and
day pushing their inquiries.  The receipt of the duplicate Bishop
notes by the leading New York morning papers had dissipated
whatever ideas Heath may have held as to Sperling's guilt; and
though he refused to put his official imprimatur on the young man's
innocence he threw himself, with his usual gusto and pertinacity,
into the task of finding another and more plausible culprit.  The
investigation which he organized and superintended was as complete
as had been that of the Greene murder case.  No avenue which held
the meagrest hope of results was overlooked; and the report he drew
up would have given joy even to those meticulous criminologists of
the University of Lausanne.

On the afternoon of the day of the murder he and his men had
searched for the cloth that had been used to wipe up the blood in
the archery-room; but no trace of it was found.  Also, a thorough
examination of the Dillard basement was made in the hope of finding
other clews; but although Heath had put the task in the hands of
experts, the result was negative.  The only point brought to light
was that the fibre rug near the door had recently been moved so as
to cover the cleansed spot on the cement floor.  This fact,
however, merely substantiated the Sergeant's earlier observation.

The post-mortem report of Doctor Doremus lent color to the now
officially accepted theory that Robin had been killed in the
archery-room and then placed on the range.  The autopsy showed that
the blow on the back of his skull had been a particularly violent
one and had been made with a heavy rounded instrument, resulting in
a depressed fracture quite different from the fissured fracture
caused by striking a flat surface.  A search was instituted for the
weapon with which the blow had been dealt; but no likely instrument
was turned up.

Though Beedle and Pyne were questioned by Heath several times,
nothing new was learned from them.  Pyne insisted that he had been
up-stairs the entire morning in Arnesson's room, except for a few
brief absences to the linen-closet and the front door, and clung
tenaciously to his denial that he had touched either the body or
the bow when sent by Professor Dillard to find Sperling.  The
Sergeant, however, was not entirely satisfied with the man's
testimony.

"That bleary-eyed old cormorant has got something up his sleeve,"
he told Markham disgustedly.  "But it would take the rubber hose
and the water cure to make him spill it."

A canvass of all the houses in 75th Street between West End Avenue
and Riverside Drive was made in the hope of finding a tenant who
had noticed some one entering or emerging from the Dillard wall
gate during the forenoon.  But nothing was gained by this tedious
campaign.  Pardee, it seemed, was the only resident within view of
the Dillard house who had observed any one in the neighborhood that
morning.  In fact, after several days of arduous inquiries along
this line the Sergeant realized that he would have to proceed
without any outside or fortuitous assistance.

The various alibis of the seven persons whom Vance had tabulated in
his notation for Markham, were gone into as thoroughly as
circumstances would permit.  It was obviously impossible to check
them completely, for, in the main, they were based solely on the
statements of the individuals involved.  Moreover the investigation
had to be made with the utmost care lest suspicion be aroused.  The
results of these inquiries were as follows:


1.  Arnesson had been seen in the university library by various
people, including an assistant librarian and two students.  But the
time covered by their evidence was neither consecutive nor specific
as to the hour.

2.  Belle Dillard had played several sets of tennis at the public
courts at 119th Street and Riverside Drive, but because there had
been more than four in her party she had twice relinquished her
place to a friend; and none of the players could state positively
that she had remained at the courts during these periods.

3.  The time that Drukker departed from the archery-room was
definitely determined by Sperling; but no one could be found who
had seen him thereafter.  He admitted he had met no one he knew in
the park, but insisted he had stopped for a few minutes to play
with some strange children.

4.  Pardee had been alone in his study.  His old cook and his
Japanese valet had been in the rear of the house, and had not seen
him until lunch time.  His alibi therefore was purely a negative
one.

5.  Mrs. Drukker's word had to be accepted as to her whereabouts
that morning, for no one had seen her between nine-thirty, when
Drukker went to call on Arnesson, and one o'clock, when the cook
brought up her luncheon.

6.  Beedle's alibi was checked with fairly satisfactory
completeness.  Pardee had seen her leave the house at 10.35; and
she was remembered by several of the hucksters at the Jefferson
Market between eleven and twelve.

7.  The fact that Sperling had taken the 11.40 train to Scarsdale
was verified; therefore he would have had to leave the Dillard
house at the time he stated--namely: 11.15.  The determination of
this point, however, was merely a matter of routine, for he had
been practically eliminated from the case.  But if, as Heath
explained, it had been found that he had not taken the 11.40 train,
he would have again become an important possibility.


Pursuing his investigations along more general lines, the Sergeant
went into the histories and associations of the various persons
involved.  The task was not a difficult one.  All were well known,
and information concerning them was readily accessible; but not one
item was unearthed that could be regarded as even remotely throwing
any light on Robin's murder.  Nothing transpired to give so much as
a hint to the motive for the crime; and after a week's intensive
inquiry and speculation the case was still cloaked in seemingly
impenetrable mystery.

Sperling had not been released.  The prima facie evidence against
him, combined with his absurd confession, made impossible such a
step on the part of the authorities.  Markham, however, had held an
unofficial conference with the attorneys whom Sperling's father had
engaged to handle the case, and some sort of a "gentleman's
agreement" had, I imagine, been reached; for although the State
made no move to apply for an indictment (despite the fact that the
Grand Jury was sitting at the time), the defense lawyers did not
institute habeas corpus proceedings.  All the indications pointed
to the supposition that both Markham and Sperling's attorneys were
waiting for the real culprit to be apprehended.

Markham had had several interviews with the members of the Dillard
household, in a persistent effort to bring out some trivial point
that might lead to a fruitful line of inquiry; and Pardee had been
summoned to the District Attorney's office to make an affidavit as
to what he had observed from his window on the morning of the
tragedy.  Mrs. Drukker had been interrogated again; but not only
did she emphatically deny having looked out of her window that
morning, but she scoffed at the idea that she had screamed.

Drukker, when re-questioned, modified somewhat his former
testimony.  He explained that he might have been mistaken as to the
source of the scream, and suggested that it could have come from
the street or from one of the court windows of the apartment house.
In fact, he said, it was highly unlikely that his mother had
uttered the scream, for when he went to her door a moment later she
was humming an old German nursery song from Humperdinck's "Hänsel
and Gretel."  Markham, convinced that nothing further was to be
learned from either him or Mrs. Drukker, finally concentrated on
the Dillard house itself.

Arnesson attended the informal conferences held in Markham's
office; but for all his voluble and cynical observations, he
appeared to be as much at sea as the rest of us.  Vance chaffed him
good-naturedly about the mathematical formula that was to solve the
case, but Arnesson insisted that a formula could not be worked out
until all the factors of the theorem were available.  He appeared
to regard the entire affair as a kind of Juvenalian lark; and
Markham on several occasions gave vent to his exasperation.  He
reproached Vance for having made Arnesson an unofficial confrère in
the investigation, but Vance defended himself on the ground that
sooner or later Arnesson would supply some piece of seemingly
irrelevant information that could be used as an advantageous point
de départ.

"His crimino-mathematical theory is of course rubbish," said Vance.
"Psychology--not abstract science--will eventually reduce this
conundrum to its elements.  But we need material to go on, and
Arnesson knows the inwardness of the Dillard home better than we
can ever know it.  He knows the Drukkers, and he knows Pardee; and
it goes without saying that a man who has had the academic honors
heaped on him that he has, possesses an unusually keen mind.  As
long as he gives his thought and attention to the case, there's the
chance that he'll hit upon something of vital importance to us."

"You may be right," grumbled Markham.  "But the man's derisive
attitude gets on my nerves."

"Be more catholic," urged Vance.  "Consider his ironies in relation
to his scientific speculations.  What could be more natural than
that a man who projects his mind constantly into the vast
interplanet'ry reaches, and deals with light-years and infinities
and hyperphysical dimensions, should sniff derisively at the
infinitesimals of this life? . . .  Stout fella, Arnesson.  Not
homey and comfortable perhaps, but dashed interestin'."

Vance himself had taken the case with unwonted seriousness.  His
Menander translations had been definitely put aside.  He became
moody and waspish--a sure sign that his mind was busy with an
absorbing problem.  After dinner each night he went into his
library and read for hours--not the classic and aesthetic volumes
on which he generally spent his time, but such books as Bernard
Hart's "The Psychology of Insanity," Freud's "Der Witz und seine
Beziehung zum Unbewussten," Coriat's "Abnormal Psychology" and
"Repressed Emotions," Lippo's "Komik und Humor," Daniel A.
Huebsch's "The Murder Complex," Janet's "Les Obsessions et la
Psychasthènie," Donath's "Uber Arithmomanie," Riklin's "Wish
Fulfillment and Fairy Tales," Leppman's "Die forensische Bedeutung
der Zwangsvorstellungen," Kuno Fischer's "Uber den Witz," Erich
Wulffen's "Kriminalpsychologie," Hollenden's "The Insanity of
Genius," and Groos's "Die Spiele des Menschen."

He spent hours going over the police reports.  He called twice at
the Dillards', and on one occasion visited Mrs. Drukker in company
with Belle Dillard.  He had a long discussion one night with
Drukker and Arnesson on de Sitter's conception of physical space as
a Lobatchewskian pseudosphere, his object being, I surmised, to
acquaint himself with Drukker's mentality.  He read Drukker's book,
"World Lines in Multidimensional Continua"; and spent nearly an
entire day studying Janowski's and Tarrasch's analyses of the
Pardee gambit.

On Sunday--eight days after the murder of Robin--he said to me:

"Eheu, Van!  This problem is unbelievedly subtle.  No ordin'ry
investigation will ever probe it.  It lies in a strange territ'ry
of the brain; and its superficial childishness is its most terrible
and bafflin' aspect.  Nor is the perpetrator going to be content
with a single coup.  Cock Robin's death serves no definitive end.
The perverted imagination that concocted this beastly crime is
insatiable; and unless we can expose the abnormal psychological
mechanism back of it there will be more grim jokes to contend
with. . . ."

The very next morning his prognostication was verified.  We went to
Markham's office at eleven o'clock to hear Heath's report and to
discuss further lines of action.  Though nine days had passed since
Robin had been found murdered, no progress had been made in the
case, and the newspapers had grown bitter in their criticisms of
the police and the District Attorney's office.  It was therefore
with considerable depression that Markham greeted us that Monday
morning.  Heath had not yet arrived; but when he came a few minutes
later it was obvious that he, too, was discouraged.

"We run up against a brick wall, sir, every way we turn," he
repined, when he had outlined the results of his men's activities.
"There ain't a sign of a motive, and outside of Sperling there's
nobody on the landscape that we can hang anything on.  I'm coming
to the conclusion that it was some stick-up man who ambled into the
archery-room that morning and messed things up."

"'Stick-up' men, Sergeant," countered Vance, "are deuced
unimaginative, and they're without a sense of humor; whereas the
johnny who sent Robin on the long, long trail had both imagination
and humor.  He wasn't content merely to kill Robin: he had to turn
the act into an insane joke.  Then, lest the public wouldn't see
the point, he wrote explanat'ry letters to the press.--Does that
sound like the procedure of an itinerant thug?"

Heath smoked unhappily for several minutes without speaking, and at
length turned a gaze of exasperated dismay upon Markham.

"There's no sense in anything that's breaking round this town
lately," he complained.  "Just this morning a guy named Sprigg was
shot in Riverside Park, up near 84th Street.  Money in his pocket--
nothing taken.  Just shot.  Young fella--student at Columbia.
Lived with his parents; no enemies.  Went out to take his usual
walk before going to class.  Found dead half an hour later by a
bricklayer."  The Sergeant chewed viciously on his cigar.  "Now we
got that homicide to worry about; and we'll probably get hell from
the newspapers if we don't clear it up pronto.  And there's
nothing--absolutely nothing--to go on."

"Still, Sergeant," said Vance consolingly, "shooting a man is an
ordin'ry event.  There are numerous commonplace reasons for that
sort of crime.  It's the scenic and dramatic appurtenances of
Robin's murder that play havoc with all our processes of deduction.
If only it wasn't a nursery affair--"

Suddenly he stopped speaking, and his eyelids drooped slightly.
Leaning forward he very deliberately crushed out his cigarette.

"Did you say, Sergeant, that this chap's name was Sprigg?"

Heath nodded gloomily.

"And I say,"--despite Vance's effort, there was a note of eagerness
in his tone--"what was his first name?"

Heath gave Vance a look of puzzled surprise; but after a brief
pause he drew forth his battered notebook and riffled the pages.

"John Sprigg," he answered.  "John E. Sprigg."

Vance took out another cigarette, and lighted it with great care.

"And tell me: was he shot with a .32?"

"Huh?"  Heath's eyes rounded, and his chin shot forward.  "Yes,
a .32. . . ."

"And was he shot through the top of his head?"

The Sergeant sprang to his feet, and stared at Vance with ludicrous
bewilderment.  Slowly his head moved up and down.

"That's right.--But how in hell, sir?"

Vance held up a silencing hand.  It was, however, the look on his
face, rather than his gesture, that cut short the query.

"Oh, my precious aunt!"  He rose like a man in a daze and gazed
fixedly before him.  Had I not known him so well I would have sworn
he was frightened.  Then going to the tall window behind Markham's
desk he stood looking down on the gray stone walls of the Tombs.

"I can't credit it," he murmured.  "It's too ghastly. . . .  But of
course it's so! . . ."

Markham's impatient voice sounded.

"What's all this mumbling about, Vance?  Don't be so damned
mysterious!  How did you happen to know that Sprigg was shot
through the crown with a .32?  And what's the point, anyway?"

Vance turned and met Markham's eyes.

"Don't you see?" he asked softly.  "It's the second act of this
devilish parody! . . .  Have you forgotten your 'Mother-Goose'?"
And in a hushed voice that brought a sense of unutterable horror
into that dingy old office he recited:


     "'There was a little man,
       And he had a little gun,
       And his bullets were made of lead, lead, lead;

       He shot Johnny Sprig
       Through the middle of his wig,
       And knocked it right off of his head, head, head.'"



CHAPTER IX

THE TENSOR FORMULA


(Monday, April 11; 11.30 a.m.)


Markham sat staring at Vance like a man hypnotized.  Heath stood
rigid, his mouth partly open, his cigar held a few inches from his
lips.  There was something almost comic in the Sergeant's attitude,
and I had a nervous inclination to laugh; but for the moment my
blood seemed frozen, and all muscular movement was impossible.

Markham was the first to speak.  Jerking his head backward, he
brought his hand down violently on the desk-top.

"What new lunacy of yours is this?"  He was fighting desperately
against Vance's dumbfounding suggestion.  "I'm beginning to think
the Robin case has affected your mind.  Can't a man with the
commonplace name of Sprigg be shot without your trying to turn it
into some grotesque hocus-pocus?"

"Still, you must admit, Markham old dear," returned Vance mildly,
"this particular Johnny Sprigg was shot with 'a little gun',
through 'the middle of his wig', so to speak."

"What if he was?"  A dull flush had crept into Markham's face.  "Is
that any reason for your going about babbling Mother-Goose rhymes?"

"Oh, I say!  I never babble, don't y' know."

Vance had dropped into a chair facing the District Attorney's desk.
"I may not be a thrillin' elocutionist; but really, now, I don't
babble."  He gave Heath an ingratiating smile.  "Do I, Sergeant?"

But Heath had no opinion to express.  He still held his astonished
pose, though his eyes had now become mere slits in his broad,
pugnacious face.

"Are you seriously suggesting--?" began Markham; but Vance
interrupted him.

"Yes!  I'm seriously suggesting that the person who killed Cock
Robin with an arrow has vented his grim humor upon the hapless
Sprigg.  Coincidence is out of the question.  Such repetitive
parallels would knock the entire foundation out from all sanity and
reason.  'Pon my soul, the world is mad enough; but such madness
would dissipate all science and rational thinking.  Sprigg's death
is rather hideous; but it must be faced.  And however much you may
force yourself to protest against its incredible implications
you'll eventually have to accept them."

Markham had risen, and was pacing nervously up and down.

"I'll grant there are inexplicable elements in this new crime."
His combativeness had gone, and his tone had moderated.  "But if we
assume, even tentatively, that some maniac is at large reconstructing
the rhymes of his nursery days, I can't see how it will help us.
It would practically close all routine lines of investigation."

"I shouldn't say that, don't y' know."  Vance was smoking
meditatively.  "I'm inclined to think that such an assumption would
supply us with a definite basis of inquiry."

"Sure!" snapped Heath with ponderous sarcasm.  All we gotta do is
to go out and find one bug among six million people.  A cinch!"

"Don't let the fumes of discouragement overcome you, Sergeant.  Our
elusive jester is a rather distinctive entomological specimen.
Moreover, we have certain clews as to his exact habitat. . . ."

Markham swung round.  "What do you mean by that?"

"Merely that this second crime is related to the first not only
psychologically, but geographically.  Both murders were committed
within a few blocks of each other,--our destructive demon at least
has a weakness for the neighborhood in which the Dillard house is
situated.  Furthermore, the very factors of the two murders
preclude the possibility of his having come from afar to give rein
to his distorted humor in unfamiliar surroundings.  As I learnedly
pointed out to you, Robin was translated into the Beyond by some
one who knew all the conditions obtaining at the Dillard house at
the exact hour the grisly drama was performed; and surely it's
obvious that this second crime could not have been so tidily staged
had not the impresario been acquainted with Sprigg's ambulat'ry
intentions this morning.  Indeed, the entire mechanism of these
weird playlets proves that the operator was intimately cognizant of
all the circumstances surrounding his victims."

The heavy silence that followed was broken by Heath.

"If you're right, Mr. Vance, then that lets Sperling out."  The
Sergeant made even this qualified admission reluctantly; but it
showed that Vance's argument had not been without its effect on
him.  He turned desperately to the District Attorney.  "What do you
think we'd better do, sir?"

Markham was still battling against the acceptance of Vance's
theory, and he did not answer.  Presently, however, he reseated
himself at his desk and drummed with his fingers upon the blotter.
Then, without looking up, he asked:

"Who's in charge of the Sprigg case, Sergeant?"

"Captain Pitts.  The local men at the 68th-Street Station grabbed
it first; but when the news was relayed to the Bureau, Pitts and a
couple of our boys went up to look into it.  Pitts got back just
before I came over here.  Says it's a washout.  But Inspector
Moran* told him to stay with it."


* Inspector William M. Moran, who died two years ago, was, at the
time of the Bishop case, the Commanding Officer of the Detective
Bureau.


Markham pressed the buzzer beneath the edge of his desk, and
Swacker, his youthful secretary, appeared at the swinging door that
led to the clerical room between the District Attorney's private
office and the main waiting-room.

"Get Inspector Moran on the wire," he ordered.

When the connection had been made he drew the telephone toward him
and spoke for several minutes.

When he had replaced the receiver, he gave Heath a weary smile.

"You're now officially handling the Sprigg case, Sergeant.  Captain
Pitts will be here presently, and then we'll know where we stand."
He began looking through a pile of papers before him.  "I've got to
be convinced," he added half-heartedly, "that Sprigg and Robin are
tied up in the same sack."

Pitts, a short, stocky man, with a lean, hard face and a black
tooth-brush moustache, arrived ten minutes later.  He was, I
learned afterwards, one of the most competent men in the Detective
Division.  His specialty was "white-collar" gangsters.  He shook
hands with Markham and gave Heath a companionable leer.  When
introduced to Vance and me he focussed suspicious eyes on us and
bowed grudgingly.  But as he was about to turn away his expression
suddenly changed.

"Mr. Philo Vance, is it?" he asked.

"Alas!  So it seems, Captain," Vance sighed.

Pitts grinned and, stepping forward, held out his hand.

"Glad to meet you, sir.  Heard the Sergeant speak of you often."

"Mr. Vance is helping us unofficially with the Robin case,
Captain," explained Markham; "and since this man Sprigg was killed
in the same neighborhood we thought we'd like to hear your
preliminary report on the affair."  He took out a box of Corona
Perfectos, and pushed it across the desk.

"You needn't put the request that way, sir."  The Captain smiled,
and selecting a cigar held it to his nose with a kind of voluptuous
satisfaction.  "The Inspector told me you had some ideas about this
new case, and wanted to take it on.  To tell you the truth, I'm
glad to get rid of it."  He sat down leisurely, and lighted his
cigar.  "What would you like to know, sir?"

"Let us have the whole story," said Markham.

Pitts settled himself comfortably.

"Well, I happened to be on hand when the case came through--a
little after eight this morning--and I took a couple of the boys
and beat it up-town.  The local men were on the job, and an
assistant Medical Examiner arrived the same time I did. . . ."

"Did you hear his report, Captain?" asked Vance.

"Sure.  Sprigg was shot through the top of the head with a .32.  No
signs of a struggle--no bruises or anything.  Nothing fancy.  Just
a straight shooting."

"Was he lying on his back when found?"

"That's right.  Stretched out nice and pretty, right in the middle
of the walk."

"And wasn't his skull fractured where he'd fallen on the asphalt?"
The question was put negligently.

Pitts took his cigar from his mouth and gave Vance a sly look.

"I guess maybe you fellows over here do know something about this
case."  He nodded his head sagaciously.  "Yes, the back of the
guy's skull was all bashed in.  He sure had a tough fall.  But I
guess he didn't feel it--not with that bullet in his brain. . . ."

"Speaking of the shot, Captain, didn't anything about it strike you
as peculiar?"

"Well . . . yes," Pitts admitted, rolling his cigar meditatively
between his thumb and forefinger.  "The top of a guy's head isn't
where I'd ordinarily look for a bullet-hole.  And his hat wasn't
touched,--it must have fallen off before he was potted.  You might
call those facts peculiar, Mr. Vance."

"Yes, Captain, they're dashed peculiar. . . .  And I take it the
pistol was held at close range."

"Not more'n a couple of inches away.  The hair was singed round the
hole."  He made a broad gesture of inconsequence.  "Still and all,
the guy might have seen the other fellow draw the gun, and ducked
forward, spilling his hat.  That would account for his getting the
shot at close range in the top of the head."

"Quite, quite.  Except that, in that case, he wouldn't have fallen
over back, but would have pitched forward on his face. . . .  But
go on with the story, Captain."

Pitts gave Vance a look of crafty agreement, and continued.

"The first thing I did was to go through the fellow's pockets.  He
had a good gold watch on him and about fifteen dollars in bills and
silver.  So it didn't look like a robbery--unless the guy that shot
him got panicky and beat it.  But that didn't seem likely, for
there's never any one round that part of the park early in the
morning; and the walk there dips under a stone bluff, so that the
view is cut off.  The bird that did the job certainly picked a
swell place for it. . . .  Anyhow, I left a couple of men to guard
the body till the wagon came for it, and went up to Sprigg's house
in 93rd Street,--I'd got his name and address from a couple of
letters in his pocket.  I found out he was a student at Columbia,
living with his parents, and that it was his habit to take a walk
in the park after breakfast.  He left home this morning about half
past seven. . . ."

"Ah!  It was his habit to promenade in the park each morning,"
murmured Vance.  "Most interestin'."

"Even so, that don't get us anywheres," returned Pitts.  "Plenty of
fellows take an early constitutional.  And there was nothing
unusual about Sprigg this morning.  He wasn't worried about
anything, his folks told me; and was cheerful enough when he said
good-bye to 'em.--After that I hopped up to the university and made
inquiries; talked to a couple of the students that knew him, and
also to one of the instructors.  Sprigg was a quiet sort of chap.
Didn't make friends and kept pretty much to himself.  Serious bird--
always working at his studies.  Stood high in his classes, and was
never seen going around with Janes.  Didn't like women, in fact.
Wasn't what you'd call sociable.  From all reports he was the last
man to get in a mess of any kind.  That's why I can't see anything
special in his getting shot.  It must have been an accident of some
kind.  Might have been taken for somebody else."

"And he was found at what time?"

"About quarter of eight.  A bricklayer on the new 79th-Street dock
was cutting across the embankment toward the railway tracks, and
saw him.  He notified one of the post officers on the Drive, who
phoned in to the local station."

"And Sprigg left his home in 93rd Street at half past seven."
Vance gazed at the ceiling meditatively.  "Therefore he would have
had just enough time to reach this point in the park before being
killed.  It looks as if some one who knew his habits was waiting
for him.  Neatness and dispatch, what? . . .  It doesn't appear
exactly fortuitous, does it, Markham?"

Ignoring the jibe Markham addressed Pitts.

"Was there nothing found that could possibly be used as a lead?"

"No, sir.  My men combed the spot pretty thoroughly, but nothing
showed up."

"And in Sprigg's pockets--among his papers. . . ?"

"Not a thing.  I've got all the stuff at the Bureau--a couple of
ordinary letters, a few odds and ends of the usual kind. . . ."  He
paused as if suddenly remembering something, and pulled out a dog-
eared note-book.  "There was this," he said unenthusiastically,
handing a torn, triangular scrap of paper to Markham.  "It was
found under the fellow's body.  It don't mean anything, but I stuck
it in my pocket--force of habit."

The paper was not more than four inches long, and appeared to have
been torn from the corner of an ordinary sheet of unruled
stationery.  It contained part of a typewritten mathematical
formula, with the lambda, the equals and the infinity sign marked
in with pencil.  I reproduce the paper here, for, despite its
seeming irrelevancy, it was to play a sinister and amazing part in
the investigation of Sprigg's death.


[Picture of formula--Formula.gif]


Vance glanced only casually at the exhibit, but Markham held it in
his hand frowning at it for several moments.  He was about to make
some comment when he caught Vance's eye; and, instead, he tossed
the paper to the desk carelessly with a slight shrug.

"Is this everything you found?"

"That's all, sir."

Markham rose.

"We're very grateful to you, Captain.  I don't know what we'll be
able to make out of this Sprigg case, but we'll look into it."  He
pointed to the box of Perfectos.  "Put a couple in your pocket
before you go."

"Much obliged, sir."  Pitts selected the cigars, and placing them
tenderly in his waistcoat pocket, shook hands with all of us.

When he had gone Vance got up with alacrity, and bent over the
scrap of paper on Markham's desk.

"My word!"  He took out his monocle and studied the symbols for
several moments.  "Most allurin'.  Now where have I seen that
formula recently? . . .  Ah!  The Riemann-Christoffel tensor--of
course!  Drukker uses it in his book for determining the Gaussian
curvature of spherical and homaloidal space. . . .  But what was
Sprigg doing with it?  The formula is considerably beyond the
college curricula. . . ."  He held the paper up to the light.
"It's the same stock as that on which the Bishop notes are written.
And you probably observed that the typing is also similar."

Heath had stepped forward, and now scrutinized the paper.

"It's the same, all right."  The fact seemed to nonplus him.
"That's a link anyway between the two crimes."

Vance's eyes took on a puzzled look.

"A link--yes.  But the presence of the formula under Sprigg's body
appears as irrational as the murder itself. . . ."

Markham moved uneasily.

"You say it is a formula that Drukker uses in his book?"

"Yes.  But the fact doesn't necessarily involve him.  The tensor is
known to all advanced mathematicians.  It is one of the technical
expressions used in non-Euclidean geometry; and though it was
discovered by Riemann in connection with a concrete problem in
physics,* it has now become of widespread importance in the
mathematics of relativity.  It's highly scientific in the abstract
sense, and can have no direct bearing on Sprigg's murder."  He sat
down again.  "Arnesson will be delighted with the find.  He may be
able to work out some astonishing conclusion from it."


* This expression was actually developed by Christoffel for a
problem on the conductivity of heat, and published by him in 1869
in the "Crelle Journal für reine und angewandte Mathematik."


"I see no reason," protested Markham, "to inform Arnesson of this
new case.  My idea would be to keep it under cover as much as
possible."

"The Bishop won't let you, I fear," returned Vance.

Markham set his jaw.

"Good God!" he burst out.  "What damnable sort of thing are we
facing?  I expect every minute to wake up and discover I've been
living a nightmare."

"No such luck, sir," growled Heath.  He took a resolute breath like
a man preparing for combat.  "What's on the cards?  Where do we go
from here?  I need action."

Markham appealed to Vance.

"You seem to have some idea about this affair.  What's your
suggestion?  I frankly admit I'm floundering about in a black
chaos."

Vance inhaled deeply on his cigarette.  Then he leaned forward as
if to give emphasis to his words.

"Markham old man, there's only one conclusion to be drawn.  These
two murders were engineered by the same brain: both sprang from the
same grotesque impulse; and since the first of them was committed
by some one intimately familiar with conditions inside the Dillard
house, it follows that we must now look for a person who, in
addition to that knowledge, had definite information that a man
named John Sprigg was in the habit of taking a walk each morning in
a certain part of Riverside Park.  Having found such a person, we
must check up on the points of time, place, opportunity, and
possible motive.  There's some interrelation between Sprigg and the
Dillards.  What it is I don't know.  But our first move should be
to find out.  What better starting-point than the Dillard house
itself?"

"We'll get some lunch first," said Markham wearily.  "Then we'll
run out there."



CHAPTER X

A REFUSAL OF AID


(Monday, April 11; 2 p.m.)


It was shortly after two o'clock when we reached the Dillard house.
Pyne answered our ring; and if our visit caused him any surprise he
succeeded admirably in hiding it.  In the look he gave Heath,
however, I detected a certain uneasiness; but when he spoke his
voice had the flat, unctuous quality of the well-trained servant.

"Mr. Arnesson has not returned from the university," he informed
us.

"Mind-reading, I see," said Vance, "is not your forte, Pyne.  We
called to see you and Professor Dillard."

The man looked ill at ease; but before he could answer Miss Dillard
appeared in the archway of the drawing-room.

"I thought I recognized your voice, Mr. Vance."  She included us
all in a smile of wistful welcome.  "Please come in. . . .  Lady
Mae dropped in for a few minutes,--we're going riding together this
afternoon," she explained, as we entered the room.

Mrs. Drukker stood by the centre-table, one bony hand on the back
of the chair from which she had evidently just risen.  There was
fear in her eyes as she stared at us unblinkingly; and her lean
features seemed almost contorted.  She made no effort to speak, but
stood rigidly as if waiting for some dread pronouncement, like a
convicted prisoner at the bar about to receive sentence.

Belle Dillard's pleasant voice relieved the tensity of the
situation.

"I'll run up and tell uncle you're here."

She had no sooner quitted the room than Mrs. Drukker leaned over
the table and said to Markham in a sepulchral, awe-stricken
whisper:  "I know why you've come!  It's about that fine young man
who was shot in the park this morning."

So amazing and unexpected were her words that Markham could make no
immediate answer; and it was Vance who replied.

"You have heard of the tragedy, then, Mrs. Drukker?  How could the
news have come to you so soon?"

A look of canniness came into the woman's expression, giving her
the appearance of an evil old witch.

"Every one is talking about it in the neighborhood," she answered
evasively.

"Indeed?  That's most unfortunate.  But why do you assume we have
come here to make inquiries about it?"

"Wasn't the young man's name Johnny Sprigg?"  A faint, terrible
smile accompanied the question.

"So it was.  John E. Sprigg.  Still, that does not explain his
connection with the Dillards."

"Ah, but it does!"  Her head moved up and down with a sort of
horrible satisfaction.  "It's a game--a child's game.  First Cock
Robin . . . then Johnny Sprig.  Children must play--all healthy
children must play."  Her mood suddenly changed.  A softness shone
on her face, and her eyes grew sad.

"It's a rather diabolical game, don't you think, Mrs. Drukker?"

"And why not?  Isn't life itself diabolical?"

"For some of us--yes."  A curious sympathy informed Vance's words
as he gazed at this strange tragic creature before us.  "Tell me,"
he went on quickly, in an altered tone; "do you know who the Bishop
is?"

"The Bishop?"  She frowned perplexedly.  "No, I don't know him.  Is
that another child's game?"

"Something of that kind, I imagine.  At any rate, the Bishop is
interested in Cock Robin and Johnny Sprig.  In fact, he may be the
person who is making up these fantastic games.  And we're looking
for him, Mrs. Drukker.  We hope to learn the truth from him."

The woman shook her head vaguely.  "I don't know him."  Then she
glared vindictively at Markham.  "But it's not going to do you
any good to try to find out who killed Cock Robin and shot Johnny
Sprig through the middle of his wig.  You'll never learn--never--
NEVER. . . ."  Her voice had risen excitedly, and a fit of trembling
seized her.

At this moment Belle Dillard re-entered the room, and going quickly
to Mrs. Drukker put her arm about her.

"Come," she said soothingly; "we'll have a long drive in the
country, Lady Mae."  Reproachfully she turned to Markham, and said
coldly:  "Uncle wishes you to come to the library."  With that she
led Mrs. Drukker from the room and down the hall.

"Now that's a queer one, sir," commented Heath, who had stood
looking on with bewildered amazement.  "She had the dope on this
Johnny-Sprig stuff all the time!"

Vance nodded.

"And our appearance here frightened her.  Still, her mind is morbid
and sensitive, Sergeant; and dwelling as she does constantly on her
son's deformity and the early days when he was like other children,
it's quite possible she merely hit accidentally upon the Mother-
Goose significance of Robin's and Sprigg's death. . . .  I wonder."
He looked toward Markham.  "There are strange undercurrents in this
case--incredible and terrifying implications.  It's like being lost
in the Dovrë-Troll caverns of Ibsen's 'Peer Gynt,' where only
monstrosities and abnormalities exist."  He shrugged his shoulders,
though I knew he had not wholly escaped the pall of horror cast on
us by Mrs. Drukker's words.  "Perhaps we can find a little solid
footing with Professor Dillard."

The professor received us without enthusiasm and with but scant
cordiality.  His desk was littered with papers, and it was obvious
that we had disturbed him in the midst of his labors.

"Why this unexpected visit, Markham?" he asked, after we had seated
ourselves.  "Have you something to report on Robin's death?"  He
marked a page in Weyl's "Space, Time and Matter" and, settling back
reluctantly, regarded us with impatience.  "I'm very busy working
on a problem of Mach's mechanics. . . ."

"I regret," said Markham, "I have nothing to report on the Robin
case.  But there has been another murder in this neighborhood to-
day, and we have reason to believe that it may be connected with
Robin's death.  What I wanted particularly to ask you, sir, is
whether or not the name of John E. Sprigg is familiar to you."

Professor Dillard's expression of annoyance changed quickly.

"Is that the name of the man who was killed?"  There was no longer
any lack of interest in his attitude.

"Yes.  A man named John E. Sprigg was shot in Riverside Park, near
84th Street, this morning shortly after half past seven."

The professor's eyes wandered to the mantelpiece, and he was silent
for several moments.  He seemed to be debating inwardly some point
that troubled him.

"Yes," he said at length, "I--we--do know a young man of that name--
though it's wholly unlikely he's the same one."

"Who is he?"  Markham's voice was eagerly insistent.

Again the professor hesitated.

"The lad I have in mind is Arnesson's prize student in mathematics--
what they'd call at Cambridge a senior wrangler."

"How do you happen to know him, sir?"

"Arnesson has brought him to the house here several times.  Wanted
me to see him and talk to him.  Arnesson was quite proud of the
boy; and I must admit he showed unusual talent."

"Then he was known to all the members of the household?"

"Yes.  Belle met him, I think.  And if by 'the household' you
include Pyne and Beedle, I should say the name was probably
familiar to them too."

Vance asked the next question.

"Did the Drukkers know Sprigg, Professor Dillard?"

"It's quite possible.  Arnesson and Drukker see each other a great
deal. . . .  Come to think of it, I believe Drukker was here one
night when Sprigg called."

"And Pardee: did he also know Sprigg?"

"As to that I couldn't say."  The professor tapped impatiently on
the arm of his chair, and turned back to Markham.  "See here"--his
voice held a worried petulance--"what's the point of these
questions?  What has our knowing a student named Sprigg to do with
this morning's affair?  Surely you don't mean to tell me that the
man who was killed was Arnesson's pupil."

"I'm afraid it's true," said Markham.

There was a note of anxiety--of fear almost, I thought--in the
professor's voice when he next spoke.

"Even so, what can that fact have to do with us?  And how can you
possibly connect his death with Robin's?"

"I admit we have nothing definite to go on," Markham told him.
"But the purposelessness of both crimes--the total lack of any
motive in either case--seems to give them a curious unity of
aspect."

"You mean, of course, that you have found no motive.  But if all
crimes without apparent motive were assumed to be connected--"

"Also there are the elements of time and proximity in these two
cases," Markham amplified.

"Is that the basis of your assumption?"  The professor's manner was
benevolently contemptuous.  "You never were a good mathematician,
Markham, but at least you should know that no hypothesis can be
built on such a flimsy premise."

"Both names," interposed Vance, "--Cock Robin and Johnny Sprig--are
the subjects of well-known nursery rhymes."

The old man stared at him with undisguised astonishment; and
gradually an angry flush mounted to his face.

"Your humor, sir, is out of place."

"It is not MY humor, alas!" replied Vance sadly.  "The jest is the
Bishop's."

"The Bishop?"  Professor Dillard strove to curb his irritation.
"Look here, Markham; I won't be played with.  That's the second
mention of a mysterious Bishop that's been made in this room; and I
want to know the meaning of it.  Even if a crank did write an
insane letter to the papers in connection with Robin's death, what
has this Bishop to do with Sprigg?"

"A paper was found beneath Sprigg's body bearing a mathematical
formula typed on the same machine as the Bishop notes."

"What!"  The professor bent forward.  "The same machine, you say?
And a mathematical formula? . . .  What was the formula?"

Markham opened his pocketbook, and held out the triangular scrap of
paper that Pitts had given him.

"The Riemaun-Christoffel tensor. . . ."  Professor Dillard sat for
a long time gazing at the paper; then he handed it back to Markham.
He seemed suddenly to have grown older; and there was a weary look
in his eyes as he lifted them to us.  "I don't see any light in
this matter."  His tone was one of hopeless resignation.  "But
perhaps you are right in following your present course.--What do
you want of me?"

Markham was plainly puzzled by the other's altered attitude.

"I came to you primarily to ascertain if there was any link between
Sprigg and this house; but, to be quite candid, I don't see how
that link, now that I have it, fits into the chain.--I would,
however, like your permission to question Pyne and Beedle in
whatever way I think advisable."

"Ask them anything you like, Markham.  You shall never be able to
accuse me of having stood in your way."  He glanced up appealingly.
"But you will, I hope, advise me before you take any drastic
steps."

"That I can promise you, sir."  Markham rose.  "But I fear we are a
long way from any drastic measures at present."  He held out his
hand, and from his manner it was evident he had sensed some hidden
anxiety in the old man and wanted to express his sympathy without
voicing his feelings.

The professor walked with us to the door.

"I can't understand that typed tensor," he murmured, shaking his
head.  "But if there's anything I can do. . . ."

"There IS something you can do for us, Professor Dillard," said
Vance, pausing at the door.  "On the morning Robin was killed we
interviewed Mrs. Drukker--"

"Ah!"

"And though she denied having sat at her window during the forenoon
there is a possibility she saw something happen on the archery
range between eleven and twelve."

"She gave you that impression?"  There was an undertone of
suppressed interest in the professor's question.

"Only in a remote way.  It was Drukker's statement that he had
heard his mother scream, and her denial of having screamed, that
led me to believe that she might have seen something she preferred
to keep from us.  And it occurred to me that you would probably
have more influence with her than any one else, and that, if she
did indeed witness anything, you might prevail upon her to speak."

"No!"  Professor Dillard spoke almost harshly; but he immediately
placed his hand on Markham's arm, and his tone changed.  "There are
some things you must not ask me to do for you.  If that poor
harassed woman saw anything from her window that morning, you must
find it out for yourself.  I'll have no hand in torturing her; and
I sincerely hope you'll not worry her either.  There are other ways
of finding out what you want to know."  He looked straight into
Markham's eyes.  "SHE must not be the one to tell you.  You
yourself would be sorry afterwards."

"We must find out what we can," Markham answered resolutely but
with kindliness.  "There's a fiend loose in this city, and I cannot
stay my hand to save any one from suffering--however tragic that
suffering may be.  But I assure you I shall not unnecessarily
torture any one."

"Have you thought," asked Professor Dillard quietly, "that the
truth you seek may be more frightful even than the crimes
themselves?"

"That I shall have to risk.  But even if I knew it to be a fact, it
would not deter me in any degree."

"Certainly not.  But, Markham, I'm much older than you.  I had gray
hair when you were a lad struggling with your logs and antilogs;
and when one gets old one learns the true proportions in the
universe.  The ratios all change.  The estimates we once placed on
things lose their meaning.  That's why the old are more forgiving:
they know that no man-made values are of any importance."

"But as long as we must live by human values," argued Markham, "it
is my duty to uphold them.  And I cannot, through any personal
sense of sympathy, refuse to take any avenue that may lead to the
truth."

"You are perhaps right," the professor sighed.  "But you must not
ask me to help you in this instance.  If you learn the truth, be
charitable.  Be sure your culprit is accountable before you demand
that he be sent to the electric chair.  There are diseased minds as
well as diseased bodies; and often the two go together."

When we had returned to the drawing-room Vance lighted a cigarette
with more than his usual care.

"The professor," he said, "is not at all happy about Sprigg's
death; and, though he won't admit it, that tensor formula convinced
him that Sprigg and Robin belong to the same equation.  But he was
convinced dashed easily.  Now, why?--Moreover, he didn't care to
admit that Sprigg was known hereabouts.  I don't say he has
suspicions, but he has fears. . . .  Deuced funny, his attitude.
He apparently doesn't want to obstruct the legal justice which you
uphold with such touchin' zeal, Markham; but he most decidedly
doesn't care to abet your crusade where the Drukkers are concerned.
I wonder what's back of his consideration for Mrs. Drukker.  I
shouldn't say, offhand, that the professor was of a sentimental
nature.--And what was that platitude about a diseased mind and a
diseased body?  Sounded like a prospectus for a physical culture
class, what? . . .  Lackaday!  Let's put a few questions to Pyne
and kin."

Markham sat smoking moodily.  I had rarely seen him so despondent.

"I don't see what we can hope for from them," he commented.
"However, Sergeant, get Pyne in here."

When Heath had stepped out Vance gave Markham a waggish look.

"Really, y' know, you shouldn't repine.  Let Terence console you:--
Nil tam difficile est, quin quaerendo investigari possit.  And,
'pon my soul, this is a difficult problem. . . ."  He became
suddenly sober.  "We're dealing with unknown quantities here.
We're pitted against some strange, abnormal force that doesn't
operate according to the accepted laws of conduct.  It's at once
subtle--oh, no end subtle--and unfamiliar.  But at least we know
that it emanates from somewhere in the environs of this old house;
and we must search in every psychological nook and cranny.
Somewhere about us lies the invisible dragon.  So don't be shocked
at the questions I shall put to Pyne.  We must look in the most
unlikely places. . . ."

Footsteps were heard approaching the archway, and a moment later
Heath entered with the old butler in tow.



CHAPTER XI

THE STOLEN REVOLVER


(Monday, April 11; 3 p.m.)


"Sit down, Pyne," said Vance, with peremptory kindness.  "We have
permission from Professor Dillard to question you; and we shall
expect answers to all our questions."

"Certainly, sir," the man answered.  "I'm sure there's nothing that
Professor Dillard has any reason to hide."

"Excellent."  Vance lay back lazily.  "To begin with, then; what
hour was breakfast served here this morning?"

"At half past eight, sir--the same as always."

"Were all the members of the family present?"

"Oh, yes, sir."

"Who calls the family in the morning?  And at what time?"

"I do myself--at half past seven.  I knock on the doors--"

"And wait for an answer?"

"Yes, sir--always."

"Now think, Pyne: did every one answer you this morning?"

The man inclined his head emphatically.  "Yes, sir."

"And no one was late to breakfast?"

"Every one was on time promptly--as usual, sir."

Vance leaned over and deposited his cigarette ash in the grate.

"Did you happen to see any one leaving the house or returning to it
this morning before breakfast?"

The question was put casually, but I noted a slight quiver of
surprise in the butler's thin drooping eyelids.

"No, sir."

"Even though you saw no one," pursued Vance, "would it not have
been possible for some member of the household to have gone out and
returned without your knowing it?"

Pyne for the first time during the interview appeared reluctant to
answer.

"Well, sir, the fact is," he said uneasily, "any one might have
used the front door this morning without my knowing it, as I was in
the dining-room setting table.  And, for the matter of that, any
one might have used the archery-room door, for my daughter
generally keeps the kitchen door closed while preparing breakfast."

Vance smoked thoughtfully a moment.  Then in an even, matter-of-
fact tone he asked:  "Does any one in the house own a revolver?"

The man's eyes opened wide.

"Not that I--know of, sir," he answered haltingly.

"Ever hear of the Bishop, Pyne?"

"Oh, no, sir!"  His face blanched.  "You mean the man who wrote
those letters to the papers?"

"I merely meant the Bishop," said Vance carelessly.  "But tell me:
have you heard anything about a man being killed in Riverside Park
this morning?"

"Yes, sir.  The janitor next door was telling me about it."

"You knew young Mr. Sprigg, didn't you?"

"I'd seen him at the house here once or twice, sir."

"Was he here recently?"

"Last week, sir.  Thursday I think it was."

"Who else was here at the time?"

Pyne frowned as if trying to remember.

"Mr. Drukker, sir," he said after a moment.  "And, as I recall, Mr.
Pardee came too.  They were together in Mr. Arnesson's room talking
until late."

"In Mr. Arnesson's room, eh?  Is it custom'ry for Mr. Arnesson to
receive callers in his room?"

"No, sir," Pyne explained; "but the professor was working in the
library, and Miss Dillard was with Mrs. Drukker in the drawing-room
here."

Vance was silent a while.

"That will be all, Pyne," he said at length.  "But please send
Beedle to us at once."

Beedle came and stood before us with sullen aggressiveness.  Vance
questioned her along the same lines as he had taken with Pyne.  Her
answers, for the most part monosyllabic, added nothing to what had
already been learned.  But at the end of the brief interview Vance
asked her if she had happened to look out of the kitchen window
that morning before breakfast.

"I looked out once or twice," she answered defiantly.  "Why
shouldn't I look out?"

"Did you see any one on the archery range or in the rear yard?"

"No one but the professor and Mrs. Drukker."

"No strangers?"  Vance strove to give the impression that the fact
of Professor Dillard's and Mrs. Drukker's presence in the rear yard
that morning was of no importance; but, by the slow, deliberate way
in which he reached into his pocket for his cigarette-case, I knew
the information had interested him keenly.

"No," the woman replied curtly.

"What time did you notice the professor and Mrs. Drukker?"

"Eight o'clock maybe."

"Were they talking together?"

"Yes.--Anyway," she emended, "they were walking up and down near
the arbor."

"Is it custom'ry for them to stroll in the yard before breakfast?"

"Mrs. Drukker often comes out early and walks about the flower
beds.  And I guess the professor has a right to walk in his own
yard any time he wants to."

"I'm not questioning his rights in the matter, Beedle," said Vance
mildly.  "I was merely wondering if he was in the habit of
exercising those rights at such an early hour."

"Well, he was exercising 'em this morning."

Vance dismissed the woman and, rising, went to the front window.
He was patently puzzled, and he stood several minutes looking down
the street toward the river.

"Well, well," he murmured.  "It's a nice day for communin' with
nature.  At eight this morning the lark was on the wing no doubt,
and--who knows?--maybe there was a snail on the thorn.  But--my
word!--all wasn't right with the world."

Markham recognized the signs of Vance's perplexity.

"What do you make of it?" he asked.  "I'm inclined to ignore
Beedle's information."

"The trouble is, Markham, we can't afford to ignore anything in
this case."  Vance spoke softly, without turning.  "I'll admit,
though, that at present Beedle's revelation is meaningless.  We've
merely learned that two of the actors in our melodrama were up
and about this morning shortly after Sprigg was snuffed out.  The
al-fresco rendezvous between the professor and Mrs. Drukker may,
of course, be just one of your beloved coincidences.  On the other
hand, it may have some bearing on the old gentleman's sentimental
attitude toward the lady. . . .  I think we'll have to make a few
discreet inquiries of him about his ante-prandial tryst, what? . . ."

He leaned suddenly toward the window.

"Ah!  Here comes Arnesson.  Looks a bit excited."

A few moments later there was the sound of a key in the front door,
and Arnesson strode down the hall.  When he saw us he came quickly
into the drawing-room and, without a word of greeting, burst forth:

"What's this I hear about Sprigg being shot?"  His eager eyes
darted from one to the other of us.  "I suppose you're here to ask
me about him.  Well, fire away."  He threw a bulky brief-case on
the centre-table and sat down abruptly on the edge of a straight
chair.  "There was a detective up at college this morning asking
fool questions and acting like a burlesque sleuth in a comic opera.
Very mysterious. . . .  Murder--horrible murder!  What did we know
about a certain John E. Sprigg?  And so on. . . .  Scared a couple
of juniors out of an entire semester's mental growth, and sent a
harmless young English instructor into incipient nervous collapse.
I didn't see the Dogberry myself--was in class at the time.  But he
had the cheek to ask what women Sprigg went around with.  Sprigg
and women!  That boy didn't have a thought in his head but his
work.  Brightest man in senior math.  Never missed a class.  When
he didn't answer roll-call this morning I knew something serious
was the matter.  At the lunch hour every one was buzzing about
murder. . . .  What's the answer?"

"We haven't the answer, Mr. Arnesson."  Vance had been watching him
closely.  "However, we have another determinant for your formula.
Johnny Sprig was shot this morning with a little gun through the
middle of his wig."

Arnesson stared at Vance for some time without moving.  Then he
threw his head back and gave a sardonic laugh.

"Some more mumbo-jumbo, eh?--like the death of Cock Robin. . . .
Read me the rune."

Vance gave him briefly the details of the crime.

"That's all we know at present," he concluded.  "Could YOU, Mr.
Arnesson, add any suggestive details?"

"Good Lord, no!"  The man appeared genuinely amazed.  "Not a thing.
Sprigg . . . one of the keenest students I ever had.  Something of
a genius, by Gad!  Too bad his parents named him John--plenty of
other names.  It sealed his doom apparently; got him shot through
the head by a maniac.  Obviously the same merry-andrew who did
Robin in with an arrow."  He rubbed his hands together,--the
abstract philosopher in him had become uppermost.  "A nice problem.
You've told me everything?  I'll need every known integer.  Maybe
I'll hit upon a new mathematical method in the process--like
Kepler."  He chuckled over the conceit.  "Remember Kepler's
'Doliometrie'?  It became the foundation of Infinitesimal Calculus.
He arrived at it trying to construct a cask for his wine--a cask
with a minimum amount of wood and a maximum cubical content.  Maybe
the formulas I work out to solve these crimes will open up new
fields of scientific research.  Ha!  Robin and Sprigg will then
become martyrs."

The man's humor, even taking into consideration his life's passion
for abstractions, struck me as particularly distasteful.  But Vance
seemed not to mind his cold-blooded cynicism.

"There's one item," he said, "that I omitted to mention."  Turning
to Markham he asked for the piece of paper containing the formula,
and handed it to Arnesson.  "This was found beneath Sprigg's body."

The other scrutinized it superciliously.

"The Bishop, I see, is again involved.  Same paper and typing as
the notes. . . .  But where did he get that Riemann-Christoffel
tensor?  Now, if it had been some other tensor--like the G-sigma-
tau, for instance--any one interested in practical physics might
have hit on it.  But this one isn't common; and the statement of it
here is arbitrary and unusual.  Certain terms omitted. . . .  BY
GEORGE!  I was talking to Sprigg about this only the other night.
He wrote it down, too."

"Pyne mentioned the fact that Sprigg had called here Thursday
night," put in Vance.

"Oh, he did, did he? . . .  Thursday--that's right.  Pardee was
here, too.  And Drukker.  We had a discussion on Gaussian co-
ordinates.  This tensor came up--Drukker mentioned it first, I
think.  And Pardee had some mad notion of applying the higher
mathematics to chess. . . ."

"Do you play chess, by the by?" asked Vance.

"Used to.  But no more.  A beautiful game, though--if it wasn't for
the players.  Queer crabs, chess players."

"Did you ever make any study of the Pardee gambit?"  (At the time I
could not understand the seeming irrelevance of Vance's questions;
and I noticed that Markham too was beginning to show signs of
impatience.)

"Poor old Pardee!"  Arnesson smiled unfeelingly.  "Not a bad
elementary mathematician.  Should have been a high-school teacher.
Too much money, though.  Took to chess.  I told him his gambit was
unscientific.  Even showed him how it could be beaten.  But he
couldn't see it.  Then Capablanca, Vidman and Tartakower came along
and knocked it into a cocked hat.  Just as I told him they would.
Wrecked his life.  He's been fussing around with another gambit for
years, but can't make it cohere.  Reads Weyl, Silberstein,
Eddington and Mach in the hope of getting inspiration."

"That's most interestin'."  Vance extended his match-case to
Arnesson, who had been filling his pipe as he talked.  "Was Pardee
well acquainted with Sprigg?"

"Oh, no.  Met him here twice--that's all.  Pardee knows Drukker
well, though.  Always asking him about potentials and scalars and
vectors.  Hopes to hit on something that'll revolutionize chess."

"Was he interested in the Riemann-Christoffel tensor when you
discussed it the other night?"

"Can't say that he was.  A bit out of his realm.  You can't hitch
the curvature of space-time to a chess-board."

"What do you make of this formula being found on Sprigg?"

"Don't make anything of it.  If it had been in Sprigg's handwriting
I'd say it dropped out of his pocket.  But who'd go to the trouble
of trying to type a mathematical formula?"

"The Bishop apparently."

Arnesson took his pipe from his mouth and grinned.

"Bishop X.  We'll have to find him.  He's full of whimsies.
Perverted sense of values."

"Obviously."  Vance spoke languidly.  "And, by the by, I almost
forgot to ask you: does the Dillard house harbor any revolvers?"

"Oho!"  Arnesson chuckled with unrestrained delight.  "Sits the
wind there? . . .  Sorry to disappoint you.  No revolvers.  No
sliding doors.  No secret stairways.  All open and above-board."

Vance sighed theatrically.

"Sad . . . sad!  And I had such a comfortin' theory."

Belle Dillard had come silently down the hall, and now stood in the
archway.  She had evidently heard Vance's question and Arnesson's
answer.

"But there ARE two revolvers in the house, Sigurd," she declared.
"Don't you remember the old revolvers I used for target practice in
the country?"

"Thought you'd thrown 'em away long ago."  Arnesson rose and drew
up a chair for her.  "I told you when we returned from Hopatcong
that summer that only burglars and bandits are allowed to own guns
in this benevolent State. . . ."

"But I didn't believe you," the girl protested.  "I never know when
you're jesting and when you're serious."

"And you kept them, Miss Dillard?" came Vance's quiet voice.

"Why--yes."  She shot an apprehensive glance at Heath.  "Shouldn't
I have done so?"

"I believe it was technically illegal.  However"--Vance smiled
reassuringly--"I don't think the Sergeant will invoke the Sullivan
law against you.--Where are they now?"

"Down-stairs--in the archery-room.  They're in one of the drawers
of the tool-chest."

Vance rose.

"Would you be so good, Miss Dillard, as to show us where you put
them?  I have a gnawin' curiosity to see 'em, don't y' know."

The girl hesitated and looked to Arnesson for guidance.  When he
nodded she turned without a word and led the way to the archery-
room.

"They're in that chest by the window," she said.

Going to it she drew out a small deep drawer in one end.  At the
rear, beneath a mass of odds and ends, was a .38 Colt automatic.

"Why!" she exclaimed.  "There's only one here.  The other is gone."

"It was a smaller pistol, wasn't it?" asked Vance.

"Yes. . . ."

"A .32?"

The girl nodded and turned bewildered eyes on Arnesson.

"Well, it's gone, Belle," he told her, with a shrug.  "Can't be
helped.  Probably one of your young archers took it to blow out his
brains with after he'd foozled at shooting arrows up the alley."

"Do be serious, Sigurd," she pleaded, a little frightened.  "Where
could it have gone?"

"Ha!  Another dark mystery," scoffed Arnesson.  "Strange
disappearance of a discarded .32."

Seeing the girl's uneasiness Vance changed the subject.

"Perhaps, Miss Dillard, you'd be good enough to take us to Mrs.
Drukker.  There are one or two matters we want to speak to her
about; and I assume, by your presence here, that the ride in the
country has been postponed."

A shadow of distress passed over the girl's face.

"Oh, you mustn't bother her to-day."  Her tone was tragically
appealing.  "Lady Mae is very ill.  I can't understand it--she
seemed so well when I was talking with her up-stairs.  But after
she'd seen you and Mr. Markham she changed: she became weak and
. . . oh, something terrible seemed to be preying on her mind.
After I'd put her to bed she kept repeating in an awful whisper:
'Johnny Sprig, Johnny Sprig.' . . .  I phoned her doctor and he
came right over.  He said she had to be kept very quiet. . . ."

"It's of no importance," Vance assured her.  "Of course we shall
wait.--Who is her doctor, Miss Dillard?"

"Whitney Barstead.  He's attended her as long as I can remember."

"A good man," nodded Vance.  "There's no better neurologist in the
country.  We'll do nothing without his permission."

Miss Dillard gave him a grateful look.  Then she excused herself.

When we were again in the drawing-room Arnesson stationed himself
before the fireplace and regarded Vance satirically.

"'Johnny Sprig, Johnny Sprig.'  Ha!  Lady Mae got the idea at once.
She may be cracked, but certain lobes of her brain are over-active.
Unaccountable piece of machinery, the human brain.  Some of the
greatest mental computers of Europe are morons.  And I know a
couple of chess masters who need nurses to dress and feed 'em."

Vance appeared not to hear him.  He had stopped by a small cabinet
near the archway and was apparently absorbed in a set of jade
carvings of ancient Chinese origin.

"That elephant doesn't belong there," he remarked casually,
pointing to a tiny figure in the collection.  "It's a bunjinga--
decadent, don't y' know.  Clever, but not authentic.  Probably a
copy of a Manchu piece."  He stifled a yawn and turned toward
Markham.  "I say, old man, there's nothing more we can do.  Suppose
we toddle.  We might have a brief word with the professor before we
go, though. . . .  Mind waiting for us here, Mr. Arnesson?"

Arnesson lifted his eyebrows in some surprise, but immediately
crinkled his face into a disdainful smile.

"Oh, no.  Go ahead."  And he began refilling his pipe.

Professor Dillard was much annoyed at our second intrusion.

"We've just learned," said Markham, "that you were speaking to Mrs.
Drukker before breakfast this morning. . . ."

The muscles of Professor Dillard's cheeks worked angrily.

"Is it any concern of the District Attorney's office if I speak to
a neighbor in my garden?"

"Certainly not, sir.  But I am in the midst of an investigation
which seriously concerns your house, and I assumed that I had the
privilege of seeking help from you."

The old man spluttered a moment.

"Very well," he acquiesced irritably.  "I saw no one except Mrs.
Drukker--if that's what you're after."

Vance projected himself into the conversation.  "That's not what we
came to you for, Professor Dillard.  We wanted merely to ask you if
Mrs. Drukker gave you the impression this morning that she
suspected what had taken place earlier in Riverside Park."

The professor was about to make a sharp retort, but checked
himself.  After a moment he said simply:

"No, she gave me no such impression."

"Did she appear in any way uneasy or, let us say, excited?"

"She did not!"  Professor Dillard rose and faced Markham.  "I
understand perfectly what you are driving at and I won't have it.
I've told you, Markham, that I'll take no part in spying or tale-
bearing where this unhappy woman is concerned.  That's all I have
to say to you."  He turned back to his desk.  "I regret I'm very
busy to-day."

We descended to the main floor and made our adieus to Arnesson.  He
waved his hand to us cordially as we went out; but his smile held
something of contemptuous patronage, as if he had witnessed, and
was gloating over, the rebuff we had just received.

When we were on the sidewalk Vance paused to light a fresh
cigarette.

"Now for a brief causerie with the sad and gentlemanly Mr. Pardee.
I don't know what he can tell us, but I have a yearnin' to commune
with him."

Pardee, however, was not at home.  His Japanese servant informed us
that his master was most likely at the Manhattan Chess Club.

"To-morrow will be time enough," Vance said to Markham, as we
turned away from the house.  "I'll get in touch with Doctor
Barstead in the morning and try to arrange to see Mrs. Drukker.
We'll include Pardee in the same pilgrimage."

"I sure hope," grumbled Heath, "that we learn more to-morrow than
we did to-day."

"You overlook one or two consolin' windfalls, Sergeant," returned
Vance.  "We've found out that every one connected with the Dillard
house was acquainted with Sprigg and could easily have known of his
early morning walks along the Hudson.  We've also learned that the
professor and Mrs. Drukker were ramblin' in the garden at eight
o'clock this morning.  And we discovered that a .32 revolver has
disappeared from the archery-room.--Not an embarrassment of riches,
but something--oh, decidedly something."

As we drove down-town Markham roused himself from gloomy
abstraction, and looked apprehensively at Vance.

"I'm almost afraid to go on with this case.  It's becoming too
sinister.  And if the newspapers get hold of that Johnny-Sprig
nursery rhyme and connect the two murders, I hate to think of the
gaudy sensation that'll follow."

"I fear you're in for it, old man," sighed Vance.  "I'm not a bit
psychic--never had dreams that came true, and don't know what a
telepathic seizure feels like--but something tells me that the
Bishop is going to acquaint the press with that bit of Mother-Goose
verse.  The point of his new joke is even obscurer than his Cock-
Robin comedy.  He'll see to it that no one misses it.  Even a grim
humorist who uses corpses for his cap-and-bells must have his
audience.  Therein lies the one weakness of his abominable crimes.
It's about our only hope, Markham."

"I'll give Quinan a ring," said Heath, "and find out if anything
has been received."

But the Sergeant was saved the trouble.  The World reporter was
waiting for us at the District Attorney's office, and Swacker
ushered him in at once.

"Howdy, Mr. Markham."  There was a breezy impudence in Quinan's
manner, but withal he showed signs of nervous excitement.  "I've
got something here for Sergeant Heath.  They told me at Headquarters
that he was handling the Sprigg case, and said he was parleying with
you.  So I blew over."

He reached in his pocket and, taking out a sheet of paper, handed
it to Heath.  "I'm being mighty high, wide and handsome with you,
Sergeant, and I expect a little inside stuff by way of reciprocity.
. . .  Cast your eye on that document.  Just received by America's
foremost family journal."

It was a plain piece of typewriting paper, and it contained the
Mother-Goose melody of Johnny Sprig, typed in élite characters with
a pale-blue ribbon.  In the lower right-hand corner was the
signature in capitals:  THE BISHOP.

"And here's the envelope, Sergeant."  Quinan again dug down into
his pocket.

The official cancellation bore the hour of 9 a.m., and, like the
first note, it had been mailed in the district of Post Office
Station "N."



CHAPTER XII

A MIDNIGHT CALL


(Tuesday, April 12; 10 a.m.)


The following morning the front pages of the metropolitan press
carried sensational stories which surpassed Markham's worst fears.
In addition to the World two other leading morning journals had
received notes similar to the one shown us by Quinan; and the
excitement created by their publication was tremendous.  The entire
city was thrown into a state of apprehension and fear; and though
half-hearted attempts were made here and there to dismiss the
maniacal aspect of the crimes on the ground of coincidence, and to
explain away the Bishop notes as the work of a practical joker, all
the newspapers and the great majority of the public were thoroughly
convinced that a new and terrible type of killer was preying upon
the community.*


* A similar state of panic obtained in London in 1888 when Jack-
the-Ripper was engaged in his grisly, abnormal debauch; and again
in Hanover in 1923 when Haarmann, the werewolf, was busy with his
anthropophagous slaughters.  But I can recall no other modern
parallel for the atmosphere of gruesome horror that settled over
New York during the Bishop murders.


Markham and Heath were beset by reporters, but a veil of secrecy
was sedulously maintained.  No intimation was given that there was
any reason to believe that the solution lay close to the Dillard
household; and no mention was made of the missing .32 revolver.
Sperling's status was sympathetically dealt with by the press.
The general attitude now was that the young man had been the
unfortunate victim of circumstances; and all criticism of Markham's
procrastination in prosecuting him was instantly dropped.

On the day that Sprigg was shot Markham called a conference at the
Stuyvesant Club.  Both Inspector Moran of the Detective Bureau and
Chief Inspector O'Brien* attended.  The two murders were gone over
in detail, and Vance outlined his reasons for believing that the
answer to the problem would eventually be found either in the
Dillard house or in some quarter directly connected with it.


* Chief Inspector O'Brien was then in command of the entire Police
Department.


"We are now in touch," he ended, "with every person who could
possibly have had sufficient knowledge of the conditions
surrounding the two victims to perpetrate the crimes successfully;
and our only course is to concentrate on these persons."

Inspector Moran was inclined to agree.  "Except," he qualified,
"that none of the dramatis personae you have mentioned strikes me
as a bloodthirsty maniac."

"The murderer is not a maniac in the conventional sense," returned
Vance.  "He's probably normal on all other points.  His brain, in
fact, may be brilliant except for this one lesion--too brilliant,
I should say.  He has lost all sense of proportion through sheer
exalted speculation."

"But does even a perverted superman indulge in such hideous jests
without a motive?" asked the Inspector.

"Ah, but there is a motive.  Some tremendous impetus is back of the
monstrous conception of these murders--an impetus which, in its
operative results, takes the form of satanic humor."

O'Brien took no part in this discussion.  Though impressed by its
vague implications, he became nettled by its impractical character.

"That sort of talk," he rumbled ponderously, "is all right for
newspaper editorials, but it ain't workable."  He shook his fat
black cigar at Markham.  "What we gotta do is to run down every
lead and get some kind of legal evidence."

It was finally decided that the Bishop notes were to be turned over
to an expert analyst, and an effort made to trace both the
typewriter and the stationery.  A systematic search was to be
instituted for witnesses who might have seen some one in Riverside
Park between seven and eight that morning.  Sprigg's habits and
associations were to be the subject of a careful report; and a man
was to be detailed to question the mail collector of the district
in the hope that, when taking the letters from the various boxes,
he had noticed the envelopes addressed to the papers and could say
in which box they had actually been posted.

Various other purely routine activities were outlined; and Moran
suggested that for a time three men be stationed day and night in
the vicinity of the murders to watch for any possible developments
or for suspicious actions on the part of those involved.  The
Police Department and the District Attorney's office were to work
hand in hand.  Markham, of course, in tacit agreement with Heath,
assumed command.

"I have already interviewed the members of the Dillard and Drukker
homes in connection with the Robin murder," Markham explained to
Moran and O'Brien: "and I've talked the Sprigg case over with
Professor Dillard and Arnesson.  To-morrow I shall see Pardee and
the Drukkers."

The next morning Markham, accompanied by Heath, called for Vance a
little before ten o'clock.

"This thing can't go on," he declared, after the meagrest of
greetings.  "If any one knows anything, we've got to find it out.
I'm going to put the screws on--and damn the consequences!"

"By all means, chivy 'em."  Vance himself appeared despondent.
"I doubt if it'll help though.  No ordin'ry procedure is going to
solve this riddle.  However, I've phoned Barstead.  He says we may
talk with Mrs. Drukker this morning.  But I've arranged to see him
first.  I have a hankerin' to know more of the Drukker pathology.
Hunchbacks, d' ye see, are not usually produced by falls."

We drove at once to the doctor's home and were received without
delay.  Doctor Barstead was a large comfortable man, whose
pleasantness of manner impressed me as being the result of schooled
effort.

Vance went straight to the point.

"We have reason to believe, doctor, that Mrs. Drukker and perhaps
her son are indirectly concerned in the recent death of Mr. Robin
at the Dillard house; and before we question either of them further
we should like to have you tell us--as far as professional
etiquette will permit--something of the neurological situation we
are facing."

"Please be more explicit, sir."  Doctor Barstead spoke with
defensive aloofness.

"I am told," Vance continued, "that Mrs. Drukker regards herself as
responsible for her son's kyphosis; but it is my understanding that
such malformations as his do not ordinarily result from mere
physical injuries."

Doctor Barstead nodded his head slowly.

"That is quite true.  Compression paraplegia of the spinal cord may
follow a dislocation or injury, but the lesion thus produced is of
the focal transverse type.  Osteitis or caries of the vertebrae--
what we commonly call Pott's disease--is usually of tubercular
origin; and this tuberculosis of the spine occurs most frequently
in children.  Often it exists at birth.  True, an injury may
precede the onset by determining the site of infection or exciting
a latent focus; and this fact no doubt gives rise to the belief
that the injury itself produces the disease.  But both Schmaus and
Horsley have exposed the true pathological anatomy of spinal
caries.  Drukker's deformity is unquestionably of tubercular
origin.  Even his curvature is of the marked rounded type, denoting
an extensive involvement of vertebrae; and there is no scholiosis
whatever.  Moreover, he has all the local symptoms of osteitis."

"You have, of course, explained the situation to Mrs. Drukker."

"On many occasions.  But I have had no success.  The fact is, a
terrific instinct of perverted martyrdom bids her cling to the
notion that she is responsible for her son's condition.  This
erroneous idea has become an idée fixe with her.  It constitutes
her entire mental outlook, and gives meaning to the life of service
and sacrifice she had lived for forty years."

"To what extent," asked Vance, "would you say this psychoneurosis
has affected her mind?"

"That would be difficult to say; and it is not a question I would
care to discuss.  I may say this, however: she is undoubtedly
morbid; and her values have become distorted.  At times there have
been--I tell you this in strictest confidence--signs of marked
hallucinosis centring upon her son.  His welfare has become an
obsession with her.  There is practically nothing she would not do
for him."

"We appreciate your confidence, doctor. . . .  And would it not be
logical to assume that her upset condition yesterday resulted from
some fear or shock connected with his welfare?"

"Undoubtedly.  She has no emotional or mental life outside of him.
But whether her temporary collapse was due to a real or imaginary
fear, one cannot say.  She has lived too long on the borderland
between reality and fantasy."

There was a short silence, and then Vance asked:

"As to Drukker himself: would you regard him as wholly responsible
for his acts?"

"Since he is my patient," returned Doctor Barstead, with frigid
reproach, "and since I have taken no steps to sequester him, I
consider your question an impertinence."

Markham leaned over and spoke peremptorily.

"We haven't time to mince words, doctor.  We're investigating a
series of atrocious murders.  Mr. Drukker is involved in those
murders--to what extent we don't know.  But it is our duty to find
out."

The doctor's first impulse was to combat Markham; but he evidently
thought better of it, for when he answered, it was in an
indulgently matter-of-fact voice.

"I have no reason, sir, to withhold any information from you.  But
to question Mr. Drukker's responsibility is to impute negligence to
me in the matter of public safety.  Perhaps, however, I misunderstand
this gentleman's question."  He studied Vance for a brief moment.
"There are, of course, degrees of responsibility," he went on, in a
professional tone.  "Mr. Drukker's mind is overdeveloped, as is
often the case with kyphotic victims.  All mental processes are
turned inward, as it were; and the lack of normal physical reactions
often tends to produce inhibitions and aberrancies.  But I've noted
no indications of this condition in Mr. Drukker.  He is excitable
and prone to hysteria; but, then, psychokinesia is a common
accompaniment of his disease."

"What form do his recreations take?" Vance was politely casual.

Doctor Barstead thought a moment.

"Children's games, I should say.  Such recreations are not unusual
with cripples.  In Mr. Drukker's case it is what we might term a
waking wish-fulfilment.  Having had no normal childhood, he grasps
at whatever will give him a sense of youthful rehabilitation.  His
juvenile activities tend to balance the monotony of his purely
mental life."

"What is Mrs. Drukker's attitude toward his instinct for play?"

"She very correctly encourages it.  I've often seen her leaning
over the wall above the playground in Riverside Park watching him.
And she always presides at the children's parties and dinners which
he holds in his home."

We took our leave a few minutes later.  As we turned into 76th
Street, Heath, as if arousing himself from a bad dream, drew a deep
breath and sat upright in the car.

"Did you get that about the kid games?" he asked, in an awe-
stricken voice.  "Good God, Mr. Vance!  What's this case going to
turn into?"

A curious sadness was in Vance's eyes as he gazed ahead toward the
misty Jersey cliffs across the river.

Our ring at the Drukker house was answered by a portly German
woman, who planted herself stolidly before us and informed us
suspiciously that Mr. Drukker was too busy to see any one.

"You'd better tell him, however," said Vance, "that the District
Attorney wishes to speak to him immediately."

His words produced a strange effect on the woman.  Her hands went
to her face, and her massive bosom rose and fell convulsively.
Then, as though panic-stricken, she turned and ascended the stairs.
We heard her knock on a door; there was a sound of voices; and a
few moments later she came back to inform us that Mr. Drukker would
see us in his study.

As we passed the woman Vance suddenly turned and, fixing his eyes
on her ominously, asked:

"What time did Mr. Drukker get up yesterday morning?"

"I--don't know," she stammered, thoroughly frightened.  "Ja, ja, I
know.  At nine o'clock--like always."

Vance nodded and moved on.

Drukker received us standing by a large table covered with books
and sheets of manuscript.  He bowed sombrely, but did not ask us to
have chairs.

Vance studied him a moment as if trying to read the secret that lay
behind his restless, hollow eyes.

"Mr. Drukker," he began, "it is not our desire to cause you
unnecess'ry trouble; but we have learned that you were acquainted
with Mr. John Sprigg, who, as you probably know, was shot near here
yesterday morning.  Now, could you suggest any reason that any one
might have had for killing him?"

Drukker drew himself up.  Despite his effort at self-control there
was a slight tremor in his voice as he answered.

"I knew Mr. Sprigg but slightly.  I can suggest nothing whatever in
regard to his death. . . ."

"There was found on his body a piece of paper bearing the Riemann-
Christoffel tensor which you introduce in your book in the chapter
on the finiteness of physical space."  As Vance spoke he moved one
of the typewritten sheets of papers on the table toward him, and
glanced at it casually.

Drukker seemed not to notice the action.  The information contained
in Vance's words had rivetted his attention.

"I can't understand it," he said vaguely.  "May I see the notation?"

Markham complied at once with his request.  After studying the
paper a moment Drukker handed it back; and his little eyes narrowed
malevolently.

"Have you asked Arnesson about this?  He was discussing this very
subject with Sprigg last week."

"Oh, yes," Vance told him carelessly.  Mr. Arnesson recalled the
incident, but couldn't throw any light on it.  We thought perhaps
you could succeed where he had failed."

"I regret I can't accommodate you."  There was the suggestion of a
sneer in Drukker's reply.  "Any one might use the tensor.  Weyl's
and Einstein's works are full of it.  It isn't copyrighted. . . ."
He leaned over a revolving book case and drew out a thin octavo
pamphlet.  Here it is in Minkowski's 'Relativitätsprinzip,' only
with different symbols--a T for the B, for instance; and Greek
letters for the indices."  He reached for another volume.
"Poincaré also uses it in his 'Hypothèses Cosmogoniques,' with
still other symbolic equivalents."  He tossed the books on the
table contemptuously.  "Why come to me about it?"

"It wasn't the tensor formula alone that led our roving footsteps
to your door," said Vance lightly.  "For instance, we have reason
to believe that Sprigg's death is connected with Robin's
murder. . . ."

Drukker's long hands caught the edge of the table, and he leaned
forward, his eyes glittering excitedly.

"Connected--Sprigg and Robin?  You don't believe that newspaper
talk, do you? . . .  It's a damned lie!"  His face had begun to
twitch, and his voice rose shrilly.  "It's insane nonsense. . . .
There's no proof, I tell you--not a shred of proof!"

"Cock Robin and Johnny Sprig, don't y' know," came Vance's soft
insistent voice.

"That rot!  That crazy rot!--Oh, good God!  Has the world gone
mad! . . ."  He swayed back and forth as he beat on the table with
one hand, sending the papers flying in all directions.

Vance looked at him with mild surprise.

"Aren't you acquainted with the Bishop, Mr. Drukker?"

The man stopped swaying and, steadying himself, stared at Vance
with terrible intensity.  His mouth was drawn back at the corners,
resembling the transverse laugh of progressive muscular dystrophy.

"You, too!  You've gone mad!"  He swept his eyes over us.  "You
damned, unutterable fools!  There's no such person as the Bishop!
There wasn't any such person as Cock Robin or Johnny Sprig.  And
here you are--men grown--trying to frighten me--ME, a mathematician--
with nursery tales! . . ."  He began to laugh hysterically.

Vance went to him quickly, and taking his arm led him to his chair.
Slowly his laughter died away, and he waved his hand wearily.

"Too bad Robin and Sprigg were killed."  His tone was heavy and
colorless.  "But children are the only persons that matter. . . .
You'll probably find the murderer.  If you don't, maybe I'll help
you.  But don't let your imaginations run away with you.  Keep to
facts . . . facts. . . ."

The man was exhausted, and we left him.

"He's scared, Markham--deuced scared," observed Vance, when we were
again in the hall.  "I could bear to know what is hidden in that
shrewd warped mind of his."

He led the way down the hall to Mrs. Drukker's door.

"This method of visiting a lady doesn't accord with the best social
usage.  Really, y' know, Markham, I wasn't born to be a policeman.
I abhor snooping."

Our knock was answered by a feeble voice.  Mrs. Drukker, paler than
usual, was lying back on her chaise-longue by the window.  Her
white prehensile hands lay along the arms of the chair, slightly
flexed; and more than ever she recalled to my mind the pictures I
had seen of the ravening Harpies that tormented Phineus in the
story of the Argonauts.

Before we could speak she said in a strained terrified voice:  "I
knew you would come--I knew you were not through torturing me. . . ."

"To torture you, Mrs. Drukker," returned Vance softly, "is the
furthest thing from our thoughts.  We merely want your help."

Vance's manner appeared to alleviate her terror somewhat, and she
studied him calculatingly.

"If only I could help you!" she muttered.  "But there's nothing to
be done--nothing. . . ."

"You might tell us what you saw from your window on the day of Mr.
Robin's death," Vance suggested kindly.

"No--no!"  Her eyes stared horribly.  "I saw nothing--I wasn't near
the window that morning.  You may kill me, but my dying words would
be No--no--NO!"

Vance did not press the point.

"Beedle tells us," he went on, "that you often rise early and walk
in the garden."

"Oh, yes."  The words came with a sigh of relief.  "I don't sleep
well in the mornings.  I often wake up with dull boring pains in my
spine, and the muscles of my back feel rigid and sore.  So I get up
and walk in the yard whenever the weather is mild enough."

"Beedle saw you in the garden yesterday morning."

The woman nodded absently.

"And she also saw Professor Dillard with you."

Again she nodded, but immediately afterward she shot Vance a
combative inquisitive glance.

"He sometimes joins me," she hastened to explain.  "He feels sorry
for me, and he admires Adolph; he thinks he's a great genius.  And
he IS a genius!  He'd be a great man--as great as Professor
Dillard--if it hadn't been for his illness. . . .  And it was all
my fault.  I let him fall when he was a baby. . . ."  A dry sob
shook her emaciated body, and her fingers worked spasmodically.

After a moment Vance asked:  "What did you and Professor Dillard
talk about in the garden yesterday?"

A sudden wiliness crept into the woman's manner.

"About Adolph mostly," she said, with a too obvious attempt at
unconcern.

"Did you see any one else in the yard or on the archery range?"
Vance's indolent eyes were on the woman.

"No!"  Again a sense of fear pervaded her.  "But somebody else was
there, wasn't there?--somebody who didn't wish to be seen."  She
nodded her head eagerly.  "Yes!  Some one else was there--and they
thought I saw them. . . .  But I didn't!  Oh, merciful God, I
didn't! . . ."  She covered her face with her hands, and her body
shook convulsively.  "If only I had seen them!  If only I knew!
But it wasn't Adolph--it wasn't my little boy.  He was asleep--
thank God, he was asleep!"

Vance went close to the woman.

"Why do you thank God that it wasn't your son?" he asked gently.

She looked up with some amazement.

"Why, don't you remember?  A little man shot Johnny Sprig with a
little gun yesterday morning--the same little man that killed Cock
Robin with a bow and arrow.  It's all a horrible game--and I'm
AFRAID. . . .  But I mustn't tell--I CAN'T tell.  The little man
might do something awful.  Maybe"--her voice became dull with
horror--"maybe he has some insane idea that I'm THE OLD WOMAN WHO
LIVED IN A SHOE! . . ."

"Come, come, Mrs. Drukker."  Vance forced a consoling smile.  "Such
talk is nonsense.  You've let these matters prey on your mind.
There's a perfectly rational explanation for everything.  And I
have a feeling that you yourself can help us find that
explanation."

"No--no!  I can't--I mustn't!  I don't understand it myself."  She
took a deep, resolute inspiration, and compressed her lips.

"Why can't you tell us?" persisted Vance.

"Because I don't know," she cried.  "I wish to God I did!  I only
know that something horrible is going on here--that some awful
curse is hanging over this house. . . ."

"How do you know that?"

The woman began to tremble violently, and her eyes roamed
distractedly about the room.

"Because"--her voice was barely audible--"because the little man
came here last night!"

A chill passed up my spine at this statement, and I heard even the
imperturbable Sergeant's sharp intake of breath.  Then Vance's calm
voice sounded.

"How do you know he was here, Mrs. Drukker?  Did you see him?"

"No, I didn't see him; but he tried to get into this room--by that
door."  She pointed unsteadily toward the entrance to the hallway
through which we had just come.

"You must tell us about it," said Vance; "or we will be driven to
conclude that you manufactured the story."

"Oh, but I didn't manufacture it--may God be my witness!"  There
could be no doubt whatever of the woman's sincerity.  Something had
occurred which filled her with mortal fear.  "I was lying in bed,
awake.  The little clock on the mantel had just struck midnight;
and I heard a soft rustling sound in the hall outside.  I turned my
head toward the door--there was a dim night-light burning on the
table here . . . and then I saw the door-knob turn slowly--
silently--as if some one were trying to get in without waking me--"

"Just a moment, Mrs. Drukker," interrupted Vance.  "Do you always
lock your door at night?"

"I've never locked it until recently--after Mr. Robin's death.
I've somehow felt insecure since then--I can't explain why. . . ."

"I quite understand.--Please go on with the story.  You say you saw
the door-knob move.  And then?"

"Yes--yes.  It moved softly--back and forth.  I lay there in bed,
frozen with terror.  But after a while I managed to call out--I
don't know how loud; but suddenly the door-knob ceased to turn, and
I heard footsteps moving rapidly away--down the hall. . . .  Then I
managed to get up.  I went to the door and listened.  I was afraid--
afraid for Adolph.  And I could hear those soft footsteps
descending the stairs--"

"Which stairs?"

"At the rear--leading to the kitchen. . . .  Then the door of the
screen porch shut, and everything was silent again. . . .  I knelt
with my ear to the keyhole a long time, listening, waiting.  But
nothing happened, and at last I rose. . . .  Something seemed to
tell me I must open the door.  I was in deadly terror--and yet I
knew I had to open the door. . . ."

A shudder swept her body.  "Softly I turned the key, and took hold
of the knob.  As I pulled the door slowly inward, a tiny object
that had been poised on the outside knob fell to the floor with a
clatter.  There was a light burning in the hall--I always keep one
burning at night,--and I tried not to look down.  I tried--I TRIED
. . . but I couldn't keep my eyes away from the floor.  And there
at my feet--oh, God in Heaven!--there lay SOMETHING! . . ."

She was unable to go on.  Horror seemed to paralyze her tongue.
Vance's cool, unemotional voice, however, steadied her.

"What was it that lay on the floor, Mrs. Drukker?"

With difficulty the woman rose and, bracing herself for a moment at
the foot of the bed, went to the dressing-table.  Pulling out a
small drawer she reached inside and fumbled among its contents.
Then she extended her open hand to us.  On the palm lay a small
chessman--ebony black against the whiteness of her skin.  It was
the bishop!



CHAPTER XIII

IN THE BISHOP'S SHADOW


(Tuesday, April 12; 11 a.m.)


Vance took the bishop from Mrs. Drukker and slipped it into his
coat pocket.

"It would be dangerous, madam," he said, with impressive solemnity,
"if what happened here last night became known.  Should the person
who played this joke on you find out that you had informed the
police, other attempts to frighten you might be made.  Therefore,
not one word of what you have told us must pass your lips."

"May I not even tell Adolph?" the woman asked distractedly.

"No one!  You must maintain a complete silence, even in the
presence of your son."

I could not understand Vance's emphasis on this point; but before
many days had passed it was all too clear to me.  The reason for
his advice was revealed with tragic force; and I realized that even
at the time of Mrs. Drukker's disclosure his penetrating mind had
worked out an uncannily accurate ratiocination, and foreseen
certain possibilities unsuspected by the rest of us.

We took our leave a few moments later, and descended the rear
stairs.  The staircase made a sharp turn to the right at a landing
eight or ten steps below the second floor, and led into a small
dark passageway with two doors--one on the left, opening into the
kitchen, and another, diagonally opposite, giving on the screen
porch.

We stepped out immediately to the porch, now flooded in sunshine,
and stood without a word trying to shake off the atmosphere cast
about us by Mrs. Drukker's terrifying experience.

Markham was the first to speak.

"Do you believe, Vance, that the person who brought that chessman
here last night is the killer of Robin and Sprigg?"

"There can be no doubt of it.  The purpose of his midnight visit is
hideously clear.  It fits perfectly with what has already come to
light."

"It strikes me merely as a ruthless practical joke," Markham
rejoined, "--the act of a drunken fiend."

Vance shook his head.

"It's the only thing in this whole nightmare that doesn't qualify
as a piece of insane humor.  It was a deadly serious excursion.
The devil himself is never so solemn as when covering his tracks.
Our particular devil's hand had been forced, and he made a bold
play.  'Pon my soul, I almost prefer his jovial mood to the one
that prompted him to break in here last night.  However, we now
have something definite to go on."

Heath, impatient of all theorizing, quickly picked up this last
remark.

"And what might that be, sir?"

"Imprimis, we may assume that our chess-playing troubadour was
thoroughly familiar with the plan of this house.  The night-light
in the upper hall may have cast its gleam down the rear stairs as
far as the landing, but the rest of the way must have been in
darkness.  Moreover, the arrangement of the rear of the house is
somewhat complicated.  Therefore, unless he knew the layout he
couldn't have found his way about noiselessly in the dark.
Obviously, too, the visitor knew in which room Mrs. Drukker slept.
Also, he must have known what time Drukker turned in last night,
for he wouldn't have chanced making his call unless he had felt
sure that the coast was clear."

"That don't help us much," grumbled Heath.  "We've been going on
the theory right along that the murderer was wise to everything
connected with these two houses."

"True.  But one may be fairly intimate with a family and still not
know at what hour each of its members retires on a certain night,
or just how to effect a surreptitious entry to the house.
Furthermore, Sergeant, our midnight caller was some one who knew
that Mrs. Drukker was in the habit of leaving her door unlocked at
night; for he had every intention of entering her room.  His object
wasn't merely to leave his little memento outside and then depart.
The silent stealthy way he tried the knob proves that."

"He may simply have wanted to waken Mrs. Drukker so she would find
it at once," suggested Markham.

"Then why did he turn the knob so carefully--as if trying NOT to
waken any one?  A rattling of the knob, or a soft tapping, or even
throwing the chessman against the door, would have answered that
purpose much better. . . .  No, Markham; he had a far more sinister
object in mind; but when he found himself thwarted by the locked
door and heard Mrs. Drukker's cry of fright, he placed the bishop
where she would find it, and fled."

"Still and all, sir," argued Heath, "any one mighta known she left
her door unlocked at night; and any one coulda learned the lay of
the house so's to find their way around in the dark."

"But who, Sergeant, had a key to the rear door?  And who could have
used it at midnight last night?"

"The door mighta been left unlocked," countered Heath; "and when we
check up on the alibis of everybody we may get a lead."

Vance sighed.

"You'll probably find two or three people without any alibi at all.
And if last night's visit here was planned, a convincing alibi may
have been prepared.  We're not dealing with a simpleton, Sergeant.
We're playing a game to the death with a subtle and resourceful
murderer, who can think as quickly as we can, and who has had long
training in the subtleties of logic. . . ."

As if on a sudden impulse he turned and passed indoors, motioning
us to follow.  He went straight to the kitchen where the German
woman who had admitted us earlier sat stolidly by a table preparing
the midday meal.  She rose as we entered and backed away from us.
Vance, puzzled by her demeanor, studied her for several moments
without speaking.  Then his eyes drifted to the table where a large
eggplant had been halved lengthwise and scooped out.

"Ah!" he exclaimed, glancing at the contents of the various dishes
standing about.  "Aubergines à la Turque, what?  An excellent dish.
But I'd mince the mutton a bit finer, if I were you.  And not too
much cheese: it detracts from the sauce espagnole which I see
you're preparing."  He looked up with a pleasant smile.  "What's
your name, by the by?"

His manner astonished the woman greatly, but it also had the effect
of alleviating her fears.

"Menzel," she answered in a dull voice.  "Grete Menzel."

"And how long have you been with the Drukkers?"

"Going on twenty-five years."

"A long time," Vance commented musingly.  "Tell me: why were you
frightened when we called here this morning?"

The woman became sullen, and her large hands closed tightly.

"I wasn't frightened.  But Mr. Drukker was busy--"

"You thought perhaps we had come to arrest him," Vance broke in.

Her eyes dilated, but she made no answer.

"What time did Mr. Drukker rise yesterday morning?" Vance went on.

"I told you . . . nine o'clock--like always."

"What time did Mr. Drukker rise?"  The insistent, detached quality
of his voice was far more ominous than any dramatic intonation
could have been.

"I told you--"

"Die Wahrheit, Frau Menzel!  Um wie viel Uhr ist er aufgestanden?"

The psychological effect of this repetition of the question in
German was instantaneous.  The woman's hands went to her face, and
a stifled cry, like a trapped animal's, escaped her.

"I don't--know," she groaned.  "I called him at half past eight,
but he didn't answer, and I tried the door. . . .  It wasn't locked
and--Du lieber Gott!--he was gone."

"When did you next see him?" asked Vance quietly.

"At nine.  I went up-stairs again to tell him breakfast was ready.
He was in the study--at his desk--working like mad, and all
excited.  He told me to go away."

"Did he come down to breakfast?"

"Ja--ja.  He came down--half an hour later."

The woman leaned heavily against the drain-board of the sink, and
Vance drew up a chair for her.

"Sit down, Mrs. Menzel," he said kindly.  When she had obeyed, he
asked:  "Why did you tell me this morning that Mr. Drukker rose at
nine?"

"I had to--I was told to."  Her resistance was gone, and she
breathed heavily like a person exhausted.  "When Mrs. Drukker came
back from Miss Dillard's yesterday afternoon she told me that if
any one asked me that question about Mr. Drukker I was to say 'Nine
o'clock.'  She made me swear I'd say it. . . ."  Her voice trailed
off, and her eyes took on a glassy stare.  "I was afraid to say
anything else."

Vance still seemed puzzled.  After several deep inhalations on his
cigarette he remarked:

"There's nothing in what you've told us to affect you this way.
It's not unnatural that a morbid woman like Mrs. Drukker should
have taken such a fantastic measure to protect her son from
possible suspicion, when a murder had been committed in the
neighborhood.  You've surely been with her long enough to realize
how she might exaggerate every remote possibility where her son is
concerned.  In fact, I'm surprised you take it so seriously. . . .
Have you any other reason to connect Mr. Drukker with this crime?"

"No--no!"  The woman shook her head distractedly.

Vance strolled to the rear window, frowning.  Suddenly he swung
about.  He had become stern and implacable.

"Where were you, Mrs. Menzel, the morning Mr. Robin was killed?"

An astounding change came over the woman.  Her face paled; her lips
trembled; and she clinched her hands with a spasmodic gesture.  She
tried to take her staring eyes from Vance, but some quality in his
gaze held her.

"Where were you, Mrs. Menzel?"  The question was repeated sharply.

"I was--here--" she began; then stopped abruptly and cast an
agitated glance at Heath, who was watching her fixedly.

"You were in the kitchen?"

She nodded.  The power of speech seemed to have deserted her.

"And you saw Mr. Drukker return from the Dillards'?"

Again she nodded.

"Exactly," said Vance.  "And he came in the rear way, by the screen
porch, and went up-stairs. . . .  And he didn't know that you saw
him through the kitchen door. . . .  And later he inquired
regarding your whereabouts at that hour. . . .  And when you told
him you had been in the kitchen he warned you to keep silent about
it. . . .  And then you learned of Mr. Robin's death a few minutes
before you saw him enter here. . . .  And yesterday, when Mrs.
Drukker told you to say he had not risen until nine, and you heard
that some one else had been killed near here, you became suspicious
and frightened. . . .  That's correct, is it not, Mrs. Menzel?"

The woman was sobbing audibly in her apron.  There was no need for
her to reply, for it was obvious that Vance had guessed the truth.

Heath took his cigar from his mouth and glared at her ferociously.

"So!  You were holding out on me," he bellowed, thrusting forward
his jaw.  "You lied to me when I questioned you the other day.
Obstructing justice, were you?"

She gave Vance a look of frightened appeal.

"Mrs. Menzel, Sergeant," he said, "had no intention of obstructing
justice.  And now that she has told us the truth, I think we may
overlook her perfectly natural deception in the matter."  Then
before Heath had time to reply he turned to the woman and asked in
a matter-of-fact tone:  "Do you lock the door leading to the screen
porch every night?"

"Ja--every night."  She spoke listlessly: the reaction from her
fright had left her apathetic.

"You are sure you locked it last night?"

"At half past nine--when I went to bed."

Vance stepped across the little passageway and inspected the lock.

"It's a snap-lock," he observed, on returning.  "Who has a key to
the door?"

"I have a key.  And Mrs. Drukker--she has one, too."

"You're sure no one else has a key?"

"No one except Miss Dillard. . . ."

"Miss Dillard?"  Vance's voice was suddenly resonant with interest.
"Why should she have one?"

"She's had it for years.  She's like a member of the family--over
here two and three times a day.  When I go out I lock the back
door; and her having a key saves Mrs. Drukker the trouble of coming
down and letting her in."

"Quite natural," Vance murmured.  Then:  "We sha'n't bother you any
more, Mrs. Menzel."  He strolled out on the little rear porch.

When the door had been closed behind us he pointed to the screen
door that opened into the yard.

"You'll note that this wire mesh has been forced away from the
frame, permitting one to reach inside and turn the latch.  Either
Mrs. Drukker's key or Miss Dillard's--probably the latter--was used
to open the door of the house."

Heath nodded: this tangible aspect of the case appealed to him.
But Markham was not paying attention.  He stood in the background
smoking with angry detachment.  Presently he turned resolutely and
was about to re-enter the house when Vance caught his arm.

"No--no, Markham!  That would be abominable technique.  Curb your
ire.  You're so dashed impulsive, don't y' know."

"But, damn it, Vance!"  Markham shook off the other's hand.
"Drukker lied to us about going out the Dillard gate before Robin's
murder--"

"Of course he did.  I've suspected all along that the account he
gave us of his movements that morning was a bit fanciful.  But it's
useless to go upstairs now and hector him about it.  He'll simply
say that the cook is mistaken."

Markham was unconvinced.

"But what about yesterday morning?  I want to know where he was
when the cook called him at half past eight.  Why should Mrs.
Drukker be so anxious to have us believe he was asleep?"

"She, too, probably went to his room and saw that he was gone.
Then when she heard of Sprigg's death her febrile imagination
became overheated, and she proceeded to invest him with an alibi.
But you're only inviting trouble when you plan to chivy him about
the discrepancies in his tale."

"I'm not so sure."  Markham spoke with significative gravity.  "I
may be inviting a solution to this hideous business."

Vance did not reply at once.  He stood gazing down at the quivering
shadows cast on the lawn by the willow trees.  At length he said in
a low voice:

"We can't afford to take that chance.  If what you're thinking
should prove to be true, and you should reveal the information
you've just received, the little man who was here last night might
prowl about the upper hall again.  And this time he might not be
content to leave his chessman OUTSIDE THE DOOR!"

A look of horror came into Markham's eyes.

"You think I might be jeopardizing the cook's safety if I used her
evidence against him at this time?"

"The terrible thing about this affair is that, until we know the
truth, we face danger at every turn."  Vance's voice was heavy with
discouragement.  "We can't risk exposing any one. . . ."

The door leading to the porch opened, and Drukker appeared on the
threshold, his little eyes blinking in the sunlight.  His gaze came
to rest on Markham, and a crafty, repulsive smile contorted his
mouth.

"I trust I am not disturbing you," he apologized, with a menacing
squint; "but the cook has just informed me that she told you she
saw me enter here by the rear door on the morning of Mr. Robin's
unfortunate death."

"Oh, my aunt!" murmured Vance, turning away and busying himself
with the selection of a fresh cigarette.  "That tears it."

Drukker shot him an inquisitive look, and drew himself up with a
kind of cynical fortitude.

"And what about it, Mr. Drukker?" demanded Markham.

"I merely desired to assure you," the man replied, "that the cook
is in error.  She has obviously confused the date,--you see, I come
and go so often by this rear door.  On the morning of Mr. Robin's
death, as I explained to you, I left the range by the 75th-Street
gate and, after a brief walk in the park, returned home by the
front way.  I have convinced Grete that she is mistaken."

Vance had been listening to him closely.  Now he turned and met the
other's smile with a look of bland ingenuousness.

"Did you convince her with a chessman, by any chance?"

Drukker jerked his head forward and sucked in a rasping breath.
His twisted frame became taut; the muscles about his eyes and mouth
began to twitch; and the ligaments of his neck stood out like
whipcord.  For a moment I thought he was going to lose his self-
control; but with a great effort he steadied himself.

"I don't understand you, sir."  There was the vibrancy of an
intense anger in his words.  "What has a chessman to do with it?"

"Chessmen have various names," suggested Vance softly.

"Are YOU telling ME about chess?"  A venomous contempt marked
Drukker's manner, but he managed to grin.  "Various names,
certainly.  There's the king and queen, the rook, the knight--"  He
broke off.  "THE BISHOP! . . ."  He lay his head against the
casement of the door and began to cackle mirthlessly.  "So!  That's
what you mean?  THE BISHOP! . . .  You're a lot of imbecile
children playing a nonsense game."

"We have excellent reason to believe," said Vance, with impressive
calmness, "that the game is being played by some one else--with the
chess bishop as the principal symbol."

Drukker sobered.

"Don't take my mother's vagaries too seriously," he admonished.
"Her imagination often plays tricks on her."

"Ah!  And why do you mention your mother in this connection?"

"You've just been talking to her, haven't you?  And your comments,
I must say, sound very much like some of her harmless hallucinations."

"On the other hand," Vance rejoined mildly, "your mother may have
perfectly good grounds for her beliefs."

Drukker's eyes narrowed, and he looked swiftly at Markham.

"Rot!"

"Ah, well," sighed Vance; "we sha'n't debate the point."  Then in
an altered tone he added:  "It might help us though, Mr. Drukker,
if we knew where you were between eight and nine yesterday
morning."

The man opened his mouth slightly as if to speak, but quickly his
lips closed again, and he stood staring calculatingly at Vance.  At
length he answered in a high-pitched insistent voice.

"I was working--in my study--from six o'clock until half past
nine."  He paused, but evidently felt that further explanation was
desirable.  "For several months I've been working on a modification
of the ether-string theory to account for the interference of
light, which the quantum theory is unable to explain.  Dillard told
me I couldn't do it";--a fanatical light came into his eyes--"but I
awoke early yesterday morning with certain factors of the problem
clarified; and I got up and went to my study. . . ."

"So that's where you were."  Vance spoke carelessly.  "It's of no
great importance.  Sorry we discommoded you to-day."  He beckoned
with his head to Markham, and moved toward the screen door.  As we
stepped upon the range he turned back and, smiling, said almost
dulcetly:  "Mrs. Menzel is under our protection.  It would pain us
deeply if anything should happen to her."

Drukker looked after us with a sort of hypnotized fascination.

The moment we were out of hearing Vance moved to Heath's side.

"Sergeant," he said in a troubled voice, "that forthright German
Hausfrau may have put her head unwittingly in a noose.  And--my
word!--I'm afraid.  You'd better have a good man watch the Drukker
house to-night--from the rear, under those willow trees.  And tell
him to break in at the first scream or call. . . .  I'll sleep
better if I know there's a plain-clothes angel guarding Frau
Menzel's slumbers."

"I get you, sir."  Heath's face was grim.  "There won't be no chess
players worrying her to-night."



CHAPTER XIV

A GAME OF CHESS


(Tuesday, April 12; 11:30 a.m.)


As we walked slowly toward the Dillard house it was decided that
immediate inquiries should be made regarding the whereabouts the
night before of every person connected in any way with this
gruesome drama.

"We must be careful, however, to drop no hint of what befell Mrs.
Drukker," warned Vance.  "Our midnight bishop-bearer did not intend
that we should learn of his call.  He believed that the poor lady
would be too frightened to tell us."

"I'm inclined to think," objected Markham, "that you're attaching
too much importance to the episode."

"Oh, my dear fellow!"  Vance stopped short and put both hands on
the other's shoulders.  "You're much too effete--that's your great
shortcomin'.  You don't feel--you are no child of nature.  The
poetry of your soul has run to prose.  Now I, on the other hand,
give my imagination full sway; and I tell you that the leaving of
that bishop at Mrs. Drukker's door was no Hallowe'en prank, but the
desperate act of a desperate man.  It was meant as a warning."

"You think she knows something?"

"I think she saw Robin's body placed on the range.  And I think she
saw something else--something she would give her life not to have
seen."

In silence we moved on.  It was our intention to pass through the
wall gate into 75th Street and present ourselves at the Dillards'
front door; but as we passed the archery-room the basement door
opened, and Belle Dillard confronted us anxiously.

"I saw you coming down the range," she said, with troubled
eagerness, addressing her words to Markham.  "For over an hour I've
been waiting to get in touch with you--phoning your office. . . ."
Her manner became agitated.  "Something strange has happened.  Oh,
it may not mean anything . . . but when I came through the archery-
room here this morning, intending to call on Lady Mae, some impulse
made me go to the tool-chest again and look in the drawer,--it
seemed so--so queer that the little revolver should have been
stolen. . . .  And there it lay--in plain sight--beside the other
pistol!"  She caught her breath.  "Mr. Markham, some one returned
it to the drawer last night!"

This information acted electrically on Heath.

"Did you touch it?" he asked excitedly.

"Why--no. . . ."

He brushed past her unceremoniously and, going to the tool-chest,
yanked open the drawer.  There, beside the larger automatic that we
had seen the day before, lay a small pearl-handled .32.  The
Sergeant's eyes glistened as he ran his pencil through the trigger-
guard and lifted it gingerly.  He held it to the light and sniffed
at the end of the barrel.

"One empty chamber," he announced, with satisfaction.  "And it's
been shot off recently. . . .  This oughta get us somewheres."  He
wrapped the revolver tenderly in a handkerchief and placed it in
his coat pocket.  "I'll get Dubois busy on this for finger-prints;
and I'll have Cap Hagedorn* check up on the bullets."


* Captain Hagedorn was the fire-arms expert of the New York Police
Department.  It was he who, in the Benson murder case, gave Vance
the data with which to establish the height of the murderer; and
who made the examination of the three bullets fired from the old
Smith & Wesson revolver in the Greene murder case.


"Really now, Sergeant," said Vance banteringly; "do you imagine
that the gentleman we're looking for would wipe a bow and arrow
clean and then leave his digital monogram on a revolver?"

"I haven't got your imagination, Mr. Vance," returned Heath
surlily.  "So I'm going ahead doing the things that oughta be
done."

"You're quite right."  Vance smiled with good-natured admiration at
the other's dogged thoroughness.  "Forgive me for trying to damp
your zeal."

He turned to Belle Dillard.

"We came here primarily to see the professor and Mr. Arnesson.  But
there's also a matter we'd like to speak about to you.--We
understand you have a key to the rear door of the Drukker house."

She gave him a puzzled nod.

"Yes; I've had one for years.  I run back and forth so much; and it
saves Lady Mae a lot of bother. . . ."

"Our only interest in the key is that it might have been used by
some one who had no right to it."

"But that's impossible.  I've never lent it to any one.  And I
always keep it in my hand-bag."

"Is it generally known you have a key to the Drukkers'?"

"Why--I suppose so."  She was obviously perplexed.  "I've never
made a secret of it.  The family certainly know about it."

"And you may perhaps have mentioned or revealed the fact when there
were outsiders present?"

"Yes--though I can't recall any specific instance."

"Are you sure you have the key now?"

She gave Vance a startled look, and without a word picked up a
small lizard-skin hand-bag which lay on the wicker table.  Opening
it she felt swiftly in one of its inner compartments.

"Yes!" she announced, with relief.  "It's where I always keep
it. . . .  Why do you ask me about it?"

"It's important that we know who had access to the Drukker house,"
Vance told her.  Then, before she could question him further, he
asked:  "Could the key possibly have left your possession last
night?--that is, could it have been extracted from your bag
without your knowledge?"

A look of fright came into her face.

"Oh, what has happened?" she began; but Vance interrupted her.

"Please, Miss Dillard!  There's nothing for you to worry about.
We're merely striving to eliminate certain remote possibilities in
connection with our investigation.--Tell me: could any one have
taken your key last night?"

"No one," she answered uneasily.  "I went to the theatre at eight
o'clock, and had my bag with me the entire time."

"When did you last make use of the key?"

"After dinner last night.  I ran over to see how Lady Mae was and
to say good-night."

Vance frowned slightly.  I could see that this information did not
square with some theory he had formed.

"You made use of the key after dinner," he recapitulated, "and kept
it with you in your hand-bag the rest of the evening, without
letting it once go out of your sight.--Is that right, Miss
Dillard?"

The girl nodded.

"I even held the bag in my lap during the play," she amplified.

Vance regarded the hand-bag thoughtfully.

"Well," he said lightly, "so ends the romance of the key.--And now
we're going to bother your uncle again.  Do you think you'd better
act as our avant-courier; or shall we storm the citadel unannounced?"

"Uncle is out," she informed us.  "He went for a walk along the
Drive."

"And Mr. Arnesson, I suppose, has not yet returned from the
university."

"No; but he'll be here for lunch.  He has no classes Tuesday
afternoons."

"In the meantime, then, we'll confer with Beedle and the admirable
Pyne.--And I might suggest that it would do Mrs. Drukker no end of
good if you'd pay her a visit."

With a troubled smile and a little nod the girl passed out through
the basement door.

Heath at once went in search of Beedle and Pyne and brought them to
the drawing-room, where Vance questioned them about the preceding
night.  No information, however, was obtained from them.  They had
both gone to bed at ten o'clock.  Their rooms were on the fourth
floor at the side of the house; and they had not even heard Miss
Dillard when she returned from the theatre.  Vance asked them about
noises on the range, and intimated that the screen-porch door of
the Drukkers might have slammed shut at about midnight.  But
apparently both of them had been asleep at that hour.  Finally they
were dismissed with a warning not to mention to any one the
questions that had just been asked them.

Five minutes later Professor Dillard came in.  Though surprised to
see us, he greeted us amiably.

"For once, Markham, you've chosen an hour for your visit when I am
not absorbed in work.--More questions, I suppose.  Well, come along
to the library for the inquisition.  It'll be more comfortable
there."  He led the way up-stairs, and when we were seated he
insisted that we join him in a glass of port which he himself
served from the sideboard.

"Drukker should be here," he remarked.  "He has a fondness for my
'Ninety-six,' though he'll drink it only on rare occasions.  I tell
him he should take more port; but he imagines it's bad for him, and
points to my gout.  But there's no connection between gout and
port--the notion is sheer superstition.  Sound port is the most
wholesome of wines.  Gout is unknown in Oporto.  A little physical
stimulation of the right kind would be good for Drukker. . . .
Poor fellow.  His mind is like a furnace that's burning his body
up.  A brilliant man, Markham.  If he had sufficient bodily energy
to keep pace with his brain, he'd be one of the world's great
physicists."

"He tells me," commented Vance, "that you twitted him on his
inability to work out a modification of the quantum theory in
regard to light-interference."

The old man smiled ruefully.

"Yes.  I knew that such a criticism would spur him to a maximum
effort.  The fact is, Drukker is on the track of something
revolutionary.  He has already worked out some very interesting
theorems. . . .  But I'm sure this isn't what you gentlemen came
here to discuss.  What can I do for you, Markham?  Or, perhaps you
came to give me news."

"Unfortunately we have no news.  We have come to solicit aid
again. . . ."  Markham hesitated as if uncertain how to proceed;
and Vance assumed the rôle of questioner.

"The situation has changed somewhat since we were here yesterday.
One or two new matters have arisen, and there is a possibility that
our investigation would be facilitated if we knew the exact
movements of the members of your household last night.  These
movements, in fact, may have influenced certain factors in the
case."

The professor lifted his head in some surprise, but made no
comment.  He said merely:  "That information is very easily given.
To what members do you refer?"

"To no member specifically," Vance hastened to assure him.

"Well, let me see. . . ."  He took out his old meerschaum pipe and
began filling it.  "Belle and Sigurd and I had dinner alone at six
o'clock.  At half past seven Drukker dropped in, and a few minutes
later Pardee called.  Then at eight Sigurd and Belle went to the
theatre, and at half past ten Drukker and Pardee went away.  I
myself turned in shortly after eleven, after locking up the house--
I'd let Pyne and Beedle go to bed early.--And that's about all I
can tell you."

"Do I understand that Miss Dillard and Mr. Arnesson went to the
theatre together?"

"Yes.  Sigurd rarely patronizes the theatre, but whenever he does
he takes Belle along.  He attends Ibsen's plays, for the most part.
He's a devout disciple of Ibsen's, by the way.  His American
upbringing hasn't in the least tempered his enthusiasm for things
Norwegian.  At heart he's quite loyal to his native country.  He's
as well grounded in Norwegian literature as any professor at the
University of Oslo; and the only music he really cares for is
Grieg's.  When he goes to concerts or the theatre you're pretty
sure to find that the programs are liberally Norwegian."

"It was an Ibsen play, then, he attended last night?"

"'Rosmersholm,' I believe.  There's a revival of Ibsen's dramas at
present in New York."

Vance nodded.  "Walter Hampden's doing them.--Did you see either
Mr. Arnesson or Miss Dillard after they returned from the theatre?"

"No; they came in rather late, I imagine.  Belle told me this
morning they went to the Plaza for supper after the play.  However,
Sigurd will be here at any minute, and you can learn the details
from him."  Though the professor spoke with patience, it was plain
that he was annoyed by the apparently irrelevant nature of the
interrogation.

"Will you be good enough, sir," pursued Vance, "to tell us the
circumstances connected with Mr. Drukker's and Mr. Pardee's visit
here after dinner?"

"There was nothing unusual about their call.  They often drop in
during the evening.  The object of Drukker's visit was to discuss
with me the work he had done on his modification of the quantum
theory; but when Pardee appeared the discussion was dropped.
Pardee is a good mathematician, but advanced physics is beyond his
depth."

"Did either Mr. Drukker or Mr. Pardee see Miss Dillard before she
went to the theatre?"

Professor Dillard took his pipe slowly from his mouth, and his
expression became resentful.

"I must say," he replied testily, "that I can see no valid object
in my answering such questions.--However," he added, in a more
indulgent tone, "if the domestic trivia of my household can be of
any possible assistance to you, I will of course be glad to go into
detail."  He regarded Vance a moment.  "Yes, both Drukker and
Pardee saw Belle last night.  All of us, including Sigurd, were
together in this room for perhaps half an hour before theatre time.
There was even a casual discussion about Ibsen's genius, in which
Drukker annoyed Sigurd greatly by maintaining Hauptmann's
superiority."

"Then at eight o'clock, I gather, Mr. Arnesson and Miss Dillard
departed, leaving you and Mr. Pardee and Mr. Drukker alone here."

"That is correct."

"And at half past ten, I think you said, Mr. Drukker and Mr. Pardee
went away.  Did they go together?"

"They went down-stairs together," the professor answered, with more
than a suggestion of tartness.  "Drukker, I believe, went home; but
Pardee had an appointment at the Manhattan Chess Club."

"It seems a bit early for Mr. Drukker to have gone home," mused
Vance, "especially as he had come to discuss an important matter
with you and had had no adequate opportunity to do so up to the
time of his departure."

"Drukker is not well."  The professor's voice was again studiously
patient.  "As I've told you, he tires easily.  And last night he
was unusually played out.  In fact, he complained to me of his
fatigue and said he was going immediately to bed."

"Yes . . . quite in keeping," murmured Vance.  "He told us a little
while ago that he was up working at six yesterday morning."

"I'm not surprised.  Once a problem has posed itself in his mind he
works on it incessantly.  Unfortunately he has no normal reactions
to counterbalance his consuming passion for mathematics.  There
have been times when I've feared for his mental stability."

Vance, for some reason, steered clear of this point.

"You spoke of Mr. Pardee's engagement at the Chess Club last
night," he said, when he had carefully lighted a fresh cigarette.
"Did he mention the nature of it to you?"

Professor Dillard smiled with patronizing lenity.

"He talked about it for fully an hour.  It appears that a gentleman
named Rubinstein--a genius of the chess world, I understand, who is
now visiting this country--had taken him on for three exhibition
games.  The last one was yesterday.  It began at two o'clock, and
was postponed at six.  It should have been played off at eight, but
Rubinstein was the lion of some dinner down-town; so the hour set
for the play-off was eleven, Pardee was on tenter-hooks, for he had
lost the first game and drawn the second; and if he could have won
last night's game he would have broken even with Rubinstein.  He
seemed to think he had an excellent chance according to the way the
game stood at six o'clock; although Drukker disagreed with him. . . .
He must have gone directly from here to the club, for it was fully
half past ten when he and Drukker went out."

"Rubinstein's a strong player," observed Vance.  A new note of
interest, which he strove to conceal, had come into his voice.
"He's one of the grand masters of the game.  He defeated Capablanca
at San Sebastian in 1911, and between 1907 and 1912 was considered
the logical contender for the world's title held by Doctor Lasker.*
. . .  Yes, it would have been a great feather in Pardee's cap to
have beaten him.  Indeed, it was no small compliment to him that he
should have been matched with Rubinstein.  Pardee, despite the fame
of his gambit, has never been ranked as a master.--Have you heard
the result of last night's game, by the by?"


* Akiba Rubinstein was then, and is to-day, the chess champion of
Poland and one of the great international masters of the game.  He
was born in Stavisk, near Lodz, in 1882, and made his début in
international chess at the Ostend tournament in 1906.  His recent
visit to America resulted in a series of new triumphs.


Again I noted a faint tolerant smile at the corners of the
professor's mouth.  He gave the impression of looking down
benevolently on the foolish capers of children from some great
intellectual height.

"No," he answered; "I didn't inquire.  But my surmise is that
Pardee lost; for when Drukker pointed out the weakness of his
adjourned position, he was more positive than usual.  Drukker by
nature is cautious, and he rarely expresses a definite opinion on
a problem without having excellent grounds for so doing."

Vance raised his eyebrows in some astonishment.

"Do you mean to tell me that Pardee analyzed his unfinished game
with Drukker and discussed the possibilities of its ending?  Not
only is such a course unethical, but any player would be
disqualified for doing such a thing."

"I'm unfamiliar with the punctilio of chess," Professor Dillard
returned acidly; "but I am sure Pardee would not be guilty of a
breach of ethics in that regard.  And, as a matter of fact, I
recall that when he was engaged with the chessmen at the table over
there and Drukker stepped up to look on, Pardee requested him to
offer no advice.  The discussion of the position took place some
time later, and was kept entirely to generalities.  I don't believe
there was a mention of any specific line of play."

Vance leaned slowly forward and crushed out his cigarette with that
taut deliberation which I had long since come to recognize as a
sign of repressed excitement.  Then he rose carelessly and moved to
the chess table in the corner.  He stood there, one hand resting on
the exquisite marquetry of the alternating squares.

"You say that Mr. Pardee was analyzing his position on this board
when Mr. Drukker came over to him?"

"Yes, that is right."  Professor Dillard spoke with forced
politeness.  "Drukker sat down facing him and studied the layout.
He started to make some remark, and Pardee requested him to say
nothing.  A quarter of an hour or so later Pardee put the men away;
and it was then that Drukker told him that his game was lost--that
he had worked himself into a position which, though it looked
favorable, was fundamentally weak."

Vance had been running his fingers aimlessly over the board; and
he had taken two or three of the men from the box and tossed them
back, as if toying with them.

"Do you remember just what Mr. Drukker said?" he asked without
looking up.

"I didn't pay very close attention--the subject was not exactly one
of burning moment to me."  There was an unescapable note of irony
in the answer.  "But, as nearly as I can recall, Drukker said that
Pardee could have won provided it had been a rapid-transit game,
but that Rubinstein was a notoriously slow and careful player and
would inevitably find the weak spot in Pardee's position."

"Did Pardee resent this criticism?"  Vance now strolled back to his
chair and selected another cigarette from his case; but he did not
sit down again.

"He did--very much.  Drukker has an unfortunately antagonistic
manner.  And Pardee is hypersensitive on the subject of his chess.
The fact is, he went white with anger at Drukker's strictures.
But I personally changed the subject; and when they went away the
incident had apparently been forgotten."

We remained but a few minutes longer.  Markham was profuse in his
apologies to the professor and sought to make amends for the patent
annoyance our visit had caused him.  He was not pleased with Vance
for his seemingly garrulous insistence on the details of Pardee's
chess game, and when we had descended to the drawing-room he
expressed his displeasure.

"I could understand your questions relating to the whereabouts of
the various occupants of this house last night, but I could see no
excuse for your harping on Pardee's and Drukker's disagreement over
a game of chess.  We have other things to do besides gossip."

"A hate of gossip parlance also crown'd Tennyson's Isabel thro'
all her placid life," Vance returned puckishly.  "But--my word,
Markham!--our life is not like Isabel's.  Speakin' seriously, there
was method in my gossip.  I prattled--and I learned."

"You learned what?" Markham demanded sharply.

With a cautious glance into the hall Vance leaned forward and
lowered his voice.

"I learned, my dear Lycurgus, that a black bishop is missing from
that set in the library, and that the chessman left at Mrs.
Drukker's door matches the other pieces up-stairs!"



CHAPTER XV

AN INTERVIEW WITH PARDEE


(Tuesday, April 12; 12.30 p.m.)


This piece of news had a profound effect on Markham.  As was his
habit when agitated, he rose and began pacing back and forth, his
hands clasped behind him.  Heath, too, though slower to grasp the
significance of Vance's revelation, puffed vigorously on his cigar--
an indication that his mind was busy with a difficult adjustment
of facts.

Before either had formulated any comment the rear door of the hall
opened and light footsteps approached the drawing-room.  Belle
Dillard, returning from Mrs. Drukker's, appeared in the archway.
Her face was troubled, and letting her eyes rest on Markham, she
asked:

"What did you say to Adolph this morning?  He's in an awful state
of funk.  He's going about testing all the door-locks and window-
catches as if he feared burglars; and he has frightened poor Grete
by telling her to be sure to bolt herself in at night."

"Ah!  He has warned Mrs. Menzel, has he?" mused Vance.  "Very
interestin'."

The girl's gaze turned swiftly to him.

"Yes; but he will give me no explanation.  He's excited and
mysterious.  And the strangest thing about his attitude is that he
refuses to go near his mother. . . .  What does it mean, Mr. Vance?
I feel as though something terrible were impending."

"I don't know just what it does mean."  Vance spoke in a low,
distressed voice.  "And I'm afraid even to try to interpret it.  If
I should be wrong. . . ."  He became silent for a moment.  "We must
wait and see.  To-night perhaps we'll know.--But there's no cause
for alarm on your part, Miss Dillard."  He smiled comfortingly.
"How did you find Mrs. Drukker?"

"She seemed much better.  But there's still something worrying her;
and I think it has to do with Adolph, for she talked about him the
whole time I was there, and kept asking me if I'd noticed anything
unusual in his manner lately."

"That's quite natural in the circumstances," Vance returned.  "But
you mustn't let her morbid attitude affect you.--And now, to change
the subject: I understand that you were in the library for half an
hour or so last night just before you went to the theatre.  Tell
me, Miss Dillard: where was your hand-bag during that time?"

The question startled her; but after a momentary hesitation she
answered:  "When I came into the library I placed it with my wrap
on the little table by the door."

"It was the lizard-skin bag containing the key?"

"Yes.  Sigurd hates evening dress, and when we go out together I
always wear my day clothes."

"So you left the bag on the table during that half-hour, and then
kept it with you the rest of the evening.--And what about this
morning?"

"I went out for a walk before breakfast and carried it with me.
Later I put it on the hat-rack in the hall for an hour or so; but
when I started for Lady Mae's at about ten I took it with me.  It
was then I discovered that the little pistol had been returned, and
I postponed my call.  I left the bag down-stairs in the archery-
room until you and Mr. Markham came; and I've had it with me ever
since."

Vance thanked her whimsically.

"And now that the peregrinations of the bag have been thoroughly
traced, please try to forget all about it."  She was on the point
of asking a question, but he anticipated her curiosity and said
quickly:  "You went to the Plaza for supper last night, your uncle
told us.  You must have been late in getting home."

"I never stay out very late when I go anywhere with Sigurd,"
she answered, with a maternal note of complaint.  "He has a
constitutional aversion to any kind of night life.  I begged him
to stay out longer, but he looked so miserable I hadn't the heart
to remain.  We actually got home at half past twelve."

Vance rose with a gracious smile.

"You've been awfully good to bear with our foolish questions so
patiently. . . .  Now we're going to drop in on Mr. Pardee and see
if he has any illuminatin' suggestions to offer.  He's generally in
at this time, I believe."

"I'm sure he's in now."  The girl walked with us to the hall.  "He
was here only a little while before you came, and he said he was
returning home to attend to some correspondence."

We were about to go out when Vance paused.

"Oh, I say, Miss Dillard; there's one point I forgot to ask you
about.  When you came home last night with Mr. Arnesson, how did
you know it was just half past twelve?  I notice you don't wear a
watch."

"Sigurd told me," she explained.  "I was rather mean to him for
bringing me home so early, and as we entered the hall here I asked
him spitefully what time it was.  He looked at his watch and said
it was half past twelve. . . ."

At that moment the front door opened and Arnesson came in.  He
stared at us in mock astonishment; then he caught sight of Belle
Dillard.

"Hallo, sis," he called to her pleasantly.  "In the hands of the
gendarmerie, I see."  He flashed us an amused look.  "Why the
conclave?  This house is becoming a regular police station.
Hunting for clews of Sprigg's murderer?  Ha!  Bright youth done
away with by his jealous professor, and that sort of thing, eh? . . .
Hope you chaps haven't been putting Diana the Huntress through a
third degree."

"Nothing of the kind," the girl spoke up.  "They've been most
considerate.  And I've been telling them what an old fogy you are--
bringing me home at half past twelve."

"I think I was very indulgent," grinned Arnesson.  "Much too late
for a child like you to be out."

"It must be terrible to be senile and--and mathematically
inclined," she retorted with some heat, and ran up-stairs.

Arnesson shrugged his shoulders and looked after her until she had
disappeared.  Then he fixed a cynical eye on Markham.

"Well, what glad tidings do you bring?  Any news about the latest
victim?"  He led the way back to the drawing-room.  "You know, I
miss that lad.  He'd have gone far.  Rotten shame he had to be
named Johnny Sprigg.  Even 'Peter Piper' would have been safer.
Nothing happened to Peter Piper aside from the pepper episode; and
you couldn't very well work that up into a murder. . . ."

"We have nothing to report, Arnesson," Markham broke in, nettled by
the man's flippancy.  "The situation remains unchanged."

"Just dropped in for a social call, I presume.  Staying for lunch?"

"We reserve the right," said Markham coldly, "to investigate the
case in whatever manner we deem advisable.  Nor are we accountable
to you for our actions."

"So!  Something HAS happened that irks you."  Arnesson spoke with
sarcasm.  "I thought I had been accepted as a coadjutor; but I see
I am to be turned forth into the darkness."  He sighed elaborately
and took out his pipe.  "Dropping the pilot!--Bismarck and me.
Alas!"

Vance had been smoking dreamily near the archway, apparently
oblivious of Arnesson's complaining.  Now he stepped into the room.

"Really, y' know, Markham, Mr. Arnesson is quite right.  We agreed
to keep him posted; and if he's to be of any help to us he must
know all the facts."

"It was you yourself," protested Markham, "who pointed out the
possible danger of mentioning last night's occurrence. . . ."

"True.  But I had forgotten at the time our promise to Mr.
Arnesson.  And I'm sure his discretion can be relied on."  Then
Vance related in detail Mrs. Drukker's experience of the night
before.

Arnesson listened with rapt attention.  I noticed that his sardonic
expression gradually disappeared, and that in its place came a look
of calculating sombreness.  He sat for several minutes in
contemplative silence, his pipe in his hand.

"That's certainly a vital factor in the problem," he commented at
length.  "It changes our constant.  I can see that this thing has
got to be calculated from a new angle.  The Bishop, it appears, is
in our midst.  But why should he come to haunt Lady Mae?"

"She is reported to have screamed at almost the exact moment of
Robin's death."

"Aha!"  Arnesson sat up.  "I grasp your implication.  She saw the
Bishop from her window on the morning of Cock Robin's dissolution,
and later he returned and perched on her door-knob as a warning for
her to keep mum."

"Something like that, perhaps. . . .  Have you enough integers now
to work out your formula?"

"I'd like to cast an eye on this black bishop.  Where is it?"

Vance reached in his pocket, and held out the chessman.  Arnesson
took it eagerly.  His eyes glittered for a moment.  He turned the
piece over in his hand, and then gave it back.

"You seem to recognize this particular bishop," said Vance
dulcetly.  "You're quite correct.  It was borrowed from your chess
set in the library."

Arnesson nodded a slow affirmative.

"I believe it was."  Suddenly he turned to Markham, and an ironic
leer came over his lean features.  "Was that why I was to be kept
in the dark?  Under suspicion, am I?  Shades of Pythagoras!  What
penalty attaches to the heinous crime of distributing chessmen
among one's neighbors?"

Markham got up and walked toward the hall.

"You are not under suspicion, Arnesson," he answered, with no
attempt to conceal his ill-humor.  "The bishop was left at Mrs.
Drukker's at exactly midnight."

"And I was half an hour too late to qualify.  Sorry to have
disappointed you."

"Let us hear if your formula works out," said Vance, as we passed
out of the front door.  "We've a little visit to pay to Mr. Pardee
now."

"Pardee?  Oho!  Calling in a chess expert on the subject of
bishops, eh?  I see your reasoning--it at least has the virtue of
being simple and direct. . . ."

He stood on the little porch and watched us, like a japish
gargoyle, as we crossed the street.

Pardee received us with his customary quiet courtesy.  The tragic,
frustrated look which was a part of his habitual expression was
even more pronounced than usual; and when he drew up chairs for us
in his study his manner was that of a man whose interest in life
had died, and who was merely going through the mechanical motions
of living.

"We have come here, Mr. Pardee," Vance began, "to learn what we can
of Sprigg's murder in Riverside Park yesterday morning.  We have
excellent reasons for every question we are about to ask you."

Pardee nodded resignedly.

"I shall not be offended at any line of interrogation you take.
After reading the papers I realize just how unusual a problem you
are facing."

"First, then, please inform us where you were yesterday morning
between seven and eight."

A faint flush overspread Pardee's face, but he answered in a low,
even voice.

"I was in bed.  I did not rise until nearly nine."

"Is it not your habit to take a walk in the park before breakfast?"
(I knew this was sheer guesswork on Vance's part, for the subject
of Pardee's habits had not come up during the investigation.)

"That is quite true," the man replied, without a moment's
hesitation.  "But yesterday I did not go,--I had worked rather late
the night before."

"When did you first hear of Sprigg's death?"

"At breakfast.  My cook repeated the gossip of the neighborhood.
I read the official account of the tragedy in the early edition of
the evening Sun."

"And you saw the reproduction of the Bishop note, of course, in
this morning's paper.--What is your opinion of the affair, Mr.
Pardee?"

"I hardly know."  For the first time his lacklustre eyes showed
signs of animation.  "It's an incredible situation.  The
mathematical chances are utterly opposed to such a series of
interrelated events being coincidental."

"Yes," Vance concurred.  "And speaking of mathematics: are you at
all familiar with the Riemann-Christoffel tensor?"

"I know of it," the man admitted.  "Drukker uses it in his book on
world lines.  My mathematics, however, are not of the physicist's
type.  Had I not become enamored of chess"--he smiled sadly--"I
would have been an astronomer.  Next to manoeuvring the factors in
a complicated chess combination, the greatest mental satisfaction
one can get, I think, is plotting the heavens and discovering new
planets.  I even keep a five-inch equatorial telescope in a pent-
house on my roof for amateur observations."

Vance listened to Pardee with close attention; and for several
minutes discussed with him Professor Pickering's recent
determination of the trans-Neptunean O,* much to Markham's
bewilderment and to the Sergeant's annoyance.  At length he brought
the conversation back to the tensor formula.


* Since this discussion took place Professor Pickering has posited
from the perturbations of Uranus, two other outer planets beyond
Neptune: P and S.


"You were, I understand, at the Dillards' last Thursday when Mr.
Arnesson was discussing this tensor with Drukker and Sprigg."

"Yes, I recall that the subject came up then."

"How well did you know Sprigg?"

"Only casually.  I had met him with Arnesson once or twice."

"Sprigg, also, it seems, was in the habit of walking in Riverside
Park before breakfast," observed Vance negligently.  "Ever run into
him there, Mr. Pardee?"

The man's eyelids quivered slightly, and he hesitated before
answering.

"Never," he said finally.

Vance appeared indifferent to the denial.  He rose and, going to
the front window, looked out.

"I thought one might be able to see into the archery range from
here.  But I note that the angle cuts off the view entirely."

"Yes, the range is quite private.  There's even a vacant lot
opposite the wall, so that no one can see over it. . . .  Were you
thinking of a possible witness to Robin's death?"

"That, and other things."  Vance returned to his chair.  "You don't
go in for archery, I take it."

"It's a trifle too strenuous for me.  Miss Dillard once tried to
interest me in the sport, but I was not a very promising acolyte.
I've been to several tournaments with her, however."

An unusually soft note had crept into Pardee's voice, and for some
reason which I could not exactly explain I got the feeling that he
was fond of Belle Dillard.  Vance, too, must have received the same
impression, for after a brief pause he said:

"You will realize, I trust, that it is not our intention to pry
unnecessarily into any one's private affairs; but the question of
motive in the two murders we are investigating still remains
obscure, and as Robin's death was at first superficially attributed
to a rivalry for Miss Dillard's affections, it might help us to
know, in a general way, what the true situation is concerning the
young lady's preference. . . .  As a friend of the family you
probably know; and we'd appreciate your confidence in the matter."

Pardee's gaze travelled out of the window, and the suggestion of a
sigh escaped him.

"I've always had the feeling that she and Arnesson would some day
be married.  But that is only conjecture.  She once told me quite
positively that she was not going to consider matrimony until she
was thirty."  (One could easily guess in what connection Belle
Dillard had made this pronouncement to Pardee.  His emotional, as
well as his intellectual life, had apparently met with failure.)

"You do not believe then," pursued Vance, "that her heart is
seriously concerned with young Sperling?"

Pardee shook his head.  "However," he qualified, "martyrdom such as
he is undergoing at present has a tremendous sentimental appeal for
women."

"Miss Dillard tells me you called on her this morning."

"I generally drop over during the day."  He was obviously
uncomfortable and, I thought, a little embarrassed.

"Do you know Mrs. Drukker well?"

Pardee gave Vance a quick, inquisitive look.

"Not particularly," he said.  "I've naturally met her several
times."

"You've called at her house?"

"On many occasions, but always to see Drukker.  I've been interested
for years in the relation of mathematics to chess. . . ."

Vance nodded.

"How did your game with Rubinstein come out last night, by the by?
I didn't see the papers this morning."

"I resigned on the forty-fourth move."  The man spoke hopelessly.
"Rubinstein found a weakness in my attack which I had entirely
overlooked when I sealed my move at the adjournment."

"Drukker, Professor Dillard tells us, foresaw the outcome when you
and he were discussing the situation last night."

I could not understand why Vance referred so pointedly to this
episode, knowing as he did how sore a point it was with Pardee.
Markham, also, frowned at what appeared to be an unforgivably
tactless remark on Vance's part.

Pardee colored, and shifted in his chair.

"Drukker talked too much last night."  The statement was not
without venom.  "Though he's not a tournament player, he should
know that such discussions are taboo during unfinished games.
Frankly, though, I put little stock in his prophecy.  I thought my
sealed move had taken care of the situation, but Drukker saw
farther ahead than I did.  His analysis was uncannily profound."
There was the jealousy of self-pity in his tone, and I felt that he
hated Drukker as bitterly as his seemingly mild nature would
permit.

"How long did the game last?" Vance asked casually.

"It was over a little after one o'clock.  There were only fourteen
moves in last night's session."

"Were there many spectators?"

"An unusually large number, considering the late hour."

Vance put out his cigarette and got up.  When we were in the lower
hall on our way to the front door he halted suddenly and, fixing
Pardee with a gaze of sardonic amusement, said:

"Y' know, the black bishop was at large again last night around
midnight."

His words produced an astonishing effect.  Pardee drew himself up
as if he had been struck in the face; and his cheeks went chalky
white.  For a full half-minute he stared at Vance, his eyes like
live coals.  His lips moved with a slight tremor, but no word came
from them.  Then, as if with superhuman effort, he turned stiffly
away and went to the door.  Jerking it open he held it for us to
pass out.

As we walked up Riverside Drive to the District Attorney's car,
which had been left in front of the Drukker house in 76th Street,
Markham questioned Vance sharply in regard to the final remark he
had made to Pardee.

"I was in hopes," explained Vance, "of surprising some look of
recognition or understanding from him.  But, 'pon my soul, Markham,
I didn't expect any effect like the one I produced.  Astonishin'
how he reacted.  I don't grasp it--I don't at all grasp it. . . ."

He became engrossed in his thoughts.  But as the car swung into
Broadway at 72nd Street he roused himself and directed the
chauffeur to the Sherman Square Hotel.

"I have a gaspin' desire to know more of that chess game between
Pardee and Rubinstein.  No reason for it--sheer vagary on my part.
But the idea has been workin' in me ever since the professor
mentioned it. . . .  From eleven until past one--that's a deuced
long time to play off an unfinished game of only forty-four moves."

We had drawn up to the curb at the corner of Amsterdam Avenue and
71st Street, and Vance disappeared into the Manhattan Chess Club.
It was fully five minutes before he returned.  In his hand he
carried a sheet of paper filled with notations.  There was,
however, no sign of jubilance in his expression.

"My far-fetched but charmin' theory," he said, with a grimace,
"has run aground on base prosaic facts.  I just talked to the
secret'ry of the club; and last night's session consumed two
hours and nineteen minutes.  It seems to have been a coruscatin'
battle, full of esoteric quirks and strategical soul-searchin's.
Along about half past eleven the onlooking genii had Pardee picked
for the winner; but Rubinstein then staged a masterly piece of
sustained analysis, and proceeded to tear Pardee's tactics to
smithereens--just as Drukker had prognosticated.  Astonishin'
mind, Drukker's. . . ."

It was plain that even now he was not entirely satisfied with what
he had learned; and his next words voiced his dissatisfaction.

"I thought while I was at it I'd take a page from the Sergeant's
book, so to speak, and indulge in a bit of routine thoroughness.
So I borrowed the score sheet of last night's game and copied down
the moves.  I may run over the game some day when time hangs
heavy."

And, with what I thought unusual care, he folded the score and
placed it in his wallet.



CHAPTER XVI

ACT THREE


(Tuesday, April 12--Saturday, April 16.)


After lunch at the Elysée Markham and Heath continued down-town.
A hard afternoon lay before them.  Markham's routine work had
accumulated; and the Sergeant, having taken on the Sprigg case in
addition to the Robin investigation, had to keep two separate
machines working, co-ordinate all his reports, answer innumerable
questions from his superiors, and attempt to satisfy the
voraciousness of an army of reporters.  Vance and I went to an
exhibition of modern French art at Knoedler's, had tea at the St.
Regis, and met Markham at the Stuyvesant Club for dinner.  Heath
and Inspector Moran joined us at half past eight for an informal
conference; but though it lasted until nearly midnight nothing of
a tangible nature came out of it.

Nor did the following day bring anything but discouragement.  The
report from Captain Dubois stated that the revolver given him by
Heath contained no sign of a finger-print.  Captain Hagedorn
identified the weapon as the one used in the shooting of Sprigg;
but this merely substantiated our already positive belief.  The man
set to guard the rear of the Drukker residence spent an uneventful
night.  No one had entered or departed from the house; and by
eleven o'clock every window had been dark.  Nor had a sound of any
kind come from the house until the next morning when the cook set
about her chores for the day.  Mrs. Drukker had appeared in the
garden a little after eight; and at half past nine Drukker went out
the front door and sat for two hours in the park reading.

Two days went by.  A watch was kept on the Dillard house; Pardee
was put under strict surveillance; and a man was stationed each
night under the willow trees behind the Drukker house.  But nothing
unusual happened; and, despite the Sergeant's tireless activities,
all promising lines of investigation seemed to be automatically
closed.  Both Heath and Markham were deeply worried.  The
newspapers were outdoing themselves in gaudy rhetoric; and the
inability of the Police Department and the District Attorney's
office to make the slightest headway against the mystery of the two
spectacular murders was rapidly growing into a political scandal.

Vance called on Professor Dillard and discussed the case along
general lines.  He also spent over an hour on Thursday afternoon
with Arnesson in the hope that the working out of the proposed
formula had brought to light some detail that could be used as a
starting-point for speculation.  But he was dissatisfied with the
interview, and complained to me that Arnesson had not been wholly
frank with him.  Twice he dropped in at the Manhattan Chess Club
and attempted to lead Pardee into conversation; but each time he
was met with the reticence of cold courtesy.  I noticed that he
made no effort to communicate with either Drukker or Mrs. Drukker;
and when I asked him his reason for ignoring them, he answered:

"The truth cannot be learned from them now.  Each is playing a
game; and both are thoroughly frightened.  Until we have some
definite evidence, more harm than good will result from any attempt
to cross-examine them."

This definite evidence was to come the very next day from a most
unexpected quarter; and it marked the beginning of the last phase
of our investigation--a phase fraught with such sinister, soul-
stirring tragedy and unspeakable horror, with such wanton cruelty
and monstrous humor, that even now, years later, as I set down this
reportorial record of it, I find it difficult to believe that the
events were not, after all, a mere grotesque dream of fabulous
wickedness.

Friday afternoon Markham, in a mood of desperation, called another
conference.  Arnesson asked permission to attend; and at four
o'clock we all met, including Inspector Moran, in the District
Attorney's private room in the old Criminal Courts Building.
Arnesson was unwontedly silent during the discussion, and not once
did he indulge in his usual flippancy.  He listened with close
attention to all that was said, and seemed purposely to avoid
expressing an opinion, even when directly appealed to by Vance.

We had been in conference perhaps half an hour when Swacker entered
quietly and placed a memorandum on the District Attorney's desk.
Markham glanced at it and frowned.  After a moment he initialed two
printed forms and handed them to Swacker.

"Fill these in right away and give them to Ben,"* he ordered.  Then
when the man had gone out through the outer-hall door, he explained
the interruption.  "Sperling has just sent a request to speak to
me.  He says he has information that may be of importance.  I
thought, in the circumstances, it might be well to see him now."


* Colonel Benjamin Hanlon, commanding officer of the Detective
Division attached to the District Attorney's office.


Ten minutes later Sperling was brought in by a deputy sheriff from
the Tombs.  He greeted Markham with a friendly boyish smile, and
nodded pleasantly to Vance.  He bowed--a bit stiffly, I thought--
to Arnesson, whose presence seemed both to surprise and disconcert
him.  Markham motioned him to a chair, and Vance offered him a
cigarette.

"I wanted to speak to you, Mr. Markham," he began, a bit
diffidently, "about a matter which may be of help to you. . . .
You remember, when you were questioning me about my being in the
archery-room with Robin, you wanted to know which way Mr. Drukker
went when he left us.  I told you I didn't notice, except that he
went out by the basement door. . . .  Well, sir, I've had a lot of
time to think lately; and I've naturally gone over in my mind all
that happened that morning.  I don't know just how to explain it,
but everything has become a lot clearer now.  Certain--what you
might call impressions--have come back to me. . . ."

He paused and looked down at the carpet.  Then lifting his head, he
went on:

"One of these impressions has to do with Mr. Drukker--and that's
why I wanted to see you.  Just this afternoon I was--well, sort of
pretending I was in the archery-room again, talking to Robin; and
all of a sudden the picture of the rear window flashed across my
mind.  And I remembered that when I had glanced out of the window
that morning to see how the weather was for my trip, I had seen Mr.
Drukker sitting in the arbor behind the house. . . ."

"At what time was this?" Markham demanded brusquely.

"Only a few seconds before I went to catch my train."

"Then you imply that Mr. Drukker, instead of leaving the premises,
went to the arbor and remained there until you departed."

"It looks that way, sir."  Sperling was reluctant to make the
admission.

"You're quite sure you saw him?"

"Yes, sir.  I remember distinctly now.  I even recall the peculiar
way he had his legs drawn up under him."

"You would swear to it," asked Markham gravely, "knowing that a
man's life might rest on your testimony?"

"I'd swear to it, sir," Sperling returned simply.

When the sheriff had escorted his prisoner from the room, Markham
looked at Vance.

"I think that gives us a foothold."

"Yes.  The cook's testimony was of little value, since Drukker
merely denied it; and she's the type of loyal stubborn German who'd
back up his denial if any real danger threatened him.  Now we're
armed with an effective weapon."

"It seems to me," Markham said, after a few moments of speculative
silence, "that we have a good circumstantial case against Drukker.
He was in the Dillard yard only a few seconds before Robin was
killed.  He could easily have seen when Sperling went away; and, as
he had recently come from Professor Dillard, he knew that the other
members of the family were out.  Mrs. Drukker denied she saw any
one from her window that morning, although she screamed at the time
of Robin's death and then went into a panic of fear when we came to
question Drukker.  She even warned him against us and called us
'the enemy.'  My belief is she saw Drukker returning home
immediately after Robin's body had been placed on the range.--
Drukker was not in his room at the time Sprigg was killed, and both
he and his mother have been at pains to cover up the fact.  He has
become excited whenever we broached the subject of the murders, and
has ridiculed the idea that they were connected.  In fact, many of
his actions have been highly suspicious.  Also, we know he is
abnormal and unbalanced, and that he is given to playing children's
games.  It's quite possible--in view of what Doctor Barstead told
us--that he has confused fantasy and reality, and perpetrated these
crimes in a moment of temporary insanity.  The tensor formula is
not only familiar to him, but he may have associated it in some
crazy way with Sprigg as a result of Arnesson's discussion with
Sprigg about it.--As for the Bishop notes, they may have been part
of the unreality of his insane games,--children all want an
approving audience when they invent any new form of amusement.  His
choice of the word 'bishop' was probably the result of his interest
in chess--a playful signature intended to confuse.  And this
supposition is further borne out by the actual appearance of a
chess bishop on his mother's door.  He may have feared that she saw
him that morning, and thus sought to silence her without openly
admitting to her that he was guilty.  He could easily have slammed
the screen-porch door from the inside, without having had a key,
and thereby given the impression that the bearer of the bishop had
entered and departed by the rear door.  Furthermore, it would have
been a simple matter for him to take the bishop from the library
the night Pardee was analyzing his game. . . ."

Markham continued for some time building up his case against
Drukker.  He was thorough and detailed, and his summation accounted
for practically all of the evidence that had been adduced.  The
logical and relentless way in which he pieced his various factors
together was impressively convincing; and a long silence followed
his résumé.

Vance at length stood up, as if to break the tension of his
thoughts, and walked to the window.

"You may be right, Markham," he admitted.  "But my chief objection
to your conclusion is that the case against Drukker is too good.
I've had him in mind as a possibility from the first; but the more
suspiciously he acted and the more the indications pointed toward
him, the more I felt inclined to dismiss him from consideration.
The brain that schemed these abominable murders is too competent,
too devilishly shrewd, to become entangled in any such net of
circumstantial evidence as you've drawn about Drukker.  Drukker
has an amazing mentality--his intelligence and intellect are
supernormal, in fact; and it's difficult to conceive of him, if
guilty, leaving so many loopholes."

"The law," returned Markham with acerbity, "can hardly be expected
to throw out cases because they're too convincing."

"On the other hand," pursued Vance, ignoring the comment, "it is
quite obvious that Drukker, even if not guilty, knows something
that has a direct and vital bearing on the case; and my humble
suggestion is that we attempt to prise this information out of him.
Sperling's testimony has given us the lever for the purpose. . . .
I say, Mr. Arnesson, what's your opinion?"

"Haven't any," the man answered.  "I'm a disinterested onlooker.
I'd hate, however, to see poor Adolph in durance vile."  Though he
would not commit himself it was plain that he agreed with Vance.

Heath thought, characteristically, that immediate action was
advisable, and expressed himself to that effect.

"If he's got anything to tell he'll tell it quick enough after he's
locked up."

"It's a difficult situation," Inspector Moran demurred, in a soft
judicial voice.  "We can't afford to make an error.  If Drukker's
evidence should convict some one else, we'd be a laughing-stock if
we had arrested the wrong man."

Vance looked toward Markham and nodded agreement.

"Why not have him on the tapis first, and see if he can't be
persuaded to unburden his soul.  You might dangle a warrant over
his head, don't y' know, as a kind of moral inducement.  Then, if
he remains coy and reticent, bring out the gyves and have the
doughty Sergeant escort him to the bastille."

Markham sat tapping indecisively on the desk, his head enveloped in
smoke as he puffed nervously on his cigar.  At last he set his chin
firmly and turned to Heath.

"Bring Drukker here at nine o'clock to-morrow morning.  You'd
better take a wagon and a John-Doe warrant in case he offers any
objection."  His face was grim and determined.  "Then I'll find out
what he knows--and act accordingly."

The conference broke up immediately.  It was after five o'clock,
and Markham and Vance and I rode up-town together to the Stuyvesant
Club.  We dropped Arnesson at the subway, and he took leave of us
with scarcely a word.  His garrulous cynicism seemed entirely to
have deserted him.  After dinner Markham pleaded fatigue, and Vance
and I went to the Metropolitan and heard Geraldine Farrar in
"Louise."*


* "Louise" was Vance's favorite modern opera, but he greatly
preferred Mary Garden to Farrar in the title rôle.


The next morning broke dark and misty.  Currie called us at half
past seven, for Vance intended to be present at the interview with
Drukker; and at eight o'clock we had breakfast in the library
before a light grate fire.  We were held up in the traffic on our
way down-town, and though it was quarter after nine when we reached
the District Attorney's office, Drukker and Heath had not yet
arrived.

Vance settled himself comfortably in a large leather-upholstered
chair and lighted a cigarette.

"I feel rather bucked this morning," he remarked.  "If Drukker
tells his story, and if the tale is what I think it is, we'll know
the combination to the lock."

His words had scarcely been uttered when Heath burst into the
office and, facing Markham without a word of greeting, lifted both
arms and let them fall in a gesture of hopeless resignation.

"Well, sir, we ain't going to question Drukkcr this morning--or no
other time," he blurted.  "He fell off a that high wall in
Riverside Park right near his house last night, and broke his neck.
Wasn't found till seven o'clock this morning.  His body's down at
the morgue now. . . .  Fine breaks we get!"  He sank disgustedly
into a chair.

Markham stared at him unbelievingly.

"You're sure?" he asked, with startled futility.

"I was up there before they removed the body.  One of the local men
phoned me about it just as I was leaving the office.  I stuck
around and got all the dope I could."

"What did you learn?"  Markham was fighting against an overwhelming
sense of discouragement.

"There wasn't much to find out.  Some kids in the park found the
body about seven o'clock this morning--lots of kids around, it
being Saturday; and the local men hopped over and called a police
surgeon.  The doc said Drukker musta fallen off the wall about ten
o'clock last night--killed instantly.  The wall at that spot--right
opposite 76th Street-is all of thirty feet above the playground.
The top of it runs along the bridle path; and it's a wonder more
people haven't broke their necks there.  Kids are all the time
walking along the stone ledge."

"Has Mrs. Drukker been notified?"

"No.  I told 'em I'd attend to it.  But I thought I'd come here
first and see what you wanted done about it."

Markham leaned back dejectedly.

"I don't see that there's much of anything we can do."

"It might be well," suggested Vance, "to inform Arnesson.  He'll
probably be the one who'll have to look after things. . . .  My
word, Markham!  I'm beginning to think that this case is a
nightmare, after all.  Drukker was our principal hope, and at the
very moment when there's a chance of our forcing him to speak,
he tumbles off of a wall--"  Abruptly he stopped.  "Off of a
wall! . . ."  As he repeated these words he leapt to his feet.
"A HUNCHBACK FALLS OFF OF A WALL! . . .  A HUNCHBACK! . . ."

We stared at him as if he had gone out of his mind; and I admit
that the look on his face sent a chill over me.  His eyes were
fixed, like those of a man gazing at a malignant ghost.  Slowly he
turned to Markham, and said in a voice that I hardly recognized:

"It's another mad melodrama--another Mother-Goose rhyme. . . .
'Humpty Dumpty' this time!"

The astonished silence that followed was broken by a strained harsh
laugh from the Sergeant.

"That's stretching things, ain't it, Mr. Vance?"

"It's preposterous!" declared Markham, studying Vance with genuine
concern.  "My dear fellow, you've let this case prey on your mind
too much.  Nothing has happened except that a man with a hump has
fallen from the coping of a wall in the park.  It's unfortunate, I
know; and it's doubly unfortunate at just this time."  He went to
Vance and put his hand on his shoulder.  "Let the Sergeant and me
run this show--we're used to these things.  Take a trip and get a
good rest.  Why not go to Europe as you generally do in the
spring?"

"Oh, quite--quite." Vance sighed and smiled wearily.  "The sea air
would do me worlds of good, and all that.  Bring me back to normal,
what?--build up the wreck of this once noble brain. . . .  I give
up!  The third act in this terrible tragedy is played almost before
your eyes, and you serenely ignore it."

"Your imagination has got the better of you," Markham returned,
with the patience of a deep affection.  "Don't worry about it any
more.  Have dinner with me to-night.  We'll talk it over then."

At this moment Swacker looked in, and spoke to the Sergeant.

"Quinan of the World is here.  Wants to see you."

Markham swung about.

"OH, MY GOD! . . .  Bring him in here!"

Quinan entered, waved us a cheery salutation, and handed the
Sergeant a letter.

"Another billet-doux--received this morning.--What privileges do I
get for being so big-hearted?"

Heath opened the letter as the rest of us looked on.  At once I
recognized the paper and the faint blue characters of the élite
type.  The note read:


     Humpty Dumpty sat on a wall,
     Humpty Dumpty had a great fall;
     All the king's horses and all the king's men
     Cannot put Humpty Dumpty together again.


Then came that ominous signature, in capitals:  THE BISHOP.



CHAPTER XVII

AN ALL-NIGHT LIGHT


(Saturday, April 16; 9.30 a.m.)


When Heath had got rid of Quinan with promises such as would have
gladdened any reporter's heart,* there were several minutes of
tense silence in the office.  "The Bishop" had been at his grisly
work again; and the case had now become a terrible triplicate
affair, with the solution apparently further off than ever.  It was
not, however, the insolubility of these incredible crimes that
primarily affected us; rather was it the inherent horror that
emanated, like a miasma, from the acts themselves.


* It may be recalled that the World's accounts of the Bishop case
were the envy of the other metropolitan newspapers.  Sergeant
Heath, though impartial in his statements of facts to the press,
nevertheless managed to save several picturesque bonnes-bouches for
Quinan, and permitted himself certain speculations which, while
having no news value, gave the World's stories an added interest
and color.


Vance, who was pacing sombrely up and down, gave voice to his
troubled emotions.

"It's damnable, Markham--it's the essence of unutterable evil. . . .
Those children in the park--up early on their holiday in search
of dreams--busy with their play and make-believe . . . and then the
silencing reality--the awful, overpowering disillusion. . . .
Don't you see the wickedness of it?  Those children found Humpty
Dumpty--their Humpty Dumpty, with whom they had played--lying dead
at the foot of the famous wall--a Humpty Dumpty they could touch
and weep over, broken and twisted and never more to be put
together. . . ."

He paused by the window and looked out.  The mist had lifted, and a
faint diffusion of spring sunlight lay over the gray stones of the
city.  The golden eagle on the New York Life Building glistened in
the distance.

"I say; one simply mustn't get sentimental," he remarked with a
forced smile, turning back to the room.  "It decomposes the
intelligence and stultifies the dialectic processes.  Now that we
know Drukker was not the capricious victim of the law of gravity,
but was given a helpin' hand in his departure from this world, the
sooner we become energetic, the better, what?"

Though his change of mood was an obvious tour de force, it roused
the rest of us from our gloomy apathy.  Markham reached for the
telephone and made arrangements with Inspector Moran for Heath to
handle the Drukker case.  Then he called the Medical Examiner's
office and asked for an immediate post-mortem report.  Heath got up
vigorously, and after taking three cups of ice-water, stood with
legs apart, his derby pulled far down on his forehead, waiting for
the District Attorney to indicate a line of action.

Markham moved restlessly.

"Several men from your department, Sergeant, were supposed to be
keeping an eye on the Drukker and Dillard houses.  Did you talk to
any of them this morning?"

"I didn't have time, sir; and, anyway, I figured it was only an
accident.  But I told the boys to hang around until I got back."

"What did the Medical Examiner have to say?"

"Only that it looked like an accident; and that Drukker had been
dead about ten hours. . . ."

Vance interpolated a question.

"Did he mention a fractured skull in addition to the broken neck?"

"Well, sir, he didn't exactly say the skull was fractured, but he
did state that Drukker had landed on the back of his head."  Heath
nodded understandingly.  "I guess it'll prove to be a fracture all
right--same like Robin and Sprigg."

"Undoubtedly.  The technique of our murderer seems to be simple and
efficacious.  He strikes his victims on the vault, either stunning
them or killing them outright, and then proceeds to cast them in
the rôles he has chosen for them in his puppet-plays.  Drukker was
no doubt leaning over the wall, perfectly exposed for such an
attack.  It was misty, and the setting was somewhat obscured.  Then
came the blow on the head, a slight heave, and Drukker fell
noiselessly over the parapet--the third sacrificial offering on the
altar of old Mother Goose."

"What gets me," declared Heath with surly anger, "is why
Guilfoyle,* the fellow I set to watch the rear of the Drukker
house, didn't report the fact that Drukker was out all night.  He
returned to the Bureau at eight o'clock, and I missed him.--Don't
you think, sir, it might be a good idea to find out what he knows
before we go up-town?"


* Guilfoyle, it may be remembered, was one of the detectives who
shadowed Tony Skeel in the Canary murder case.


Markham agreed, and Heath bawled an order over the telephone.
Guilfoyle made the distance between Police Headquarters and the
Criminal Courts Building in less than ten minutes.  The Sergeant
almost pounced on him as he entered.

"What time did Drukker leave the house last night?" he bellowed.

"About eight o'clock--right after he'd had dinner."  Guilfoyle was
ill at ease, and his tone had the wheedling softness of one who had
been caught in a dereliction of duty.

"Which way did he go?"

"He came out the back door, walked down the range, and went into
the Dillard house through the archery-room."

"Paying a social visit?"

"It looked that way, Sergeant.  He spends a lot of time at the
Dillards'."

"Huh!  And what time did he come back home?"

Guilfoyle moved uneasily.

"It don't look like he came back home, Sergeant."

"Oh, it don't?"  Heath's retort was ponderous with sarcasm.  "I
thought maybe after he'd broke his neck he mighta come back and
passed the time of day with you."

"What I meant was, Sergeant--"

"You meant that Drukker--the bird you were supposed to keep an eye
on--went to call on the Dillards at eight o'clock, and then you set
down in the arbor, most likely, and took a little beauty nap. . . ."
What time did you wake up?"

"Say, listen!"  Guilfoyle bristled.  "I didn't take no nap.  I was
on the job all night.  Just because I didn't happen to see this guy
come back home don't mean I was laying down on the watch."

"Well, if you didn't see him come back, why didn't you phone in
that he was spending his week-end out of town or something?"

"I thought he musta come in by the front door."

"Thinking again, were you?  Ain't your brain worn out this
morning?"

"Have a heart, Sergeant.  My job wasn't to tail Drukker.  You told
me to watch the house and see who went in and out, and that if
there was any sign of trouble to bust in.--Now, here's what
happened.  Drukker went to the Dillards' at eight o'clock, and I
kept my eye on the windows of the Drukker house.  Along about nine
o'clock the cook goes up-stairs and turns on the light in her room.
Half an hour later the light goes out, and says I:  'She's put to
bed.'  Then along about ten o'clock the lights are turned on in
Drukker's room--"

"What's this?"

"Yeh--you heard me.  The lights go on in Drukker's room about ten
o'clock; and I can see a shadow of somebody moving about.--Now, I
ask you, Sergeant: wouldn't you yourself have took it for granted
that the hunchback had come in by the front door?"

Heath grunted.

"Maybe so," he admitted.  "You're sure it was ten o'clock?"

"I didn't look at my watch; but I'm here to tell you it wasn't far
off of ten."

"And what time did the lights go out in Drukker's room?"

"They didn't go out.  They stayed on all night.  He was a queer
bird.  He didn't keep regular hours, and twice before his lights
were on till nearly morning."

"That's quite understandable," came Vance's lazy voice.  "He has
been at work on a difficult problem lately.--But tell us,
Guilfoyle: what about the light in Mrs. Drukker's room?"

"Same as usual.  The old dame always keeps a light burning in her
room all night."

"Was there any one on guard in front of the Drukker house last
night?" Markham asked Heath.

"Not after six o'clock, sir.  We've had a man tailing Drukker
during the day, but he goes off duty at six when Guilfoyle takes up
his post in the rear."

There was a moment's silence.  Then Vance turned to Guilfoyle.

"How far away were you last night from the door of the alleyway
between the two apartment houses?"

The man paused to visualize the scene.

"Forty or fifty feet, say."

"And between you and the alleyway were the iron fence and some tree
branches."

"Yes, sir.  The view was more or less cut off, if that's what you
mean."

"Would it have been possible for any one, coming from the direction
of the Dillard house, to have gone out and returned by that door
without your noticing him?"

"It mighta been done," the detective admitted; "provided, of
course, the guy didn't want me to see him.  It was foggy and dark
last night, and there's always a lot of traffic noises from the
Drive that woulda drowned out his movements if he was being extra
cautious."

When the Sergeant had sent Guilfoyle back to the Bureau to await
orders, Vance gave voice to his perplexity.

"It's a dashed complicated situation.  Drukker called on the
Dillards at eight o'clock, and at ten o'clock he was shoved over
the wall in the park.  As you observed, the note that Quinan just
showed us was postmarked 11 p.m.--which means that it was probably
typed BEFORE THE CRIME.  The Bishop therefore had planned his
comedy in advance and prepared the note for the press.  The
audacity of it is amazin'.  But there's one assumption we can tie
to--namely, that the murderer was some one who knew of Drukker's
exact whereabouts and proposed movements between eight and ten."

"I take it," said Markham, "your theory is that the murderer went
and returned by the apartment-house alley."

"Oh, I say!  I have no theory.  I asked Guilfoyle about the alley
merely in case we should learn that no one but Drukker was seen
going to the park.  In that event we could assume, as a tentative
hypothesis, that the murderer had managed to avoid detection by
taking the alleyway and crossing to the park in the middle of the
block."

"With that possible route open to the murderer," Markham observed
gloomily, "it wouldn't matter much who was seen going out with
Drukker."

"That's just it.  The person who staged this farce may have walked
boldly into the park under the eyes of an alert myrmidon, or he may
have hied stealthily through the alley."

Markham nodded an unhappy agreement.

"The thing that bothers me most, however," continued Vance, "is
that light in Drukker's room all night.  It was turned on at about
the time the poor chap was tumbling into eternity.  And Guilfoyle
says that he could see some one moving about there after the light
went on--"

He broke off, and stood for several seconds in an attitude of
concentration.

"I say, Sergeant; I don't suppose you know whether or not Drukker's
front-door key was in his pocket when he was found."

"No, sir; but I can find out in no time.  The contents of his
pockets are being held till after the autopsy."

Heath stepped to the telephone, and a moment later he was talking
to the desk sergeant of the 68th-Street Precinct Station.  Several
minutes of waiting passed; then he grunted and banged down the
receiver.

"Not a key of any kind on him."

"Ah!"  Vance drew a deep puff on his cigarette and exhaled the
smoke slowly.  "I'm beginnin' to think that the Bishop purloined
Drukker's key and paid a visit to his room after the murder.
Sounds incredible, I know; but, for that matter, so does everything
else that's happened in this fantastic business."

"But what, in God's name, would have been his object?" protested
Markham incredulously.

"We don't know yet.  But I have an idea that when we learn the
motive of these astonishin' crimes, we'll understand why that visit
was paid."

Markham, his face set austerely, took his hat from the closet.

"We'd better be getting out there."

But Vance made no move.  He remained standing by the desk smoking
abstractedly.

"Y' know, Markham," he said, "it occurs to me that we should see
Mrs. Drukker first.  There was tragedy in that house last night:
something strange took place there that needs explaining; and now
perhaps she'll tell us the secret that has been locked up in her
brain.  Moreover, she hasn't been notified of Drukker's death, and
with all the rumor and gossip in the neighborhood, word of some
kind is sure to leak through to her before long.  I fear the result
of the shock when she hears the news.  In fact, I'd feel better if
we got hold of Barstead right away and took him with us.  What do
you say to my phoning him?"

Markham assented, and Vance briefly explained the situation to the
doctor.

We drove up-town immediately, called for Barstead, and proceeded at
once to the Drukker house.  Our ring was answered by Mrs. Menzel,
whose face showed plainly that she knew of Drukker's death.  Vance,
after one glance at her, led her into the drawing-room away from
the stairs, and asked in a low tone:

"Has Mrs. Drukker heard the news?"

"Not yet," she answered, in a frightened, quavering voice.  "Miss
Dillard came over an hour ago, but I told her the mistress had gone
out.  I was afraid to let her up-stairs.  Something's wrong. . . ."
She began to tremble violently.

"What's wrong, Mrs. Menzel?"  Vance placed a quieting hand on her
arm.

"I don't know.  But she hasn't made a sound all morning.  She
didn't come down for breakfast . . . and I'm afraid to go and call
her."

"When did you hear of the accident?"

"Early--right after eight o'clock.  The paper boy told me; and I
saw all the people down on the Drive."

"Don't be frightened," Vance consoled her.  "We have the doctor
here, and we'll attend to everything."

He turned back to the hall and led the way upstairs.  When we came
to Mrs. Drukker's room he knocked softly and, receiving no answer,
opened the door.  The room was empty.  The night-light still burned
on the table, and I noticed that the bed had not been slept in.

Without a word Vance retraced his steps down the hall.  There were
only two other main doors, and one of them, we knew, led to
Drukker's study.  Unhesitatingly Vance stepped to the other and
opened it without knocking.  The window shades were drawn, but they
were white and semi-transparent, and the gray daylight mingled with
the ghastly yellow radiation from the old-fashioned chandelier.
The lights which Guilfoyle had seen burning all night had not been
extinguished.

Vance halted on the threshold, and I saw Markham, who was just in
front of me, give a start.

"Mother o' God!" breathed the Sergeant, and crossed himself.

On the foot of the narrow bed lay Mrs. Drukker, fully clothed.  Her
face was ashen white; her eyes were set in a hideous stare; and her
hands were clutching her breast.

Barstead sprang forward and leaned over.  After touching her once
or twice he straightened up and shook his head slowly.

"She's gone.  Been dead probably most of the night."  He bent over
the body again and began making an examination.  "You know, she's
suffered for years from chronic nephritis, arteriosclerosis, and
hypertrophy of the heart. . . .  Some sudden shock brought on an
acute dilatation. . . .  Yes, I'd say she died about the same time
as Drukker . . . round ten o'clock."

"A natural death?" asked Vance.

"Oh, undoubtedly.  A shot of adrenalin in the heart might have
saved her if I'd been here at the time. . . ."

"No signs of violence?"

"None.  As I told you, she died from dilatation of the heart
brought on by shock.  A clear case--true to type in every respect."



CHAPTER XVIII

THE WALL IN THE PARK


(Saturday, April 16; 11 a.m.)


When the doctor had straightened Mrs. Drukker's body on the bed and
covered it with a sheet, we returned down-stairs.  Barstead took
his departure at once after promising to send the death certificate
to the Sergeant within an hour.

"It's scientifically correct to talk of natural death from shock,"
said Vance, when we were alone; "but our immediate problem, d' ye
see, is to ascertain the cause of that sudden shock.  Obviously
it's connected with Drukker's death.  Now, I wonder. . . ."

Turning impulsively, he entered the drawing-room.  Mrs. Menzel was
sitting where we had left her, in an attitude of horrified
expectancy.  Vance went to her and said kindly:

"Your mistress died of heart failure during the night.  And it's
much better that she should not have outlived her son."

"Gott geb' ihr die ewige Ruh'!" the woman murmured piously.  "Ja,
it is best. . . ."

"The end came at about ten last night.--Were you awake at that
time, Mrs. Menzel?"

"All night I was awake."  She spoke in a low, awed voice.

Vance contemplated her with eyes half shut.

"Tell us what you heard?"

"Somebody came here last night!"

"Yes, some one came at about ten o'clock--by the front door.  Did
you hear him enter?"

"No; but after I had gone to bed I heard voices in Mr. Drukker's
room."

"Was it unusual to hear voices in his room at ten o'clock at
night?"

"But it wasn't HIM!  He had a high voice, and this one was low and
gruff."  The woman looked up in bewildered fright.  "And the other
voice was Mrs. Drukker's . . . and she never went in Mr. Drukker's
room at night!"

"How could you hear so plainly with your door shut?"

"My room is right over Mr. Drukker's," she explained.  "And I was
worried--what with all these awful things going on; so I got up and
listened at the top of the steps."

"I can't blame you," said Vance.  "What did you hear?"

"At first it was like as though the mistress was moaning, but right
away she began to laugh, and then the man spoke angry-like.  But
pretty soon I heard him laugh, too.  After that it sounded like the
poor lady was praying--I could hear her saying 'Oh, God--oh, God!'
Then the man talked some more--very quiet and low. . . .  And
in a little while it seemed like the mistress was--reciting--
a poem. . . ."

"Would you recognize the poem if you heard it again? . . .  Was it


     Humpty Dumpty sat on a wall;
     Humpty Dumpty had a great fall. . . ."


"Bei Gott, das ist's!  It sounded just like that!"  A new horror
came into the woman's expression.  "And Mr. Drukker fell from the
wall last night. . . ."

"Did you hear anything else, Mrs. Menzel?"  Vance's matter-of-fact
voice interrupted her confused correlation of Drukker's death to
the verse she had heard.

Slowly she shook her head.

"No.  Everything was quiet after that."

"Did you hear any one leave Mr. Drukker's room?"

She gave Vance a panic-stricken nod.

"A few minutes later some one opened and shut the door, very soft;
and I heard steps moving down the hall in the dark.  Then the
stairs creaked, and pretty soon the front door shut."

"What did you do after that?"

"I listened a little while, and then I went back to bed.  But I
couldn't sleep. . . ."

"It's all over now, Mrs. Menzel," Vance told her comfortingly.
"There's nothing for you to fear.--You'd best go to your room and
wait till we need you."

Reluctantly the woman went up-stairs.

"I think now," said Vance, "we can make a pretty close guess as to
what happened here last night.  The murderer took Drukker's key and
let himself in by the front door.  He knew Mrs. Drukker's quarters
were at the rear, and he no doubt counted on accomplishing his
business in Drukker's room and departing as he had come.  But Mrs.
Drukker heard him.  It may be she associated him with 'the little
man' who had left the black bishop at her door, and feared that her
son was in danger.  At any rate, she went at once to Drukker's
room.  The door may have been slightly open, and I think she saw
the intruder and recognized him.  Startled and apprehensive, she
stepped inside and asked him why he was there.  He may have
answered that he had come to inform her of Drukker's death--which
would account for her moans and her hysterical laughter.  But that
was only a prelimin'ry on his part--a play for time.  He was
devising some means of meeting the situation--he was planning how
he would kill her!  Oh, there can be no doubt of that.  He couldn't
afford to let her leave that room alive.  Maybe he told her so in
as many words--he spoke 'angry-like,' you recall.  And then he
laughed.  He was torturing her now--perhaps telling her the whole
truth in a burst of insane egoism; and she could say only 'Oh God--
oh God!'  He explained how he had pushed Drukker over the wall.
And did he mention Humpty Dumpty?  I think he did; for what more
appreciative audience could he have had for his monstrous jest than
the victim's own mother?  That last revelation proved too much for
her hypersensitive brain.  She repeated the nursery rhyme in a
spell of horror; and then the accumulated shock dilated her heart.
She fell across the bed, and the murderer was saved the necessity
of sealing her lips with his own hands.  He saw what had happened,
and went quietly away."

Markham took a turn up and down the room.

"The least comprehensible part of last night's tragedy," he said,
"is why this man should have come here after Drukker's death."

Vance was smoking thoughtfully.

"We'd better ask Arnesson to help us explain that point.  Maybe he
can throw some light on it."

"Yeh, maybe he can," chimed in Heath.  Then after rolling his cigar
between his lips for a moment, he added sulkily:  "There's several
people around here, I'm thinking, that could do some high-class
explaining."

Markham halted before the Sergeant.

"The first thing we'd better do is to find out what your men know
about the movements of the various persons hereabouts last night.
Suppose you bring them here and let me question them.--How many
were there, by the way?--and what were their posts?"

The Sergeant had risen, alert and energetic.

"There were three, sir, besides Guilfoyle.  Emery was set to tail
Pardee; Snitkin was stationed at the Drive and 75th Street to watch
the Dillard house; and Hennessey was posted on 75th Street up near
West End Avenue.--They're all waiting down at the place where
Drukker was found.  I'll get 'em up here pronto."


[Map1.gif]


He disappeared through the front door, and in less than five
minutes returned with the three detectives.  I recognized them all,
for each had worked on one or more of the cases in which Vance had
figured.*  Markham questioned Snitkin first as the one most likely
to have information bearing directly on the previous night's
affair.  The following points were brought out by his testimony:


* Hennessey had kept watch with Doctor Drumm over the Greene
mansion from the Narcoss Flats, in the Greene murder case.  Snitkin
also had taken part in the Greene investigation, and had played a
minor rôle in both the Benson and the Canary case.  The dapper
Emery was the detective who had unearthed the cigarette stubs from
beneath the fire-logs in Alvin Benson's living-room.


[Map2.gif]


Pardee had emerged from his house at 6.30 and gone straight to the
Dillards'.

At 8.30 Belle Dillard, in an evening gown, had got into a taxi and
been driven up West End Avenue.  (Arnesson had come out of the
house with her and helped her into the taxicab, but had immediately
returned indoors.)

At 9.15 Professor Dillard and Drukker had left the Dillard house
and walked slowly toward Riverside Drive.  They had crossed the
Drive at 74th Street, and turned up the bridle path.

At 9.30 Pardee had come out of the Dillard house, walked down to
the Drive, and turned up-town.

At a little after 10.00 Professor Dillard had returned to his house
alone, recrossing the Drive at 74th Street.

At 10.20 Pardee had returned home, coming from the same direction
he had taken when going out.

Belle Dillard had been brought home at 12.30 in a limousine filled
with young people.


Hennessey was interrogated next; but his evidence merely
substantiated Snitkin's.  No one had approached the Dillard house
from the direction of West End Avenue; and nothing of a suspicious
nature had happened.

Markham then turned his attention to Emery, who reported that,
according to Santos whom he had relieved at six, Pardee had spent
the early part of the afternoon at the Manhattan Chess Club and had
returned home at about four o'clock.

"Then, like Snitkin and Hennessey said," Emery continued, "he went
to the Dillards' at half past six, and stayed till half past nine.
When he came out I followed, keeping half a block or so behind him.
He walked up the Drive to 79th Street, crossed to the upper park,
and walked round the big grass bowl, past the rocks, and on up
toward the Yacht Club. . . ."

"Did he take the path where Sprigg was shot?" Vance asked.

"He had to.  There ain't any other path up that way unless you walk
along the Drive."

"How far did he go?"

"The fact is, he stopped right about where Sprigg was bumped off.
Then he came back the same way he'd gone and turned into the little
park with the playground on the south side of 79th Street.  He went
slowly down the walk under the trees along the bridle path; and as
he passed along the top of the wall under the drinking fountain,
who should he run into but the old man and the hunchback, resting
up against the ledge and talking. . . ."

"You say he met Professor Dillard and Drukker at the very spot
where Drukker fell over the wall?"  Markham leaned forward
hopefully.

"Yes, sir.  Pardee stopped to visit with them; and I naturally kept
on going.  As I passed 'em I heard the hunchback say:  'Why ain't
you practising chess this evening?'  And it sounded to me like he
was sore at Pardee for stopping, and was hinting that he wasn't
wanted.  Anyhow, I ambled along the wall till I got to 74th Street
where there was a couple of trees to hide under. . . ."

"How well could you see Pardee and Drukker after you'd reached 74th
Street?" interrupted Markham.

"Well, sir, to tell you the truth, I couldn't see 'em at all.  It
was getting pretty misty about that time, and there isn't any lamp-
post at that part of the walk where they were confabulating.  But I
figured Pardee would be along pretty soon, so I waited for him."

"This must have been well on toward ten o'clock."

"About a quarter of, I should say, sir."

"Were there any people on the walk at that time?"

"I didn't see anybody.  The fog musta driven 'em indoors--it wasn't
no warm balmy evening.  And it was on account of there being nobody
around that I went as far ahead as I did.  Pardee's nobody's fool,
and I'd already caught him looking at me once or twice as though he
suspected I was tailing him."

"How long was it before you picked him up again?"

Emery shifted his position.

"My figuring wasn't so good last night," he confessed, with a weak
grin.  "Pardee musta gone back the way he came and recrossed the
Drive at 79th Street; for a half-hour or so later I saw him heading
home in front of the apartment-house light on the corner of 75th
Street."

"But," interposed Vance; "if you were at the 74th Street entrance
to the park until a quarter past ten you must have seen Professor
Dillard pass you.  He returned home about ten o'clock by that
route."

"Sure, I saw him.  I'd been waiting for Pardee about twenty minutes
when the professor came strolling along all alone, crossed the
Drive, and went home.  I naturally thought Pardee and the hunchback
were still gabbing,--that's why I took it easy and didn't go back
to check up."

"Then, as I understand, about fifteen minutes after Professor
Dillard passed you, you saw Pardee returning home from the opposite
direction along the Drive."

"That's right, sir.  And, of course, I took up my post again on
75th Street."

"You realize, Emery," said Markham gravely, "that it was during the
time you waited at 74th Street that Drukker fell over the wall."

"Yes, sir.  But you're not blaming me, are you?  Watching a man on
a foggy night on an open path when there ain't anybody around to
screen you, is no easy job.  You gotta take a few chances and do a
little figuring if you don't want to get spotted."

"I realize your difficulty," Markham told him; "and I'm not
criticizing you."

The Sergeant dismissed the three detectives gruffly.  He was
obviously dissatisfied with their reports.

"The farther we go," he complained, "the more gummed up this case
gets."

"Sursum corda, Sergeant," Vance exhorted him.  "Let not dark
despair o'ercome you.  When we have Pardee's and the Professor's
testimony as to what took place while Emery was watchfully waiting
beneath the trees at 74th Street, we may be able to fit some very
interestin' bits together."

As he spoke Belle Dillard entered the front hall from the rear of
the house.  She saw us in the drawing-room and came in at once.

"Where's Lady Mae?" she asked in a troubled voice.  "I was here an
hour ago, and Grete told me she was out.  And she's not in her room
now."

Vance rose and gave her his chair.

"Mrs. Drukker died last night of heart failure.  When you were here
earlier Mrs. Menzel was afraid to let you go up-stairs."

The girl sat very quiet for some time.  Presently the tears welled
to her eyes.

"Perhaps she heard of Adolph's terrible accident."

"Possibly.  But it's not quite clear what happened here last night.
Doctor Barstead thinks Mrs. Drukker died at about ten o'clock."

"Almost the same time Adolph died," she murmured.  "It seems too
terrible. . . .  Pyne told me of the accident when I came down to
breakfast this morning,--every one in the quarter was talking about
it,--and I came over at once to be with Lady Mae.  But Grete said
she had gone out, and I didn't know what to think.  There's
something very strange about Adolph's death. . . ."

"What do you mean by that, Miss Dillard?"  Vance stood by the
window watching her covertly.

"I--don't know--what I mean," she answered brokenly.  "But only
yesterday afternoon Lady Mae spoke to me about Adolph and the--
wall. . . ."

"Oh, did she, now?"  Vance's tone was more indolent than usual, but
every nerve in his body was, I knew, vigilantly alert.

"On my way to the tennis courts," the girl went on, in a low,
hushed voice, "I walked with Lady Mae along the bridle path above
the playground--she often went there to watch Adolph playing with
the children,--and we stood for a long time leaning over the stone
balustrade of the wall.  A group of children were gathered around
Adolph: he had a toy aeroplane and was showing them how to fly it.
And the children seemed to regard him as one of themselves; they
didn't look upon him as a grown-up.  Lady Mae was very happy and
proud about it.  She watched him with shining eyes, and then she
said to me: 'They're not afraid of him, Belle, because he's a
hunchback.  They call him Humpty Dumpty--he's their old friend of
the story-book.  My poor Humpty Dumpty!  It was all my fault for
letting him fall when he was little.' . . ."  The girl's voice
faltered, and she put her handkerchief to her eyes.

"So she mentioned to you that the children called Drukker Humpty
Dumpty."  Vance reached slowly in his pocket for his cigarette-
case.

She nodded, and a moment later lifted her head as if forcing
herself to face something she dreaded.

"Yes!  And that's what was so strange; for after a little while she
shuddered and drew back from the wall.  I asked her what was the
matter, and she said in a terrified voice:  'Suppose, Belle--
suppose that Adolph should ever fall off of this wall--the way the
real Humpty Dumpty did!'  I was almost afraid myself; but I forced
a smile, and told her she was foolish.  It didn't do any good,
though.  She shook her head and gave me a look that sent a chill
through me.  'I'm not foolish,' she said.  'Wasn't Cock Robin
killed with a bow and arrow, and wasn't Johnny Sprig shot with a
little gun--RIGHT HERE IN NEW YORK?'"  The girl turned a frightened
gaze upon us.  "And it DID happen, didn't it--just as she foresaw?"

"Yes, it happened," Vance nodded.  "But we mustn't be mystical
about it.  Mrs. Drukker's imagination was abnormal.  All manner of
wild conjectures went through her tortured mind; and with these two
other Mother-Goose deaths so vivid in her memory, it's not
remarkable that she should have turned the children's sobriquet for
her son into a tragic speculation of that kind.  That he should
actually have been killed in the manner she feared is nothing more
than a coincidence. . . ."

He paused and drew deeply on his cigarette.

"I say, Miss Dillard," he asked negligently; "did you, by any
chance, repeat your conversation with Mrs. Drukker to any one
yesterday?"

She regarded him with some surprise before answering.

"I mentioned it at dinner last night.  It worried me all the
afternoon, and--somehow--I didn't want to keep it to myself."

"Were any comments made about it?"

"Uncle told me I shouldn't spend so much time with Lady Mae--that
she was unhealthily morbid.  He said the situation was very tragic,
but that there was no need for me to share Lady Mae's suffering.
Mr. Pardee agreed with uncle.  He was very sympathetic, and asked
if something could not be done to help Lady Mae's mental
condition."

"And Mr. Arnesson?"

"Oh, Sigurd never takes anything seriously,--I hate his attitude
sometimes.  He laughed as though it was a joke; and all he said
was:  'It would be a shame if Adolph took his tumble before he got
his new quantum problem worked out.'"

"Is Mr. Arnesson at home now, by the by?" asked Vance.  "We want to
ask him about the necess'ry arrangements in regard to the
Drukkers."

"He went to the university early this morning; but he'll be back
before lunch.  He'll attend to everything, I am sure.  We were
about the only friends Lady Mae and Adolph had.  I'll take charge
in the meantime and see that Grete gets the house in order."

A few minutes later we left her and went to interview Professor
Dillard.



CHAPTER XIX

THE RED NOTE-BOOK


(Saturday, April 16; noon)


The professor was plainly perturbed when we entered the library
that noon.  He sat in an easy chair with his back to the window,
a glass of his precious port on the table beside him.

"I've been expecting you, Markham," he said, before we had time to
speak.  "There's no need to dissemble.  Drukker's death was no
accident.  I'll admit I felt inclined to discount the insane
implications arising from the deaths of Robin and Sprigg; but the
moment Pyne related the circumstances of Drukker's fall I realized
that there was a definite design behind these deaths: the
probabilities of their being accidental would be incalculable.
You know it, as well as I; otherwise you wouldn't be here."

"Very true."  Markham had seated himself facing the professor.
"We're confronted by a terrific problem.  Moreover, Mrs. Drukker
died of shock last night at almost the same time her son was
killed."

"That, at least," returned the old man after a pause, "may be
regarded as a blessing.  It's better she didn't survive him--her
mind unquestionably would have collapsed."  He looked up.  "In what
way can I help?"

"You were probably the last person, with the exception of the
actual murderer, to see Drukker alive; and we would like to know
everything you can tell us of what took place last night."

Professor Dillard nodded.

"Drukker came here after dinner--about eight, I should say.  Pardee
had dined with us; and Drukker was annoyed at finding him here--in
fact, he was openly hostile.  Arnesson twitted him good-naturedly
about his irascibility--which only made him more irritable; and,
knowing that Drukker was anxious to thrash out a problem with me,
I finally suggested that he and I stroll down to the park. . . ."

"You were not gone very long," suggested Markham.

"No.  An unfortunate episode occurred.  We walked up the bridle
path to almost the exact spot where, I understand, the poor fellow
was killed.  We had been there for perhaps half an hour, leaning
against the stone balustrade of the wall, when Pardee walked up.
He stopped to speak to us, but Drukker was so antagonistic in his
remarks that, after a few minutes, Pardee turned and walked away in
the direction he had come.  Drukker was very much upset, and I
suggested we postpone the discussion.  Furthermore, a damp mist had
fallen, and I was beginning to get some twinges in my foot.
Drukker straightway became morose, and said he didn't care to go
indoors just yet.  So I left him alone by the wall, and came home."

"Did you mention the episode to Arnesson?"

"I didn't see Sigurd after I got back.  I imagine he'd gone to
bed."

Later as we rose to take our leave, Vance asked casually:  "Can you
tell us where the key to the alley door is kept?"

"I know nothing about it, sir," the professor replied irritably,
but added in a more equable tone:  "However, as I remember, it used
to hang on a nail by the archery-room door."

From Professor Dillard we went straight to Pardee, and were
received at once in his study.  His manner was rigid and detached,
and even after we had seated ourselves he remained standing by the
window, staring at us with unfriendly eyes.

"Do you know, Mr. Pardee," asked Markham, "that Mr. Drukker fell
from the wall in the park at ten o'clock last night--shortly after
you stopped and spoke to him?"

"I heard of the accident this morning."  The man's pallor became
more noticeable, and he toyed nervously with his watch chain.
"It's very unfortunate."  His eyes rested vacantly for a while on
Markham.  "Have you asked Professor Dillard about it?  He was with
Drukker--"

"Yes, yes; we've just come from him," interrupted Vance.  "He said
there was a ruffled atmosphere between you and Mr. Drukker last
night."

Pardee slowly walked to the desk and sat down stiffly.

"Drukker was displeased for some reason to find me at the Dillards'
when he came over after dinner.  He hadn't the good taste to hide
his displeasure, and created a somewhat embarrassing situation.
But, knowing him as I did, I tried to pass the matter off.  Soon,
however, Professor Dillard took him out for a walk."

"You didn't remain long afterward," observed Vance indolently.

"No--about a quarter of an hour.  Arnesson was tired and wanted to
turn in, so I went for a walk myself.  On my return I took the
bridle path instead of the Drive, and came on Professor Dillard and
Drukker standing by the wall talking.  Not wishing to appear rude,
I stopped for a moment.  But Drukker was in a beastly mood and made
several sneering remarks.  I turned and walked back to 79th Street,
crossed the Drive, and came home."

"I say; didn't you loiter a bit by the wayside?"

"I sat down near the 79th-Street entrance and smoked a cigarette."

For nearly half an hour Markham and Vance interrogated Pardee, but
nothing more could be learned from him.  As we came out into the
street Arnesson hailed us from the front porch of the Dillard house
and stalked forward to meet us.

"Just heard the sad news.  Got home from the university a little
while ago, and the professor told me you'd gone to rag Pardee.
Learn anything?"  Without waiting for an answer he ran on:
"Frightful mess.  I understand the entire Drukker family is wiped
out.  Well, well.  And more story-book mumbo-jumbo to boot. . . .
Any clews?"

"Ariadne has not yet favored us," responded Vance.  "Are you an
ambassador from Crete?"

"One never knows.  Bring out your questionnaire."  Vance had led
the way toward the wall gate, and we now stepped down on the range.

"We'll repair to the Drukker house first," he said.  "There'll be a
number of things to settle.  I suppose you'll look after Drukker's
affairs and the funeral arrangements."

Arnesson made a grimace.

"Elected!  I refuse, however, to attend the funeral.  Obscene
spectacles, funerals.  But Belle and I will see to everything.
Lady Mae probably left a will.  We'll have to find it.  Now, where
do women generally hide their wills? . . ."

Vance halted by the Dillards' basement door and stepped into the
archery-room.  After glancing along the door's moulding he rejoined
us on the range.

"The alley key isn't there.--By the by, what do you know about it,
Mr. Arnesson?"

"You mean the key to yon wooden door in the fence? . . .  Haven't
an idea on the subject.  Never use the alley myself--much simpler
going out the front door.  No one uses it, as far as I know.  Belle
locked it up years ago: thought some one might sneak in off the
Drive and get an arrow in the eye.  I told her, let 'em get popped--
serve 'em right for being interested in archery."

We entered the Drukker house by the rear door.  Belle Dillard and
Mrs. Menzel were busy in the kitchen.

"Hallo, sis," Arnesson greeted the girl.  His cynical manner had
been dropped.  "Hard lines for a young 'un like you.  You'd better
run home now.  I'll assume command."  And taking her arm in a
jocularly paternal fashion, he led her to the door.

She hesitated and looked back at Vance.

"Mr. Arnesson is right," he nodded.  "We'll carry on for the
present.--But just one question before you go.  Did you always keep
the key to the alley door hanging in the archery-room?"

"Yes--always.  Why?  Isn't it there now?"

It was Arnesson who answered, with burlesque irony.

"Gone!  Disappeared!--Most tragic.  Some eccentric key-collector
has evidently been snooping around."  When the girl had left us, he
cocked an eye at Vance.  "What, in the name of all that's unholy,
has a rusty key to do with the case?"

"Perhaps nothing," said Vance carelessly.  "Let's go to the
drawin'-room.  It's more comfortable there."  He led the way down
the hall.  "We want you to tell us what you can about last night."

Arnesson took an easy chair by the front window, and drew out his
pipe.

"Last night, eh? . . .  Well, Pardee came to dinner--it's a sort of
habit with him on Fridays.  Then Drukker, in the throes of quantum
speculation, dropped in to pump the professor; and Pardee's
presence galled him.  Showed his feelings too, by Gad!  No control.
The professor broke up the contretemps by taking Drukker for an
airing.  Pardee moped for fifteen minutes or so, while I tried to
keep awake.  Then he had the goodness to depart.  I looked over a
few test papers . . . and so to bed."  He lighted his pipe.  "How
does that thrilling recital explain the end of poor Drukker?"

"It doesn't," said Vance.  "But it's not without interest.--Did you
hear Professor Dillard when he returned home?"

"Hear him?"  Arnesson chuckled.  "When he hobbles about with his
gouty foot, thumping his stick down and shaking the banisters,
there's no mistaking his arrival on the scene.  Fact is, he was
unusually noisy last night."

"Offhand, what do you make of these new developments?" asked Vance,
after a short pause.

"I'm somewhat foggy as to the details.  The professor was not
exactly phosphorescent.  Sketchy, in fact.  Drukker fell from the
wall, like Humpty Dumpty, round ten o'clock, and was found this
morning--that's all plain.  But under what conditions did Lady Mae
succumb to shock?  Who, or what, shocked her?  And how?"

"The murderer took Drukker's key and came here immediately after
the crime.  Mrs. Drukker caught him in her son's room.  There was a
scene, according to the cook, who listened from the head of the
stairs; and during it Mrs. Drukker died from dilatation of the
heart."

"Thereby relieving the gentleman of the bother of killing her."

"That seems clear enough," agreed Vance.  "But the reason for the
murderer's visit here is not so lucid.  Can you suggest an
explanation?"

Arnesson puffed thoughtfully on his pipe.

"Incomprehensible," he muttered at length.  "Drukker had no
valuables, or no compromising documents.  Straightforward sort of
cuss--not the kind to mix in any dirty business. . . .  No possible
reason for any one prowling about his room."

Vance lay back and appeared to relax.

"What was this quantum theory Drukker was working on?"

"Ha!  Big thing!"  Arnesson became animated.  "He was on the path
of reconciling the Einstein-Bohr theory of radiation with the facts
of interference, and of overcoming the inconsistencies inherent in
Einstein's hypothesis.  His research had already led him to an
abandonment of causal space-time coordination of atomic phenomena,
and to its replacement by a statistical description.* . . .  Would
have revolutionized physics--made him famous.  Shame he was told
off before he'd put his data in shape."


* An important step toward the solution of these complex problems
was taken a few years later by the de Broglie-Schrödinger theory as
laid down in de Broglie's "Ondes et Mouvements" and Schrödinger's
"Abhandlungen zur Wellenmechanik."


"Do you happen to know where Drukker kept the records of these
computations?"

"In a loose-leaf note-book--all tabulated and indexed.  Methodical
and neat about everything.  Even his chirography was like
copperplate."

"You know, then, what the note-book looked like?"

"I ought to.  He showed it to me often enough.  Red limp-leather
cover--thin yellow pages--two or three clips on every sheet
holding notations--his name gold-stamped in large letters on the
binding. . . .  Poor devil!  Sic transit. . . ."

"Where would this note-book be now?"

"One of two places--either in the drawer of his desk in the study
or else in the escritoire in his bedroom.  In the daytime, of
course, he worked in the study; but he fussed day and night when
wrapped up in a problem.  Kept an escritoire in his bedroom, where
he put his current records when he retired, in case he got an
inspiration to monkey with 'em during the night.  Then, in the
morning, back they'd go to the study.  Regular machine for system."

Vance had been gazing lazily out of the window as Arnesson rambled
on.  The impression he gave was that he had scarcely heard the
description of Drukker's habits; but presently he turned and fixed
Arnesson with a languid look.

"I say," he drawled; "would you mind toddling up-stairs and
fetching Drukker's note-book?  Look in both the study and the
bedroom."

I thought I noticed an almost imperceptible hesitation on
Arnesson's part; but straightway he rose.

"Good idea.  Too valuable a document to be left lying round."  And
he strode from the room.

Markham began pacing the floor, and Heath revealed his uneasiness
by puffing more energetically on his cigar.  There was a tense
atmosphere in the little drawing-room as we waited for Arnesson's
return.  Each of us was in a state of expectancy, though just what
we hoped for or feared would have been difficult to define.

In less than ten minutes Arnesson reappeared at the door.  He
shrugged his shoulders and held out empty hands.

"Gone!" he announced.  "Looked in every likely place--couldn't find
it."  He threw himself into a chair and relighted his pipe.  "Can't
understand it. . . .  Perhaps he hid it."

"Perhaps," murmured Vance.



CHAPTER XX

THE NEMESIS


(Saturday, April 16; 1 p.m.)


It was past one o'clock, and Markham, Vance and I rode to the
Stuyvesant Club.  Heath remained at the Drukker house to carry on
the routine work, to draw up his report, and to deal with the
reporters who would be swarming there shortly.

Markham was booked for a conference with the Police Commissioner at
three o'clock; and after lunch Vance and I walked to Stieglitz's
Intimate Gallery and spent an hour at an exhibition of Georgia
O'Keeffe's floral abstractions.  Later we dropped in at Aeolian
Hall and sat through Debussy's G-minor quartette.  There were some
Cézanne water-colors at the Montross Galleries; but by the time we
had pushed our way through the late-afternoon traffic of Fifth
Avenue the light had begun to fail, and Vance ordered the chauffeur
to the Stuyvesant Club, where we joined Markham for tea.

"I feel so youthful, so simple, so innocent," Vance complained
lugubriously.  "So many things are happenin', and they're bein'
manipulated so ingeniously that I can't grasp 'em.  It's very
disconcertin', very confusin'.  I don't like it--I don't at all
like it.  Most wearin'."  He sighed drearily and sipped his tea.

"Your sorrows leave me cold," retorted Markham.

"You've probably spent the afternoon inspecting arquebuses and
petronels at the Metropolitan Museum.  If you'd had to go through
what I've suffered--"

"Now, don't be cross," Vance rebuked him.  "There's far too much
emotion in the world.  Passion is not going to solve this case.
Cerebration is our only hope.  Let us be calm and thoughtful."  His
mood became serious.  "Markham, this comes very near being the
perfect crime.  Like one of Morphy's great chess combinations, it
has been calculated a score of moves ahead.  There are no clews;
and even if there were, they'd probably point in the wrong
direction.  And yet . . . and yet there's something that's trying
to break through.  I feel it: sheer intuition--that is to say,
nerves.  There's an inarticulate voice that wants to speak, and
can't.  A dozen times I've sensed the presence of some struggling
force, like an invisible ghost trying to make contact without
revealing its identity."

Markham gave an exasperated sigh.

"Very helpful.  Do you advise calling in a medium?"

"There's something we've overlooked," Vance went on, disregarding
the sarcasm.  "The case is a cipher, and the key-word is somewhere
before us, but we don't recognize it.  'Pon my soul, it's dashed
annoyin'. . . .  Let's be orderly.  Neatness--that's our desideratum.
First, Robin is killed.  Next, Sprigg is shot.  Then Mrs. Drukker
is frightened with a black bishop.  After that, Drukker is shoved
over a wall.  Makin' four distinct episodes in the murderer's
extravaganza.  Three of 'em were carefully planned. One--the
leaving of the bishop at Mrs. Drukker's door--was forced on the
murderer, and was therefore decided on without preparation. . . ."

"Clarify your reasoning on that point."

"Oh, my dear fellow!  The conveyor of the black bishop was
obviously acting in self-defence.  An unexpected danger developed
along his line of campaign, and he took this means of averting it.
Just before Robin's death Drukker departed from the archery-room
and installed himself in the arbor of the yard, where he could look
into the archery-room through the rear window.  A little later he
saw some one in the room talking to Robin.  He returned to his
house, and at that moment Robin's body was thrown on the range.
Mrs. Drukker saw it, and at the same time she probably saw Drukker.
She screamed--very natural, what?  Drukker heard the scream, and
told us of it later in an effort to establish an alibi for himself
after we'd informed him that Robin had been killed.  Thus the
murderer learned that Mrs. Drukker had seen something--how much, he
didn't know.  But he wasn't taking any chances.  He went to her
room at midnight to silence her, and took the bishop to leave
beside her body as a signature.  But he found the door locked, and
left the bishop outside, by way of warning her to say nothing on
pain of death.  He didn't know that the poor woman suspected her
own son."

"But why didn't Drukker tell us whom he saw in the archery-room
with Robin?"

"We can only assume that the person was some one whom he couldn't
conceive of as being guilty.  And I'm inclined to believe he
mentioned the fact to this person and thus sealed his own doom."

"Assuming the correctness of your theory, where does it lead us?"

"To the one episode that wasn't elaborately prepared in advance.
And when there has been no preparation for a covert act there is
pretty sure to be a weakness in one or more of the details.--Now,
please note that at the time of each of the three murders any one
of the various persons in the drama could have been present.  No
one had an alibi.  That, of course, was cleverly calculated: the
murderer chose an hour when all of the actors were, so to speak,
waiting in the wings.  But that midnight visit!  Ah!  That was a
different matter.  There was no time to work out a perfect set of
circumstances,--the menace was too immediate.  And what was the
result?  Drukker and Professor Dillard were, apparently, the only
persons on hand at midnight.  Arnesson and Belle Dillard were
supping at the Plaza and didn't return home until half past twelve.
Pardee was hornlocked with Rubinstein over a chess-board from
eleven to one.  Drukker is now of course eliminated. . . .  What's
the answer?"

"I could remind you," returned Markham irritably, "that the alibis
of the others have not been thoroughly checked."

"Well, well, so you could."  Vance lay back indolently and sent a
long regular series of smoke-rings toward the ceiling.  Suddenly
his body tensed, and with meticulous care he leaned over and put
out his cigarette.  Then he glanced at his watch and got to his
feet.  He fixed Markham with a quizzical look.

"Allons, mon vieux.  It's not yet six.  Here's where Arnesson makes
himself useful."

"What now?" expostulated Markham.

"Your own suggestion," Vance replied, taking him by the arm and
leading him toward the door.  "We're going to check Pardee's
alibi."

Half an hour later we were seated with the professor and Arnesson
in the Dillard Library.

"We've come on a somewhat unusual errand," explained Vance; "but it
may have a vital bearing on our investigation."  He took out his
wallet, and unfolded a sheet of paper.  "Here's a document, Mr.
Arnesson, I wish you'd glance over.  It's a copy of the official
scoresheet of the chess game between Pardee and Rubinstein.  Very
interestin'.  I've toyed with it a bit, but I'd like your expert
analysis of it.  The first part of the game is usual enough, but
the play after the adjournment rather appeals to me."

Arnesson took the paper and studied it with cynical amusement.

"Aha!  The inglorious record of Pardee's Waterloo, eh?"

"What's the meaning of this, Markham?" asked professor Dillard
contemptuously.  "Do you hope to run a murderer to earth by dilly-
dallying over a chess game?"

"Mr. Vance hoped something could be learned from it."

"Fiddlesticks!"  The professor poured himself another glass of port
and, opening a book, ignored us completely.

Arnesson was absorbed in the notations of the chess score.

"Something a bit queer here," he muttered.  "The time's askew.
Let's see. . . .  The scoresheet shows that, up to the time of
adjournment, White--that is, Pardee--had played one hour and forty-
five minutes, and Black, or Rubinstein, one hour and fifty-eight
minutes.  So far, so good.  Thirty moves.  Quite in order.  But the
time at the end of the game, when Pardee resigned, totals two hours
and thirty minutes for White, and three hours and thirty-two
minutes for Black--which means that, during the second session of
the game, White consumed only forty-five minutes whereas Black used
up one hour and thirty-four minutes."

Vance nodded.

"Exactly.  There were two hours and nineteen minutes of play
beginning at 11 p.m., which carried the game to 1.19 a.m.  And
Rubinstein's moves during that time took forty-nine minutes longer
than Pardee's.--Can you make out what happened?"

Arnesson pursed his lips and squinted at the notations.

"It's not clear.  I'd need time."

"Suppose," Vance suggested, "we set up the game in the adjourned
position and play it through.  I'd like your opinion on the
tactics."

Arnesson rose jerkily and went to the little chess table in the
corner.

"Good idea."  He emptied the men from the box.  "Let's see now. . . .
Oho!  A black bishop is missing.  When do I get it back, by the
way?"  He gave Vance a plaintive leer.  "Never mind.  We don't need
it here.  One black bishop was swapped."  And he proceeded to
arrange the men to accord with the position of the game at the time
of adjournment.  Then he sat down and studied the set-up.

"It doesn't strike me as a particularly unfavorable position for
Pardee," ventured Vance.

"Me either.  Can't see why he lost the game.  Looks drawish to me."
After a moment Arnesson referred to the scoresheet.  "We'll run
through the play and find out where the trouble lay."  He made half
a dozen moves; then, after several minutes' study, gave a grunt.
"Ha!  This is rather deep stuff of Rubinstein's.  Amazing
combination he began working up here.  Subtle, by Gad!  As I know
Rubinstein, it took him a long time to figure it out.  Slow,
plodding chap."

"It's possible, isn't it," suggested Vance, "that the working out
of that combination explains the discrepancy in time between Black
and White?"

"Oh, undoubtedly.  Rubinstein must have been in good form not to
have made the discrepancy greater.  Planning the combination took
him all of forty-five minutes--or I'm a duffer."

"At what hour, would you say," asked Vance carelessly, "did
Rubinstein use up that forty-five minutes?"

"Well, let's see.  The play began at eleven: six moves before the
combination started. . . .  Oh, say, somewhere between half past
eleven and half past twelve. . . .  Yes, just about.  Thirty moves
before the adjournment: six moves beginning at eleven--that makes
thirty-six: then on the forty-fourth move Rubinstein moved his pawn
to Bishop-7-check, and Pardee resigned. . . .  Yes--the working out
of the combination was between eleven-thirty and twelve-thirty."

Vance regarded the men on the board, which were now in the position
they had occupied at the time of Pardee's resignation.*


* For the benefit of the expert chess-player who may be
academically interested I append the exact position of the game
when Pardee resigned:--WHITE: King at QKtsq; Rook at QB8; Pawns at
QR2 and Q2.  BLACK: King at Q5; Knight at QKt5; Bishop at QR6;
Pawns at QKt7 and QB7.


"Out of curiosity," he said quietly, "I played the game through to
the checkmate the other night.--I say, Mr. Arnesson; would you mind
doin' the same.  I could bear to hear your comment on it."

Arnesson studied the position closely for a few minutes.  Then he
turned his head slowly and lifted his eyes to Vance.  A sardonic
grin overspread his face.

"I grasp the point.  Gad!  What a situation!  Five moves for Black
to win through.  And an almost unheard-of finale in chess.  Can't
recall a similar instance.  The last move would be Bishop to
Knight-7, mating.  In other words, Pardee was beaten by the black
bishop!  Incredible!"*


* The final five unplayed moves for Black to mate, as I later
obtained them from Vance, were:--45.  RxP; KtxR.  46.  KxKt; P--Kt8
(Queen).  47.  KxQ; K--Q6.  48.  K--Rsq; K--B7.  49.  P--Q3; B--Kt7
mate.


Professor Dillard put down his book.

"What's this?" he exclaimed, joining us at the chess table.
"Pardee was defeated by the bishop?"  He gave Vance a shrewd,
admiring look.  "You evidently had good reason, sir, for
investigating that chess game.  Pray overlook an old man's temper."
He stood gazing down at the board with a sad, puzzled expression.

Markham was frowning with deep perplexity.

"You say it's unusual for a bishop alone to mate?" he asked
Arnesson.

"Never happens--almost unique situation.  And that it should happen
to Pardee of all people!  Incomprehensible!"  He gave a short
ironic laugh.  "Inclines one to believe in a nemesis.  You know,
the bishop has been Pardee's bête noir for twenty years--it's
ruined his life.  Poor beggar!  The black bishop is the symbol of
his sorrow.  Fate, by Gad!  It's the one chessman that defeated the
Pardee gambit.  Bishop-to-Knight-5 always broke up his calculations--
disqualified his pet theory--made a hissing and a mocking of his
life's work.  And now, with a chance to break even with the great
Rubinstein, the bishop crops up again and drives him back into
obscurity."

A few minutes later we took our departure and walked to West End
Avenue, where we hailed a taxicab.

"It's no wonder, Vance," commented Markham, as we rode down-town,
"that Pardee went white the other afternoon when you mentioned the
black bishop's being at large at midnight.  He probably thought you
were deliberately insulting him--throwing his life's failure in his
face."

"Perhaps. . . ."  Vance gazed dreamily out into the gathering
shadows.  "Dashed queer about the bishop being his incubus all
these years.  Such recurring discouragements affect the strongest
minds sometimes; create a desire for revenge on the world, with the
cause of one's failure exalted to an Astraean symbol."

"It's difficult to picture Pardee in a vindictive rôle," objected
Markham.  Then, after a moment:  "What was your point about the
discrepancy in time between Pardee's and Rubinstein's playing?
Suppose Rubinstein did take forty-five minutes or so to work out
his combination.  The game wasn't over until after one.  I don't
see that your visit to Arnesson put us ahead in any way."

"That's because you're unacquainted with the habits of chess
players.  In a clock game of that kind no player sits at the table
all the time his opponent is figuring out moves.  He walks about,
stretches his muscles, takes the air, ogles the ladies, imbibes
ice-water, and even indulges in food.  At the Manhattan Square
Masters Tournament last year there were four tables, and it was a
common sight to see as many as three empty chairs at one time.
Pardee's a nervous type.  He wouldn't sit through Rubinstein's
protracted mental speculations."

Vance lighted a cigarette slowly.

"Markham, Arnesson's analysis of that game reveals the fact that
Pardee had three-quarters of an hour to himself around midnight."



CHAPTER XXI

MATHEMATICS AND MURDER


(Saturday, April 16; 8.30 p.m.)


Little was said about the case during dinner, but when we had
settled ourselves in a secluded corner of the club lounge-room
Markham again broached the subject.

"I can't see," he said, "that finding a loophole in Pardee's alibi
helps us very much.  It merely complicates an already intolerable
situation."

"Yes," sighed Vance.  "A sad and depressin' world.  Each step
appears to tangle us a little more.  And the amazin' part of it is,
the truth is staring us in the face; only, we can't see it."

"There's no evidence pointing to any one.  There's not even a
suspect against whose possible culpability reason doesn't revolt."

"I wouldn't say that, don't y' know.  It's a mathematician's crime;
and the landscape has been fairly cluttered with mathematicians."

Throughout the entire investigation no one had been indicated by
name as the possible murderer.  Yet each of us realized in his own
heart that one of the persons with whom we had talked was guilty;
and so hideous was this knowledge that we instinctively shrank from
admitting it.  From the first we had cloaked our true thoughts and
fears with generalities.

"A mathematician's crime?" repeated Markham.  "The case strikes me
as a series of senseless acts committed by a maniac running amuck."

Vance shook his head.

"Our criminal is supersane, Markham.  And his acts are not
senseless: they're hideously logical and precise.  True, they have
been conceived with a grim and terrible humor, with a tremendously
cynical attitude; but within themselves they are exact and
rational."

Markham regarded Vance thoughtfully.

"How can you reconcile these Mother-Goose crimes with the
mathematical mind?" he asked.  "In what way can they be regarded as
logical?  To me they're nightmares, unrelated to sanity."

Vance settled himself deeper in his chair, and smoked for several
minutes.  Then he began an analysis of the case, which not only
clarified the seeming madness of the crimes themselves, but brought
all the events and the characters into a uniform focus.  The
accuracy of this analysis was brought home to us with tragic and
overwhelming force before many days had passed.*


* I am obviously unable to set down Vance's exact words, despite
the completeness of my notes; but I sent him a proof of the
following passages with a request that he revise and edit them; so
that, as they now stand, they represent an accurate paraphrase of
his analysis of the psychological factors of the Bishop murders.


"In order to understand these crimes," he began, "we must consider
the stock-in-trade of the mathematician, for all his speculations
and computations tend to emphasize the relative insignificance of
this planet and the unimportance of human life.--Regard, first, the
mere scope of the mathematician's field.  On the one hand he
attempts to measure infinite space in terms of parsecs and light-
years, and, on the other, to measure the electron which is so
infinitely small that he has to invent the Rutherford unit--a
millionth of a millimicron.  His vision is one of transcendental
perspectives, in which this earth and its people sink almost to the
vanishing point.  Some of the stars--such as Arcturus, Canopus and
Betelgeuse--which he regards merely as minute and insignificant
units, are many times more massive than our entire solar system.
Shapleigh's estimate of the diameter of the Milky Way is 300,000
light-years; yet we must place 10,000 Milky Ways together to get
the diameter of the universe--which gives us a cubical content a
thousand milliard times greater than the scope of astronomical
observation.  Or, to put it relatively in terms of mass:--the sun's
weight is 324,000 times greater than the weight of the earth; and
the weight of the universe is postulated as that of a trillion*--a
milliard times a milliard--suns. . . .  Is it any wonder that
workers in such stupendous magnitudes should sometimes lose all
sense of earthly proportions?"


* Vance was here using the English connotation of "trillion," which
is the third power of a million, as opposed to the American and
French system of numeration which regards a trillion as a mere
million millions.


Vance made an insignificant gesture.

"But these are element'ry figures--the every-day facts of
journeyman calculators.  The higher mathematician goes vastly
further.  He deals in abstruse and apparently contradict'ry
speculations which the average mind can not even grasp.  He lives
in a realm where time, as we know it, is without meaning save as a
fiction of the brain, and becomes a fourth co-ordinate of three-
dimnensional space; where distance also is meaningless except for
neighboring points, since there are an infinite number of shortest
routes between any two given points; where the language of cause
and effect becomes merely a convenient shorthand for explanat'ry
purposes; where straight lines are non-existent and insusceptible
of definition; where mass grows infinitely great when it reaches
the velocity of light; where space itself is characterized by
curvatures; where there are lower and higher orders of infinities;
where the law of gravitation is abolished as an acting force and
replaced by a characteristic of space--a conception that says, in
effect, that the apple does not fall because it is attracted by the
earth, but because it follows a geodesic, or world-line. . . .

"In this realm of the modern mathematician, curves exist without
tangents.  Neither Newton nor Leibnitz nor Bernoulli even dreamed
of a continuous curve without a tangent--that is, a continuous
function without a differential co-efficient.  Indeed, no one is
able to picture such a contradiction,--it lies beyond the power of
imagination.  And yet it is a commonplace of modern mathematics to
work with curves that have no tangents.--moreover, pi--that old
friend of our school-days, which we regarded as immutable--is no
longer a constant; and the ratio between diameter and circumference
now varies according to whether one is measuring a circle at rest
or a rotating circle. . . .  Do I bore you?"

"Unquestionably," retorted Markham.  "But pray continue, provided
your observations have an earthly direction."

Vance sighed and shook his head hopelessly, but at once became
serious again.

"The concepts of modern mathematics project the individual out of
the world of reality into a pure fiction of thought, and lead to
what Einstein calls the most degenerate form of imagination--
pathological individualism.  Silberstein, for instance, argues the
possibility of five- and six-dimensional space, and speculates on
one's ability to see an event before it happens.  The conclusions
contingent on the conception of Flammarion's Lumen--a fictive
person who travels faster than the velocity of light and is
therefore able to experience time extending in a reverse direction--
are in themselves enough to distort any natural and sane point of
view.*  But there is another conceptual Homunculus even weirder
than Lumen from the standpoint of rational thinking.  This
hypothetical creature can traverse all worlds at once with infinite
velocity, so that he is able to behold all human history at a
glance.  From Alpha Centauri he can see the earth as it was four
years ago; from the Milky Way he can see it as it was 4,000 years
ago; and he can also choose a point in space where he can witness
the ice-age and the present day simultaneously! . . ."


* Lumen was invented by the French astronomer to prove the
possibility of the reversal of time.  With a speed of 250,000 miles
per second, he was conceived as soaring into space at the end of
the battle of Waterloo, and catching up all the light-rays that had
left the battlefield.  He attained a gradually increasing lead,
until at the end of two days he was witnessing, not the end, but
the beginning of the battle; and in the meantime he had been
viewing events in reverse order.  He had seen projectiles leaving
the objects they had penetrated and returning to the cannon; dead
men coming to life and arranging themselves in battle formation.
Another hypothetical adventure of Lumen was jumping to the moon,
turning about instantaneously, and seeing himself leaping from the
moon to the earth backwards.


Vance settled himself more deeply in his chair.

"Toying with the simple idea of infinity is enough to unhinge the
average man's mind.  But what of the well-known proposition of
modern physics that we cannot take a straight and ever-advancing
path into space without returning to our point of departure?  This
proposition holds, in brief, that we may go straight to Sirius and
a million times further without changing direction, but we can
never leave the universe: we at last return to our starting-point
FROM THE OPPOSITE DIRECTION!  Would you say, Markham, that this
idea is conducive to what we quaintly call normal thinking?  But
however paradoxical and incomprehensible it may seem, it is almost
rudiment'ry when compared with other theorems advanced by
mathematical physics.  Consider, for example, what is called the
problem of the twins.  One of two twins starts to Arcturus at
birth--that is, with accelerated motion in a gravitational field--
and, on returning, discovers that he is much younger than his
brother.  If, on the other hand, we assume that the motion of the
twins is Galilean and that they are therefore travelling with
uniform motion relative to each other, then each twin will find
that his brother is younger than himself! . . .

"These are not paradoxes of logic, Markham: they're only paradoxes
of feeling.  Mathematics accounts for them logically and
scientifically.*  The point I'm trying to make is that things which
seem inconsistent and even absurd to the lay mind, are commonplaces
to the mathematical intelligence.  A mathematico-physicist like
Einstein announces that the diameter of space--of SPACE, mind you--
is 100,000,000 light-years, or 700 trillion miles; and considers
the calculation abecedarian.  When we ask what is beyond this
diameter, the answer is:  'There is no beyond: these limitations
include everything.'  To wit, infinity is finite!  Or, as the
scientist would say, space is unbounded but finite.--Let your mind
meditate on this idea for half an hour, Markham, and you'll have a
sensation that you're going mad."


* Vance requested me to mention here A. d'Abro's recent scholarly
work, "The Evolution of Scientific Thought," in which there is an
excellent discussion of the paradoxes associated with spacetime.


He paused to light a cigarette.

"Space and matter--that's the mathematician's speculative
territ'ry.  Eddington conceives matter as a characteristic of
space--a bump in nothingness; whereas Weil conceives space as a
characteristic of matter,--to him empty space is meaningless.  Thus
Kant's noumenon and phenomenon become interchangeable; and even
philosophy loses all significance.  But when we come to the
mathematical conceptions of finite space all rational laws are
abrogated.  De Sitter's conception of the shape of space is
globular, or spherical.  Einstein's space is cylindrical; and
matter approaches zero at the periphery, or 'border condition.'
Weyl's space, based on Mach's mechanics, is saddle-shaped. . . .
Now, what becomes of nature, of the world we live in, of human
existence, when we weigh them against such conceptions?  Eddington
suggests the conclusion that there are no natural laws--namely,
that nature is not amenable to the law of sufficient reason.  Alas,
poor Schopenhauer!*  And Bertrand Russell sums up the inevitable
results of modern physics by suggesting that matter is to be
interpreted merely as a group of occurrences, and that matter
itself need not be existent! . . .  Do you see what it all leads
to?  If the world is non-causative and non-existent, what is a mere
human life?--or the life of a nation?--or, for that matter,
existence itself? . . ."


* Vance's M. A. thesis, I recall, dealt with Schopenhauer's "Ueber
die vierfache Wurzel des Satzes vom zureichenden Grunde."


Vance looked up, and Markham nodded dubiously.

"So far I follow you, of course," he said.  "But your point seems
vague--not to say esoteric."

"Is it surprising," asked Vance, "that a man dealing in such
colossal, incommensurable concepts, wherein the individuals of
human society are infinitesimal, might in time lose all sense of
relative values on earth, and come to have an enormous contempt for
human life?  The comparatively insignificant affairs of this world
would then become mere petty intrusions on the macrocosmos of his
mental consciousness.  Inevitably such a man's attitude would
become cynical.  In his heart he would scoff at all human values,
and sneer at the littleness of the visual things about him.
Perhaps there would be a sadistic element in his attitude; for
cynicism is a form of sadism. . . ."

"But deliberate, planned murder!" objected Markham.

"Consider the psychological aspects of the case.  With the normal
person, who takes his recreations daily, a balance is maintained
between the conscious and the unconscious activities: the emotions,
being constantly dispersed, are not allowed to accumulate.  But
with the abnormal person, who spends his entire time in intense
mental concentration and who rigorously suppresses all his
emotions, the loosening of the subconscious is apt to result in a
violent manifestation.  This long inhibition and protracted mental
application, without recreation or outlet of any kind, causes an
explosion which often assumes the form of deeds of unspeakable
horror.  No human being, however intellectual, can escape the
results.  The mathematician who repudiates nature's laws is
nevertheless amenable to those laws.  Indeed, his rapt absorption
in hyperphysical problems merely increases the pressure of his
denied emotions.  And outraged nature, in order to maintain her
balance, produces the most grotesque fulminations--reactions which,
in their terrible humor and perverted gaiety, are the exact reverse
of the grim seriousness of abstruse mathematical theories.  The
fact that Sir William Crookes and Sir Oliver Lodge--both great
mathematical physicists--became confirmed spiritists, constitutes a
similar psychological phenomenon."

Vance took several deep inhalations on his cigarette.

"Markham, there's no escaping the fact: these fantastic and
seemingly incredible murders were planned by a mathematician as
forced outlets to a life of tense abstract speculation and
emotional repression.  They fulfil all the indicated requirements:
they are neat and precise, beautifully worked out, with every
minute factor fitting snugly in place.  No loose ends, no
remainders, apparently no motive.  And aside from their highly
imaginative precision, all their indications point unmistakably to
an abstrusely conceptive intelligence on the loose--a devotee of
pure science having his fling."

"But why their grisly humor?" asked Markham.  "How do you reconcile
the Mother-Goose phase of them with your theory?"

"The existence of inhibited impulses," explained Vance, "always
produces a state favorable to humor.  Dugas designates humor as a
'détente'--a release from tension; and Bain, following Spencer,
calls humor a relief from restraint.  The most fertile field for a
manifestation of humor lies in accumulated potential energy--what
Freud calls Besetzungsenergie--which in time demands a free
discharge.  In these Mother-Goose crimes we have the mathematician
reacting to the most fantastic of frivolous acts in order to
balance his superserious logical speculations.  It's as if he were
saying cynically:  'Behold!  This is the world that you take so
seriously because you know nothing of the infinitely larger
abstract world.  Life on earth is a child's game--hardly important
enough to make a joke about.' . . .  And such an attitude would be
wholly consistent with psychology; for after any great prolonged
mental strain one's reactions will take the form of reversals--
that is to say, the most serious and dignified will seek an
outlet in the most childish games.  Here, incidentally, you
have the explanation for the practical joker with his sadistic
instincts. . . .

"Moreover, all sadists have an infantile complex.  And the child is
totally amoral.  A man, therefore, who experiences these infantile
psychological reversals is beyond good and evil.  Many modern
mathematicians even hold that all convention, duty, morality,
good, and the like, could not exist except for the fiction of
free will. To them the science of ethics is a field haunted by
conceptual ghosts; and they even arrive at the disintegrating
doubt as to whether truth itself is not merely a figment of the
imagination. . . .  Add to these considerations the sense of earthly
distortion and the contempt for human life which might easily result
from the speculations of higher mathematics, and you have a perfect
set of conditions for the type of crimes with which we are dealing."

When Vance had finished speaking Markham sat silent for a long
time.  Finally he moved restively.

"I can understand," he said, "how these crimes might fit almost any
of the persons involved.  But, on the basis of your argument, how
do you account for the notes to the press?"

"Humor must be imparted," returned Vance.  "'A jest's prosperity
lies in the ear of him who hears it.'  Also, the impulse toward
exhibitionism enters into the present case."

"But the 'Bishop' alias?"

"Ah!  That's a most vital point.  The raison d'être of this
terrible orgy of humor lies in that cryptic signature."

Markham turned slowly.

"Does the chess player and the astronomer fulfil the conditions of
your theory as well as the mathematical physicist?"

"Yes," Vance replied.  "Since the days of Philidor, Staunton and
Kieseritzki, when chess was something of a fine art, the game has
degenerated almost into an exact science; and during Capablanca's
régime it has become largely a matter of abstract mathematical
speculation.  Indeed, Maroczy, Doctor Lasker and Vidmar are all
well-known mathematicians. . . .  And the astronomer, who actually
views the universe, may get an even more intense impression of the
unimportance of this earth than the speculative physicist.
Imagination runs riot through a telescope.  The mere theory of
existing life on distant planets tends to reduce earthly life to
second'ry consideration.  For hours after one has looked at Mars,
for instance, and dallied with the notion that its inhabitants
outnumber and surpass in intelligence our own population, one has
difficulty in readjusting oneself to the petty affairs of life here
on earth.  Even a reading of Percival Lowell's romantic book*
temporarily takes away from the imaginative person all consciousness
of the significance of any single planet'ry existence."


* I do not know whether Vance was here referring to "Mars and Its
Canals" or "Mars as the Abode of Life."


There was a long silence.  Then Markham asked:

"Why should Pardee have taken Arnesson's black bishop that night
instead of one from the club where it would not have been missed?"

"We don't know enough of the motive to say.  He may have taken it
with some deliberate purpose in view.--But what evidence have you
of his guilt?  All the suspicions in the world would not permit you
to take any step against him.  Even if we knew indubitably who the
murderer was, we'd be helpless. . . .  I tell you, Markham, we're
facing a shrewd brain--one that figures out every move, and
calculates all the possibilities.  Our only hope is to create our
own evidence by finding a weakness in the murderer's combination."

"The first thing in the morning," declared Markham grimly, "I'm
going to put Heath to work on Pardee's alibi that night.  There'll
be twenty men checking it up by noon, questioning every spectator
at that chess game, and making a door-to-door canvass between the
Manhattan Chess Club and the Drukker house.  If we can find some
one who actually saw Pardee in the vicinity of the Drukkers' around
midnight, then we'll have a very suspicious piece of circumstantial
evidence against him."

"Yes," agreed Vance; "that would give us a definite starting-point.
Pardee would have considerable difficulty in explaining why he was
six blocks away from the club during his set-to with Rubinstein at
the exact hour that a black bishop was being left at Mrs. Drukker's
door. . . .  Yes, yes.  By all means have Heath and his minions
tackle the problem.  It may lead us forward."

But the Sergeant was never called upon to check the alibi.  Before
nine o'clock on the following morning Markham called at Vance's
house to inform him that Pardee had committed suicide.



CHAPTER XXII

THE HOUSE OF CARDS


(Sunday, April 17; 9 a.m.)


The astounding news of Pardee's death had a curiously disturbing
effect on Vance.  He stared at Markham unbelievingly.  Then he rang
hastily for Currie and ordered his clothes and a cup of coffee.
There was an eager impatience in his movements as he dressed.

"My word, Markham!" he exclaimed.  "This is most extr'ordin'ry. . . .
How did you hear of it?"

"Professor Dillard phoned me at my apartment less than half an hour
ago.  Pardee killed himself in the archery-room of the Dillard home
some time last night.  Pyne discovered the body this morning and
informed the professor.  I relayed the news to Sergeant Heath, and
then came here.  In the circumstances I thought we ought to be on
hand."  Markham paused to light his cigar.  "It looks as if the
Bishop case was over. . . .  Not an entirely satisfactory ending,
but perhaps the best for every one concerned."

Vance made no immediate comment.  He sipped his coffee abstractedly,
and at length got up and took his hat and stick.

"Suicide. . . ," he murmured, as we went down the stairs.  "Yes,
that would be wholly consistent.  But, as you say, unsatisfact'ry--
dashed unsatisfact'ry. . . ."

We rode to the Dillard house, and were admitted by Pyne.  Professor
Dillard had no more than joined us in the drawing-room when the
door-bell rang, and Heath, pugnacious and dynamic, bustled in.

"This'll clean things up, sir," he exulted to Markham, after the
usual ritualistic handshake.  "Those quiet birds . . . you never
can tell.  Yet, who'd've thought. . . ?"

"Oh, I say, Sergeant," Vance drawled; "let's not think.  Much too
wearin'.  An open mind--arid like a desert--is indicated."

Professor Dillard led the way to the archery-room.  The shades at
all the windows were drawn, and the electric lights were still
burning.  I noticed, too, that the windows were closed.

"I left everything exactly as it was," explained the professor.

Markham walked to the large wicker centre-table.  Pardee's body was
slumped in a chair facing the range door.  His head and shoulders
had fallen forward over the table; and his right arm hung at his
side, the fingers still clutching an automatic pistol.  There was
an ugly wound in his right temple; and on the table beneath his
head was a pool of coagulated blood.

Our eyes rested but a moment on the body, for a startling and
incongruous thing diverted our attention.  The magazines on the
table had been pushed aside, leaving an open space in front of the
body; and in this cleared area rose a tall and beautifully
constructed house of playing cards.  Four arrows marked the
boundaries of the yard, and matches had been laid side by side to
represent the garden walks.  It was a reproduction that would have
delighted a child's heart; and I recalled what Vance had said the
night before about serious minds seeking recreation in children's
games.  There was something unutterably horrible in the
juxtaposition of this juvenile card structure and violent death.

Vance stood looking down at the scene with sad, troubled eyes.

"Hic jacet John Pardee," he murmured, with a sort of reverence.
"And this is the house that Jack built . . . a house of cards. . . ."

He stepped forward as if to inspect it more closely; but as his
body struck the edge of the table there was a slight jar, and the
flimsy edifice of cards toppled over.

Markham drew himself up and turned to Heath.

"Have you notified the Medical Examiner?"

"Sure."  The Sergeant seemed to find it difficult to take his eyes
from the table.  "And Burke's coming along, in case we need him."
He went to the windows and threw up the shades, letting in the
bright daylight.  Then he returned to Pardee's body and stood
regarding it appraisingly.  Suddenly he knelt down and leaned over.

"That looks to me like the .38 that was in the tool-chest," he
remarked.

"Undoubtedly," nodded Vance, taking out his cigarette-case.

Heath rose and, going to the chest, inspected the contents of its
drawer.  "I guess that's it, all right.  We'll get Miss Dillard to
identify it after the doc has been here."

At this moment Arnesson, clothed in a brilliant red-and-yellow
dressing-gown, burst excitedly into the room.

"By all the witches!" he exclaimed.  "Pyne just told me the news."
He came to the table and stared at Pardee's body.  "Suicide,
eh? . . .  But why didn't he choose his own home for the performance?
Damned inconsiderate of him to muss up some one else's house this
way.  Just like a chess player."  He lifted his eyes to Markham.
"Hope this won't involve us in more unpleasantness.  We've had
enough notoriety.  Distracts the mind.  When'll you be able to take
the beggar's remains away?  Don't want Belle to see him."

"The body will be removed as soon as the Medical Examiner has seen
it," Markham told him in a tone of frosty rebuke.  "And there will
be no necessity to bring Miss Dillard here."

"Good."  Arnesson still stood staring at the dead man.  Slowly a
look of cynical wistfulness came over his face.  "Poor devil!  Life
was too much for him.  Hypersensitive--no psychic stamina.  Took
things too seriously.  Brooded over his fate ever since his gambit
went up in smoke.  Couldn't find any other diversion.  The black
bishop haunted him; probably tipped his mind from its axis.  By
Gad!  Wouldn't be surprised if the idea drove him to self-
destruction.  Might have imagined he was a chess bishop--trying to
get back at the world in the guise of his nemesis."

"Clever idea," returned Vance.  "By the by, there was a house of
cards on the table when we first saw the body."

"Ha!  I wondered what the cards were doing there.  Thought he might
have sought solace in solitaire during his last moments. . . .  A
card house, eh?  Sounds foolish.  Do you know the answer?"

"Not all of it.  'The house that Jack built' might explain
something."

"I see."  Arnesson looked owlish.  "Playing children's games to the
end--even on himself.  Queer notion."  He yawned cavernously.
"Guess I'll get some clothes on."  And he went up-stairs.

Professor Dillard had stood watching Arnesson with a look at once
distressed and paternal.  Now he turned to Markham with a gesture
of annoyance.

"Sigurd's always protecting himself against his emotions.  He's
ashamed of his feelings.  Don't take his careless attitude too
seriously."

Before Markham could make a reply Pyne ushered Detective Burke into
the room; and Vance took the opportunity of questioning the butler
about his discovery of Pardee.

"How did it happen you entered the archery-room this morning?" he
asked.

"It was a bit close in the pantry, sir," the man returned, "and I
opened the door at the foot of the stairs to get a little more air.
Then I noticed that the shades were down--"

"It's not custom'ry to draw the shades at night, then?"

"No, sir--not in this room."

"How about the windows?"

"I always leave them slightly open from the top at night."

"Were they left open last night?"

"Yes, sir."

"Very good.--And after you opened the door this morning?"

"I started to put out the lights, thinking Miss Dillard had
forgotten to turn the switch last night; but just then I saw the
poor gentleman there at the table, and went straight up and
informed Professor Dillard."

"Does Beedle know about the tragedy?"

"I told her of it right after you gentlemen arrived."

"What time did you and Beedle retire last night?"

"At ten o'clock, sir."

When Pyne had left us Markham addressed Professor Dillard.

"It might be well for you to give us what details you can while
we're waiting for Doctor Doremus.--Shall we go up-stairs?"

Burke remained in the archery-room, and the rest of us went to the
library.

"I'm afraid there's little I can tell you," the professor began,
settling himself and taking out his pipe.  There was a noticeable
reserve in his manner--a kind of detached reluctance.  "Pardee came
here last night after dinner, ostensibly to chat with Arnesson, but
actually, I imagine, to see Belle.  Belle, however, excused herself
early and went to bed--the child had a bad headache--and Pardee
remained until about half past eleven.  Then he went out; and that
was the last I saw of him until Pyne brought me the terrible news
this morning. . . ."

"But if," put in Vance, "Mr. Pardee came to see your niece, how do
you account for his staying so late after she had retired?"

"I don't account for it."  The old man exhibited perplexity.  "He
gave the impression, though, that there was something on his mind
and that he desired a sense of human contact.  The fact is, I had
to hint rather broadly about being tired before he finally got up
to go."

"Where was Mr. Arnesson during the evening?"

"Sigurd remained here talking with us for an hour or so after Belle
had retired, and then went to bed.  He'd been busy with Drukker's
affairs all afternoon, and was played out."

"What time would that have been?"

"About half past ten."

"And you say," continued Vance, "that Mr. Pardee impressed you as
being under a mental strain?"

"Not a strain exactly."  The professor drew on his pipe, frowning.
"He appeared depressed, almost melancholy.

"Did it strike you that he was in fear of something?"

"No; not in the least.  He was more like a man who had suffered a
great sorrow and couldn't shake the effects of it."

"When he went out did you go with him into the hall--that is, did
you note which direction he took?"

"No.  We always treated Pardee very informally here.  He said good-
night and left the room.  I took it for granted he went to the
front door and let himself out."

"Did you go to your own room at once?"

"In about ten minutes.  I stayed up only long enough to arrange
some papers I'd been working on."

Vance lapsed into silence--he was obviously puzzled over some phase
of the episode; and Markham took up the interrogation.

"I suppose," he said, "that it is useless to ask if you heard any
sound last night that might have been a shot."

"Everything in the house was quiet," Professor Dillard replied.
"And anyway no sound of a shot would carry from the archery-room to
this floor.  There are two flights of stairs, the entire length of
the lower hall and a passageway, and three heavy doors between.
Moreover, the walls of this old house are very thick and solid."

"And no one," supplemented Vance, "could have heard the shot from
the street, for the archery-room windows were carefully closed."

The professor nodded and gave him a searching look.

"That is true.  I see you, too, noticed that peculiar circumstance.
I don't quite understand why Pardee should have shut the windows."

"The idiosyncrasies of suicides have never been satisfactorily
explained," returned Vance casually.  Then, after a short pause, he
asked:  "What were you and Mr. Pardee talking about during the hour
preceding his departure?"

"We talked very little.  I was more or less engaged with a new
paper of Millikan's in the Physics Review on alkali doublets, and
I tried to interest him in it; but his mind, as I've said, was
noticeably preoccupied, and he amused himself at the chess-board
for the best part of the hour."

"Ah!  Did he, now?  That's most interestin'."

Vance glanced at the board.  A number of pieces were still standing
on the squares; and he rose quickly and crossed the room to the
little table.  After a moment he came back and reseated himself.

"Most curious," he murmured, and very deliberately lighted a
cigarette.  "He was evidently pondering over the end of his game
with Rubinstein just before he went down-stairs last night.  The
pieces are set up exactly as they were at the time he resigned the
contest--with the inevitable black-bishop-mate only five moves
off."

Professor Dillard's gaze moved to the chess table wonderingly.

"The black bishop," he repeated in a low tone.  "Could that have
been what was preying on his mind last night?  It seems unbelievable
that so trivial a thing could affect him so disastrously."

"Don't forget, sir," Vance reminded him, "that the black bishop was
the symbol of his failure.  It represented the wreckage of his
hopes.  Less potent factors have driven men to take their own
lives."

A few minutes later Burke informed us that the Medical Examiner had
arrived.  Taking leave of the professor we descended again to the
archery-room, where Doctor Doremus was busy with his examination of
Pardee's body.

He looked up as we entered and waved one hand perfunctorily.  His
usual jovial manner was gone.

"When's this business going to stop?" he grumbled.  "I don't like
the atmosphere round here.  Murders--death from shock--suicides.
Enough to give any one the creeps.  I'm going to get a nice
uneventful job in a slaughter house."

"We believe," said Markham, "that this is the end."

Doremus blinked.  "So!  That's it, is it?--the Bishop suicides
after running the town ragged.  Sounds reasonable.  Hope you're
right."  He again bent over the body, and, unflexing the fingers,
tossed the revolver to the table.

"For your armory, Sergeant."

Heath dropped the weapon in his pocket.

"How long's he been dead, doc?"

"Oh, since midnight, or thereabouts.  Maybe earlier, maybe later.--
Any other fool questions?"

Heath grinned.  "Is there any doubt about it being suicide?"

Doremus glared passionately at the Sergeant.

"What does it look like?  A black-hand bombing?"  Then he became
professional.  "The weapon was in his hand.  Powder marks on the
temple.  Hole the right size for the gun, and in the right place.
Position of the body natural.  Can't see anything suspicious.--Why?
Got any doubts?"

It was Markham who answered.

"To the contrary, doctor.  Everything from our angle of the case
points to suicide."

"It's suicide all right, then.  I'll check up a little further,
though.--Here, Sergeant, give me a hand."

When Heath had helped to lift Pardee's body to the divan for a more
detailed examination, we went to the drawing-room where we were
joined shortly by Arnesson.

"What's the verdict?" he asked, dropping into the nearest chair.
"I suppose there's no question that the chap committed the act
himself."

"Why should you raise the point, Mr. Arnesson?" Vance parried.

"No reason.  An idle comment.  Lots of queer things going on
hereabouts."

"Oh, obviously."  Vance blew a wreath of smoke upward.  "No; the
Medical Examiner seems to think there's no doubt in the matter.
Did Pardee, by the by, impress you as bent on self-destruction last
night?"

Arnesson considered.  "Hard to say," he concluded.  "He was never a
gay soul.  But suicide? . . .  I don't know.  However, you say
there's no question about it; so there you are."

"Quite, quite.  And how does this new situation fit into your
formula?"

"Dissipates the whole equation, of course.  No more need for
speculation."  Despite his words, he appeared uncertain.  "What I
can't understand," he added, "is why he should choose the archery-
room.  Lot of space in his own house for a felo-de-se."

"There was a convenient gun in the archery-room," suggested Vance.
"And that reminds me: Sergeant Heath would like to have Miss
Dillard identify the weapon, as a matter of form."

"That's easy.  Where is it?"

Heath handed it to him, and he started from the room.

"Also"--Vance halted him--"you might ask Miss Dillard if she kept
playing cards in the archery-room."

Arnesson returned in a few minutes and informed us that the gun was
the one which had been in the tool-chest drawer, and that not only
were playing cards kept in the table drawer of the archery-room but
that Pardee knew of their presence there.

Doctor Doremus appeared soon afterwards and iterated his conclusion
that Pardee had shot himself.

"That'll be my report," he said.  "Can't see any way out of it.
To be sure, lots of suicides are fakes--but that's YOUR province.
Nothing in the least suspicious here."

Markham nodded with undisguised satisfaction.

"We've no reason to question your findings, doctor.  In fact,
suicide fits perfectly with what we already know.  It brings this
whole Bishop orgy to a logical conclusion."  He got up like a man
from whose shoulders a great burden had been lifted.  "Sergeant,
I'll leave you to arrange for the removal of the body for the
autopsy; but you'd better drop in at the Stuyvesant Club later.
Thank Heaven today is Sunday!  It gives us time to turn round."

That night at the club Vance and Markham and I sat alone in the
lounge-room.  Heath had come and gone, and a careful statement had
been drawn up for the press announcing Pardee's suicide and
intimating that the Bishop case was thereby closed.  Vance had said
little all day.  He had refused to offer any suggestion as to the
wording of the official statement, and had appeared reluctant even
to discuss the new phase of the case.  But now he gave voice to the
doubts that had evidently been occupying his mind.

"It's too easy, Markham--much too easy.  There's an aroma of
speciousness about it.  It's perfectly logical, d' ye see, but it's
not satisfyin'.  I can't exactly picture our Bishop terminating his
debauch of humor in any such banal fashion.  There's nothing witty
in blowin' one's brain out--it's rather commonplace, don't y' know.
Shows a woeful lack of originality.  It's not worthy of the
artificer of the Mother-Goose murders."

Markham was disgruntled.

"You yourself explained how the crimes accorded with the
psychological possibilities of Pardee's mentality; and to me it
appears highly reasonable that, having perpetrated his gruesome
jokes and come to the end of his rope, he should have done away
with himself."

"You're probably right," sighed Vance.  "I haven't any coruscatin'
arguments to combat you with.  Only, I'm disappointed.  I don't
like anticlimaxes, especially when they don't jibe with my idea of
the dramatist's talent.  Pardee's death at this moment is too
deuced neat--it clears things up too tidily.  There's too much
utility in it, and too little imagination."

Markham felt that he could afford to be tolerant.

"Perhaps his imagination was exhausted on the murders.  His suicide
might be regarded merely as a lowering of the curtain when the play
was over.  In any event, it was by no means an incredible act.
Defeat and disappointment and discouragement--a thwarting of all
one's ambitions--have constituted cause for suicide since time
immemorial."

"Exactly.  We have a reasonable motive, or explanation, for his
suicide, but no motive for the murders."

"Pardee was in love with Belle Dillard," argued Markham; "and he
probably knew that Robin was a suitor for her hand.  Also, he was
intensely jealous of Drukker."

"And Sprigg's murder?"

"We have no data on that point."

Vance shook his head.

"We can't separate the crimes as to motive.  They all sprang from
one underlying impulse: they were actuated by a single urgent
passion."

Markham sighed impatiently.

"Even if Pardee's suicide is unrelated to the murders, we're at a
dead end, figuratively and literally."

"Yes, yes.  A dead end.  Very distressin'.  Consolin' for the
police, though.  It lets them out--for a while, anyway.  But don't
misinterpret my vagaries.  Pardee's death is unquestionably related
to the murders.  Rather intimate relationship, too, I'd say."

Markham took his cigar slowly from his mouth and scrutinized Vance
for several moments.

"Is there any doubt in your mind," he asked, "that Pardee committed
suicide?"

Vance hesitated before answering.

"I could bear to know," he drawled, "why that house of cards
collapsed so readily when I deliberately leaned against the table--"

"Yes?"

"--and why it didn't topple over when Pardee's head and shoulders
fell forward on the table after he'd shot himself."

"Nothing to that," said Markham.  "The first jar may have loosened
the cards--"  Suddenly his eyes narrowed.  "Are you implying that
the card-house was built AFTER Pardee was dead?"

"Oh, my dear fellow!  I'm not indulgin' in implications.  I'm
merely givin' tongue to my youthful curiosity, don't y' know."



CHAPTER XXIII

A STARTLING DISCOVERY


(Monday, April 25; 8.30 p.m.)


Eight days went by.  The Drukker funeral was held in the little
house on 76th Street, attended only by the Dillards and Arnesson
and a few men from the university who came to pay a last tribute of
respect to a scientist for whose work they had a very genuine
admiration.

Vance and I were at the house on the morning of the funeral when a
little girl brought a small cluster of spring flowers she had
picked herself, and asked Arnesson to give them to Drukker.  I
almost expected a cynical response from him, and was surprised when
he took the flowers gravely and said in a tone almost tender:

"I'll give them to him at once, Madeleine.  And Humpty Dumpty
thanks you for remembering him."  When the child had been led
away by her governess, he turned to us.  "She was Drukker's
favorite. . . .  Funny fellow.  Never went to the theatre.
Detested travel. His only recreation was entertaining youngsters."

I mention this episode because, in spite of its seeming
unimportance, it was to prove one of the most vital links in the
chain of evidence that eventually cleared up, beyond all question
of doubt, the problem of the Bishop murders.

The death of Pardee had created a situation almost unique in the
annals of modern crime.  The statement given out by the District
Attorney's office had only intimated that there was a possibility
of Pardee's being guilty of the murders.  Whatever Markham may have
personally believed, he was far too honorable and just to cast any
direct doubt on another's character without overwhelming proofs.
But the wave of terror arising from these strange murders had
reached such proportions that he could not, in view of the duty he
owed to the community, refrain from saying that he believed the
case to be closed.  Thus, while no open accusation of guilt was
made against Pardee, the Bishop murders were no longer regarded as
a source of menace to the city, and a sigh of relief went up from
all quarters.

In the Manhattan Chess Club there was probably less discussion of
the case than anywhere else in New York.  The members felt perhaps
that the club's honor was in some way involved.  Or there may have
been a sense of loyalty toward a man who had done as much for chess
as Pardee.  But whatever the cause of the club's avoidance of the
subject, the fact remained that its members attended, almost to a
man, Pardee's funeral.  I could not help admiring this tribute to a
fellow chess player; for, whatever his personal acts, he had been
one of the great sustaining patrons of the royal and ancient game
to which they were devoted.*


* Pardee left in his will a large sum for the furtherance of chess;
and in the autumn of that same year, it will be remembered, the
Pardee Memorial Tournament was held at Cambridge Springs.


Markham's first official act on the day after Pardee's death was to
secure Sperling's release.  The same afternoon the Police
Department moved all its records of the Bishop murders to the file
marked "shelved cases," and withdrew the guards from the Dillard
house.  Vance protested mildly against this latter step; but, in
view of the fact that the Medical Examiner's post-mortem report had
substantiated in every particular the theory of suicide, there was
little that Markham could do in the matter.  Furthermore, he was
thoroughly convinced that the death of Pardee had terminated the
case; and he scoffed at Vance's wavering doubts.

During the week following the finding of Pardee's body Vance was
restive and more distrait than usual.  He attempted to interest
himself in various matters, but without any marked success.  He
showed signs of irritability; and his almost miraculous equanimity
seemed to have deserted him.  I got the impression that he was
waiting for something to happen.  His manner was not exactly
expectant, but there was a watchfulness in his attitude amounting
at times almost to apprehension.

On the day following the Drukker funeral Vance called on Arnesson,
and on Friday night accompanied him to a performance of Ibsen's
"Ghosts"--a play which, I happened to know, he disliked.  He
learned that Belle Dillard had gone away for a month's visit to the
home of a relative in Albany.  As Arnesson explained, she had begun
to show the effects of all she had been through, and needed a
change of scene.  The man was plainly unhappy over her absence, and
confided to Vance that they had planned to be married in June.
Vance also learned from him that Mrs. Drukker's will had left
everything to Belle Dillard and the professor in the event of her
son's death--a fact which appeared to interest Vance unduly.

Had I known, or even suspected, what astounding and terrible things
were hanging over us that week, I doubt if I could have stood the
strain.  For the Bishop murder case was not ended.  The climactic
horror was still to come; but even that horror, terrific and
staggering as it proved, was only a shadow of what it might have
been had not Vance reasoned the case out to two separate
conclusions, only one of which had been disposed of by Pardee's
death.  It was this other possibility, as I learned later, that had
kept him in New York, vigilant and mentally alert.

Monday, April 25, was the beginning of the end.  We were to dine
with Markham at the Bankers Club and go afterwards to a performance
of "Die Meistersinger";* but we did not witness the triumphs of
Walther that night.  I noticed that when we met Markham in the
rotunda of the Equitable Building he seemed troubled; and we were
no more than seated in the club grill when he told us of a phone
call he had received from Professor Dillard that afternoon.


* Of the Wagnerian operas this was Vance's favorite.  He always
asserted that it was the only opera that had the structural form of
a symphony; and more than once he expressed the regret that it had
not been written as an orchestral piece instead of as a conveyance
for an absurd drama.


"He asked me particularly to come to see him tonight," Markham
explained; "and when I tried to get out of it he became urgent.
He made a point of the fact that Arnesson would be away the entire
evening, and said that a similar opportunity might not present
itself until it was too late.  I asked him what he meant by that;
but he refused to explain, and insisted that I come to his house
after dinner.  I told him I'd let him know if I could make it."

Vance had listened with the intensest interest.

"We must go there, Markham.  I've been rather expecting a call of
this kind.  It's possible we may at last find the key to the
truth."

"The truth about what?"

"Pardee's guilt."

Markham said no more, and we ate our dinner in silence.

At half past eight we rang the bell of the Dillard house, and were
taken by Pyne direct to the library.

The old professor greeted us with nervous reserve.

"It's good of you to come, Markham," he said, without rising.
"Take a chair and light a cigar.  I want to talk to you--and I want
to take my time about it.  It's very difficult. . . ."  His voice
trailed off as he began filling his pipe.

We settled ourselves and waited.  A sense of expectancy invaded me
for no apparent reason, except perhaps that I caught some of the
radiations of the professor's obviously distraught mood.

"I don't know just how to broach the subject," he began; "for it
has to do, not with physical facts, but with the invisible, human
consciousness.  I've struggled all week with certain vague ideas
that have been forcing themselves upon me; and I see no way to rid
myself of them but by talking with you. . . ."

He looked up hesitantly.

"I preferred to discuss these ideas with you when Sigurd was not
present, and as he has gone to-night to see Ibsen's 'Pretenders'--
his favorite play, by the way--I took the opportunity to ask you
here."

"What do these ideas concern?" asked Markham.

"Nothing specifically.  As I have said, they're very vague; but
they have nevertheless grown fairly insistent. . . .  So insistent,
in fact," he added, "that I thought it best to send Belle away for
a while.  It's true that she was in a tortured state of mind as a
result of all these tragedies; but my real reason for shipping her
north was that I was beset by intangible doubts."

"Doubts?"  Markham leaned forward.  "What sort of doubts?"

Professor Dillard did not reply at once.

"Let me answer that question by asking another," he countered
presently.  "Are you wholly satisfied in your mind that the
situation in regard to Pardee is exactly as it appears?"

"You mean the authenticity of his suicide?"

"That and his presumptive culpability."

Markham settled back contemplatively.

"Are YOU not wholly satisfied?" he asked.

"I can't answer that question."  Professor Dillard spoke almost
curtly.  "You have no right to ask me.  I merely wanted to be sure
that the authorities, having all the data in their hands, were
convinced that this terrible affair was a closed book."  A look of
deep concern came over his face.  "If I knew that to be a fact, it
would help me to repulse the vague misgivings that have haunted me
day and night for the past week."

"And if I were to say that I am not satisfied?"

The old professor's eyes took on a distant, distressed look.  His
head fell slightly forward, as if some burden of sorrow had
suddenly weighed him down.  After several moments he lifted his
shoulders and drew a deep breath.

"The most difficult thing in this world," he said, "is to know
where one's duty lies; for duty is a mechanism of the mind, and
the heart is forever stepping in and playing havoc with one's
resolutions.  Perhaps I did wrong to ask you here; for, after all,
I have only misty suspicions and nebulous ideas to go on.  But
there was the possibility that my mental uneasiness was based on
some deep hidden foundation of whose existence I was unaware. . . .
Do you see what I mean?"  Evasive as were his words, there was no
doubt as to the disturbing mien of the shadowy image that lurked at
the back of his mind.

Markham nodded sympathetically.

"There is no reason whatever to question the findings of the
Medical Examiner."  He made the statement in a forced matter-of-
fact voice.  "I can understand how the proximity of these tragedies
might have created an atmosphere conducive to doubts.  But I think
you need have no further misgivings."

"I sincerely hope you're right," the professor murmured; but it was
clear he was not satisfied.  "Suppose, Markham--" he began, and
then stopped.  "Yes, I hope you're right," he repeated.

Vance had sat through this unsatisfactory discussion smoking
placidly; but he had been listening with unwonted concentration,
and now he spoke.

"Tell me, Professor Dillard, if there has been anything--no matter
how indefinite--that may have given birth to your uncertainty."

"No--nothing."  The answer came quickly and with a show of spirit.
"I have merely been wondering--testing every possibility.  I dared
not be too sanguine without some assurance.  Pure logic is all very
well for principles that do not touch us personally.  But where
one's own safety is concerned the imperfect human mind demands
visual evidence."

"Ah, yes."  Vance looked up, and I thought I detected a flash of
understanding between these two disparate men.

Markham rose to make his adieu; but Professor Dillard urged him to
remain a while.

"Sigurd will be here before long.  He'd enjoy seeing you again.
As I said, he's at 'The Pretenders,' but I'm sure he will come
straight home. . . .  By the way, Mr. Vance," he went on, turning
from Markham; "Sigurd tells me you accompanied him to 'Ghosts' last
week.  Do you share his enthusiasm for Ibsen?"

A slight lift of Vance's eyebrows told me that he was somewhat
puzzled by this question; but when he answered there was no hint of
perplexity in his voice.

"I have read Ibsen a great deal; and there can be little doubt that
he was a creative genius of a high order, although I've failed to
find in him either the aesthetic form or the philosophic depth that
characterizes Goethe's 'Faust,' for instance."

"I can see that you and Sigurd would have a permanent basis of
disagreement."

Markham declined the invitation to stay longer, and a few minutes
later we were walking down West End Avenue in the brisk April air.

"You will please take note, Markham old dear," observed Vance, with
a touch of waggishness, as we turned into 72nd Street and headed
for the park, "that there are others than your modest collaborator
who are hag-ridden with doubts as to the volition of Pardee's
taking-off.  And I might add that the professor is not in the least
satisfied with your assurances."

"His suspicious state of mind is quite understandable," submitted
Markham.  "These murders have touched his house pretty closely."

"That's not the explanation.  The old gentleman has fears.  And he
knows something which he will not tell us."

"I can't say that I got that impression."

"Oh, Markham--my dear Markham!  Weren't you listening closely to
his halting, reluctant tale?  It was as if he were trying to convey
some suggestion to us without actually putting it into words.  We
were supposed to guess.  Yes!  That was why he insisted that you
visit him when Arnesson was safely away at an Ibsen revival--"

Vance ceased speaking abruptly and stood stock-still.  A startled
look came in his eyes.

"Oh, my aunt!  Oh, my precious aunt!  So that was why he asked me
about Ibsen! . . .  My word!  How unutterably dull I've been!"  He
stared at Markham, and the muscles of his jaw tightened.  "The
truth at last!" he said with impressive softness.  "And it is
neither you nor the police nor I who has solved this case: it is a
Norwegian dramatist who has been dead for twenty years.  In Ibsen
is the key to the mystery."

Markham regarded him as though he had suddenly gone out of his
mind; but before he could speak Vance hailed a taxicab.

"I'll show you what I mean when we reach home," he said, as we rode
east through Central Park.  "It's unbelievable, but it's true.  And
I should have guessed it long ago; but the connotation of the
signature on those notes was too clouded with other possible
meanings. . . ."

"If it were midsummer instead of spring," commented Markham
wrathfully, "I'd suggest that the heat had affected you."

"I knew from the first there were three possible guilty persons,"
continued Vance.  "Each was psychologically capable of the murders,
provided the impact of his emotions had upset his mental
equilibrium.  So there was nothing to do but to wait for some
indication that would focus suspicion.  Drukker was one of my three
suspects, but he was murdered; and that left two.  Then Pardee to
all appearances committed suicide, and I'll admit that his death
made reasonable the assumption that he had been the guilty one.
But there was an eroding doubt in my mind.  His death was not
conclusive; and that house of cards troubled me.  We were
stalemated.  So again I waited, and watched my third possibility.
Now I know that Pardee was innocent, and that he did not shoot
himself.  He was murdered--just as were Robin and Sprigg and
Drukker.  His death was another grim joke--he was a victim thrown
to the police in the spirit of diabolical jest.  And the murderer
has been chuckling at our gullibility ever since."

"By what reasoning do you arrive at so fantastic a conclusion?"

"It's no longer a question of reasoning.  At last I have the
explanation for the crimes; and I know the meaning of the 'Bishop'
signature to the notes.  I'll show you a piece of amazing and
incontrovertible evidence very soon."

A few minutes later we reached his apartment, and he led us
straight to the library.

"The evidence has been here within arm's reach all the time."

He went to the shelves where he kept his dramas, and took down
Volume II of the collected works of Henrik Ibsen.*  The book
contained "The Vikings at Helgeland" and "The Pretenders"; but with
the first of these plays Vance was not concerned.  Turning to "The
Pretenders" he found the page where the dramatis personae were
given, and laid the book on the table before Markham.


* Vance's set was the William Archer copyright edition, published
by Charles Scribner's Sons.


"Read the cast of characters of Arnesson's favorite play," he
directed.

Markham, silent and puzzled, drew the volume toward him; and I
looked over his shoulder.  This is what we saw:


     HÅKON HÅKONSSON, the King elected by the Birchlegs.

     INGA OF VARTEIG, his mother.

     EARL SKULE.

     LADY RAGNHILD, his wife.

     SIGRID, his sister.

     MARGRETE, his daughter.

     GUTHORM INGESSON.

     SIGURD RIBBUNG.

     NICHOLAS ARNESSON, Bishop of Oslo.

     DAGFINN THE PEASANT, Hakon's marshal.

     IVAR BODDE, his chaplain.

     VEGARD VAERADAL, one of his guard.

     GREGORIUS JONSSON, a nobleman.

     PAUL FLIDA, a nobleman.

     INGEBORG, Andres Skialdarband's wife.

     PETER, her son, a young priest.

     SIRA VILIAM, Bishop Nicholas's chaplain.

     MASTER SIGARD OF BRABANT, a physician.

     JATGEIR SKALD, an Icelander.

     BÅRD BRATTE, a chieftain from the Trondhiem district.


But I doubt if either of us read beyond the line:


     NICHOLAS ARNESSON, Bishop of Oslo.


My eyes became riveted on that name with a set and horrified
fascination.  And then I remembered. . . .  Bishop Arnesson was one
of the most diabolical villains in all literature--a cynical,
sneering monster who twisted all the sane values of life into
hideous buffooneries.



CHAPTER XXIV

THE LAST ACT


(Tuesday, April 26; 9 a.m.)


With this astounding revelation the Bishop murder case entered its
final and most terrible phase.  Heath had been informed of Vance's
discovery; and it was arranged that we should meet in the District
Attorney's office early the following day for a counsel of war.

Markham, when he took leave of us that night, was more troubled and
despondent than I had ever seen him.

"I don't know what can be done," he said hopelessly.  "There's no
legal evidence against the man.  But we may be able to devise some
course of action that will give us the upper hand. . . .  I never
believed in torture, but I almost wish we had access today to the
thumbscrew and the rack."

Vance and I arrived at his office a few minutes after nine the next
morning.  Swacker intercepted us and asked us to wait in the
reception room for a little while.  Markham, he explained, was
engaged for the moment.  We had no more than seated ourselves when
Heath appeared, grim, pugnacious and sullen.

"I gotta hand it to you, Mr. Vance," he proclaimed.  "You sure got
a line on the situation.  But what good it's going to do us I don't
see.  We can't arrest a guy because his name's in a book."

"We may be able to force the issue some way," Vance rejoined.  "In
any event, we now know where we stand."

Ten minutes later Swacker beckoned to us and indicated that Markham
was free.

"Sorry to have kept you waiting," Markham apologized.  "I had an
unexpected visitor."  His voice had a despairing ring.  "More
trouble.  And, curiously enough, it's connected with the very
section of Riverside Park where Drukker was killed.  However,
there's nothing I can do about it. . . ."  He drew some papers
before him.  "Now to business."

"What's the new trouble in Riverside Park?" asked Vance casually.

Markham frowned.

"Nothing that need bother us now.  A kidnapping, in all likelihood.
There's a brief account of it in the morning papers, in case you're
interested. . . ."

"I detest reading the papers."  Vance spoke blandly, but with an
insistence that puzzled me.  "What happened?"

Markham drew a deep breath of impatience.

"A child disappeared from the playground yesterday after talking
with an unknown man.  Her father came here to solicit my help.  But
it's a job for the Bureau of Missing Persons; and I told him so.--
Now, if your curiosity is appeased--"

"Oh, but it isn't," persisted Vance.  "I simply must hear the
details.  That section of the park fascinates me strangely."

Markham shot him a questioning glance through lowered lids.

"Very well," he acquiesced.  "A five-year-old girl, named Madeleine
Moffat, was playing with a group of children at about half past
five last evening.  She crawled up on a high mound near the
retaining wall, and a little later, when her governess went to get
her, thinking she had descended the other side, the child was
nowhere to be found.  The only suggestive fact is that two of the
other children say they saw a man talking to her shortly before she
disappeared; but, of course, they can give no description of him.
The police were notified, and are investigating.  And that's all
there is to the case so far."

"'Madeleine.'"  Vance repeated the name musingly.  "I say, Markham;
do you know if this child knew Drukker?"

"Yes!"  Markham sat up a little straighter.  "Her father mentioned
that she often went to parties at his house. . . ."

"I've seen the child."  Vance rose and stood, hands in pockets,
gazing down at the floor.  "An adorable little creature . . .
golden curls.  She brought a handful of flowers for Drukker the
morning of his funeral. . . .  And now she has disappeared after
having been seen talking with a strange man. . . ."

"What's going on in your mind?" demanded Markham sharply.

Vance appeared not to have heard the question.

"Why should her father appeal to you?"

"I've known Moffat slightly for years--he was at one time connected
with the city administration.  He's frantic--grasping at every
straw.  The proximity of the affair to the Bishop murders has made
him morbidly apprehensive. . . .  But see here, Vance; we didn't
come here to discuss the Moffat child's disappearance. . . ."

Vance lifted his head: there was a look of startled horror on his
face.

"Don't speak--oh, don't speak. . . ."  He began pacing up and down,
while Markham and Heath watched him in mute amazement.  "Yes--yes;
that would be it," he murmured to himself.  "The time is right . . .
it all fits. . . ."

He swung about, and going to Markham seized his arm.

"Come--quickly!  It's our only chance--we can't wait another
minute."  He fairly dragged Markham to his feet and led him toward
the door.  "I've been fearing something like this all week--"

Markham wrenched his arm free from the other's grip.

"I won't move from this office, Vance, until you explain."

"It's another act in the play--the last act!  Oh, take my word for
it."  There was a look in Vance's eyes I had never seen before.
"It's 'Little Miss Muffet' now.  The name isn't identical, but that
doesn't matter.  It's near enough for the Bishop's jest; he'll
explain it all to the press.  He probably beckoned the child to the
tuffet, and sat down beside her.  And now she's gone--frightened
away. . . ."

Markham moved forward in a sort of daze; and Heath, his eyes
bulging, leapt to the door.  I have often wondered what went on
in their minds during those few seconds of Vance's importunate
urgings.  Did they believe in his interpretation of the episode?
Or were they merely afraid not to investigate, in view of the
remote possibility that another hideous joke had been perpetrated
by the Bishop?  Whatever their convictions or doubts, they accepted
the situation as Vance saw it; and a moment later we were in the
hall, hastening toward the elevator.  At Vance's suggestion we
picked up Detective Tracy from the branch office of the Detective
Bureau in the Criminal Courts Building.

"This affair is serious," he explained.  "Anything may happen."

We emerged through the Franklin-Street entrance, and in a few
minutes were on our way up-town in the District Attorney's car,
breaking speed regulations and ignoring traffic signals.  Scarcely
a word was spoken on that momentous ride; but as we swung through
the tortuous roads of Central Park Vance said:

"I may be wrong, but we will have to risk it.  If we wait to see
whether the papers get a note, it'll be too late.  We're not
supposed to know yet; and that's our one chance. . . ."

"What do you expect to find?"  Markham's tone was husky and a
little uncertain.

Vance shook his head despondently.

"Oh, I don't know.  But it'll be something devilish."

When the car drew up with a lurch in front of the Dillard house
Vance leapt out and ran up the steps ahead of us.  Pyne answered
his insistent ring.

"Where's Mr. Arnesson?" he demanded.

"At the university, sir," the old butler replied; and I imagined
there was fright in his eyes.  "But he'll be home for an early
lunch."

"Then take us at once to Professor Dillard."

"I'm sorry, sir," Pyne told him; "but the professor is also out.
He went to the Public Library--"

"Are you alone here?"

"Yes, sir.  Beedle's gone to market."

"So much the better."  Vance took hold of the butler and turned him
toward the rear stairs.  "We're going to search the house, Pyne.
You lead the way."

Markham came forward.

"But, Vance, we can't do that!"

Vance wheeled round.

"I'm not interested in what you can do or can't do.  I'm going to
search this house. . . .  Sergeant, are you with me?"  There was a
strange look on his face.

"You bet your sweet life!"  (I never liked Heath as much as at that
moment.)

The search was begun in the basement.  Every hallway, every closet,
every cupboard and waste space was inspected.  Pyne, completely
cowed by Heath's vindictiveness, acted as guide.  He brought keys
and opened doors for us, and even suggested places we might
otherwise have overlooked.  The Sergeant had thrown himself into
the hunt with energy, though I am sure he had only a vague idea as
to its object.  Markham followed us disapprovingly; but he, too,
had been caught in the sweep of Vance's dynamic purposefulness; and
he must have realized that Vance had some tremendous justification
for his rash conduct.

Gradually we worked our way upward through the house.  The library
and Arnesson's room were gone over carefully.  Belle Dillard's
apartment was scrutinized, and close attention was given to the
unused rooms on the third floor.  Even the servants' quarters on
the fourth floor were overhauled.  But nothing suspicious was
discovered.  Though Vance suppressed his eagerness I could tell
what a nervous strain he was under by the tireless haste with which
he pushed the search.

Eventually we came to a locked door at the rear of the upper hall.

"Where does that lead?" Vance asked Pyne.

"To a little attic room, sir.  But it's never used--"

"Unlock it."

The man fumbled for several moments with his bunch of keys.

"I don't seem to find the key, sir.  It's supposed to be here. . . ."

"When did you have it last?"

"I couldn't say, sir.  To my knowledge no one's been in the attic
for years."

Vance stepped back and crouched.

"Stand aside, Pyne."

When the butler had moved out of the way Vance hurled himself
against the door with terrific force.  There was a creaking and
straining of wood; but the lock held.

Markham rushed forward and caught him round the shoulders.

"Are you mad!" he exclaimed.  "You're breaking the law."

"The law!"  There was scathing irony in Vance's retort.  "We're
dealing with a monster who sneers at all law.  You may coddle him
if you care to, but I'm going to search that attic if it means
spending the rest of my life in jail.--Sergeant, open that door!"

Again I experienced a thrill of liking for Heath.  Without a
moment's hesitation he poised himself on his toes and sent his
shoulders crashing against the door's panel just above the knob.
There was a splintering of wood as the lock's bolt tore through the
moulding.  The door swung inward.

Vance, freeing himself from Markham's hold, ran stumbling up the
steps with the rest of us at his heels.  There was no light in the
attic, and we paused for a moment at the head of the stairs to
accustom our eyes to the darkness.  Then Vance struck a match and,
groping forward, sent up the window shade with a clatter.  The
sunlight poured in, revealing a small room, scarcely ten feet
square, cluttered with all manner of discarded odds and ends.  The
atmosphere was heavy and stifling, and a thick coating of dust lay
over everything.

Vance looked quickly about him, and an expression of disappointment
came over his face.

"This is the only place left," he remarked, with the calmness of
desperation.

After a more careful scrutiny of the room, he stepped to the corner
by the little window and peered down at a battered suit-case which
lay on its side against the wall.  I noticed that it was unlatched
and that its straps hung free.  Leaning over he threw the cover
back.

"Ah!  Here, at least, is something for you, Markham."

We crowded about him.  In the suit-case was an old Corona
typewriter.  A sheet of paper was in the carriage; and on it had
already been typed, in pale-blue élite characters, the two lines:


     Little Miss Muffet
     Sat on a tuffet


At this point the typist had evidently been interrupted, or for
some other reason had not completed the Mother-Goose rhyme.

"The new Bishop note for the press," observed Vance.  Then reaching
into the suit-case he lifted out a pile of blank paper and
envelopes.  At the bottom, beside the machine, lay a red-leather
note-book with thin yellow leaves.  He handed it to Markham with
the terse announcement:

"Drukker's calculations on the quantum theory."

But there was still a look of defeat in his eyes; and again he
began inspecting the room.  Presently he went to an old dressing-
table which stood against the wall opposite to the window.  As he
bent over to peer behind it he suddenly drew back and, lifting his
head, sniffed several times.  At the same moment he caught sight of
something on the floor at his feet, and kicked it toward the centre
of the room.  We looked down at it with astonishment.  It was a
gas-mask of the kind used by chemists.

"Stand back, you chaps!" he ordered; and holding one hand to his
nose and mouth he swung the dressing-table away from the wall.
Directly behind it was a small cupboard door about three feet high,
set into the wall.  He wrenched it open and looked inside, then
slammed it shut immediately.

Brief as was my view of the interior of the cupboard, I was able to
glimpse its contents clearly.  It was fitted with two shelves.  On
the lower one were several books lying open.  On the upper shelf
stood an Erlenmeyer flask clamped to an iron support, a spirit-
lamp, a condenser tube, a glass beaker, and two small bottles.

Vance turned and gave us a despairing look.

"We may as well go: there's nothing more here."

We returned to the drawing-room, leaving Tracy to guard the door to
the attic.

"Perhaps, after all, you were justified in your search,"
acknowledged Markham, studying Vance gravely.  "I don't like such
methods, however.  If we hadn't found the typewriter--"

"Oh, that!"  Vance, preoccupied and restless, went to the window
overlooking the archery range.  "I wasn't hunting for the
typewriter--or the note-book, either.  What do they matter?"  His
chin fell forward on his breast, and his eyes closed in a kind of
lethargy of defeat.  "Everything's gone wrong--my logic has failed.
We're too late."

"I don't pretend to know what you're grumbling about," said
Markham.  "But at least you've supplied me evidence of a sort.
I'll now be able to arrest Arnesson when he returns from the
university."

"Yes, yes; of course.  But I wasn't thinking of Arnesson, or the
arrest of the culprit, or the triumph of the District Attorney's
office.  I was hoping--"

He broke off and stiffened.

"We're NOT too late!  I didn't think far enough. . . ."  He went
swiftly to the archway.  "It's the Drukker house we must
search. . . .  Hurry!"  He was already half-running down the hall,
Heath behind him, and Markham and I bringing up the rear.

We followed him down the rear stairs, across the archery-room, and
out on the range.  We did not know, and I doubt if any of us even
guessed, what was in his mind; but some of his inner excitation had
been communicated to us, and we realized that only a vital urgency
could have shaken him so completely out of his usual attitude of
disinterest and calm.

When we came to the screen-porch of the Drukker house he reached
through the broken wire-netting and released the catch.  The
kitchen door, to my astonishment, was unlocked; but Vance seemed to
expect this, for he unhesitatingly turned the knob and threw it
open.

"Wait!" he directed, pausing in the little rear hallway.  "There's
no need to search the entire house.  The most likely place. . . .
Yes!  Come along . . . up-stairs . . . somewhere in the centre of
the house . . . a closet most likely . . . where no one could
hear. . . ."  As he spoke he led the way up the rear stairs, past
Mrs. Drukker's room and the study, and thence to the third floor.
There were but two doors on this upper hall--one at the extreme end,
and a smaller door set midway in the right wall.

Vance went straight to the latter.  There was a key protruding from
the lock, and, turning it, he drew open the door.  Only a shadowy
blackness met our eyes.  Vance was on his knees in a second,
groping inside.

"Quick, Sergeant.  Your flash-light."

Almost before he had uttered the words a luminous circle fell on
the floor of the closet.  What I saw sent a chill of horror over
me.  A choked exclamation burst from Markham; and a soft whistle
told me that Heath too was appalled by the sight.  Before us on the
floor, in a limp, silent heap, lay the little girl who had brought
flowers to her broken Humpty Dumpty on the morning of his funeral.
Her golden hair was dishevelled; her face was deathly pale, and
there were streaks down her cheeks where the futile tears had
welled forth and dried.

Vance bent over and put his ear to her heart.  Then he gathered her
tenderly in his arms.

"Poor little Miss Muffet," he whispered, and rising went toward the
front stairs.  Heath preceded him, flashing his light all the way
so there would be no chance of his stumbling.  In the main lower
hall he paused.

"Unbolt the door, Sergeant."

Heath obeyed with alacrity, and Vance stepped out on the sidewalk.

"Go to the Dillards' and wait for me there," he flung back over his
shoulder.  And with the child clasped closely to his breast he
started diagonally across 76th Street to a house on which I could
make out a doctor's brass name-plate.



CHAPTER XXV

THE CURTAIN FALLS


(Tuesday, April 26; 11 a.m.)


Twenty minutes later Vance rejoined us in the Dillard drawing-room.

"She's going to be all right," he announced, sinking into a chair
and lighting a cigarette.  "She was only unconscious, had fainted
from shock and fright; and she was half-suffocated."  His face
darkened.  "There were bruises on her little wrist.  She probably
struggled in that empty house when she failed to find Humpty
Dumpty; and then the beast forced her into the closet and locked
the door.  No time to kill her, d' ye see.  Furthermore, killing
wasn't in the book.  'Little Miss Muffet' wasn't killed--merely
frightened away.  She'd have died, though, from lack of air.  And
HE was safe: no one could hear her crying. . . ."

Markham's eyes rested on Vance affectionately.

"I'm sorry I tried to hold you back," he said simply.  (For all his
conventionally legal instincts, there was a fundamental bigness to
his nature.)  "You were right in forcing the issue, Vance. . . .
And you, too, Sergeant.  We owe a great deal to your determination
and faith."

Heath was embarrassed.

"Oh, that's all right, sir.  You see, Mr. Vance had me all worked
up about the kid.  And I like kids, sir."

Markham turned an inquisitive look on Vance.

"You expected to find the child alive?"

"Yes; but drugged or stunned perhaps.  I didn't think of her as
dead, for that would have contravened the Bishop's joke."

Heath had been pondering some troublous point.

"What I can't get through my head," he said, "is why this Bishop,
who's been so damn careful about everything else, should leave the
door of the Drukker house unlocked."

"We were expected to find the child," Vance told him.  "Everything
was made easy for us.  Very considerate of the Bishop, what?  But
we weren't supposed to find her till to-morrow--after the papers
had received the Little-Miss-Muffet notes.  They were to have been
our clew.  But we anticipated the gentleman."

"But why weren't the notes sent yesterday?"

"It was no doubt the Bishop's original intention to post his poetry
last night; but I imagine he decided it was best for his purpose to
let the child's disappearance attract public attention first.
Otherwise the relationship between Madeleine Moffat and little Miss
Muffet might have been obscured."

"Yeh!" snarled Heath through his teeth.  "And by to-morrow the kid
woulda been dead.  No chance then of her identifying him."

Markham looked at his watch and rose with determination.

"There's no point in waiting for Arnesson's return.  The sooner we
arrest him the better."  He was about to give Heath an order when
Vance intervened.

"Don't force the issue, Markham.  You haven't any real evidence
against the man.  It's too delicate a situation for aggression.
We must go carefully or we'll fail."

"I realize that the finding of the typewriter and the note-book is
not conclusive," concurred Markham.  "But the identification by the
child--"

"Oh, my dear fellow!  What weight would a jury attach to a
frightened five-year-old girl's identification without powerful
contribut'ry evidence?  A clever lawyer could nullify it in five
minutes.  And even assuming you could make the identification hold,
what would it boot you?  It wouldn't connect Arnesson in any way
with the Bishop murders.  You could only prosecute him for attempted
kidnapping,--the child's unharmed, remember.  And if you should,
through a legal miracle, get a doubtful conviction, Arnesson would
receive at most a few years in the bastille.  That wouldn't end this
horror. . . .  No, no.  You mustn't be precipitate."

Reluctantly Markham resumed his seat.  He saw the force of Vance's
argument.

"But we can't let this thing go on," he declared ferociously.  "We
must stop this maniac some way."

"Some way--yes."  Vance began pacing the room restlessly.  "We may
be able to wangle the truth out of him by subterfuge: he doesn't
know yet that we've found the child. . . .  It's possible Professor
Dillard could assist us--"  He halted and stood looking down at the
floor.  "Yes!  That's our one chance.  We must confront Arnesson
with what we know when the professor is present.  The situation is
sure to force an issue of some kind.  The professor now will do all
in his power to help convict Arnesson."

"You believe he knows more than he had told us?"

"Undoubtedly.  I've told you so from the first.  And when he hears
of the Little-Miss-Muffet episode, it's not unlikely he'll supply
us with the evidence we need."

"It's a long chance."  Markham was pessimistic.  "But it can do no
harm to try.  In any event, I shall arrest Arnesson before I leave
here, and hope for the best."

A few moments later the front door opened and Professor Dillard
appeared in the hall opposite the archway.  He scarcely acknowledged
Markham's greeting--he was scanning our faces as if trying to read
the meaning of our unexpected visit.  Finally he put a question.

"You have, perhaps, thought over what I said last night?"

"Not only have we thought it over," said Markham, "but Mr. Vance
has found the thing that was disturbing you.  After we left here he
showed me a copy of 'The Pretenders.'"

"Ah!"  The exclamation was like a sigh of relief.  "For days that
play has been in my mind, poisoning every thought. . . ."  He
looked up fearfully.  "What does it mean?"

Vance answered the question.

"It means, sir, that you've led us to the truth.  We're waiting now
for Mr. Arnesson.--And I think it would be well if we had a talk
with you in the meantime.  You may be able to help us."

The old man hesitated.

"I had hoped not to be made an instrument in the boy's conviction."
His voice held a tragic paternal note.  But presently his features
hardened; a vindictive light shone in his eyes; and his hand
tightened over the knob of his stick.  "However, I can't consider
my own feelings now.  Come; I will do what I can."

On reaching the library he paused by the sideboard and poured
himself a glass of port.  When he had drunk it he turned to Markham
with a look of apology.

"Forgive me.  I'm not quite myself."  He drew forward the little
chess table and placed glasses on it for all of us.  "Please
overlook my discourtesy."  He filled the glasses and sat down.

We drew up chairs.  There was none of us, I think, who did not feel
the need of a glass of wine after the harrowing events we had just
passed through.

When we had settled ourselves the professor lifted heavy eyes to
Vance, who had taken a seat opposite to him.

"Tell me everything," he said.  "Don't try to spare me."

Vance drew out his cigarette-case.

"First, let me ask you a question.  Where was Mr. Arnesson between
five and six yesterday afternoon?"

"I--don't know."  There was a reluctance in the words.  "He had tea
here in the library; but he went out about half past four, and I
didn't see him again until dinner time."

Vance regarded the other sympathetically for a moment, then he
said:

"We've found the typewriter on which the Bishop notes were printed.
It was in an old suit-case hidden in the attic of this house."

The professor showed no sign of being startled.

"You were able to identify it?"

"Beyond any doubt.  Yesterday a little girl named Madeleine Moffat
disappeared from the playground in the park.  There was a sheet of
paper in the machine, and on it had already been typed:  'Little
Miss Muffet sat on a tuffet.'"

Professor Dillard's head sank forward.

"Another insane atrocity!  If only I hadn't waited till last night
to warn you--!"

"No great harm has been done," Vance hastened to inform him.  "We
found the child in time: she's out of danger now."

"Ah!"

"She had been locked in the hall-closet on the top floor of the
Drukker house.  We had thought she was here somewhere--which is how
we came to search your attic."

There was a silence; then the professor asked:

"What more have you to tell me?"

"Drukker's note-book containing his recent quantum researches was
stolen from his room the night of his death.  We found this note-
book in the attic with the typewriter."

"He stooped even to that?"  It was not a question, but an
exclamation of incredulity.  "Are you sure of your conclusions?
Perhaps if I had made no suggestion last night--had not sowed the
seed of suspicion. . . ."

"There can be no doubt," declared Vance softly.  "Mr. Markham
intends to arrest Mr. Arnesson when he returns from the university.
But to be frank with you, sir: we have practically no legal
evidence, and it is a question in Mr. Markham's mind whether or not
the law can even hold him.  The most we can hope for is a conviction
for attempted kidnapping through the child's identification."

"Ah, yes . . . the child would know."  A bitterness crept into the
old man's eyes.  "Still, there should be some means of obtaining
justice for the other crimes."

Vance sat smoking pensively, his eyes on the wall beyond.  At last
he spoke with quiet gravity.

"If Mr. Arnesson were convinced that our case against him was a
strong one, he might choose suicide as a way out.  That perhaps
would be the most humane solution for every one."

Markham was about to make an indignant protest, but Vance
anticipated him.

"Suicide is not an indefensible act per se.  The Bible, for
instance, contains many accounts of heroic suicide.  What finer
example of courage than Rhazis', when he threw himself from the
tower to escape the yoke of Demetrius?*  There was gallantry, too,
in the death of Saul's sword-bearer, and in the self-hanging of
Ahithophel.  And surely the suicides of Samson and Judas Iscariot
had virtue.  History is filled with notable suicides--Brutus and
Cato of Utica, Hannibal, Lucretia, Cleopatra, Seneca. . . .   Nero
killed himself lest he fall into the hands of Otho and the
Pretorian guards.  In Greece we have the famous self-destruction of
Demosthenes; and Empedocles threw himself in the crater of Etna.
Aristotle was the first great thinker to advance the dictum that
suicide is an anti-social act, but, according to tradition, he
himself took poison after the death of Alexander.  And in modern
times let us not forget the sublime gesture of Baron Nogi. . . ."


* I admit that the name of Rhazis was unfamiliar to me; and when I
looked it up later I found that the episode to which Vance referred
does not appear in the Anglican Bible, but in the second book of
Maccabees in the Apocrypha.


"All that is no justification of the act," Markham retorted.  "The
law--"

"Ah, yes--the law.  In Chinese law every criminal condemned to
death has the option of suicide.  The Codex adopted by the French
National Assembly at the end of the eighteenth century abolished
all punishments for suicide; and in the Sachsenspiegel--the
principal foundation of Teuton law--it is plainly stated that
suicide is not a punishable act.  Moreover, among the Donatists,
Circumcellions and Patricians suicide was considered pleasing to
the gods.  And even in More's Utopia there was a synod to pass on
the right of the individual to take his own life. . . .  Law,
Markham, is for the protection of society.  What of a suicide that
makes possible that protection?  Are we to invoke a legal
technicality, when, by so doing, we actually lay society open to
continued danger?  Is there no law higher than those on the statute
books?"

Markham was sorely troubled.  He rose and walked the length of the
room and back, his face dark with anxiety.  When he sat down again
he looked at Vance a long while, his fingers drumming with nervous
indecision on the table.

"The innocent of course must be considered," he said in a voice of
discouragement.  "As morally wrong as suicide is, I can see your
point that at times it may be theoretically justified."  (Knowing
Markham as I did, I realized what this concession had cost him; and
I realized, too, for the first time, how utterly hopeless he felt
in the face of the scourge of horror which it was his duty to wipe
out.)

The old professor nodded understandingly.

"Yes, there are some secrets so hideous that it is well for the
world not to know them.  A higher justice may often be achieved
without the law taking its toll."

As he spoke the door opened, and Arnesson stepped into the room.

"Well, well.  Another conference, eh?"  He gave us a quizzical
leer, and threw himself into a chair beside the professor.  "I
thought the case had been adjudicated, so to speak.  Didn't
Pardee's suicide put finis to the affair?"

Vance looked straight into the man's eyes.

"We've found little Miss Muffet, Mr. Arnesson."

The other's eyebrows went up with sardonic amusement.

"Sounds like a charade.  What am I supposed to answer:  'How's
little Jack Horner's thumb?'  Or, should I inquire into the health
of Jack Sprat?"

Vance did not relax his steady gaze.

"We found her in the Drukker house, locked in a closet," he
amplified, in a low, even tone.

Arnesson became serious, and an involuntary frown gathered on his
forehead.  But this slackening of pose was only transient.  Slowly
his mouth twisted into a smirk.

"You policemen are so efficient.  Fancy finding little Miss Muffet
so soon.  Remarkable."  He wagged his head in mock admiration.
"However, sooner or later it was to be expected.--And what, may I
ask, is to be the next move?"

"We also found the typewriter," pursued Vance, ignoring the
question.  "And Drukker's stolen notebook."

Arnesson was at once on his guard.

"Did you really?"  He gave Vance a canny look.  "Where were these
tell-tale objects?"

"Up-stairs--in the attic."

"Aha!  Housebreaking?"

"Something like that."

"Withal," Arnesson scoffed, "I can't see that you have a cast-iron
case against any one.  A typewriter is not like a suit of clothes
that fits only one person.  And who can say how Drukker's note-book
found its way into our attic?--You must do better than that, Mr.
Vance."

"There is, of course, the factor of opportunity.  The Bishop is a
person who could have been on hand at the time of each murder."

"That is the flimsiest of contributory evidence," the man
countered.  "It would not help much toward a conviction."

"We might be able to show why the murderer chose the sobriquet of
Bishop."

"Ah!  That unquestionably would help."  A cloud settled on
Arnesson's face, and his eyes became reminiscent.  "I'd thought of
that, too."

"Oh, had you, now?"  Vance watched him closely.  "And there's
another piece of evidence I haven't mentioned.  Little Miss Muffet
will be able to identify the man who led her to the Drukker house
and forced her into the closet."

"So!  The patient has recovered?"

"Oh, quite.  Doing nicely, in fact.  We found her, d' ye see,
twenty-four hours before the Bishop intended us to."

Arnesson was silent.  He was staring down at his hands which,
though folded, were working nervously.  Finally he spoke.

"And if, in spite of everything, you were wrong. . . ."

"I assure you, Mr. Arnesson," said Vance quietly, "that I KNOW who
is guilty."

"You positively frighten me!"  The man had got a grip on himself,
and he retorted with biting irony.  "If, by any chance, I myself
were the Bishop, I'd be inclined to admit defeat. . . .  Still,
it's quite obvious that it was the Bishop who took the chessman to
Mrs. Drukker at midnight; and I didn't return home with Belle until
half past twelve that night."

"So you informed her.  As I recall, you looked at your watch and
told her what time it was.--Come, now: what time was it?"

"That's correct--half past twelve."

Vance sighed and tapped the ash from his cigarette.

"I say, Mr. Arnesson; how good a chemist are you?"

"One of the best," the man grinned.  "Majored in it.--What then?"

"When I was searching the attic this morning I discovered a little
wall-closet in which some one had been distilling hydrocyanic acid
from potassium ferrocyanide.  There was a chemist's gas-mask on
hand, and all the paraphernalia.  Bitter-almond odor still lurking
in the vicinity."

"Quite a treasure-trove, our attic.  A sort of haunt of Loki, it
would seem."

"It was just that," returned Vance gravely, "--the den of an evil
spirit."

"Or else the laboratory of a modern Doctor Faustus. . . .  But why
the cyanide, do you think?"

"Precaution, I'd say.  In case of trouble the Bishop could step out
of the picture painlessly.  Everything in readiness, don't y' know."

Arnesson nodded.

"Quite a correct attitude on his part.  Really decent of him, in
fact.  No use putting people to unnecessary bother if you're
cornered.  Yes, very correct."

Professor Dillard had sat during this sinister dialogue with one
hand pressed to his eyes, as though in pain.  Now he turned
sorrowfully to the man he had fathered for so many years.

"Many great men, Sigurd, have justified suicide--" he began; but
Arnesson cut him short with a cynical laugh.

"Faugh!  Suicide needs no justification.  Nietzsche laid the
bugaboo of voluntary death.  'Auf eine stolze Art sterben, wenn es
nicht mehr möglich ist, auf eine stolze Art zu leben.  Der Tod
unter den veräcktlichsten Bedingungen, ein unfreier Tod, ein Tod
zur unrechten Zeit ist ein Feiglings-Tod.  Wir haben es nicht in
der Hand, zu verhindern, geboren zu werden: aber wir können diesen
Fehler--denn bisweilen ist es ein Fehler--wieder gut machen.  Wenn
man sich abschafft, tut man die achtungswürdigste Sache, die es
giebt: man verdient beinahe damit, zu leben.'*--Memorized that
passage from 'Götzen-Dämmerung' in my youth.  Never forgot it.  A
sound doctrine."


* "One should die proudly when it is no longer possible to live
proudly.  The death which takes place in the most contemptible
circumstances, the death that is not free, the death which occurs
at the wrong time, is the death of a coward.  We have not the power
to prevent ourselves from being born; but this error--for sometimes
it is an error--can be rectified if we choose.  The man who does
away with himself, performs the most estimable of deeds; he almost
deserves to live for having done so."


"Nietzsche had many famous predecessors who also upheld suicide,"
supplemented Vance.  "Zeno the Stoic left us a passionate dithyramb
defending voluntary death.  And Tacitus, Epictetus, Marcus Aurelius,
Cato, Kant, Fichte, Diderot, Voltaire and Rousseau, all wrote
apologias for suicide.  Schopenhauer protested bitterly against the
fact that suicide was regarded as a crime in England. . . .  And
yet, I wonder if the subject can be formulated.  Somehow I feel that
it's too personal a matter for academic discussion."

The professor agreed sadly.

"No one can know what goes on in the human heart in that last dark
hour."

During this discussion Markham had been growing impatient and
uneasy; and Heath, though at first rigid and watchful, had begun
to unbend.  I could not see that Vance had made the slightest
progress; and I was driven to the conclusion that he had failed
signally in accomplishing his purpose of ensnaring Arnesson.
However, he did not appear in the least perturbed.  I even got the
impression that he was satisfied with the way things were going.
But I did notice that, despite his outer calm, he was intently
alert.  His feet were drawn back and poised; and every muscle in
his body was taut.  I began to wonder what the outcome of this
terrible conference would be.

The end came swiftly.  A short silence followed the professor's
remark.  Then Arnesson spoke.

"You say you know who the Bishop is, Mr. Vance.  That being the
case, why all this palaver?"

"There was no great haste."  Vance was almost casual.  "And there
was the hope of tying up a few loose ends,--hung juries are so
unsatisfact'ry, don't y' know. . . .  Then again, this port is
excellent."

"The port? . . .  Ah yes."  Arnesson glanced at our glasses, and
turned an injured look on the professor.  "Since when have I been a
teetotaler, sir?"

The other gave a start, hesitated, and rose.

"I'm sorry, Sigurd.  It didn't occur to me . . . you never drink in
the forenoon."  He went to the sideboard and, filling another
glass, placed it, with an unsteady hand, before Arnesson.  Then he
refilled the other glasses.

No sooner had he resumed his seat than Vance uttered an exclamation
of surprise.  He had half risen and was leaning forward, his hands
resting on the edge of the table, his eyes fixed with astonishment
on the mantel at the end of the room.

"My word!  I never noticed that before. . . .  Extr'ordin'ry!"

So unexpected and startling had been his action, and so tense was
the atmosphere, that involuntarily we swung about and looked in the
direction of his fascinated gaze.

"A Cellini plaque!" he exclaimed.  "The Nymph of Fontainebleau!
Berenson told me it was destroyed in the seventeenth century.  I've
seen its companion piece in the Louvre. . . ."

A red flush of angry indignation mounted to Markham's cheeks; and
for myself I must say that, familiar as I was with Vance's
idiosyncrasies and intellectual passion for rare antiques, I had
never before known him to exhibit such indefensible bad taste.  It
seemed unbelievable that he would have let himself be distracted by
an objet-d'art in such a tragic hour.

Professor Dillard frowned at him with consternation.

"You've chosen a strange time, sir, to indulge your enthusiasm for
art," was his scathing comment.

Vance appeared abashed and chagrined.  He sank back in his seat,
avoiding our eyes, and began turning the stem of his glass between
his fingers.

"You are quite right, sir," he murmured.  "I owe you an apology."

"The plaque, incidentally," the professor added, by way of
mitigating the severity of his rebuke, "is merely a copy of the
Louvre piece."

Vance, as if to hide his confusion, raised his wine to his lips.
It was a highly unpleasant moment: every one's nerves were on edge;
and, in automatic imitation of his action, we lifted our glasses
too.

Vance gave a swift glance across the table and, rising, went to the
front window, where he stood, his back to the room.  So unaccountable
was his hasty departure that I turned and watched him wonderingly.
Almost at the same moment the edge of the table was thrust violently
against my side, and simultaneously there came a crash of glassware.

I leapt to my feet and gazed down with horror at the inert body
sprawled forward in the chair opposite, one arm and shoulder flung
across the table.  A short silence of dismay and bewilderment
followed.  Each of us seemed momentarily paralyzed.  Markham stood
like a graven image, his eyes fastened on the table; and Heath,
staring and speechless, clung rigidly to the back of his chair.

"Good Gad!"

It was Arnesson's astonished ejaculation that snapped the tension.

Markham went quickly round the table and bent over Professor
Dillard's body.

"Call a doctor, Arnesson," he ordered.

Vance turned wearily from the window and sank into a chair.

"Nothing can be done for him," he said, with a deep sigh of
fatigue.  "He prepared for a swift and painless death when he
distilled his cyanide.--The Bishop case is over."

Markham was glaring at him with dazed incomprehension.

"Oh, I've half-suspected the truth ever since Pardee's death,"
Vance went on, in answer to the other's unspoken question.  "But I
wasn't sure of it until last night when he went out of his way to
hang the guilt on Mr. Arnesson."

"Eh?  What's that?"  Arnesson turned from the telephone.

"Oh, yes," nodded Vance.  "You were to pay the penalty.  You'd been
chosen from the first as the victim.  He even suggested the
possibility of your guilt to us."

Arnesson did not seem as surprised as one would have expected.

"I knew the professor hated me," he said.  "He was intensely
jealous of my interest in Belle.  And he was losing his
intellectual grip--I've seen that for months.  I've done all the
work on his new book, and he's resented every academic honor paid
me.  I've had an idea he was back of all this deviltry; but I
wasn't sure.  I didn't think, though, he'd try to send me to the
electric-chair."

Vance got up and, going to Arnesson, held out his hand.

"There was no danger of that.--And I want to apologize for the way
I've treated you this past half hour.  Merely a matter of tactics.
Y' see, we hadn't any real evidence, and I was hopin' to force his
hand."

Arnesson grinned sombrely.

"No apology necessary, old son.  I knew you didn't have your eye on
me.  When you began riding me I saw it was only technique.  Didn't
know what you were after, but I followed your cues the best I
could.  Hope I didn't bungle the job."

"No, no.  You turned the trick."

"Did I?"  Arnesson frowned with deep perplexity.  "But what I don't
understand is why he should have taken the cyanide when he thought
it was I you suspected."

"That particular point we'll never know," said Vance.  "Maybe he
feared the girl's identification.  Or he may have seen through my
deception.  Perhaps he suddenly revolted at the idea of shouldering
you with the onus. . . .  As he himself said, no one knows what
goes on in the human heart during the last dark hour."

Arnesson did not move.  He was looking straight into Vance's eyes
with penetrating shrewdness.

"Oh, well," he said at length; "we'll let it go at that. . . .
Anyway, thanks!"



CHAPTER XXVI

HEATH ASKS A QUESTION


(Tuesday, April 26; 4 p.m.)


When Markham and Vance and I departed from the Dillard house an
hour later, I thought the Bishop affair was over.  And it was over
as far as the public was concerned.  But there was another
revelation to come; and it was, in a way, the most astounding of
all the facts that had been brought to light that day.

Heath joined us at the District Attorney's office after lunch, for
there were several delicate official matters to be discussed; and
later that afternoon Vance reviewed the entire case, explaining
many of its obscure points.

"Arnesson has already suggested the motive for these insane
crimes," he began.  "The professor knew that his position in the
world of science was being usurped by the younger man.  His mind
had begun to lose its force and penetration; and he realized that
his new book on atomic structure was being made possible only
through Arnesson's help.  A colossal hate grew up in him for his
foster son; Arnesson became in his eyes a kind of monster whom he
himself, like Frankenstein, had created, and who was now rising to
destroy him.  And this intellectual enmity was augmented by a
primitive emotional jealousy.  For ten years he had centred in
Belle Dillard the accumulated affection of a life of solit'ry
bachelorhood--she represented his one hold on every-day existence--
and when he saw that Arnesson was likely to take her from him, his
hatred and resentment were doubled in intensity."

"The motive is understandable," said Markham.  "But it does not
explain the crimes."

"The motive acted as a spark to the dry powder of his pent-up
emotions.  In looking about for a means to destroy Arnesson, he hit
upon the diabolical jest of the Bishop murders.  These murders gave
relief to his repressions; they met his psychic need for violent
expression; and at the same time they answered the dark question in
his mind how he could dispose of Arnesson and keep Belle Dillard
for himself."

"But why," Markham asked, "didn't he merely murder Arnesson and
have done with it?"

"You overlook the psychological aspects of the situation.  The
professor's mind had disintegrated through long intense repression.
Nature was demanding an outlet.  And it was his passionate hatred
of Arnesson that brought the pressure to an explosion point.  The
two impulses were thus combined.  In committing the murders he was
not only relieving his inhibitions, but he was also venting his
wrath against Arnesson, for Arnesson, d' ye see, was to pay the
penalty.  Such a revenge was more potent, and hence more
satisfying, than the mere killing of the man would have been,--it
was the great grim joke behind the lesser jokes of the murders
themselves. . . .

"However, this fiendish scheme had one great disadvantage, though
the professor did not see it.  It laid the affair open to
psychological analysis; and at the outset I was able to postulate a
mathematician as the criminal agent.  The difficulty of naming the
murderer lay in the fact that nearly every possible suspect was a
mathematician.  The only one I knew to be innocent was Arnesson,
for he was the only one who consistently maintained a psychic
balance--that is, who constantly discharged the emotions arising
from his protracted abstruse speculations.  A general sadistic and
cynical attitude that is volubly expressed, and a violent homicidal
outburst, are psychologically equivalent.  Giving full rein to
one's cynicism as one goes along produces a normal outlet and
maintains an emotional equilibrium.  Cynical, scoffing men are
always safe, for they are farthest removed from sporadic physical
outbreaks; whereas the man who represses his sadism and accumulates
his cynicism beneath a grave and stoical exterior is always liable
to dangerous fulminations.  This is why I knew Arnesson was
incapable of the Bishop murders and why I suggested your letting
him help us with the investigation.  As he admitted, he suspected
the professor; and his request to assist us was, I believe,
actuated by a desire to keep posted so that he could better protect
Belle Dillard and himself in case his suspicions should prove
correct."

"That sounds reasonable," acceded Markham.  "But where did Dillard
get his fantastic ideas for the murders?"

"The Mother-Goose motif was probably suggested to him when he heard
Arnesson jestingly tell Robin to beware of an arrow from Sperling's
bow.  He saw in that remark a means of venting his hatred against
the man who had made it; and he bided his time.  The opportunity to
stage the crime came shortly after.  When he saw Sperling pass up
the street that morning, he knew that Robin was alone in the
archery-room.  So he went below, engaged Robin in conversation,
struck him over the head, drove a shaft into his heart, and shoved
him out on the range.  He then wiped up the blood, destroyed the
cloth, posted his notes at the corner, put one in the house letter-
box, returned to the library, and called up this office.  One
unforeseen factor cropped up, however:--Pyne was in Arnesson's room
when the professor said he went out on the balcony.  But no harm
came of it, for though Pyne knew something was amiss when he caught
the professor lying, he certainly didn't suspect the old gentleman
of being a murderer.  The crime was a decided success."

"Still and all," put in Heath, "you guessed that Robin hadn't been
shot with a bow and arrow."

"Yes.  I saw from the battered condition of the nock of the arrow
that it had been hammered into Robin's body; and I concluded
therefore that the chap had been killed indoors, after having first
been stunned with a blow on the head.  That was why I assumed that
the bow had been thrown to the range from the window,--I didn't
know then that the professor was guilty.  The bow of course was
never on the range.--But the evidence on which I based my deductions
cannot be held as an error or oversight on the professor's part.
As long as his Mother-Goose joke was accomplished, the rest didn't
matter to him."

"What instrument do you think he used?" Markham put the question.

"His walking stick, most likely.  You may have noticed it has an
enormous gold knob perfectly constructed as a lethal weapon.*
Incidentally, I'm inclined to think he exaggerated his gout to
attract sympathy and to shunt any possible suspicion from himself."


* It was discovered later that the large weighted gold handle,
which was nearly eight inches long, was loose and could be easily
removed from the stick.  The handle weighed nearly two pounds and,
as Vance had observed, constituted a highly efficient "black jack."
Whether or not it had been loosened for the purpose to which it was
put, is of course wholly a matter of conjecture.


"And the suggestion for the Sprigg murder?"

"After Robin's death he may have deliberately looked about for
Mother-Goose material for another crime.  In any event, Sprigg
visited the house the Thursday night preceding the shooting; and it
was at that time, I imagine, that the idea was born.  On the day
chosen for the gruesome business he rose early and dressed, waited
for Pyne's knock at half past seven, answered it, and then went to
the park--probably through the archery-room and by way of the
alley.  Sprigg's habit of taking daily morning walks may have been
casually mentioned by Arnesson, or even by the lad himself."

"But how do you explain the tensor formula?"

"The professor had heard Arnesson talking to Sprigg about it a few
nights before; and I think he placed it under the body to call
attention--through association--to Arnesson.  Moreover, that
particular formula subtly expressed the psychological impulse
beneath the crimes.  The Riemann-Christoffel tensor is a statement
of the infinity of space--the negation of infinitesimal human life
on this earth; and subconsciously it no doubt satisfied the
professor's perverted sense of humor, giving added homogeneity to
his monstrous conception.  The moment I saw it I sensed its
sinister significance; and it substantiated my theory that the
Bishop murders were the acts of a mathematician whose values had
become abstract and incommensurable."

Vance paused to light another cigarette, and after a moment's
thoughtful silence continued.

"We come now to the midnight visit to the Drukker house.  That was
a grim entr'acte forced on the murderer by the report of Mrs.
Drukker's scream.  He feared the woman had seen Robin's body thrown
to the range; and when, on the morning of Sprigg's murder, she had
been in the yard and met him returning from the kill, he was more
worried than ever that she would put two and two together.  No
wonder he tried to prevent our questioning her!  And at the
earliest opportunity he attempted to silence her for all time.  He
took the key from Belle Dillard's handbag before the theatre that
night, and replaced it the next morning.  He sent Pyne and Beedle
to bed early; and at half past ten Drukker complained of fatigue
and went home.  At midnight he figured that the coast was clear for
his grisly visit.  His taking the black bishop as a symbolic
signature to the contemplated murder was probably suggested by the
chess discussion between Pardee and Drukker.  Then again, it was
Arnesson's chessman, and I even suspect him of telling us of the
chess discussion to call attention to Arnesson's chess set in case
the black bishop should fall into our hands."

"Do you think he had any idea of involving Pardee at that time?"

"Oh, no.  He was genuinely surprised when Arnesson's analysis of
the Pardee-Rubinstein game revealed the fact that the bishop had
long been Pardee's nemesis. . . .  And you were undoubtedly right
about Pardee's reaction to my mention of the black bishop the next
day.  The poor chap thought I was deliberately ridiculing him as a
result of his defeat at Rubinstein's hands. . . ."

Vance leaned over and tapped the ashes from his cigarette.

"Too bad," he murmured regretfully.  "I owe him an apology, don't
y' know."  He shrugged his shoulders slightly, and, settling back
in his chair, took up his narrative.  "The professor got his idea
for Drukker's murder from Mrs. Drukker herself.  She expressed her
imaginative fears to Belle Dillard, who repeated them at dinner
that night; and the plan took shape.  There were no complications
to its execution.  After dinner he went to the attic and typed the
notes.  Later he suggested a walk to Drukker, knowing Pardee
wouldn't remain long with Arnesson; and when he saw Pardee on the
bridle path he of course knew Arnesson was alone.  As soon as
Pardee had walked away, he struck Drukker and tipped him over the
wall.  Immediately he took the little path to the Drive, crossed to
76th Street, and went to Drukker's room, returning by the same
route.  The whole episode couldn't have occupied more than ten
minutes.  Then he calmly walked past Emery and went home with
Drukker's note-book under his coat. . . ."

"But why," interposed Markham, "if you were sure that Arnesson was
innocent, did you make such a point of locating the key to the
alley door?  Only Arnesson could have used the alley on the night
of Drukker's death.  Dillard and Pardee both went out by the front
door."

"I wasn't interested in the key from the standpoint of Arnesson's
guilt.  But if the key was gone, d' ye see, it would have meant
that some one had taken it in order to throw suspicion on Arnesson.
How simple it would have been for Arnesson to slip down the alley
after Pardee had gone, cross the Drive to the little path and
attack Drukker after the professor had left him. . . .  And,
Markham, that is what we were supposed to think.  It was, in fact,
the obvious explanation of Drukker's murder."

"What I can't get through my head, though," complained Heath, "is
why the old gent should have killed Pardee.  That didn't throw any
suspicion on Arnesson, and it made it look like Pardee was guilty
and had got disgusted and croaked himself."

"That spurious suicide, Sergeant, was the professor's most
fantastic joke.  It was at once ironical and contemptuous; for all
during that comic interlude plans were being made for Arnesson's
destruction.  And, of course, the fact that we possessed a
plausible culprit had the great advantage of relaxing our
watchfulness and causing the guards to be removed from the house.
The murder, I imagine, was conceived rather spontaneously.  The
professor invented some excuse to accompany Pardee to the archery-
room, where he had already closed the windows and drawn the shades.
Then, perhaps pointing out an article in a magazine, he shot his
unsuspecting guest through the temple, placed the gun in his hand,
and, as a bit of sardonic humor, built the house of cards.  On
returning to the library he set up the chessmen to give the
impression that Pardee had been brooding over the black bishop. . . .

"But, as I say, this piece of grim grotesquerie was only a side-
issue.  The Little-Miss-Muffet episode was to be the dénouement;
and it was carefully planned so as to bring the heavens crashing
down on Arnesson.  The professor was at the Drukker house the
morning of the funeral when Madeleine Moffat brought the flowers
for Humpty Dumpty; and he undoubtedly knew the child by name--she
was Drukker's favorite and had been to the house on numerous
occasions.  The Mother-Goose idea being now firmly implanted in his
mind, like a homicidal obsession, he very naturally associated the
name Moffat with Muffet.  Indeed, it's not unlikely that Drukker or
Mrs. Drukker had called the child 'Little Miss Muffat' in his
presence.  It was easy for him to attract her attention and summon
her to the mound by the wall yesterday afternoon.  He probably told
her that Humpty Dumpty wanted to see her; and she came with him
eagerly, following him under the trees by the bridle path, thence
across the Drive, and through the alley between the apartment
houses.  No one would have noticed them, for the Drive is teeming
with children at that hour.  Then last night he planted in us the
seed of suspicion against Arnesson, believing that when the Little-
Miss-Muffet notes reached the press we would look for the child and
find her, dead from lack of air, in the Drukker house. . . .
A clever, devilish plan!"

"But did he expect us to search the attic of his own home?"

"Oh, yes; but not until to-morrow.  By then he would have cleaned
out the closet and put the typewriter in a more conspicuous place.
And he would have removed the note-book, for there's little doubt
that he intended to appropriate Drukker's quantum researches.  But
we came a day too soon, and upset his calculations."

Markham smoked moodily for a time.

"You say you were convinced of Dillard's guilt last night when you
remembered the character of Bishop Arnesson. . . ."

"Yes--oh, yes.  That gave me the motive.  At that moment I realized
that the professor's object was to shoulder Arnesson with the
guilt, and that the signature to the notes had been chosen for that
purpose."

"He waited a long time before he called our attention to 'The
Pretenders,'" commented Markham.

"The fact is, he didn't expect to have to do it at all.  He thought
we'd discover the name for ourselves.  But we were duller than he
anticipated; and at last, in desperation, he sent for you and beat
cleverly round the bush, accentuating 'The Pretenders.'"

Markham did not speak for several moments.  He sat frowning
reproachfully, his fingers tapping a tattoo on the blotter.

"Why," he asked at length, "did you not tell us last night that the
professor and not Arnesson was the Bishop?  You let us think--"

"My dear Markham!  What else could I do?  In the first place, you
wouldn't have believed me, and would most likely have suggested
another ocean trip, what?  Furthermore, it was essential to let the
professor think we suspected Arnesson.  Otherwise, we'd have had no
chance to force the issue as we did.  Subterfuge was our only hope;
and I knew that if you and the Sergeant suspected him you'd be sure
to give the game away.  As it was, you didn't have to dissemble;
and lo! it all worked out beautifully."

The Sergeant, I noticed, had, for the past half hour, been
regarding Vance from time to time with a look of perplexed
uncertainty; but for some reason he had seemed reluctant to give
voice to his troubled thoughts.  Now, however, he shifted his
position uneasily and, taking his cigar slowly from his mouth,
asked a startling question.

"I ain't complaining about your not putting us wise last night, Mr.
Vance, but what I would like to know is: why, when you hopped up
and pointed at that plate on the mantel, did you switch Arnesson's
and the old gent's glasses?"

Vance sighed deeply and gave a hopeless wag of the head.

"I might have known that nothing could escape your eagle eye,
Sergeant."

Markham thrust himself forward over the desk, and glared at Vance
with angry bewilderment.

"What's this!" he spluttered, his usual self-restraint deserting
him.  "You changed the glasses?  You deliberately--"

"Oh, I say!" pleaded Vance.  "Let not your wrathful passions rise."
He turned to Heath with mock reproach.  "Behold what you've got me
in for, Sergeant."

"This is no time for evasion."  Markham's voice was cold and
inexorable.  "I want an explanation."

Vance made a resigned gesture.

"Oh, well.  Attend.  My idea, as I've explained to you, was to fall
in with the professor's plan and appear to suspect Arnesson.  This
morning I purposely let him see that we had no evidence, and that,
even if we arrested Arnesson, it was doubtful if we could hold him.
I knew that, in the circumstances, he would take some action--that
he would try to meet the situation in some heroic way--for the sole
object of the murders was to destroy Arnesson utterly.  That he
would commit some overt act and give his hand away, I was
confident.  What it would be I didn't know.  But we'd be watching
him closely. . . .  Then the wine gave me an inspiration.  Knowing
he had cyanide in his possession, I brought up the subject of
suicide, and thus planted the idea in his mind.  He fell into the
trap, and attempted to poison Arnesson and make it appear like
suicide.  I saw him surreptitiously empty a small phial of
colorless fluid into Arnesson's glass at the sideboard when he
poured the wine.  My first intention was to halt the murder and
have the wine analyzed.  We could have searched him and found the
phial, and I could have testified to the fact that I saw him poison
the wine.  This evidence, in addition to the identification by the
child, might have answered our purpose.  But at the last moment,
after he had refilled all our glasses, I decided on a simpler
course--"

"And so you diverted our attention and switched the glasses!"

"Yes, yes.  Of course.  I figured that a man should be willing to
drink the wine he pours for another."

"You took the law in your own hands!"

"I took it in my arms--it was helpless. . . .  But don't be so
righteous.  Do you bring a rattlesnake to the bar of justice?  Do
you give a mad dog his day in court?  I felt no more compunction in
aiding a monster like Dillard into the Beyond than I would have in
crushing out a poisonous reptile in the act of striking."

"But it was murder!" exclaimed Markham in horrified indignation.

"Oh, doubtless," said Vance cheerfully.  "Yes--of course.  Most
reprehensible. . . .  I say, am I by any chance under arrest?"



The "suicide" of Professor Dillard terminated the famous Bishop
murder case, and automatically cleared Pardee's reputation of all
suspicion.  The following year Arnesson and Belle Dillard were
married quietly and sailed for Norway, where they made their home.
Arnesson had accepted the chair of applied mathematics at the
University of Oslo; and it will be remembered that two years later
he was awarded the Nobel prize for his work in physics.  The old
Dillard house in 75th Street was torn down, and on the site now
stands a modern apartment house on whose façade are two huge terra-
cotta medallions strongly suggestive of archery targets.  I have
often wondered if the architect was deliberate in his choice of
decoration.



THE END





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