A group of us meet for an occasional evening of, talk and nonsense, followed by coffee and doughnuts and one of the group scored a coup by persuading a well-known entertainer to attend the session. The well-known enter tainer made one condition, however. He was not to enter tain, or even be asked to entertain. This was agreed to.

Now there arose a problem. If the meeting were left to,its own devices, someone was sure to begin badgering the entertainer. Consequently, other entertainment had to be supplied, so one of the boys turned to me and said,

"Say, you know what?" l,knew what and I objected at once. I said, "How can

I stand up there and talk with everyone staring at this other fellow in the audience and wishing he were up there instead? You'd be throwing me to the wolves!"

But they all smiled very toothily and told me about the wonderful talks I give. (Somehow everyone quickly dis covers the fact that I soften into putty as soon as the flat tery is turned on.) In no time at all, I agreed to be thrown to the wolves. Surprisingly, it worked, which speaks highly for the audience's intellect-or perhaps their magnanimity.

I As it happened, the meeting was held on "leap day" and so my topic of conversation was ready-made and the gist of it went as follows:

I suppose there's no question but that the earliest unit of time-telling was the day. It forces itself upon the aware ness of even the most primitive of humanoids. However, the day is not convenient for long intervals of time. Even allowing a primitive Iife-span of @ years, a man would live some 11,000 days and it is very easy to lose track among all those days.

Since the Sun governs the day-unit, it seems natural to turn to the next most prominent heavenly body, the Moon, for another unit. One offers itself at once, ready-made the period of the phases. The Moon waxes from nothing to a full Moon and back to nothing in a definite period of time. This period of time is called the "month" in English

(clearly from the word "mooif') or, more specifically, the

"lunar month," since we have other months, representing periods of time slightly shorter or slightly longer than the one that is strictly tied to the phases of the moon.

The lunar month is roughly equal to 291/2 days. More exactly, it is equal to 29 days, 12 hours, 44 minutes, 2.8 seconds, or 29.5306 days.

In pre-agricultural times, it may well have been that no, special significance attached itself to the month, which re mained only a convenient device for measuring moderately long periods of time. The life expectancy of primitive man was probably something like 350 months, which is a much more convenient figure than that of I 1,000 days.

In fact, there has been speculation that the extended lifetimes of the patriarchs reported in the fifth chapter of the Book of Genesis may have arisen out of a confusion of years with lunar months. For instance, suppose Me thuselah had lived 969 lunar months. This would be just about 79 years, a very reasonable figure. However, once that got twisted to 969 years by later tradition, we gained the "old as Methuselah" bit.

However, I mention this only in passing, for this idea is not really taken seriously by any biblical scholars. It is much more likely that these lifetimes are a hangover from

Babylonian traditions about the times before the Flood.

...But I am off the subject.

It is my feeling that the month gained a new and enhanced importance with the introduction of agriculture.

An agricultural society was much more closely and pre cariously tied-to the season amp; than a hunting or herding society was. Nomads could wander in search of grain or grass but farmers had to stay where they were and hope for rain. To increase their chances, farmers had to be cer tain to sow at a proper time to take advantage of sea sonal rains and seasonal warmth; and a mistake in the sowing period might easily spell disaster. What's more, the development of agriculture made possible a denser popu lation, and that intensified the scope of the possible dis aster.

Man had to pay attention, then, to the cycle of seasons, and while he was still in the prehistoric stage he must have noted that those seasons came fall cycle in roughly twelve months. In other words, if crops were planted at a par ticular time of the year and all went well, then, ff twelve months were counted from the first planting and crops were planted again, all would again go well.

Counting the months can be tricky in a primitive so ciety, especially when a miscount can be ruinous, so it isn't surprising that the count was usually left in the hands of a specialized caste, the priesthood. The priests could not only devote their time to accurate counting, but could also use their experience and skill to propitiate the gods.

After all, the cycle of the seasons was by no, means as rigid and unvarying as was the cycle of day and night or the cycle of the phases of the moon. A late frost or a failure of rain could blast that season's crops, and since such flaws in weather were bound to follow any little mista e in ritual (at least so men often believed), the priestly func tions were of importance indeed.

It is not surprising then, that the lunar month grew to have enormous religious significance. There were new

Moon festivals and special priestly proclamations of each one of them, so that the lunar month came to be called the "synodic month."

The cycle of seasons is called the "year" and twelve lunar months therefore make up a "lunar year." The use of lunar years in measuring time is referred to as the use of a "lunar calendar." The only important group of people in modem times, using a strict lunar calendar, are the Moh ammedans. Each of the Moharmnedan years is made up of 12 months which are, in turn, usually made up of 29 and 30 days in alternation.

Such months average 29.5 days, but the length of the true lunar month is, as I've pointed out, 29.5306 days.

The lunar year built up out of twelve 29.5-day months is 354 days long, whereas twelve lunar months are actually 354.37 days long.

You may say "So what?" but don't. A true lunar year should always start on the day of the new Moon. If, how ever, you start one lunar year on the day of the new Moon and then simply alternate 29-day and 30-day months, the third year will start the day before the new Moon, and the sixth year will start two days before the new Moon. To properly religious people, this would be unthinkable.

Now it so happens that 30 true lunar years come out to be almost exactly an even number of days-10,631.016.

Thirty years built up out of 29.5-day months come to

10,620 days-just 1 1 days short of keeping time with the

Moon' For that reason, the Mohammedans scatter 1 1 days through the 30 years in some fixed pattern which prevents any individual year from starting as much, as a full day ahead or behind the new Moon. In each 30-year cycle there are nineteen 354-day years and eleven 355-day years, and the calendar remains even with the Moon.

An extra day, inserted in this way to keep the calendar even with the movements of a heavenly body, is called an

"intercalary day"; a day inserted "between the calendar," so to speak.

The lunar year, whether it is 354 or 355 days in length, does not, however, match the cycle of the seasons. By the dawn of historic times the Babylonian astronomers had noted that the Sun moved against the background of stars

(see Chapter 4). This passage was followed with absorp tion because it grew apparent that a complete circle of the sky by the Sun matched the complete cycle of the seasons closely. (This apparent influence of the stars on the sea sons probably started the Babylonian fad of astrology which is still with us today.)

The Sun makes its complete cycle about the zodiac in roughly 365 days, so that the lunar year is'about II days shorter than the season-cycle, or "solar year." Three lunar years fall 33 days, or a little more than a full month be hind the season-cycle.

This is important. If you use a lunar calendar and start it so that the first day of the year is planting time, then three years later you are planting a month too soon, and by the time a decade has passed you are planting in mid winter. After 33 years the first day of the year is back where it is supposed to be, having traveled through the entire solar year.

This is exactly what happens in the Mohammedan year. The ninth month of the Mohammedan year is named

Ramadan, and it is especially holy because it was the month in which Mohammed began to receive the revela tion of the Koran. In Ramadan, therefore, Moslems ab stain from food and water during the daylight hours.

But each year, Ramadan falls a bit earlier in the cycle of the seasons, and at 33-year intervals it is to be found in the hot season of the year; at this time abstaining from drink is particularly wearing, and Moslem tempers grow particularly short.

The Mohammedan years are numbered from the Hegira; that is, from the date when Mohammed fled from Mecca to Medina. That event took place in A.D. 622. Ordinarily, you nught suppose, therefore, that to find the number of the Mohammedan year, one need only subtract 622 from the number of the Christian year. This is not quite so, since the Mohammedan year is shorter than ours. I write this chapter in A.D. 1964 and it is now 1342 solar years since the Hegira. However, it is 1384 lunar years since the

Hegira, so that, as I write, the Moslem year is A.H. 1384.

I've calculated that the Mohammedan year will catch up to the Christian year in about nineteen millennia. The year A.D. 20,874 will also be A.H. 20,874, and the Moslems will then be able to switch to our year with a minimum of trouble.

But what can we do about the lunar year in order to make it keep even with the seasons and the solar year? We can't just add II days at the end, for then the next year would not start with the new Moon and to the ancient

Babylonians, for instance, a new Moon start was essential.

However, if we start a solar year with the new Moon and wait, we will find that the twentieth solar year there after starts once again on the day of the new Moon. You see, 19 solar years contain just about 235 lunar months.

Concentrate on those 235 lunar months. That is equiva lent to 19 lunar years (made up of 12 lunar months each) plus 7 lunar months left over. We could, then, if we wanted to, let the lunar years progress as the Moham medans do, until 19 such years had passed. At this time the calendar would be exactly 7 months behind the sea sons, and by adding 7 months to the 19th year (a 19th year of 19 months-very neat) we could start a new 19 year cycle, exactly even with both the Moon and the sea sons.

The Babylonians were unwilling, however, to let them selves fall 7 months behind the seasons. Instead, they added that 7-month discrepancy through the 19-year cycle, one month at a time and as nearly evenly as possible. Each cycle had twelve 12-month years and seven 13-montb years. The "intercalary month" was added in the 3rd, 6th, 8tb, I lth, 14th, 17th, and 19th year of each cycle, so that the year was never more than about 20 days behind or ahead of the Sun.

Such a calendar, based on the lunar months, but gim micked so as to keep up with the Sun, is a "lunar-solar calendar."

The Babylonian lunar-solar calendar was popular in ancient times since it adjusted the seasons while preserving the sanctity of the Moon. The Hebrews and Greeks both adopted this calendar and, in fact, it is still the basis for the Jewish calendar today. The individual dates in the

Jewish calendar are allowed to fall slightly behind the Sun until the intercalary month is added, when they suddenly shoot slightly ahead of the Sun. That is why holidays like

Passover and Yom Kippur occur on different days of the civil calendar (kept strictly even with the Sun) each year.

These holidays occur on the same day of the year each year in the Jewish calendar.

The early Christians continued to use the Jewish calen dar for three centuries, and established the dayof Easter on that basis. As the centuries passed, matters grew some what complicated, for the Romans (who were becoming

Christian in swelling numbers) were no longer used to a lunar-solar calendar and were puzzled at the erratic jump ing about of Easter. Some formula had to be found by which the correct date for Easter could be calculated in advance, using the Roman calendar.

It was decided at the Council of Nicaea, in A.D. 325 (by which time Rome had become officially Christian), that Easter was to fall on the Sunday after the first full Moon after the vernal equinox, the date of the vernal equinox being established as March 21. However, the full Moon referred to is not the actual full Moon, but a fic titious one called the "Paschal Full Moon" ("Paschal" being derived from Pesach, which is the Hebrew word for Passover). The date of the Paschal Full Moon is calcu lated according to a formula involving Golden Numbers and Dominical Letters, which I won't go into.

The result is that Easter still jumps about the days of the civil year and can fall as early as March 22 and as late as April 25. Many other church holidays are tied to Easter and likewise move about from year to year.

Moreover, all Christians have not always agreed on the exact formula by which the date of Easter was to be cal culated. Disagreement on this detail was one of the reasons for the schism between the Catholic Church of the West and the Orthodox Church of the East. In the early Middle

Ages there was a strong Celtic Church which had its own formula.

Our own calendar is inherited from Egypt, where sea sons were unimportant. The one great event of the year was the Nile flood, and this took place (on the average) every 365 days. From a very early date, certainly as early as 2781 B.C., the Moon was abandoned and a "solar calen 19 dar," adapted to a constant-length 365-day year, was adopted.

The solar calendar kept to the tradition of 12 months, however. As the year was of constant length, the months were of constant length, too-30 days each. This meant that the new Moon could fall on any day of the month, but the Egyptians didn't care. (A month not based on the Moon is a "calendar month.")

Of course 12 months of 30 days each add up only to 360 days, so at the end of each 12-month cycle, 5 addi tional days were added and treated as holidays.

The solar year, however, is not exactly 365 days long.

There are several kinds of solar years, differing slightly in length, but the one upon which the seasons depend is the "tropical year," and this is about 3651/4 days long.

This means that each year, the Egyptian 365-day year falls 1/4 day behind the Sun. As time went on the Nile flood occurred later and later in the year, until finally it had made a complete circuit of the year. In 1460 tropical years, in other words, there would be 1461 Egyptian years.

This period of 1461 Egyptian yea'rs was called the "Sothic cycle," from Sothis, the Egyptian name for the star Sirius. If, at the beginning of one Sothic cycle, Sirius rose with the Sun on the first day of the Egyptian year, it would rise later and later during each succeeding year until finally, 1461 Egyptian years later, a new cycle would begin as Sothis rose with the Sun on New Year's Day once more.

The Greeks bad learned about that extra quarter day as early as 380 B.C., when Eudoxus of Cnidus made the discovery. In 239 B.c. Ptolemy Euergetes, the Macedonian king of Egypt, tried to adjust the Egyptian calendar to take that quarttr day into account, but the ultra-conserva tive Egyptians would have none of such a radical innova tion.

Meanwhile, the Roman Republic had a lunar-solar calendar, one in which an intercalary month was added every once in a while. The priestly officials in charge were elected politicians, however, and were by no means as con 20 scientious as those in the East. The Roman priests added a month or not according to whether they wanted a long year (when the other annually elected officials in power were of their own party) or a short one (when they were not). By 46 B.C., the Roman calendar was 80 days behind the Sun.

Julius Caesar was in power then and decided to put an end to this nonsense. He had just returned from Egypt where he had observed the convenience and simplicity of a solar year, and imported an Egyptian astronomer, Sosig enes, to help him. Together, they let 46 B.C. continue for 445 days so that it was later known as "The Year of Con fusion." However, this brought the calendar even with the Sun so that 46 B.C. was the last year of confusion.

With 45 B.C. the Romans adopted a modified Egyptian calendar in which the five extra days at the end of the year were distributed throughout the year, giving us our months of uneven length. Ideally, we should have seven 30-day months and five 31-day months. Unfortunately, the Ro mans considered February an unlucky month and short ened it, so that we ended with a silly arrangement of seven 31-day months, four 30-day months, and one 28-day month.

In order to take care of that extra 1/4 day, Caesar and Sosigenes established every fourth year with a length of 366 days. (Under the numbering of the years of the Chris tian era, every year divisible by 4 has the intercalary day - set as February 29. Since 1964 divided by 4 is 491, without a remainder, there is a February 29 in 1964.)

This is the "Julian year," after Julius Caesar' At the Council of Nicaea, the Christian Church adopted the Julian calendar. Christmas was finally accepted as a Church holiday after the Council of Nicaea, and given a date in the Julian year. It does not, therefore, bounce about from year to year as Easter does.

The 365-day year is just 52 weeks and I day long. This means that if February 6, for instance, is on a Sunday in one year, it is on a Monday the next year, on a Tuesday the year after, and so on. If there were only 365-day years, then any given date would move through the days of the week in steady progression. If a 366-day year is involved, however, that year is 52 weeks and 2 days long, and if February 6 is on Tuesday that year, it is on Thursday the year after. The day has leaped over Wednesday. It is for that reason that the 366-day year is called "leap yearip and February 29 is "leap day."

All would have been well if the tropical year were really exactly 365.25 days long; but it isn't. The tropical year is 365 days, 5 hours, 48 minutes, 46 seconds, or 365.24220 days long. The Julian year is, on the average, 11 minutes 14 seconds, or 0.0078 days, too long.

This may not seem much, but it means that the Julian year gains a full day on the tropical year in 128 years. As the Julian year gains, the vernal equinox, falling behind, comes earlier and earlier in the year. At the Council of Nicaea in A.D. 325, the vernal equinox was on March 21.

By A.D. 453 it was on March 20, by A.D. 581 on March 19, and so on. By A.D. 1263, in the lifetime of Roger Bacon, the Julian year had gained eight days on the Sun and the vernal equinox was on March 13.

Still not fatal, but the Church looked forward to an indefinite future and Easter was tied to a vernal equinox at March 21. If this were allowed to go on, Easter would come to be celebrated in midsummer, while Christmas would ed e into the spring. In 1263, therefore, Roger Bacon wrote a letter to Pope Urban IV explaining the situation. The Church, however, took over three centuries to consider the matter.

By 1582 the Julian calendar had gained two more days and the vernal equinox was falling on March I 1. Pope Gregory XIII finally took action. First, he dropped ten days, changing October 5, 1582 to October 15, 1582. That brought the calendar even with the Sun and the vernal equinox in 1583 fell on March 21 as the Council of Nicaea had decided it should.

The next step was to prevent the calendar from getting out of step again. Since the Julian year gains a full day every 128 years, it gains three full days in 384 years or, to approximate slightly, three full days in four centuries.

That means that every 400 years, three leap years (accord ing to the Julian system) ought to be omitted..

Consider the century years-1500, 1600, 1700, and so on. In the Julian year, all century years are divisible by 4 and are therefore leap years. Every 400 years there are 4 such century years, so why not keep 3 of them ordinary years, and allow onl one of them (the one that is divisible by 400) to be a leap year? This arrangement will match the year more closely to the Sun and give us the "Gre 'gorian calendar."

To summarize: Every 400 years, the Julian calendar allows 100 leap years for a total of 146,100 days. In that same 400 years, the Gregorian calendar allows only 97 leap years for a total of 146,097 days. Compare these lengths with that of 400 tropical years, which comes to 146,096.88. Whereas, in that stretch of time, the Julian year had gained 3.12 days on the Sun, the Gregorian year had gained only 0.12 days.

Still, 0.12 days is nearly 3 hours, and this means that in 3400 years the Gregorian calendar will have gained a full day on the Sun. Around A.D. 5000 we will have to consider dropping out one extra leap year., But the Church had waited a little too long to take action. Had it done the job a century earlier, all western Europe would have changed calendars without trouble.

By A.D. 1582, however, much of northern Europe bad turned Protestant. These nations would far sooner remain out of step with the Sun in accordance with the dictates of the pagan Caesar, than consent to be corrected by the Pope. Therefore they kept the Julian year.

The year 1600 introduced no crisis. It was a century year but one that was divisible by 400. Therefore, it was a leap year by both the Julian and Gregorian calendars.

But 1700 was a different matter. The Julian calendar had it as a leap year and the Gregorian di 'd not. By March 1, 1700, the Julian calendar was going to be an additional day ahead of the Sun (eleven days altogether). Denmark, the Netherlands, and Protestant Germany gave in and adopted the Gregorian calendar.

Great Britain and the American colonies held out until 1752 before giving in. Because of the additional day gained in 1700, they had to drop eleven days and changed September 2, 1752 to September 13, 1752. There were riots all over England as a result, for many people came quickly to the conclusion that they had suddenly been made eleven days older by legislation.

"Give us back our eleven days!" they cried in despair.

(A more rational objection was the fact that although the third quarter of 1752 was short eleven days, landlords calmly charged a full quarter's rent.)

As a result of this, it turns out that Washington was not born on "Washington's birthday." He was born on Febru ary 22, 1732 on the Gregorian calendar, to be sure, but the date recorded in the family Bible had to be the Julian date, February 11, 1732. When the changeover took place, Washington-a remarkably sensible man changed the date of his birthday and thus preserved the actual day.

The Eastern Orthodox nations of Europe were more stubborn than the Protestant nations. The years 1800 and 1900 went by. Both were leap years by the Julian calendar, but not by the Gregorian calendar. By 1900, then, the Julian vernal equinox was on March 8 and the Julian calendar was 13 days ahead of the Sun. It was not until after World War I that the Soviet Union, for instance, adopted the Gregorian calendar. (In doing so, the Soviets made a slight modification of the leap year pattern which made matters even more accurate. The Soviet calendar will not gain a day on the Sun until fully 35,000 years pass.)

The Orthodox churches themselves, however, still cling to the Julian year, which is why the Orthodox Christmas falls on January 6 on our calendar. It is still December 25 by their calendar.

In fact, a horrible thought occurs to me I was myself born at a time when the Julian calendar was still in force in the-ahem-old country. [Well, the Soviet Union, if you must know. I came here at the age of 3] Unlike George Washington, I never changed the birthdate and, as a result, each year I celebrate my birthday 13 days earlier than I should, making myseff 13 days older than I have to be.

And this 13-day older me is in all the records and I can't ever change it back.

Give me back my 13 days! Give me back my 13 days!

Give me back...