How Britain got the Calendar Wrong
by Duncan Steel

How long is a year? One source of definitive information should be the Astronomical Almanac (an annual publication of the US Naval Observatory and the Royal Greewich Observatory). Trouble is, the definition therein is wrong, in a fundamental way which rather upsets all those accounts you have read in books, newspapers and magazines about the history of the calendar and how the year length is "correct to within seconds".

Today, as I write, is June 24, the traditional Midsummer's Day. But the summer solstice, astronomically-specified, oscillates between June 21 and 22. This year, 1999, it was at 8.49 p.m. (British Summer Time) on the 21st.

Similarly Christmas Day became December 25 because it was the traditional winter solstice date. But the solstice has slipped to the 21st/22nd.

Even more extreme is the spring equinox. Traditionally that is March 25, the Feast of the Annunciation or Lady Day. Nowadays the spring equinox varies between instants on March 19 - 21, and so it may fall five or six days before the traditional date. How can this be? The answer is that the length of the year depends upon your reference points. The time from one spring equinox to the next is not the same as from one summer solstice to the next, and this causes them to move relative to each other.

The reason for the movement is simple astronomy. The terrestrial orbit is not circular, but slightly egg-shaped. Our closest approach to the Sun — called perihelion — occurs on about January 3, and at that time Earth's speed is greatest. This makes winters in the northern hemisphere shorter but milder than those in the south, as a general trend.

But the date of the perihelion is changing. Compared to the equinox and solstice points it takes 21,000 years to swivel around the sky, meaning that every 60 years perihelion shifts one day later on the calendar. This causes the lengths of the seasons to oscillate: currently summer, autumn, winter and spring last for 93.7, 89.9, 88.8 und 92.8 days, respectively, but over the millennia those values alter. Thus the time differential between Midsummer's Day (today June 24) and the summer solstice will move back and forth, and similarly for the equinoxes and the winter solstice.

Doing the detailed calculations the average times in days between the annual marker points are as follows (they vary over centuries and millennia):

spring equinox:365.2424
summer solstice:365.2416
autumn equinox:365.2420
winter solstice:365.2427

Resolving this problem has proved a headache for calendar makers and they have tried to make up the difference by inserting leap year days. The Julian calendar, deriving from an edict by Julius Caesar, has a leap year once in four, so its average duration is 365.25 days. In 1582 Pope Gregory XIII introduced the Gregorian Calendar which has one leap year in four, except that three out of four century years are skipped (1700, 1800 und 1900 were not leap years, but 2000 is). This makes 97 leap years in 400, rendering a mean length of 365.2425 days. So those final decimals places are critical.

The Astronomical Almanac which I have chastised is wrong on two counts. First it gives the average of the above four values (just below 365.2422 days, called the tropical year) as being the time between equinoxes. Second it states that this is the appropriate length for the calendar year.

Mistaken on both counts and this is not trivial, because so many religious questions rest upon the distinctions.

One common mistake is the idea that Britain has adopted the Gregorian Calendar. We use what should be called the British calendar, as defined in Lord Chesterfield's Calendar act of 1751. As a result all the Commonwealth and the colonies of the time including what became the United States use an incorrectly defined dating system.

If one wanted to keep the seasons in step then the tropical year might be a justifiable target length. In fact the Calendar Act of 1751 does specify keeping all of the equinoxes and solstices stable, so one might take a target of 365.2422 days as being appropiate. In that case the leap year cycle defined by the Act, copying the Gregorian without saying so, leads to a discrepancy of 0.0003 days, or 26 seconds per year. (On that basis some people have claimed that a "correction" of one day every three or four millennia is needed, but that is misguided because the day is getting longer as the Earth's spin rate falls due to the tidal drag imposed by the Moon.)

But the Gregorian reform was not based on keeping the seasons in step. Its aim was to regularise the date of Easter which falls on the first Sunday after the first full moon after the spring equinox — which means it can fall any time between March 22 and April 25. As the Gregorian calendar depends on the spring equinox only, its target year length is 365.2424 days, only 0.0001 days (eight or nine seconds) away from what it actually achieves.

Timely Words
'Ah fill the cup — what
boots it to repeat
How time is slipping
underneath our feet.'

The dilemma of the calendar makers is reflected in these lines from Edward Fitzgerald's translation of the Rubaiyat of Omar Khayyam. Khayyam was much more than a poet. A skilled astronomer and mathematician, he was commissioned in 1074 by the sultan Malik shah to build an observatory in Esfahan in Iran and reform the calendar on an astronomical basis. His work is reckoned to be far more accurate than the later Gregorian reform.
Easter has been a bone of contention among churches for 17 centuries. The Eastern Orthodox churches often celebrate their Easter up to five weeks later than Western churches, because they persist in using the Julian calendar. In 1923 the Orthodox churches considered altering their calendar to use a leap year scheme with seven leap years dropped from nine centuries, rendering a fraction 218/900 = 0.242222 which was claimed to be superior to the Gregorian because it is closer to 0.2422 than is 0.2425. But their analysis was based upon the false target propagated by the Astronomical Almanac and its predecessors.

Similarly the Persian calendar, which also uses the equinox as its defining juncture, currently employs a cycle of eight leap years in 33, and 8/33 = 0.242424. But moves are afoot in Iran to upset that superior scheme based on the false assumption that British and American Astronomers have got it right. They would do far better to stick with Omar Khayyam (see box).

Let's summarize, then. Britain mis-defined its calendar in 1751, and that system has been inherited by the USA (which has no specific calendar statute of its own) and much of the rest of the world. The underlying cause was anti-Catholic feeling.

Britain could not openly admit to adopting the Gregorian calendar, and in consequence got itself into a tangle.

Similarly for anti-Jewish reasons the definition of Easter in the Act is garbled, because the authors avoided mentioning the Hebrew calendar or Passover.

If one follows the rubric then the Easter dates calculated differ from those tabulated in the Anglican Book of Common Prayer, the table being a simple copy of the Catholic computation.

But that is no reason to persist in supplying disinformation to others, as does the Astronomical Almanac. Calendars are important: witness the confusion over the US/UK attack in Iraq last December when Ramadan was called a day earlier than expected. If Iran degrades its calendar through assuming that Western astronomers are right, then resentment in the very least will be engendered. And what if at last all Christians agree to celebrate Easter on the same day, but then realise that the astronomical basis is in error?

Copyright 1999 Duncan Steel

This article first appeared in the "Science" section of The Guardian, 1999-06-24,
and is reproduced with the permission of the author.

Duncan Steel's book about the history and astronomy of the calendar,
Marking Time, was published in October 1999 by Wiley (New York).
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