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February 29, 2016. A Leap Day!

THE JULIAN VS. THE GREGORIAN CALENDAR By 2500 BC when the first of the Pyramids were built, the length of the year was reckoned by Egyptian mathematician/priests as 360 days. They had erected pairs of gnomons (posts with notches cut out at their tops) and positioned them vertically so that at the Summer Solstice, light...

THE JULIAN VS. THE GREGORIAN CALENDAR Statue of Pope Gregory XIII, in St. Peter’s Basilica in Rome. Photo courtesy of Terez Anon.

By 2500 BC when the first of the Pyramids were built, the length of the year was reckoned by Egyptian mathematician/priests as 360 days. They had erected pairs of gnomons (posts with notches cut out at their tops) and positioned them vertically so that at the Summer Solstice, light from the star Sirius, the brightest star in the Northern heavens, would be aligned in the notches. (Of course, the sun itself is a star, but it would not be identified as a star until Aristarchus introduced the heliocentric picture of the universe in the 3rd century BC, and Copernicus resurrected the idea in the mid-sixteenth century.) The Egyptian priests counted the days as Sirius wandered away, and then returned to the notches in the same pair of gnomons. Along with their determination of the length of the year, they introduced a year of 10 months of 36 days each. It is believed that they also introduced the number of degrees in a circle at this time as 360°.

By 1000 BC, the Egyptian priests had realized that the seasons were occurring at the wrong time of year, and that a considerable error had accumulated in the preceding two millennia since. They also reckoned 365 days to be a much better approximation for the length of the year. However, they stayed with their traditional 10-month calendar of 36 days each, but modified it by adding 5 days of festivities at the end. By 800 BC, the Etruscans, the predecessors of Romans on the Italian Peninsula, adopted the Egyptian Calendar.

Initially, the Romans continued with the calendar that had been developed by the Etruscans. But following their practice of naming children in their own families — with the first 4 children being assigned proper names, but after the fourth child, being assigned numbers — the first four months would bear the names of Roman Gods, “March” for “Mars,” “April” (for “Aphrodite”), “May” (for the God of Spring, “Jupiter Mayo”), “June” (for the wife of Jupiter, “Juno”) followed by the fifth month, “Quintillus;” the sixth month, “Sextillus;” the seventh, “Septillus;” etc. By the 3rd Century BC, when the Romans were engaged in the Punic Wars against the Carthaginians led by Hannibal, they ran out of money to pay their soldiers. They solved the problem, by revising the calendar to have 12 months of 30 days each, and then add 5 days of festivities at the end. The months of January and February, without pay, were inserted in the beginning of the calendar, with all the others shifted by two. Thus, March became the third month; April, the fourth… and “Septillus,” literally the seventh month became the ninth; “Octillus,” literally the eighth month, became the tenth month, and so on. These, of course, are the present scheme of names of months.

The exact length of the year is not 365 days.They had been watching Sirius appear and disappear, but failing to return to precisely the same spot after one year, that it took 1461 days for it to be at the same spot, but in the interim, the Nile had flooded four times… four years had passed. Accordingly, a tangible error had again begun to creep in by the first century BC. During the reign of Julius Caesar in 46 BC, the Alexandrian astronomer, Sosigenes, proposed a year of 365 1/4 days, and include a leap year. He proposed the months would alternate with 31 and 30 days through the year, except for February, which would have 29 days on three years, followed by 30 days on the fourth year. Thus, January would be 31 days long; Feb 29 and 30; March, 31; April, 30; May, 31; June, 30; July, 31; August, 30; September, 31; October 30, November, 31; and December, 30. Julius Caesar adopted the new calendar, but only after renaming the month with the longest daylight hours, viz. the seventh month, Quintillus, “Julius’s month,” or July.

The emperor following Julius was his nephew, Gauis Octavius, who chose the name Augustus Caesar. Augustus, like Julius, initially thought of usurping his uncle’s month, but was dissuaded by his advisors that this would be impolitic. But, it would alright to take away a day from February, which was already short and add it to the eighth month, Sextillus, and rename it “Augustus’s month,” August. Meanwhile, February would have 28 days for three years and 29th day on the Leap Year.


Refining the calendar has been a constant quest. But 16 centuries would pass before another drastic correction. By the 1580s it was clear that another accumulation of error had taken place with the seasons occurring too late. Pope Gregory XIII in 1582 convened his astronomers and commissioned them to get a better calendar. The year is slightly shorter than the 365 ¼ days (365.25 days) prescribed by the Julian Calendar. If three leap years could be eliminated from 400 years, a far more accurate calendar would be on hand they proposed. Thus the calendar would have 365 97/400 days (or 365.242 5 days). This could be accomplished by accepting all years divisible by 4 as a Leap Year, except century marks, which must be divisible by 400. Thus in the 101 years spanning 1500 to 1600, the Gregorian Calendar does not accept 1500, but it accepts 1504, 1508, 1512…1596 and 1600 as Leap years, whereas the Julian would have accepted 1500.

Moreover, in order to get the date correct for Easter determined by the Nicene Council of AD 325, the corrections to the Julian Calendar would have to be made dating back to that date. The next century mark after the meeting of the Nicene Council would have been 400, a date acceptable to both the Julian and the Gregorian as a Leap years. In short, the two calendars would have been in synch in 400. But the year 500, would be a Leap Year in the Julian, but not in the Gregorian. The Calendars would be off by one day. In 600 they would be off by two days, in 700 by three days, but in 800, they would still be off by three days. In 900, four days; in 1000, five days; in 1100, six days; in 1200, still by six days. In 1300, they would be out of sync by seven days, in 1400 by eight days, and in 1500 by nine days.

Thus in October 1582 when the Gregorian Calendar went into effect, it was declared that the nine days had to be shaved back from the Julian date. The governments in Catholic countries complied. In Elizabethan England, however, the government declared, “Thank you very much, but we are not about to accept the Gregorian Calendar,” as they went merrily on their way. By 1752, however, it had become amply clear that the “Catholic Calendar” of 365.242 5 days was far superior to the Julian, and in September of that year, the British made a change. By then 11 days had to be shaved off the Julian. It was announced, “Everyone will go to bed on September the 9th, and wake up on September 21nd.” The public was not overjoyed by the announcement, with protests ringing out, “The birds will not know when to fly South,” or “We are going to lose 11 days of our lives!” or “This is a ploy of the Bank of England, to sit on 11 days of interest.” The transition went relatively smoothly. Many dates in history had to be corrected, however. The greatest of all scientist Isaac Newton had been born on December 25, 1642, and he had taken that Christmas birth seriously. On the corrected Gregorian Calendar, he was born on the ordinary day of January 4, 1643. And George Washington, whose birthday we celebrate on February 22, 1732, was actually born in the British Colony of Virginia on February 11, 1732 on the Julian Calendar.

Again, the Gregorian Calendar is based on 365.242 5 days. In distinction, the Maya of a millennium past in Central America employed a calendar of 364.242 2 days, derived from a discovery of a 52-years cycle in the heavens. Since the invention of the Atomic Clock by Norman Ramsey, we have known that a far more precise calendar calls for the length of the year as 365.242 199 days, making the Mayan Calendar considerably more accurate than our own Gregorian. Directed by the National Institute of Science and Technology (NIST), we periodically add or subtract a Leap Second as a correction, in order to synchronize the Gregorian Calendar with the most accurate of all, the Atomic Clock.

In 1987 Norman Ramsey of Harvard received the Nobel Prize in Physics for the invention of the Atomic Clock. And following his death in 2011, I wrote a blog as a tribute to a a personal hero and friend, The Passing of a Scientific Giant.

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Bulent Atalay
Bulent Atalay, a scientist, artist and author, has been described by NPR, PBS and the Washington Post as a “Modern Renaissance Man.” He is the author of two successful books on the intersection of art, science and mathematics, with Leonardo, the pre-eminent Renaissance man, serving as the foil. His best selling book, "Math and the Mona Lisa," (Smithsonian Books, 2004) has appeared in 13 languages. Professor Atalay's academic background is in theoretical physics. He travels around the world lecturing at academic institutions and on cruise ships on the "A-subjects," art, archaeology, astrophysics, atomic physics and Ataturk, confessing that he knows much less about the "B-subjects," business, banking, biology and botany... He is the President of the Ataturk Society of America (ASA), dedicated to promoting Ataturk's ideals of science and reason over dogma and superstition, of a secular state with full equality of genders. For more details click on Bulent Atalay