What on Earth is Epact?

By Andrew E. Rothovius
April 8, 2020
Sun Moon
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Here’s a little something deliciously arcane for those who long for the “simplicity” of life before computers. Listed in the Astronomical Glossary of The Old Farmer’s Almanac is the word Epact, expressed as a number from 1 to 30. What is epact? It all goes back to the early days of calculating Easter. 

What is Epact?

First, let’s review some basics. We witness a Full Moon about every 29.5 days. And our regular calendar month has 28 to 31 days each. It turns out that the lunar year is about 11 days shorter than our 365-day calendar year.  (Our calendar is the Gregorian calendar which is a solar calendar, though it grew out of a lunar calendar.)

These days by which the solar year exceeds the lunar year are called epacts. If you wish to convert from the lunar year to the solar year, you need to add the extra days.

With today’s Gregorian calendar, an epact is a number representing the age of the Moon on January 1 in order to harmonize the lunar and solar calendars. Occasionally (as happened in 1992) a year will have two epacts. So, why do we need an epact — let alone two?

Early Formulas to Calculate Easter

It all goes back to the early years of the Christian era and the need to determine in advance the date for Easter, which is dependent on the vernal equinox and the nearest full Moon.

For several hundred years it had been known that the phases of the Moon went through a 19-year cycle, in which no new Moon ever recurred on the same date.

After several bouts of trial and error, another regularly repeating cycle of 28 years was discovered, in which every possible day-of-month and day-of-week combination in the Western 12-month calendar occurs at least once.

By multiplying these two cycles together (19 x 28), a grand cycle of 532 years was derived, from which it was simple to construct a perpetual almanac that would readily give the date of Easter for any year within it. At the end of the 532 years, the same sequence starts all over again. Problem solved — or so they thought.

Alas, they overlooked the fact that the 19-year lunar cycle falls short by one hour and 29 minutes of being 19 full years. This amounts to one whole day every 308 years. One obvious answer would have been to revise the perpetual almanac every 308 years (and pray for the invention of the computer). But the Middle Ages, suspicious of any intervention in these matters, took no corrective action, and by 1570 the perpetual almanac was already four days in arrears.

Yes, we know this is confusing. Don’t worry too much about the math. It didn’t work. 

Introducing Epact 

In 1572 a commission of astronomers appointed by Pope Gregory XIII undertook a general revision of the calendar.

At this point it would have been easy to revise the perpetual almanac for Easter dates, but one member of the commission, a scholar named Christopher Clavius, conceived the idea of scrapping the perpetual almanac—and substituting a new mode of calculation he called the epact.

Clavius’s epact is based on the number of days between the last new Moon in December and January 1. This number varies from 1 to 30 within each 19-year cycle. Upon this foundation, which requires adjustment every three centuries, Clavius built a complicated edifice of numbers that could serve for 7,000 years before being recalculated.

In fact, Clavius’s calculations hardly ever agree exactly with the real astronomical full Moon, but are usually a day or two off, either earlier or later. The same is true of the December new Moon, which is the basis of the epact. Nevertheless, the system works after a fashion, and in pre-computer times it did provide a rough-and-ready means of determining Easter dates for many years ahead.

Clavius was proud of his complex brainchild, and Western calendar makers adopted it universally. There are no less than 30 different epact sequences, each lasting either 300 or 400 years and all requiring some intermediate corrections. In the current sequence, the 19-year lunar cycle has two years in which the December new Moon would occur 25 days before January 1. Astronomically, however, the new Moon never occurs twice on the same day of any month in a given lunar cycle. To get around that, Clavius devised the use of a second epact, in which a number not already used in the 19-year cycle is used instead

Confused Yet?

No matter. The irony of this curious provision is that even in Clavius’s pre-computer age, epact was an unnecessary complication; today it is totally unneeded, although still a traditional element of this Almanac (computers can figure the date of Easter for the next million years if need be).

As one modern critic said, Clavius shrouded the whole concept in such a mass of erudite detail that “few have really mastered it and fewer have dared to criticize. Like the squid or cuttlefish, Clavius protected his scheme by the cloud of ink with which he surrounded it.

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Source: 

The 1994 Old Farmer’s Almanac

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When this astrological phenomenon is computed electronically...

is it called e-pact?