The Gregorian calendar reform

The Julian calendar, introduced by Julius Caesar in RomBC 46, was a reform of the ancient Roman calendar which had got out of hands as the calendar had drifted out of alignment with the tropical year so that e.g. harvest festivals no longer fell at harvest time. The Julian reform took effect in RomBC 45 and was the predominant calendar in most of Europe and in European settlements in the Americas and elsewhere, until it was refined and superseded by the Gregorian calendar.

The Julian calendar has a regular year of 365 days divided into 12 months. A leap day is added to February every four years. The Julian year is, therefore, on average 365.25 days long. It was intended to approximate the tropical (solar) year. Although Greek astronomers had known, at least since Hipparchus, that the tropical year was a few minutes shorter than 365.25 days, the calendar did not compensate for that difference. As a result, the calendar year gained about three days every four centuries (or more exactly 1 day per 128.2 years) compared to observed equinox times and the seasons. When this discrepancy became obvious it was corrected by the Gregorian calendar reform of 1582. The Gregorian calendar has the same months and month lengths as the Julian calendar, but inserts leap days according to a different rule.

By 1582, the vernal equinox had moved backward in the calendar so that it occurred astronomically about  March 11, i.e. 10 days earlier than March 21 which was the nominal (given) date used as the benchmark for the calculation when the Christian feast of Easter should be celebrated. Referring to the first council of Nicaea in 325, Pope Gregory XIII wrote in his papal bull "Inter Gravissimas":

So thus that the vernal equinox, which was fixed by the fathers of the [first] Nicene Council at XII calends April [March 21], is replaced on this date, we prescribe and order that there is removed, from October of the year 1582, the ten days which go from the third before Nones [the 5th] through the day before the Ides [the 14th] inclusively.

The removal of 10 days from the calendar in October 1582 compensated for the drift during 1282 years (10 x 128.2) between the astronomical date for the vernal equinox and its nominal date (March 21). The expected number of years between 1582 and the council of Nicaea in 325 is almost the same (1257 years, though the correction could only be done with full days). Therefore we would presuppose that March 21 was both the nominal date and the astronomical date for the vernal equinox in both 325 and after 1582.

We know that this statement was true after 1582 (as this was the intention of the calendar reform), but was it true in 325? The nominal difference between 1582 and 325 is indeed 1257 years, though if we have invented (phantom) years within that period then our calculations above are misleading (and actually based on some sort of circular reasoning). Are there any observations of the vernal equinox around the Nicaea council or before? For this we have to rely on the oldest texts available which acknowledge the Julian calendar.

Anatolius of Alexandria (dead 283) relates in his "Paschal Canon" to the Julian calendar and says:

... with respect to the day of Easter, that attention must be given not only to the course of the moon and the transit of the equinox, but also to the passage (transcensum) of the sun ...

There is, then, in the first year, the new moon of the first month, which is the beginning of every cycle of nineteen years, on the six and twentieth day of the month called by the Egyptians Phamenoth. But, according to the months of the Macedonians, it is on the two-and-twentieth day of Dystrus. And, as the Romans would say, it is on the eleventh day before the Kalends of April. Now the sun is found on the said six-and-twentieth day of Phamenoth, not only as having mounted to the first segment, but as already passing the fourth day in it. And this segment they are accustomed to call the first dodecatemorion (twelfth part), and the equinox, and the beginning of months, and the head of the cycle, and the starting-point of the course of the planets. And the segment before this they call the last of the months, and the twelfth segment, and the last dodecatemorion, and the end of the circuit of the planets. And for this reason, also, we maintain that those who place the first month in it, and who determine the fourteenth day of the Paschal season by it, make no trivial or common blunder.

Alden Mosshammer's (ref.1) and our interpretation of what Anatolius says is that Easter may not be celebrated before the vernal equinox has passed, and that the nominal day for the vernal equinox is March 22. And that at this date the sun already has passed the equinox astronomically with four days, meaning that the astronomical equinox was on March 19 in the late 3rd century AD.

This interpretation of Anatolius' statements presupposes that somebody living near his time, or he himself, has determined the date for the vernal equinox experimentally. This is not at all impossible, as Anatolius had been a scholar in Alexandria and had expert knowledge in astronomy (ref.1, p.130):

Eusebius says that Anatolius was an Alexandrian by birth and one of the most eminent scholars of the time. He excelled in mathematics, astronomy, physical science, philosophy, and rhetoric. At the invitation of his fellow citizens, he founded a school of Aristotelian philosophy at Alexandria.

If the vernal equinox was astronomically on March 19 in the late 3rd century AD, it was on March 21 or 22 when the Julian calendar was introduced about 300 years before. Several scientists have noted the brisance of this fact and concluded accordingly that Anatolius must have erred. There is also a latin version of Anatolius' Paschal Canon, mentioning March 25 instead of March 22 for the vernal equinox. This version is regarded as a 7th century forgery. Read the complete discussion in ref.1, ch.8.

If we assume that Anatolius has not erred, the vernal equinox was astronomically on March 19 also at the Nicaea Council in 325, only a few years after Anatolius' death. As the vernal equinox was astronomically on March 11 in 1582, there are only eight days offset between the two observations. This equals 1026 years if we multiply 8 with 128.2 which is the number of years per one day offset (see above).

However, the nominal difference between the date for the Gregorian reform and Nicaea is instead 1257 years (see above). This means that the historical time line between 325 and 1582 counts 231 "phantom" years too much.

Note: The calculation of the size of the calendar error is only a very rough estimation as the offset increases with one day every 128 years. So the close compliance of the 231 phantom years with our 232 postulated years is only a chimera.


1. Mosshammer A.A.: The Easter Computus and the Origins of the Christian Era. Oxford Early Christian Studies. Xi + 474 pp (Oxford 2008). Read here.