The Knights of Pythias invite you to relax.
This cordial message in white script ran across the green backs of the several wrought-iron benches anchor-bolted to the concrete walk that skirted the small urban park. At the moment, time and clime were hardly propitious to acceptance of the fraternal offer. A bleak dawn, lowering with a sleety mist, had already turned yesterday’s snow into a dingy slush. Yet one of the benches had a guest, and he appeared to be relaxed utterly. Sitting in the slumped position of one who has dozed off, the man’s hatless head of thick peppery hair sagged sidewise on his left shoulder. The drizzle, freezing as a crust on his coat collar, failed to disturb him. Nor was he bothered by the semicircle of sound — shuffling feet and muttering voices — that grew steadily around him in number and volume. Even the icy voice of Captain Thomas McFate left him totally unmoved.
McFate said, “All right. Cover the poor devil up.”
A police sergeant, who had already fetched a spare raincoat from the nearby cruiser, draped it like a stiff yellow shroud over the dead man’s head and forefront.
McFate next said, “Get rid of these damned gawks.”
Behind him a patrolman turned to face the crowd that had been gathering for the past fifteen minutes and gradually inching closer. “Okay, folks. Move along now. That’s it. Right on home or wherever you’re going or you’ll all catch cold and die.”
“A high-powered rifle job if I ever saw one,” McFate was saying to the sergeant. “At long range, too.” Half turning, he aimed his sallow, hollow-cheeked face across the street. “From somewhere in that hotel. Sixth or seventh floor.”
“Could be, sir. I’m no coroner but—”
“I’ll take odds, Hanson. As soon as Bergeron gets back here with this Damroth, I want you and a couple of men to go through that trap with a fine-toothed comb.”
Just then a second police cruiser ranged along the curb, sending a sheet of dirty water among the reluctantly dispersing onlookers, and parked behind the first. A lieutenant, surprisingly youthful, leaped out and opened the rear door to assist an elderly man who obviously didn’t desire assistance. He waved the young lieutenant aside and emerged by himself. Erect, he was a few inches over six feet and looked much taller because of his nearly excruciating thinness. His face was thin, too, and long to the point of fragility, but the wide mouth was strong and the dark eyes were alive with intelligence and a glint of humor.
McFate approached him, holding out his right hand. “Sorry to get you up so early, doctor.”
“Just call me mister,” said the newcomer. “All my doctorates are honorary. Useful on the Foundation letterhead but preposterous in normal human intercourse. Now, what’s the crisis?”
“Bergeron told you nothing?”
“The lieutenant was most discreet.”
McFate nodded grimly. “He was following orders, Dr. Damroth.”
“To the letter. And may I remind you again that I prefer to be addressed as mister.”
“Pardon me. I’m Tom McFate.”
“I know. I’ve lived in this city for twenty of my seventy years, sir, and in the course of that time I have familiarized myself through the newspapers with your name, your face, and your exploits. Whenever a journalistic account of the day’s news included the name of Captain Thomas McFate, there also was a crisis involving life or death. Generally death, and generally death due to homicide. That is the reason I have already asked you what crisis concerns you now. And more to the point, why does it concern me at this ungodly hour of such an inclement day?”
McFate’s cheeks grew perceptibly more hollow, as if he were suppressing the cold cackle that sometimes served him for laughter. “Well, Mr. Damroth, you’re right about homicide. We got a clean one.”
“Clean is not, I suppose, an incongruency.”
“A thirty-caliber slug is my guess. Through the heart. Death instantaneous.”
“Clean indeed,” said Mr. Damroth with a thin smile. From a silver case he took a honey-colored cigarillo. “Am I acquainted with the victim?”
“We don’t know. But he seemed to be acquainted with you.”
“Who is he? Or who was he?”
“We don’t know that yet either.” McFate held a match for Mr. Damroth’s cigarillo. “Nothing on him but an empty wallet with one of those cards, ‘Notify in case of accident.’ ”
Mr. Damroth bent toward the flame. “I can see my name on it.”
“That’s right, sir,” said McFate. “Would you like to take a look at him for I.D.?”
“Naturally.”
“This way then, doc — pardon me. Force of habit.”
Smiling, the old man accompanied McFate to the bench and watched with clinical intentness as the upper part of the raincoat was drawn back from the face. The clinical intentness remained but now was joined by the light of recognition. “You know him?” asked McFate.
“Very well, yes.”
“Who is he?”
But Mr. Damroth was posing questions to himself and to the cigarillo. “To go like this. A month or so before his time. Incredible. Poor Ketch. I wonder why?”
“That his name? Ketch?”
The old man nodded. “Yes, that’s his name. Harlan Ketch. Dr. Harlan Ketch. A superb mathematician.” He turned to look sternly at McFate. “In this case, the doctorate was not honorary.”
Hanson, the sergeant, said, “I knew he wasn’t no hood. Tell by his hands.”
McFate said to Hanson, “Tell me something I want to hear when you come back from that hotel across the street.” Then to Mr. Damroth: “Was he associated with the Foundation?”
“For the past ten years.”
“You said something about a month before his time. Or did I hear wrong?”
“You heard correctly,” said the old man, still musing with his own thoughts. “The unfortunate man was dying of cancer. He would have been dead within a month. Two months at the most.”
“When did you see him last, Mr. Damroth?”
“Just yesterday afternoon. At tea we had our usual discussion, jocular on my part but quite serious on his, about his mathematical approach to ethics.”
“A little out of my line.” McFate drew a crumpled handkerchief from the pocket of his yellow slicker. “Did he have a cold at the time?”
“A curious question, McFate.” The old man looked outward now with a searching interest. “The answer is no. In fact, he had been immune to the common cold for the past six months.”
“Some new drug at the Foundation?”
“One of the oldest drugs in the world, McFate. Morphine. It not only kills pain but in many cases it appears to kill the cold virus.”
“Be damned,” said McFate. “Well, that proves something, sir.”
He shook open the handkerchief and held it up. Near the center was a ragged hole the size of a dime. “We found this in his lap. Hanson thought Ketch had been shot while getting ready to blow his nose. I thought different. I guess I was right.”
Mr. Damroth appreciatively regarded the captain. “What a bizarre implication! The handkerchief was an effective target.”
“Held over his heart. White threads in the black fabric of his coat where the bullet entered. A man in a room in that hotel over there needed that kind of a target at dawn. With a scope on a rifle he could guarantee a clean job.”
“Clean, again. I see the meaning now. But why should Dr. Ketch have himself assassinated when he was so near death anyway? Have you considered that?”
“I’m considering it, sir. Intolerable pain maybe.”
“I think not. The morphine kept him tolerably comfortable. He assured me of this himself. He tired easily. He ate little. He was losing considerable weight. But, those were the only symptoms evident to me or his other colleagues, and we saw him daily.”
“Then it must have been something else. Insurance. Double indemnity for accidental death.”
Mr. Damroth slowly rotated the cigarillo between his lips and nodded. “Yes, that might be it. It sounds more in character.”
“Then he had insurance of that sort?”
“His financial arrangements were never a topic of discussion between us. I don’t know.”
“Was he married?”
“Yes. He remarried a few years ago. His first wife died shortly after he joined the Foundation. I hardly knew her. I hardly know his present wife — his widow, rather — but I deduced overtly that the union was not a huge success.”
Thirty minutes later, A.B.C. Damroth, president of the Tillary Foundation, and Thomas McFate, chief of the Homicide Division, debouched from a cruiser and made their way along a wet walk to the entrance of a modest apartment building. It required five well-spaced but prolonged pressings of a button under a mailbox bearing Ketch’s name to gain a response. And not a very civil one at that, until Mr. Damroth identified himself. Then the tone of sleepy annoyance left Mrs. Ketch’s somewhat hoarse voice to be replaced by gushing surprise and apology. The buzzer sounded to admit the oddly assorted pair, and they moved without a word down a long, echoing hallway to a brownish door marked B-22. At their knock it was opened by an opulently endowed woman in her early thirties who was still folding a fluffy negligee around herself while at the same time trying to do something with her orange-colored hair. As, moving backward, she ushered them into the foyer and thence into the living room, she again expressed surprise, apology, and even a feeling of honor in having the famous Dr. Damroth in her presence.
When the torrent of feminine exclamations and non sequiturs was over, Mr. Damroth said softly, “I’m afraid we have some bad news about Harlan.”
Mrs. Ketch didn’t quite get the gist. “I’m afraid he’s not here.”
McFate said, “We know that.” Then stiffly, “He’s dead.”
Mrs. Ketch looked momentarily baffled, but she didn’t sit down. “Dead,” she said, an expression just short of delight flitting across her face. “Well, that’s, that’s, that’s—” her eyes widened now in complete comprehension. “That was to be expected.” She sat down in a chair.
McFate’s jaundiced eyes studied her sternly. “You expected him to die today?”
“Not today necessarily.” Then the woman reacted to McFate’s icy stare. “Just who is this man, Dr. Damroth?”
The old gentleman performed the introduction and, while Mrs. Ketch was repeating the word “police” to herself, he added to McFate, “With your permission, may I ask her a few questions?”
“Take it. Sure.”
“I assume you were aware that Harlan was mortally ill.”
Mrs. Ketch, mollified by this approach, said, “Yeah, I knew. Cancer. I didn’t believe it at first. But then he had me talk to his doctor. It was incurable, just a matter of time.”
“When did he tell you about it, my dear?” said Mr. Damroth with a silkiness that caused McFate to suck in his cheeks.
“A couple of weeks ago.”
“I see. And why didn’t you believe him at first?”
“Because of all his rigamarole about the insurance policies,” said Mrs. Ketch. “Meek as a lamb, but sly as a fox when it suited him.”
McFate cleared his throat; Damroth prevailed, however, by saying, “Exactly how did a discussion of insurance make you doubt that your husband was a dying man?”
“It was so out of character,” replied Mrs. Ketch. “Or so in character. His ethical self, as he called it. Making me the sole beneficiary of his policy and cutting his darling daughter out.”
“And he actually did that?” Even the old man’s life-riven face betrayed another wrinkle: surprise.
“Yes, he did,” said Mrs. Ketch a bit defiantly. “And why shouldn’t he? After all, his daughter has a husband now, another poor bookworm like Harlan. But what do I have?”
“Do you recall the face amount of the policy?” asked Damroth.
“Twenty-five thousand.”
“Then that’s what you have, Mrs. Ketch.”
Her face softened with satisfaction. “Why, that’s right. So I do.”
McFate interposed. “Maybe more, with a double indemnity clause.”
“No, he didn’t have that in his policy, and they wouldn’t let him add it. But they put it in mine because I was so much younger.” She was proud of this.
“In yours?” Damroth took over again. “Then you now have an insurance policy, Mrs. Ketch?”
“Why, sure. For the same amount but with that indemnity thing. That was the deal. That’s what made me suspicious when he first brought it up.”
“And who, may I ask, is the beneficiary of your policy?”
“Who but his precious daughter? But I can always change that now. And don’t bet I won’t.”
Damroth smiled oddly. “I see. You agreed to take out a policy on yourself, naming Harlan’s daughter sole beneficiary, providing he made you sole beneficiary of his existing policy. Is that right?”
“Yes, but I’m no dummy. That ethics stuff he liked to spout — acting for the greatest good — I didn’t swallow that one little bit. Before I signed on the dotted line, I made him take me to his doctor. He had cancer all right, no doubt of it.”
Damroth remained thoughtfully silent, but McFate didn’t. “It wasn’t cancer that killed him,” he said.
“No? Then what did?”
“A rifle bullet.”
“You mean he was shot?”
“Yeah, that’s it.”
“Who by?” Mrs. Ketch was obviously intrigued.
“We don’t know yet. Any ideas?”
“Who, me? No. But what a funny coincidence! Just last night — spooky, very spooky.” Her frown was more perplexed than fearful.
Damroth interposed quietly, “What is the coincidence, my dear lady?”
“Well, he gave me this envelope that was written on the front of it not to be opened until after his death. Sealed with wax and all. And inside was this key and a note saying—” She stopped, lips pursed.
“May we see the note?” asked Damroth.
“Of course not,” snapped Mrs. Ketch. “Things like that are private between a man and his wife.”
“Indeed, yes,” the old man said, again with that odd smile.
Back in the cruiser five minutes later, McFate said to Damroth, “This is the first time ethics ever came into a case with me. Could you educate me as we drive along?”
The old man chuckled. “On that subject, I’m not too well educated myself, but perhaps I can communicate the gist of Ketch’s theory. He was a mathematician, not a philosopher. But since mathematics is a logical science, the pure practitioner invariably begins to think that equations can be devised for the chief aspects of philosophy, which are said to be logic, aesthetics, and ethics. Descartes once wrote, ‘Omnia apud me mathematica fiunt’ — with me everything turns into mathematics. It was the same with Harlan Ketch.”
McFate said, “I hear you but that’s all.”
“You were probably exposed to algebra once. You remember the simple equation a + b = c. Well, Ketch used equations like that, though much more complex, to determine a course of action when he was faced by a problem. In the simple algebraic example, a might represent two apples and b might represent three apples. Thus, when you saw the symbol c, you knew it meant five apples. If squared, it became twenty-five apples. Now in Ketch’s immediate history, he may have used c, let’s say, for cancer and perhaps d for death, t for the time remaining, m for money, h for his daughter’s welfare—”
“Mr. Damroth, I’m lost. Why h for his daughter’s welfare instead of d or w?”
“Well, not d because we assigned that to death. Possibly w, though. I picked h, since her name is Honora.”
“She’s married?”
“Yes, to a grammar school teacher named Speares whom I’ve met possibly twice. Amiable lad. They’re both quite young.”
“And not much liked by the widow.”
“Evidently. In fact, I believe it was this antagonism, especially between the... ah... widow and Honora that precipitated the wedding. The young people planned to wait until Bill — that’s Speares’s first name — took his master’s degree. But the situation in the Ketch household grew intolerable. Finally, but reluctantly, Harlan gave his consent. His only child, you know, and she wasn’t more than eighteen at the time. Still, unlike so many young-love matches, this one has turned out well. I gather that Harlan helped them out with a little money from time to time. Very little, however, for Mrs. Ketch apparently was voracious.” The old man produced another cigarillo. “Enough of this gossip, McFate. Let’s return to your education.”
“Not now, sir, thank you.” The cruiser was pulling to the curb in the city’s financial district. “I’ve got to learn something here first.”
“Where in the world are we?”
“At the headquarters of an insurance company. Want to come in?”
“I must if my own education is to be complete.”
After passing through a receptionist and several white collar personnel of progressively higher rank, Damroth and McFate finally gained access to a glass enclosure occupied by an assistant vice-president named Melrose. After listening to the police request, he spoke on an intercom. A few minutes later a pretty girl placed two perforated cards on his desk and, with a polite smile, withdrew. Melrose exchanged the glasses he was wearing for a pair from his pocket and examined each card quickly.
“Ketch, Mrs. Harlan B. parentheses Melanie,” he said, “is insured for twenty-five thousand dollars. A clause doubles this sum in case of accidental death, except when such death occurs in a nonscheduled aircraft flight. The premium was paid in advance two weeks ago for a full year.
“Ketch, Mr. Harlan B., for Broadbent, was insured by us in the same amount, but without the so-called double indemnity clause, until four days ago. At that time, he terminated the policy and was paid its accumulated cash value of seven thousand three hundred and forty dollars and twenty-six cents. By check. The check was honored the next day by the Pioneer Bank and Trust.” Melrose dropped the cards and removed his glasses. “Does that answer your questions, gentlemen?”
“All but two,” said McFate. “Who is the beneficiary on Mrs. Ketch’s policy?”
Melrose picked up a card, replacing glasses. “Speares, Mrs. William S. parentheses Honora.”
“And on the other policy?”
“Speares, Mrs. — no, that had been changed. At the time of termination, the sole beneficiary was Ketch, Mrs. Harlan B.”
Again outside the building, Damroth said, “McFate, I begin to discern the shadow on an equation involving logic and ethics.”
“Then stick close.”
“I also believe I know where we’ll go next. The Pioneer Bank and Trust.”
“I’ll say one thing, sir. If I learned algebra as fast as you pick up police procedure, I’d be a deputy commissioner tomorrow.”
They arrived at the bank a few minutes before ten o’clock and approached a starchy blue-haired lady sitting nearest the door behind a mahogany railing. The nameplate on the desk identified her as second assistant treasurer. After a keen glance at Damroth’s cigarillo and McFate’s badge, she murmured something about a Mr. Kessler and left to go to another desk, a larger desk three rows back. When she returned, she pointed to it, saying Mr. Kessler would see them. This gentleman, brisk and prematurely bald, to judge from his youngish unlined face, proved to be the assistant treasurer, and he got down to the business at hand immediately.
“Dr. Harlan Ketch cashed a check here in the amount mentioned just four days ago,” said Kessler, consulting memoranda and several files that seemed to be miraculously at his fingertips. “He did not deposit any of the cash. In fact, he closed out his savings account of two hundred and three dollars and eighty-three cents.”
“And walked out with all that cash?” asked McFate.
“Not all of it. Five thousand he took in twenty-dollar bills. We provided the heavy manila envelope. The approximate remainder was converted into a treasurer’s check in the amount of twenty-five hundred dollars. I handled the transaction personally, and I particularly remember it because of his insistence on the date.”
“Who was named on the check?” asked McFate.
“George Tinker. It seems Dr. Ketch hoped to consummate a business deal with Mr. Tinker and wanted the check to bind it.”
Damroth spoke around the cigarillo. “You referred to the date. I presume that means the date of the check.”
“Oh, yes.” Kessler consulted another document. “He was quite insistent that the check be dated ahead to — yes — it did not become negotiable until today.”
“I wonder,” said Damroth, that odd smile on his old face, “if that check has already been cashed this morning, Mr. Kessler.”
“The banks have only been open an hour, sir. But... well, let me see. With a treasurer’s ticket for that sum we usually get prompt reports.” He lifted a phone, spoke, waited, spoke again with a frown of faint surprise, and hung up. “Dr. Ketch and Mr. Tinker are early birds, gentlemen. Mr. Tinker cashed the check at nine fifteen with the Merchant Savings. We must assume the business deal was favorably concluded.” He smiled with commercial pleasure.
“Irrevocably concluded, at least,” said Damroth, smiling oddly.
An hour later Captain Thomas McFate’s cramped office was the scene of a report, a coffee break, and an analytical conversation. The report came from the youthful lieutenant named Bergeron on the results of a preliminary investigation he had conducted in the hotel across the street from the Knights of Pythias bench. Room 727 had been rented the previous afternoon to one W. Collins who had checked out this morning shortly after daybreak.
Nobody could recall what W. Collins looked like because he checked in at the latter part of the afternoon, when, as usual, a lot of people were checking in. And he checked out during the last few minutes of the night clerk’s shift when the night clerk was half asleep and trying to keep his eyes open just long enough to finish the essential closeout paperwork.
“Mr. Collins is a pro,” said McFate after Bergeron left.
“Mr. Collins is also Mr. Tinker,” said Damroth.
“And a couple of other guys, too.”
A sergeant brought in two containers of coffee and four sugared crullers. The practical man and the academic man, looking out the grimy window at the leaden day, sipped and chewed for a few minutes in silence. Then the practical man said, “How would a gent like Dr. Ketch ever find a way to meet a hood like this Tinker?”
The academic man said, “That thought has occurred to me, too. A year ago Harlan’s interest in the inevitable logic of numbers as they appear in games of chance turned him toward the gambling tables. Purely experimental, I assure you. The sums wagered were small, and the profits small, too. But he definitely had worked out some sort of system, and for a few months used the gambling dives as a laboratory. The system was not perfected, however, as I recall. He told me once that the house limit in most places prevented numbers from progressing to a real conclusion.”
“This Ketch was quite a thinker.”
“The treasurer’s check was typical,” said Damroth.
“Tell me about it.”
“As it appears to me, the key to the transaction between Ketch and Tinker was the payment. Each had to be sure that the other didn’t default on his part of the deal. Obviously, nobody could pay Tinker for assassinating Ketch at his own request, except Ketch himself. And since this type of agreement isn’t exactly adjudicable, Ketch could not afford to pay in advance. Men like Tinker, I imagine, might not honor the contract. Hence, Ketch devised a way to pay Tinker only after the service was satisfactorily rendered. That accounts for the time — before the banks opened today. And the predated treasurer’s check.”
“If Ketch was still alive when the banks opened, he would have stopped payment on the check. That it?”
“Correct. In the business world this is called incentive. Ketch gave Tinker a strong incentive to kill him this morning before the banks opened.”
McFate swallowed more coffee and then suddenly sat erect. “Incentive, that’s the word. He also must have given this Tinker a strong incentive to kill Mrs. Ketch.”
“Correct again.” The old man wiped crumbs from his chin. “You’re getting a knack for these ethical equations, McFate.”
“A good gamble. Seventy-five hundred bucks against fifty thousand.”
“With his daughter as sole heir. A nice equation. A slightly postdated check, a slightly postdated death, plus an ethical assassination equals an estate for the deserving daughter minus any possible litigation from the undeserving wife.”
“All right, sir,” said McFate impatiently. “But now that the sitting duck is dead, how can he pay off Tinker for killing Mrs. Ketch?”
“Tinker will collect from Mrs. Ketch herself,” Damroth replied.
“Five thousand bucks in a manila envelope. She doesn’t look the type. He’d have to kill her for it.”
“And he will. That’s his business, isn’t it?”
McFate was now on his feet. “I’m beginning to get it, yeah. The key he gave her last night. And that note.”
“In an envelope not to be opened until after his death. He judged her well, didn’t he? Timed it well, too. When she broke the wax seal last night and read the note, it was probably too late to use the key. But she would have used it this morning whether Ketch was dead or not. Greed and curiosity. She’s probably using it at this very minute.”
“You think it’s a key to a safety deposit box?”
“Definitely not. If I know my Dr. Harlan Ketch — and I’m growing to know him better today — he placed that manila envelope in a baggage locker at some out-of-the-way depot or bus station, a place that would be fairly deserted after the morning commuters left. A place, in short, where Mr. Tinker could work unmolested.”
McFate reached for the phone and issued a command to the switchboard. To Damroth he said, “Maybe I can get her at home before she leaves.”
Damroth smiled. “I’d wager it’s too late.”
It was. Nobody answered.
Therefore, McFate took the next practical police step. With a coded municipal map spread out on his desk and the phone still in hand, he began assigning men to every location within the city limits that had public baggage lockers, adding a personal description of Mrs. Ketch.
“She’s one of these orange-haired dames about thirty-five,” he was saying for the sixth time when he stopped abruptly to listen, his face cold and expressionless. Then he hung up and swiveled his chair around to face Damroth. “He got her. With a knife. They just found the body of an orange-haired dame in an alley near Brixon bus terminal. That’s the end of the line.”
Damroth said nothing for a moment. Taking another cigarillo from his case, he placed it thoughtfully between his yellow teeth. “Well, sir,” he finally said, “the ethical question that now comes to my mind is this: does crime sometimes pay? Or shouldn’t I ask?”
“Sometimes,” answered McFate. “Why?”
“I’m trying to put myself in Ketch’s frame of mind when he was working out his equation. He must have considered the fact that the insurance company would try to invalidate the policy on the basis of collusion.”
“That’s automatic, under these circumstances,” said McFate. “But, of course, they’ve got to prove it.”
“It takes at least two to collude, doesn’t it?”
“That’s what the lawyers say.”
“Then all that has to be done is find Mr. Tinker.”
“That’s all.”
“To humor an old man, would you tell me candidly what your chances are?”
“Off the record, yeah. About one in a hundred. Hell, one in a thousand.”
Damroth nodded as if this confirmed a tentatively held opinion. Then, lighting the cigarillo, he said, “You know, McFate, I’m just learning to appreciate that mathematics is a terrifying science.”