Ellery Queen’s Mystery Magazine. Vol. 105, Nos. 3 & 4. Whole Nos. 640 & 641, March 1995

The Mathematics of Murder by Michael Gilbert

Legal settings often enter into Michael Gilbert’s crime fiction, and it is a profession the author, himself a London solicitor, knows well. Mr. Gilbert was a writer, however, long before he became a lawyer. His first book was completed in 1930 (though not published until much later) and he was one of the founding members of the Crime Writers Association of Britain. His new story for us introduces a senior managing clerk to a firm of London solicitors who seems to know, or be able to figure out, just about anything...

Friday, March 18th, was a date Hugo Bracknell was destined to remember. Having missed by two minutes the fast 6:30 train from Liverpool Street to Colchester, he had been forced to take, instead, the 6:55 train on the Braintree line. Anxious study of the timetable had shown him that it would, if it ran to time, reach Witham at 7:55. The snag was that it seemed to be a commuter special, stopping no fewer than nine times before it reached Shenfield; discharging at each of these stops a number of businessmen on the way back to their residences at Chadwell Heath, Gidea Park, Brentwood, and other portions of the suburban sprawl which separated East London from Essex.

After Shenfield it seemed to get a move on, stopping only at Ingatestone, Chelmsford, and Hatfield Peverel before reaching Witham.

It was important that it should run to time. He had been invited to spend the weekend with his aunt. She was a formidable old lady who liked to dine promptly at eight. If the train dallied, or there was any difficulty over picking up a taxi at the station, he was going to keep her from her grub. Unthinkable.

“Then don’t think about it,” he said. “Either you make it or you don’t. So stop worrying.”

His thoughts reverted to personal matters; and there was much to think about.

For he had reached a milestone.

After leaving Oxford he had been allowed two years to widen his horizons, to enlarge his knowledge of human nature, to improve his mind; in fact, to enjoy himself, before plunging into the job for which he had been destined from birth.

He was now, and had been for the past ten days, articled to his father, Bob Bracknell, who, with Francis Fearne, constituted the partnership of Fearne and Bracknell, solicitors, in Little Bethel, an odd backwater near the northern end of Tower Bridge, flanked by the offices and warehouse of Ridolfi Brothers on one side and on the other by the Roaring Forties public house. When spoken of in the City — and for a small firm they were spoken of a good deal — they were naturally referred to as Fern and Bracken and strangers sometimes wrote to them under this name. It made no difference. The postmen all knew them.

Ingatestone was briefly stopped at, and left behind them. Three stations to go. Still only 7:45. Relax. Plenty of time.

Fearne and Bracknell was not a big firm. Far from it. But they had that mysterious, indefinable, unchallengeable something. Reputation. People said of them, “Fern and Bracken. Very practical firm, that. Get on with the job, you know. No highfalutin law about them, but sound. Break the law? Of course not. They’re not sharp. Just reliable.”

Hugo sometimes wondered how much of this reputation stemmed from their senior managing clerk, Horace Piggin. He had met Mr. Piggin on many occasions when visiting the office in his school days and had sat kicking his heels in the waiting room whilst his father dealt with some long-winded client. Mr. Piggin had put himself out to entertain the boy.

He remembered one conversation which had taken place when he was in his last year at Rugby. Mr. Piggin had set the ball rolling by asking him why he had decided to take up law. With a brashness which made him blush when he thought about it, he had said, “Oh, I knew Dad would give me my articles here. And after all, being a solicitor isn’t difficult. Look at some of the types you see doing it.”

Mr. Piggin had agreed with him, gravely.

“Of course, I don’t mean you, Piggy. And I don’t mean this firm. We’re different. I mean the stooges in Lincoln’s Inn and Bedford Row who read it all up in books and copy it out.”

“That’s one fault,” Mr. Piggin had agreed, “that you’ll not find in this firm. We have hardly a law book in the place.”

“But surely, Piggy, you must want to look things up sometimes.”

To which Mr. Piggin’s memorable reply had been, “If reference to the authorities is required, I trot along to the public library, scribble down the information, and trot back with it.”

The thought of Mr. Piggin trotting up Tower Bridge Road with his white hair streaming in the wind had enchanted Hugo.

Chelmsford. A rather larger place. Might that mean a longer stop? But no. Quite a few men got off the now nearly empty train, but there were no passengers waiting to get on. Hatfield Peverel next. No one got off, no one got on. Excellent. Minutes were important.

It occurred to Hugo, who was in the rear coach, that he could save a little time on arrival at Witham if he moved up to a point nearer the centre. There was no difficulty about this. The train consisted of twelve coaches in three blocks of four, and it was possible to move from one block to the other. He passed two men, one at either end of the first carriage. The next two were empty. In the fourth carriage there were a woman with a dog and a man and a girl who were sitting close together and getting on with some very private business. Hugo skirted them and passed through the cubicle which joined the rear four carriages to the central four.

Again an empty carriage. In the next, there was one man slouched in his seat and blocking the door in the centre of the carriage that Hugo had been planning to use. As the train jerked to a stop, the man rolled over and lay across the two seats, staring up at the roof with a puzzled look on his face, and Hugo saw the narrow wound in the back of his neck with the dark blood oozing out of it.

It was instinct that led his hand to the handle of the door. Must have help. Must have air. Get the door open. He stumbled onto the platform and stood holding on desperately to the handle.

The guard shouted, “Stand away,” an order which Hugo was unable and unwilling to obey. A louder shout brought out the station master, peremptory and indignant at the sight of a young man, apparently drunk, holding himself up by the door handle.

By this time the guard had come up. Hugo used his free hand to wave towards the interior of the carriage.

After that, things happened slowly.

First the arrival of a local constable. Then a more senior policeman. Then the business of evacuating the few remaining passengers and shunting the train onto a lay-by. Then the arrival of photographers and a police surgeon and a string of questions which Hugo answered as best he could while trying to control his rebellious stomach. Finally the body was moved and Hugo, his identity established and checked, was at last allowed to take possession of the taxi he had secured and to depart and endeavour to placate his aunt.

He was able in the circumstances to excuse himself from carrying out his projected weekend visit; but he further disrupted his aunt’s domestic arrangements by asking to be called at six-thirty. He reached his office at nine o’clock. Fearne and Bracknell — old-fashioned in this as in everything else — worked on Saturday mornings and he arrived, as planned, before either of the partners put in an appearance and made his way straight to the sanctum of their managing clerk. It was Mr. Piggin’s advice and support that he wanted.

“So you are the young man,” said Mr. Piggin, “described, but tactfully unnamed, whose exploits I have been reading about in the morning papers.”

“That’s me, Piggy,” said Hugo. “And I’ll tell you something mighty strange. Nobody I encountered seemed in the least surprised at what I told them. Disturbed, excited, even shocked, but not surprised. The official people at Witham were clearly keeping something back, and my aunt, when she’d heard my story, simply closed her mind to it and discussed a problem she was having with the committee of the Women’s Institute. But she knew something. I’m sure of it.”

Mr. Piggin seemed to be faintly amused. He said, “If you had opened a newspaper three or four months ago you’d have read little or nothing about indiscretions in Whitehall or massacres in Kurdistan. The front page of the paper and other pages as well would have been full of the activities of the creature they christened the Knifeman.”

“Are you telling me that yesterday was not the first—”

“It was the sixth known occasion on which he has struck. You have not seen one of today’s papers? No. Well, I can assure you that he has regained his position on the front page. Was there nothing in the papers where you were?”

“The Italian press don’t pay much attention to crime in other countries. They’ve got plenty of their own. Though now that you mention it, I do recall a brief comment about a serial murderer. When did it all start?”

Mr. Piggin had been turning over the pages of his working diaries. He said, “The first one was sixteen months ago, on Tuesday, November tenth. The next, near the beginning of last year, on Friday, February nineteenth. Then on June fifteenth, August thirteenth — which was also a Friday — and on Monday, October eleventh.”

“How did they know that these were all the same man?”

“It could not, of course, be known,” said Mr. Piggin precisely, “but the evidence that it was so was almost conclusive. His procedure in every case was the same. He waited until he was alone with one other man in the carriage, walked up to him as though he was making for the door, and struck him on the head with a loaded stick or life preserver. As his victim crumpled up he produced his second weapon. This the pathologists, in every case, thought to be a long, slender surgical-type lancet. He drove this upward, through the back of his victim’s neck, into his brain, killing him instantly.”

Although Mr. Piggin was speaking flatly, as though he was explaining a legal problem, his words recalled the horror of the moment and Hugo found himself shuddering. He said, “The man who does this — he must be mad — but he must also be wholly ordinary in appearance, so as not to excite any suspicion of his intentions.”

“Wholly so. And this agrees with the only description we have of him.”

“You mean — he was seen—”

“Exercise a little patience,” said Mr. Piggin, “and I will endeavour to explain. After five attacks, commuters — as you can imagine — became careful. They took precautions. They travelled, where possible, in parties. Then came this period of more than three months in which nothing happened. Precautions were relaxed — prematurely, you may think — but such is human nature.”

Mr. Piggin was now studying his current year’s diary.

“On Thursday, January twentieth, a Mr. Osbaldistone was travelling to Bures, where he planned to spend a long weekend with an old friend. This involved changing at Marks Tey. The train was slowing as it approached Kelvedon, the station before Marks Tey, when he suddenly realised that he was alone in the carriage with one other man and that this man was advancing on him, with his left hand in his overcoat pocket. The consciousness of his peril deprived him, he said, of the power to move or shout. He was mesmerised. Most fortunately, at that moment a young man — the son of the house that he was visiting — came through the connecting vestibule into the carriage. He said, ‘Mr. Osbaldistone, isn’t it? I guessed it might be you. You’re spending the weekend with us.’ By this time the other man had opened the carriage door and departed. When Mr. Osbaldistone related his experience, as he did, with some embarrassment, that evening, his hosts impressed on him that it was his duty to communicate with the police. Whether he was right or wrong in his suspicions, it was at least possible that he was the first man to come face-to-face with the killer and live to tell the tale. ‘You must describe him,’ they said.”

Because the first victim, a Mr. Mathieson, had worked in Stepney and lived in Romford, both places being in No. 2 Area East, the case had been assigned to the head of that area, Chief Superintendent Oliphant. He had delegated the routine handling of it to Chief Inspector Mayburgh at Cable Street, and it was to Mayburgh that Mr. Osbaldistone duly reported.

Mr. Piggin said, “I gathered from them — Osbaldistone is, by the way, a client of this firm and an old friend of your father’s — that it was not a happy experience. I’m sure he did his best, but it amounted to very little. He said, quite reasonably, that he wasn’t examining the man’s face. His attention was fixed on his left hand, which appeared to be drawing some sort of weapon out of his coat pocket. He couldn’t see more than the handle, but yes, it might have been a life preserver, something like that. ‘Or the whole thing might have been your imagination,’ says Mayburgh. ‘Yes, it might have been,’ Osbaldistone agreed. ‘But I was too worked up to notice precise details.’ All this was in answer to a series of bad-tempered questions and grunts. The inspector considered that Mr. Osbaldistone had no right to get worked up. He should have been making a careful inspection of his assailant.”

“Mayburgh sounds a bit of a brute,” said Hugo.

“He’s an old-fashioned rhinoceros who tries to arrive at the truth by butting at it, head first. His second-in-command, Inspector Barley, on the other hand, is what you might call — hum — a scientific policeman.”

Hugo gathered from Mr. Piggin’s tone that his description of Inspector Barley was not intended to be entirely complimentary.

“In the end,” he said, “he got nothing out of Mr. O. except that his presumed attacker looked, in every way, like a normal City worker. Pale face, clean-shaven, indeterminate features, no distinguishing marks. When he said that the man was ‘ordinary’ he had said it all. His failure on that occasion may account for the inspector’s wish to question you.”

“For God’s sake! Why me? I never even saw the man.”

“The working of the inspector’s mind is a closed book to me. All I can tell you is that there was a message on our answer-phone when I arrived that he would like to see you at ten o’clock. It’s a quarter to ten now. Better not keep the rhinoceros waiting.”

When Hugo was ushered into Mayburgh’s office he saw a man who could have been nothing but a middle-ranking policeman. One who had started at the bottom and crashed upwards not caring what toes he trod on. The red face, bristling hair, and angry eyes said it all. He barked at Hugo to sit down and opened fire with the observation that Hugo should not have disturbed the body.

“But I had to be certain the man was dead.”

“Were you in any doubt about it?”

“Not really, no.”

“Then why did you touch him?”

“If I hadn’t, he’d have fallen onto the floor. You wouldn’t have wanted that, surely.”

“It’s not what I want, it’s what the medical experts want. They can make useful deductions if they find the body exactly as it was at the point of death.”

This seemed like nonsense to Hugo, but had evidently gained the approval of the young man in glasses who was sitting quietly in the corner. The scientific Inspector Barley?

“Reverting to a point where you might be able to help us. It is fairly clear that the attack took place between Ingatestone and Chelmsford and that the assassin left the train at Chelmsford. Did you take any note of the people who got off?”

“I was in the rear, carriage at the time, but yes, I did look out. I was anxious about the possibility of the train being held up and I was glad to see that no one was waiting to get on.”

“It’s the people who got off that I’m interested in.”

“Well, there were a fair number of them. All men. The usual home-going crowd, I thought.”

“Nothing more?”

“I’m sorry. No.”

“If members of the public kept their eyes open and their wits about them,” said Mayburgh, “we might make some progress.”

This not being a question, Hugo did not feel called on to answer it, and five minutes later he had been bundled out of the room. As he closed the door, Mayburgh said to Inspector Barley, “What did you make of that? Was he holding out on us?”

“I made nothing of it, because there was nothing to make.”

“He’s old Bracknell’s son. He’s just joined the firm. And you know what they’re like. Do anything they can to obstruct the police.”

“I don’t think,” said Barley primly, “that we can pin anything onto this young man if he only came back to England a fortnight ago.”

“I suppose that’s right,” said Mayburgh.

It was evident that he was in some awe of his learned junior.

Hugo, meanwhile, had reported the outcome of this unsatisfactory interview to Mr. Piggin.

“The man’s a hog,” he said. “If he’d been even remotely civil, I might have given him one useful piece of information. I’m fairly certain I recognised the man who was killed.”

“Did you indeed?” said Mr. Piggin. “That could be of major importance.” He sounded faintly aggrieved. His own sources of information were wide and various. It piqued him that a newcomer should know something that he did not.

“I spent six very enjoyable months at Perugia University and got to know a lot of the students and the younger professors. We used to meet for drinks in the evening and — well, you know how people talk. This particular man — an economics don called Carlo Frossinone — told me — I think he was three parts drunk at the time because the next day he denied that he had ever said it — that he had been approached by the capo of the local mafia to do a job for them and that he’d refused and was now in their black books. He sounded rather proud of this, as though it was a distinction.”

Mr. Piggin, who had been listening carefully, had now extracted, from a locked drawer, his private address book. He was thumbing through the section under the letter A.

“Arbuthnot,” he said. “That’s the man. Colonel Arbuthnot. I’ll give him a ring. I’m sure he’ll be very interested in what you’ve told me. It may take a day or two to get hold of him. He’s much abroad.”

On the surface, the next few days were uneventful, but there was a disturbing undercurrent to them. The opposition, spearheaded by a claque of members with constituencies in Essex, raised a number of questions in Parliament. The Home Secretary sidestepped them with practised agility, but was not as easy as he managed to appear; and his uneasiness was passed down, in a series of minutes, to the assistant commissioner, and through him to Chief Superintendent Brace, and, finally, to Superintendent Oliphant, who arrived at Cable Street with an ultimatum in his pocket.

“Bring me up to date,” he said. “Particularly with regard to this last episode.”

“We’ve got a certain way,” said Mayburgh cautiously. “We’ve circulated a photograph of the victim, which produced a number of identifications, none of them reliable, I’m afraid.”

“Had the man no papers on him?”

“Yes. He had an Italian passport. We telexed the details to Interpol, who say that the details in it were false and the whole passport a clever piece of forgery.”

“And that’s all?” said Oliphant.

“All except an enormous amount of routine work,” said Mayburgh rather bitterly. He indicated the six fat folders on a side table, rocks in a torrent of other documents. “The real trouble is that the carriages concerned were of the open type, with thirty-two seats and a gangway down the middle. At the start of a commuter rush, all the seats would be occupied and a number of people standing in the gangway. As people got off, the standers would take over the seats and be replaced by other passengers coming in from even more crowded carriages. Our enquiry produced forty-one people who thought they might have been in the carriage concerned. All of them had to be questioned and their answers recorded.”

By the time he had finished this spiel Mayburgh was even redder in the face than usual. Oliphant said, “I’m not suggesting that you haven’t done your best with the resources at your disposal. But the official view is that the enquiry needs wider handling. I’m to tell you that unless you can produce concrete results in the next fortnight, the matter will have to be handed over to Central. Meanwhile, I’ll alert all the other stations in the area to give you any help you need. So, if you do chance on a line, you can hunt it hard.”

When he had departed, it was Inspector Barley who broke the silence. He said, “I feel, sir, that the first thing to do is to subject the case to a complete reassessment. If I might take all the papers home and be allowed a few days off routine duty...”

“You’ll need a pantechnicon to get that lot home,” said Mayburgh sourly. “But go ahead.”

Barley was not dismayed. He foresaw days of a kind of work that was much to his taste.

On that same day, Hugo was summoned to the office of Colonel Arbuthnot. It was in a building which overlooked St. James’s Park and seemed to be connected with the Ministry of Pensions. The colonel dismissed a pretty, dark-haired girl to whom he was dictating and listened with interest to what Hugo had to tell him. (The girl, who had managed to arrange things so that she could overhear what went on in the colonel’s office, also listened with interest and spent some time that evening on the telephone.)

“What you say,” said the colonel, “fits in with our information from other sources. You spent some time in Italy, I believe. Then I expect you know how the drug trade is organised there.”

“I know what every schoolchild seems to know. That the raw opium comes across from Turkey and is processed into morphia and heroin under the auspices of the mafia, who attend to its export and sale.”

“Remarkably well-informed schoolchildren,” said the colonel. “The one point they may not have appreciated is that the mafia control the export of the hard stuff to North America and to many European countries — Belgium in particular. But they do not, at the moment, handle its export to this country, though they would much like to do so. If the victim of this latest killing was, in fact, Carlo Frossinone — equipped with a forged passport and having overcome his reluctance to help—”

“Or, more likely, been frightened into helping.”

“Quite so. Then it follows that the assassin was one of the London-based gangs which do handle the import and sale of hard drugs and would do anything to stop the mafia muscling in.”

“And the method of killing was designed to suggest that it was the work of the Knifeman?”

“Typical camouflage. And now that we appreciate the position, we can get the Metropolitan Police Drugs Squad and the Customs and Excise Investigators — a very shrewd bunch — onto the killer. Working together they should soon be able to lay hands on him. And I am much obliged to you—”

“Different sort of man to Mayburgh,” said Hugo, reporting to Mr. Piggin. “Very pleasant, I thought.”

“So I’ve always found,” said Mr. Piggin. “I wound up his father and his grandfather. Talking of which, I’ve got a job for you. An old lady called Mrs. Trumpington — a new client, so handle her carefully — wants to make a will. She is bedridden and cannot come to us, so you are to go round tomorrow and take her instructions. Here’s the address. Carlton Mansions—”

As he surveyed Carlton Mansions Hugo surmised, from the appearance of the building, that Mrs. Trumpington must be a lady of means. His surprise was increased by the appearance of the man who opened the door to him and ushered him into a handsomely furnished flat. Had he met him casually he would have taken him for a senior businessman, a man of authority, who would have taken the chair at board meetings. A second equally impressive but younger man was standing with his back to the fire.

Hugo, hearing the door click shut behind him, had the uncomfortable feeling that he had walked into something that it might be difficult to get out of.

Before he could open his mouth, the older man said, in a voice that matched his appearance, “Let us cut all corners. There is no Mrs. Trumper here.”

“Trumpington,” amended the younger man.

“Trumpington. Yes. She was, in any event, a myth. I am glad your father sent you, because it is specifically with you that we wished to speak. To discuss with you a professor of economics at Perugia University called Carlo Frossinone.”

Now how the devil, thought Hugo, would they know anything about him. Then he remembered the black-haired girl in Colonel Arbuthnot’s office and ceased wondering.

“I understand that you identified the man who was killed on the train as being this professor and have accordingly alerted the security services to the possibility that he was murdered by one of the London drug gangs. Correct?”

Hugo nodded.

“Then let me clarify two points. First, Frossinone is still alive and it can only have been his heated imagination that led him to think that he was threatened by anyone. The man who died was Umberto Bardi, the son of Arturo Bardi and Janina Ridolfi, the youngest sister of Eugenio Ridolfi, whom I expect you know. His office is next door to yours.”

“Ridolfi Brothers?”

“Importers and Exporters,” said the young man with a half-smile.

“My immediate objective,” said the older man, ignoring him, “is to convince you that I am telling you the truth. Have you made the connection?”

“He’s ready and waiting.” The young man lifted the receiver and handed it to Hugo, who looked at it blankly and then said, “Hullo.”

“Ullo, Ugo,” said a voice he recognised. “Is that you? What can I do for you this fine morning?”

“I gather that the main thing is to assure me that you are alive and that there is no truth in your statement that you are being threatened by the mafia?”

“Whenever did I say such a thing?” The conversation was now in Italian.

“It was, I recollect, at a party with the Roncoronis.”

“Tony’s drinks are always stronger than they seem. If I said any such thing I must have been — what is the expression? — talking out of the back of my neck. But what is all this about? Why does it worry you?”

“It only worries me because I thought you were dead.”

“If you were back in Perugia I could soon convince you that I was alive.”

“I’m sure of it.”

The older man, who had been listening on an extension, put out a hand and the young man killed the call.

“I apologise for terminating a reunion with your friend, but there is one further matter and time presses. Not only had we no hand in the killing of Umberto, but he was, in fact, our emissary, doing a job for us in this country. Consequently he was under our protection. Our honour is involved. We shall be taking steps to see that the killer is identified and punished. You follow me?”

Hugo nodded. The atmosphere in the room was so oppressive that he was finding it difficult to speak. Two things were clear. He had made a fool of himself, and he had upset some formidable people.

“You will appreciate that the activities of Colonel Arbuthnot and his friends make it more difficult for us to succeed in our task. So, in return for reassuring you about your friend, Frossinone, might we look to you to assure the colonel that we had no hand in the killing of Umberto and are ourselves seeking his killer?”

Hugo nodded again. All he wanted to do was to get out of the flat. The young man held the door open for him.

By the time he got back to the office he was on balance again. He found Mr. Piggin deep in discussion with Eugenio Ridolfi, the older of the Ridolfi Brothers. He said, “I asked Mr. Ridolfi to call. As I suspected, he had not been shown the photograph of the murdered man — a curious omission on the part of the police. For as soon as he saw it he identified it.”

“As his nephew Umberto.”

“Precisely. You have just obtained that information from another quarter?”

“Yes.”

“From Mrs. Trumpington, no doubt,” said Mr. Piggin drily.

Hugo was saved embarrassment by Eugenio, who said, “But certainly it is Umberto. He has dyed his hair and shaved off the handsome side whiskers that he usually wore. Although it is all of twenty years since I last spoke to him, I am in no doubt about it. My wife agrees. You must understand, Mr. Bracknell, that my youngest sister, Janina — let us speak no ill of the dead — was a foolish girl, but not a wicked woman. On the other hand, the man she ran away to marry in Italy was a bad man. An associate of criminals. Since we learned of the marriage, I and my brother-in-law, Gino Alvaro, have had nothing to do with the Bardis.”

“Is it possible,” said Mr. Piggin slowly, “that Umberto was coming to England in an attempt to reconcile the two sides of the family?”

“It is possible. There are people who would like to see the Ridolfi and the Bardi firms working as a unit. But if that was his task, I do not think he would have been able to accomplish it.”

“Meanwhile,” said Hugo, who had lost his way in the intricacies of the Ridolfi-Bardi clan, “I have to persuade Colonel Arbuthnot to leave it to the mafia to find the killer.”

“Nor must we forget,” said Mr. Piggin, “that an equally efficient body of people will be engaged on the same task. From what I have learned from my friends in the City, the police have embarked on an entirely new tack—”

The new tack had been the brainchild of Inspector Barley. After three days of study, he had propounded a novel solution to his superior officer.

He said, “The science of psychological fingerprinting is still in its infancy, but if you apply it to the evidence in this case, an out-line — you might call it a silhouette of the killer — appears on the screen. It is necessary to accommodate two widely different aspects. On the one hand, the pathologists who studied the body all arrived at the same conclusion. That the killer must have been trained — though not necessarily practised — as a surgeon. He used a surgeon’s knife with a surgeon’s skill. That is the left-hand aspect. The right-hand aspect is the nature of the persons selected — apparently arbitrarily — for slaughter. A bill broker, a stock jobber in a small way of business, an assistant bank manager, and two accountants.”

“And one Italian, now identified for us as Umberto Bardi, possibly a criminal, and sent here by the mafia.”

“The sixth victim,” said Barley severely, “had nothing to do with the other five. His killing in that particular manner was a blind, calculated to deceive us.” He looked severely over his glasses at Mayburgh, who said, “Please go on.”

“The picture of the killer must combine these two facets. A man trained as a surgeon abandons that profession for reasons we can only speculate on and sets up a business of some sort in the City. His business collapses. His bank manager refuses further credit. A receiver, probably an accountant, is appointed. Either he himself is adjudged bankrupt, or his company is placed in compulsory liquidation. Since the fury inflamed by these happenings was fresh and compelling, I deduce that the business collapse must have occurred shortly before the first of the killings. They were random, in the sense that the victims were not selected personally. They were chosen as types. Just as Jack the Ripper is said to have been revenging himself on all prostitutes, he was taking his revenge on the City.”

“Could be something in that,” said Mayburgh. “But where does it take us?”

“Surely, if you accept my analysis, what we have to do is to study the record of business failures in the twelve months prior to the first killing. If the party involved has a background of surgical training — not a difficult matter to ascertain — then we have our hands on our man.”

Several weeks later Mr. Piggin reported to Hugo, with some amusement, “A business friend of mine tells me that Mayburgh is behaving — as he puts it — like a buffalo in a swamp. Raging to get out and attack, but too clogged to move fast in any direction. When he started he can have had no idea of the number of failures of small businesses. More than seven hundred in London alone in the year before the killings started. Nevertheless, he is plodding steadily forward, convinced that he will reach firm ground at last. He may do so. Inspector Barley is a clever young man. He may well, in fact, have arrived at the motive for the killings. But that only takes him halfway to the winning post.”

Hugo said, “I have been doing some thinking myself and have made some calculations.”

“Excellent. Most problems in this life can be solved by mathematics.”

“Actually, I was calculating what forces the police would have to deploy to protect the public. If the killings continue to be confined to the seven commuter lines from Liverpool Street—”

“Yes,” agreed Mr. Piggin. “I think we can take that as a basis for calculation.”

“Then since many of the early evening trains consist of twelve coaches, eighty-four men would be needed. Suppose that this degree of cover is maintained for, let us say, three months. If you ignore the weekends, this would mean sixty-five working days, necessitating a total deployment of five thousand, four hundred and sixty man hours. It’s a daunting total, but an effort of this magnitude wouldn’t be out of place to trap a serial killer.”

Mr. Piggin steepled his fingers and said, “Allow me to correct your factors. In making your calculations you have fallen into the same error as the police and the mafia. You have studied the killer’s method, but not his mind. So please think about him. He is a loner, sitting at home, working out his revenge on the City. Someone you might describe — odd though it seems in the circumstances — as an old maid, with an old maid’s love of neatness and regularity. Just consider how methodically he has conducted his campaign. One killing on each of the seven available lines. Upminster, Southend, Southminster, Clacton, and Norwich. And — this was the one you were involved in — Braintree. Then we have the aborted attempt on Mr. Osbaldistone — a most important episode. It took place on the Colchester line. And it was a failure. A man like ours abhors a failure. It upsets his pattern. Can we doubt that his next, and possibly his final effort will be a repeated attempt on the Colchester line which will round out the pattern?”

“Seems logical,” agreed Hugo.

“And since he always selects a latish commuter train I’d lay very heavy odds on the six-ten.”

“Well,” said Hugo, “if you’re right, I agree that my first factor should be one, not seven. What about my other factors. Do you question them?”

“In mentioning twelve carriages you overlooked the fact that this man has always seated himself in the centre of the train, clearly in order to be as close as possible to the exit point on the platform when he leaves the train. I agree that he might choose either the fifth or the sixth carriage, so I’m prepared to allow you a second factor of two.”

“Thank you,” said Hugo. “But even if you’re right, two men on your selected train on every working day in the year — it’s still quite a substantial total, isn’t it?”

“That,” said Mr. Piggin, “is where you make your gravest error. I invited you to consider the mind of the killer. Lonely, methodical, introverted. Is it not clear that he would be a numerologist?”

“You’ve lost me.”

“A numerologist is a man who places such importance on numbers that he regulates his life by them. There are lucky and unlucky numbers. The unluckiest is, of course, thirteen. Some people carry it forward through the multiplication table and consider twenty-six, thirty-nine, fifty-two, and so on as equally unfortunate. I once had a client who believed so firmly in this that when I presented him with a bill for thirty-nine pounds he came round in person to protest. I could only pacify him by increasing it to forty pounds. On the other hand, there are lucky numbers. They are based on the number seven and all its multiples up to sixty-three, which was, historically, deemed to be the grand climacteric. A particularly lucky number in this series was twenty-one, additionally important as being the age of majority. The law on that point may have changed, but the number has never lost its supreme power. And clearly it rules this killer absolutely.”

“How do you mean, Piggy?”

“You haven’t seen it? Look at the dates he selected. November tenth, February nineteenth, June fifteenth, August thirteenth, October eleventh. Write them numerically: 10/11, 19/2, 15/6, 13/8, and 11/10. You see? The total, in every case, is twenty-one. The Osbaldistone attempt on January twentieth fits in also. One or two might have been a coincidence. Certainly not six. Quite impossible.”

Hugo, who was feeling breathless, said, “Good God!” and “You don’t really think.” And then, “And what about the one I was involved in. That was March eighteenth — 18/3.”

“Quite so,” said Mr. Piggin. “And it is significant in two ways. First, it means that it was unquestionably one of the sequence we have been discussing. I refuse to believe that chance could have dictated this particular date. Second, it means that your mafia acquaintances are quite wrong in supposing that the killing was anything to do with Umberto’s mission for them in this country. He simply happened to offer an ideal chance for the Knifeman, whose opportunities had been much diminished as men tended to travel in groups. But Umberto, who had been living in Italy, would have known nothing about all this. Indeed, if the mafia had thought about it, they must have realised that their rivals in the drug trade would have had no time to organise the attack. Umberto had arrived from Italy, unannounced, that same day. No, no. It is quite clear that the man the mafia should be pursuing is not a professional rival but the Knifeman himself.”

Hugo had started scribbling dates on a piece of paper. He said, “April seventeenth adds up to twenty-one. Why did nothing happen on that day?”

“Because it happens to have been a Sunday.”

“Oh. So it was. Well then, look here—”

“Yes?”

“The next one is May sixteenth.”

“Yes.”

“Which is next Monday.”

“Quite so.”

“And do you really think—”

“Either you accept the laws of mathematics or you reject them.”

“Then shouldn’t we tell someone.”

“Can you imagine explaining it to Chief Inspector Mayburgh?”

“Perhaps not,” said Hugo. “But we must do something.”

“Certainly. Next Monday we will catch the six-ten train to Colchester. I will occupy a seat in carriage number five. You will occupy one in carriage number six.”

Hugo said, “Oh!” rather feebly. And then, “I suppose it would be the logical way of doing it.”

His carriage, which had been crammed to start with, was emptying rapidly. Hugo’s mouth was dry and he had an uncomfortable feeling in the pit of his stomach. Although he kept telling himself that Mr. Piggin’s theory was moonshine, one corner of his mind concentrated obstinately on the idea of a knife: long, thin, sharp-edged, with a needle point.

Shenfield, Ingatestone.

He stole another look at the man occupying the far corner seat. A very ordinary man. The only thing that had attracted Hugo’s attention was his immobility. His evening paper was on the seat beside him, but he was making no attempt to read it. Nothing suspicious in that, surely?

At Chelmsford, most of the other passengers got out. Apart from this character in the corner, there was now only one other occupant of the carriage, a stout, red-faced man who was sitting in the seat beside the carriage door. The train lurched forward again. The next stop would be Hatfield Peverel and it was clear that both men were preparing to get out. The stout man had stowed his paper away into his briefcase. The suspicious character had got to his feet and was moving across. He was carrying no luggage and seemed to be feeling for something in the inside of his coat. For God’s sake, thought Hugo, surely he daren’t attempt anything with me watching him.

As the train stopped, the stout man got up and politely opened the carriage door. The suspect pulled out the season ticket he had been feeling for and both men descended onto the platform. They were laughing at something.

Hugo let out all the breath he had been holding. Then he sat back in his seat as his heart resumed its normal rhythm. Of course nothing had happened. Mr. Piggin had been talking nonsense. He got up, strolled down the now empty carriage, and peered into the next one.

What he saw stopped him in his tracks.

Mr. Piggin, apparently deep in the study of his evening paper, was occupying the seat next to the door. There was only one other man in the carriage, and as the train slowed he got up and started to move across. It was clear that his route to the door was going to take him very close to Mr. Piggin, who looked up with a bland smile as he approached.

It was the sort of smile, thought Hugo, that might have illuminated the face of Pythagoras when, at long last, he saw the proof of something he had previously only suspected. He croaked out, “Why, hullo, Mr. Piggin. I didn’t expect to see you on this train.”

Hardly pausing in his stride, the unknown man thrust the door open, climbed down onto the platform, and slammed the door shut behind him, without looking round.

Hugo said, “Was that—?”

“Certainly that was our man. One hand was actually on the handle of the life preserver he intended to use. He had it half out of his pocket. I must confess that I was glad when you intervened. If I may say so,” — Mr. Piggin sounded mildly reproachful — “I thought you left it rather late.”

“I’m sorry, Piggy. It was just that, at the last moment, I couldn’t believe it was really going to happen. What do we do now?”

“We alight at the next station and take the train back to London. I’ve no doubt that our man will be doing the same. He would only have to cross the footbridge and keep out of sight until the train arrived. There’s an up train reaches Kelvedon at seven-fifteen. We should be in plenty of time to transfer to it. On this occasion, we’ll spread our net a little wider. You get into the front carriage. I’ll travel in the rear one. We’ll get off when he does, but we can’t plan further ahead until we see what he does. Fortunately, I have used this line so frequently that I know most of the station staffs well.”

Hugo’s confidence in Mr. Piggin was now so complete that it was no surprise to him when he saw their man come out of the little hutchlike waiting room at Witham and climb onto the train. It would have surprised him if he hadn’t.

It was a stopping train. And as station succeeded station without their man making a move, Hugo began to worry. Might he be going all the way back to Liverpool Street? Which could be awkward. But no. It was at Manor Park, three stations from the terminus, that they saw him emerge and watched him disappear into the ticket office. Mr. Piggin seemed to be in no hurry to follow. He was deep in conversation with the ticket collector. As Hugo came up, he heard, “That man who went out just now? That’s Mr. Appleyard. Lives along South Park Road. If you hurried you could catch him.”

Mr. Piggin thanked him and as soon as they were clear of the station, said, “They sell a very nice line of beer at the Green Man. I think this calls for a drink, don’t you?”

“Seconded and carried unanimously,” said Hugo fervently.

It was when they were seated, with pint glasses in front of them, that Hugo started to see rocks ahead. He said, “You’ve done a marvellous job, Piggy. An absolutely incredible job, and we now know who the killer is. But tell me this. How are we going to prove it? Think what a meal you’ll be for defending counsel. ‘How did you identify the accused, Mr. Piggin? By mathematics? Really, sir, if the matter was not so serious, I’d imagine you were joking—’ ”

Mr. Piggin took a long pull at his beer, replaced the half-empty glass on the table, and said, “It had not been my intention to trouble our overworked police force or our notoriously inefficient prosecution service with this matter.”

“Then what—?”

“You have some means, I imagine, of getting in touch with your mafia acquaintances. I think, don’t you, that once they understood that it was Mr. Appleyard who killed their protégé, they would take appropriate steps.”

A week later the householder at Number Twenty-seven South Park Road telephoned the police to say that a dangerous escape of gas seemed to be taking place at Number Twenty-five and no one seemed to be doing anything about it.

This brought Chief Inspector Mayburgh onto the scene. Normally he would not have become involved in such a routine matter, but he had received a telephone call earlier that morning from a man who had refused to give his name but had said, “If you want the Knifeman, go to Twenty-five South Park Road. Don’t forget to look in the desk.”

The coincidence of the address had stirred him into action. He brought Inspector Barley with him.

They found that the fire brigade, equipped with respirators, had entered the house, turned off the gas, which was pouring into the kitchen, and succeeded in clearing the atmosphere. They had not disturbed the body of the householder, a Mr. Appleyard, which had been found on the floor beside the kitchen table, on which two pillows and a rug had been placed.

“Made himself comfortable, didn’t he?” said Mayburgh.

“It’s often the way they go,” said the police surgeon. “When he finally lost consciousness he must have rolled off the table onto the floor. That would account, no doubt, for the bruising on the back of his head.”

When Mayburgh examined the desk, he was delighted to find in one of the drawers a surgical knife, a homemade life preserver, and Mr. Appleyard’s private diary, which contained a full account of the difficulties and final collapse of the company selling medical equipment which he had founded when he left his post as assistant in the surgical wing at St. Christopher’s Hospital.

Chief Inspector Mayburgh was not a man who threw compliments around, but he felt that something special was called for on this occasion.

He said to Inspector Barley, “I regard this as a triumph for the theory of psychological fingerprinting. Clearly what happened was that this man heard of our enquiries, felt the net closing round him, and took this way out. You must write it up for the Police Gazette.” The inspector smiled modestly and said that he would see what he could do.

Mr. Piggin said nothing. He was too busy. Fearne and Bracknell had been instructed by one of their City clients in a particularly unpleasant case of blackmail.