Avalon interrupted. “Never mind that, Roger. You've got your pattern. How do you use it?”
'The easiest thing in the world. Say the thirteenth falls on a Friday in a leap year, where you remember to start the leap year on March 1 before the actual leap year. Then you represent it by A, and you will see that the thirteenth of that same month will fall whenever the A shows up, five years later and six years after that, and then eleven years after that.
“Now this is December 13, 1974, and by our convention of leap years this is the year before leap year. That means that it can be represented by the letter E, whose first appearance is under 3, the year before L. Well then, by following the E's we see that there will be another Friday the thirteenth in December eleven years from now, then in six more years, then in five years. That is, there will be a Friday the thirteenth in December 1985, in December 1991, and in December 1996.
“You can do that for any date for any month, using that little series I've just written out, and make up a perpetual calendar that runs for twenty-eight years and then repeats itself over and over. You can run it forward or backward and catch every Friday the thirteenth as far as you like in either direction, or at least as far back as 1752. In fact, you can find such perpetual calendars in reference books like the World Almanac.”
Gonzalo said, “Why 1752?”
“That's an unusual year, at least for Great Britain and what were then the American colonies. The old Julian calendar which had been used since Julius Caesar's time had gained on the season because there were a few too many leap years in it. The Gregorian calendar, named for Pope Gregory XIII, was adopted in 1582 in much of Europe, and by that time the calendar was ten days out of synchronization with the seasons, so that ten days were dropped from the calendar, and every once in a while thereafter a leap year was omitted to keep the same thing from happening again. Great Britain and the colonies didn't go along till 1752, by which time another day had been added, so they had to drop eleven days.”
“That's right,” said Rubin. “And for a while they used both calendars, referring to a particular date as O.S. or N.S. for Old Style and New Style. George Washington was born on February 11, 1732 O.S., but instead of keeping the date, as many people did, he switched to February 22, 1732 N.S. I've won considerable money by betting that George Washington wasn't born on Washington's birthday.”
Halsted said, “The reason Great Britain hesitated so long was that the new calendar was initiated by the papacy, and Great Britain, being Protestant, preferred going against the Sun than along with the Pope. Russia didn't switch till 1923, and the Russian Orthodox Church is on the Julian calendar to this day, which is why the Orthodox Christmas comes on January 7 now, since the number of accumulated days' difference is thirteen.
“Great Britain went from September 2, 1752, directly to September 14, dropping the days in between. There were riots against that, with people shouting, 'Give us back our eleven days.'“
Rubin said indignantly, “That wasn't as crazy as you might think. Landlords charged the full quarter's rent, without giving an eleven-day rebate. I’d have rioted too.”
“In any case,” said Halsted, “that's why the perpetual calendar only goes back to 1752. Those eleven missing days mess everything up and you have to set up a different arrangement for days before September 14, 1752.”
Fletcher, who had listened to everything with evident interest, said, “I must say I didn't know any of this, Mr. Halsted. I don't pretend that I followed you perfectly, or that I can duplicate what you've just done, but I didn't know that I could find a perpetual calendar in the World Almanac. It would have saved me a lot of trouble—but of course, knowing where all the Friday the thirteenths are wouldn't help me determine which Friday the thirteenth might be the Friday the thirteenth.”
Henry interposed suddenly and said in his soft, polite voice, “I'm not sure of that, Mr. Fletcher. May I ask you a few questions?”
Fletcher looked startled and, for a short moment, was silent
Avalon said quickly, “Henry is a member of the club, Evan. I hope you don't mind—”
“Of course not,” said Fletcher at once. “Ask away, Henry.”
'Thank you, sir. —What I want to know is whether Mr. Hennessy knew of this pattern of date variations that Mr. Halsted has so kindly outlined for us.”
Fletcher looked thoughtful. “I can't say for certain; I certainly haven't heard of it, if he did. —Still, it's very likely he would have. He prided himself, for instance, on being able to cast a horoscope and, for all the nonsense there is in astrology, casting a proper horoscope takes a bit of mathematics, I understand. Hennessy did not have much of a formal education, but he was fearfully intelligent, and he was interested in numbers. In fact, as I think of it, I am sure he couldn't possibly have been as interested in Friday the thirteenth as he was, without being impelled to work out the pattern.”
“In that case, sir,” said Henry, “if I ask you what Mr. Hennessy was doing on a certain day, could you call up someone to check your notes on the matter, and tell us?”
Fletcher looked uncertain. “I'm not sure. My wife is home, but she wouldn't know where to look, and it's not likely I'll be able to give her adequate directions. —I could try, I suppose.”
“In that case, do you suppose you could tell me what Mr. Hennessy was doing on Friday, March 12, 1920?”
Fletcher's chair scraped backward and for a long moment Fletcher stared openmouthed. “What makes you ask that?”
“It seems logical, sir,” said Henry softly.
“But I do know what he was doing that day. It was one of the important days of his life. He swung the labor organization of which he was one of the leaders into supporting Debs for the presidency. Debs ran that year on the Socialist ticket even though he was still in jail, and he polled over 900,000 votes—the best the Socialists were ever able to do in the United States.”
Henry said, “Might not the labor organization have ordinarily supported the Democratic candidate for that year?”
“James M. Cox, yes. He was strongly supported by Wilson.”
“So to swing the vote away from Wilson's candidate might be, in Mr. Hennessy's flamboyant style, the finishing of the job that the finger of God had begun.”
“I'm sure he would think of that in that fashion.”
“In which case the letter would have been written on Friday, February 13, 1920.”
“It's a possibility,” said Fletcher, “but how can you prove it?”
“Dr. Fletcher,” said Henry, “in Mr. Hennessy's note he thanks God that there is no Friday the thirteenth the month after and even considers it a miracle. If he knew the perpetual calendar pattern he certainly wouldn't think it a miracle. There are seven months that have thirty-one days, and are therefore four weeks and three days long. If a particular date falls on a particular weekday in such a month, it falls on a weekday three past it the next month. In other words, if the thirteenth falls on a Friday in July, then it will fall on a Monday in August. Is that not so, Mr. Halsted?”
“You're perfectly right, Henry. And if the month has thirty days it moves two weekdays along, so that if the thirteenth falls on a Friday in June it falls on a Sunday in July,” said Halsted.
“In that case, in any month that has thirty or thirty-one days, there cannot possibly be a Friday the thirteenth followed the next month by another Friday the thirteenth, and Hennessy would know that and not consider it a miracle at all.
“But, Mr. Fletcher, there is one month that has only twenty-eight days and that is February. It is exactly four weeks long, so that March begins on the same day of the week that February does, and repeats the weekdays for every date, at least up to the twenty-eighth. If there is a Friday the thirteenth in February, there must be a Friday the Thirteenth in March as well—unless it is leap year.
“In leap year, February has twenty-nine days and is four weeks and one day long. That means that every day in March falls one weekday later. If the thirteen
th falls on a Friday in February, it falls on a Saturday in March, so that, though February has a Friday the thirteenth, March has a Friday the twelfth.
“My new appointment book has calendars for both 1975 and 1976. The year 1976 is a leap year and, in it, I can see that there is a Friday, February 13, and a Friday, March 12. Mr. Halsted has pointed out that calendars repeat every twenty-eight years. That means that the 1976 calendar would also hold for 1948 and for 1920.
“It is clear that once every twenty-eight years there is a Friday the thirteenth in February that is not followed by one in March, and Mr. Hennessy, knowing that the meeting of his labor group was scheduled for the second Friday in March, something perhaps maneuvered by his opposition to keep him at home, was delighted and relieved at the fact that it was at least not a second Friday the thirteenth.”
There was a silence all about the table and then Avalon said, “That's very nicely argued. It convinces me.”
But Fletcher shook his head. “Nicely argued, I admit, but I'm not sure—”
Henry said, 'There is, possibly, more. I couldn't help wonder why Mr. Hennessy called it a 'forty-year miracle.'“
“Oh well,” said Fletcher indulgently, “there's no mystery about that, I'm sure. Forty is one of those mystic numbers that crops up in the Bible all the time. You know, the Flood rained down upon the Earth for forty days and forty nights.”
“Yes,” said Rubin eagerly, “and Moses remained forty days on Mount Sinai, and Elijah was fed forty days by the ravens, and Jesus fasted forty days in the wilderness, and so on. Talking about God's mercy would just naturally bring the number forty to mind.”
“Perhaps that is so,” said Henry, “but I have a thought. Mr. Halsted, in talking about the conversion of the Julian to the Gregorian calendar, said that the new Gregorian calendar omitted a leap year occasionally.”
Halsted brought his fist down on the table. “Good God, I forgot. Manny, if you hadn't made that stupid joke about equations, I wouldn't have been so anxious to simplify and I wouldn't have forgotten. —The Julian calendar had one leap year every four years without fail, which would have been correct if the year were exactly 365 1/4 days long, but it's a tiny bit shorter than that. To make up for that tiny falling-short, three leap years have to be omitted every four centuries, and by the Gregorian calendar those omissions come in any year ending in 00 that is not divisible by 400, even though such a year would be leap in the Julian calendar.
“That means,” and he pounded his fist on the table again, “that 1900 was not a leap year. There was no leap year between 1896 and 1904. There were seven consecutive years of 365 days each, instead of three.”
Henry said, “Doesn't that upset the perpetual calendar that you described?”
“Yes, it does. The perpetual calendar for the 1800s meets the one for the 1900s in the middle, so to speak.”
“In that case, what was the last year before 1920 in which a Friday the thirteenth in February fell in a leap year?”
“I’ll have to figure it out,” said Halsted, his pen racing over a new napkin. “Ah, ah,” he muttered, then threw his pen down on the table and said, “In 1880, by God.”
“Forty years before 1920,” said Henry, “so that on the day that Hennessy wrote his note, an unlucky day in February was not followed by an unlucky day in March for the first time in forty years, and it was quite fair for him to call it, flamboyantly, a forty-year miracle. It seems to me that February 13, 1920, is the only possible day in his entire lifetime on which that note could have been written.”
“And so it does to me,” said Halsted.
“And to me,” said Fletcher. “I thank you, gentlemen. And especially you, Henry. If I can argue this out correctly now—”
“I'm sure,” said Henry, “that Mr. Halsted will be glad to help out.”
10 Afterword
I had to write this one. On Friday, December 13, 1974, I was co-host for that month's meeting of the Trap Door Spiders. (The Trap Door Spiders have two hosts and twice the membership of the Black Widowers, you see.) I had picked a new restaurant and was particularly anxious that everything go well.
I had guaranteed that twelve to fifteen members would show up and I feared that we might not make the number and that I would have a bad time with the restaurant. I counted them as they came in and when number twelve arrived I was relieved. (And the restaurant was pleased too. We were served an excellent meal with superb service— though, of course, no Henry.)
Then, just as the cocktail hour was over and we sat down to dinner, in came member number thirteen. Personally, I think it's a credit to the membership that not one person present seemed the least bit concerned that we were thirteen at the table on Friday the thirteenth (and as far as I know, nothing has happened as a result).
I must admit I was concerned, because I could not let such an event pass without beginning to work on a Black Widower plot at once. Again Ellery Queen's Mystery Magazine felt this to be too complicated a situation, and I passed it on to F & SF, which took it. It appeared in the January 1976 issue.
*Joseph Hennessy never existed and, as far as I know, there was never an assassination attempt on Calvin Coolidge. All other historical references in the story, not involving Hennessy, are accurate—IA
To Table of Contents
11 The Unabridged
Roger Halsted, normally an equable person (as one would have to be to survive the teaching of mathematics at a junior high school), arrived at the monthly banquet of the Black Widowers in a highly apparent state of the sulks.
'I’ll have a bloody Mary, Henry,” he said. “Light on the blood and an extra slug of Mary.”
Silently and deftly, Henry produced the drink, complete with slug, and James Drake, who was the host for the evening, stared at him over the smoke of his cigarette and let his inconsiderable gray mustache twitch. “What's the matter, Rog?” he asked in his soft, hoarse voice.
Roger said, Tm late.”
“So?” said Drake, who had to come in from New Jersey and had been known to be late himself. “Drink fast and catch up.”
“It's why I'm late that bothers me,” said Halsted. His high forehead had turned pink past the place where the vanished hairline had once been. “I was looking for my cuff links. My favorite pair. —My only pair, actually. I spent twenty minutes. I looked everywhere.”
“Did you find them?*'
“No! Have you got any idea how many hiding places there are in a two-story three-bedroom house? I could have spent twenty hours and ended with nothing.”
Geoffrey Avalon drifted over, with the second drink at the halfway mark. “You don't have to look through the whole house, Rog. You didn't paste them over the molding or inside the drainpipe, did you? Where do you usually keep them?”
“In a little box I've got in the drawer. I looked there first. They weren't there.”
His voice had risen past its usual quiet pitch and Emmanuel Rubin called out from the other side of the banquet table, “You left them in your shirt the last time you wore them and they got sent to the laundry and you'll never see them again.”
“That's not so,” said Halsted, clenching his left hand into a fist and waving it. “This is the only darned shirt I've got with French cuffs and I haven't worn it in three months and I saw the cuff links in the box just the other night when I was looking for something else.”
“Then look for something else again,” said Rubin, “and they'll turn up.”
“Ha-ha,” said Halsted grimly, and finished his drink. Mario Gonzalo said, “Is that shirt you're wearing the one with the French cuffs, Rog?” “Yes, it is.”
“Well then, if that's the only shirt you've got with French cuffs, and you couldn't find your only pair of cuff links, what are you using to hold the cuffs together?”
“Thread,” said Halsted bitterly, shooting his cuffs for inspection. “I had Alice tie them with white thread.”
Gonzalo, himself an example of faultless sartorial splendor, with a predomina
nt bluish touch in shirt and jacket, shading into the darker tints of his tie, winced. “Why didn't you put on a different shirt?”
“My blood was up,” said Halsted, “and I wasn't going to be forced into changing the shirt.”
Drake said, “Well, if you'll cool down a bit, Rog, I'll introduce my guest. Jason Leominster, this is Roger Halsted, and coming up the stairs for a scotch and soda is the final member, Thomas Trumbull.”
Leominster smiled dutifully. He was not quite as tall as Avalon's six feet two, but he was thinner. He was clearly in his forties though he looked younger, and under his tan jacket he wore a black turtleneck sweater which managed to seem not out of place. He had high and pronounced cheekbones over a narrow and pointed chin.
He said, “I'm afraid you're not getting much sympathy, Mr. Halsted, but you may have mine for what it's worth. When it comes to not finding things, my heart bleeds.”
Before Halsted could express what gratitude he felt for that, Henry signaled the beginning of dinner, the Black Widowers took their seats, and Trumbull loudly and rapidly, proclaimed the ritualistic toast to Old King Cole.
Rubin, staring hard at what was before him, lifted his straggly beard skyward in an access of indignation and said to Henry, “This thing looks like an egg roll. What is it, Henry?”
“It's an egg roll, sir.”
“What's it doing here?
Henry said, The chef has put together a Chinese meal for the club this month.”
“In an Italian restaurant?”
“I believe he considers it a challenge, sir.”
Trumbull said, “Shut up and eat, Manny, will you? It's good.”
Rubin bit into it, then reached for the mustard. “It's all right,” he said discontentedly, “for an egg roll.”
Even Rubin melted with the birds' nest soup, and when the first of the seven platters proved to be Peking duck, he grew positively mellow.
“Actually,” he said, “it's not that you lose things. You forget them. It's that way with me. It's that way with everyone. You're holding something, and put it down with your mind on something else. Two minutes later you can't for the life of you tell where that something you put down is. Even if, by sheer accident, you find it, you still can't remember putting it down there. Roger hasn't lost his cuff links. He put them somewhere and he doesn't remember where.”