Julian and Gregorian Calendars
What Day is It?
This ageold question has been answered by various calendar systems
since the beginning of history. Ancient civilizations made logical use of
the length of the day, lunar month, and solar year in these systems. But,
the desire to know when a particular date falls over the years is foiled by
the fact that the length of a day, or lunar month, is not an integer number
of units to the length of a solar year. Solar year is the time it takes
the Earth to return to the same spot on its orbit  about 365.2422 mean
solar days.
The problem was compounded in ancient times by the fact that it would
take many generations of observation to determine the length of the year
with great precision. Also, computational techniques, such as decimal
notation, were not available. Eventually, some societies did learn the
length of the solar year to good precision and had to decide what to do
with the fractional day at the end of the year. The simple solution would
be to have the 366th day, after the start of the year, as a shared day
between two years, but I know of no system that adapted this method. It
seems that day sharing was universally considered inconvenient. This is
fortunate since, in our modern computer age, it avoids having a Y2Ktype
catastrophe at the end of each year.
What if the fractional day at the end of the year was ignored and a
year of 365 days was instituted? After the first 365day year it would
take ¼ of the first day, of the next year, for the Earth to reach its
yearly starting position. After four years of this it would take the whole
first day, of the fifth year, to reach this point. In 40 years it would take
the first ten days, of the 41st year, to reach the start point. To observers
on the ground this meant that the seasons of the year were starting 10
days later every 40 years. In 120 years the accumulated error would be 30
days  about a lunar month. The four seasons found in the Temperate Zone
would completely shift over, into alien months, in 360 years. In this system,
the proper time to plant crops or celebrate holidays would require
recomputation every few years. This would not be a big problem today, but
in the ancient world only a few persons in the entire kingdom would have
the knowledge, or time, to carry out the computation. Even with these faults,
the Egyptians used this system. They employed 12months of 30days and 5
extra days after the last month to create their 365day calendar.
The Romans, under Julius Caesar, thought they had the seasondrifting
problem solved by inserting an extra day in their 365day calendar, every
four years. But the system was not perfect because the 0.2422 fractional
day, at the end of the year, is about 11.25 minutes short of the 0.25 day
the Romans had calculated. So, the leap year corrections were putting the
calendar eleven minutes ahead every four years. This was still a
big improvement over the Egyptian system because the date of various
holidays and seasonal events would remain fixed over many generations. It
would take 128 years of accumulated 11.25 minute error for the calendar
seasons to be permanently a day ahead of the actual seasons. In 400 years
the error would be 3.12 days. Yet, when a system is in use by many people
it becomes unpopular to change it. So after 16centuries of use, the Julian
calendar had moved the calendar seasons 12days ahead of their observed
arrival.
Calendar Reform
The modern Gregorian calendar was introduced by Pope Gregory XIII, in
1582 AD, to replace the Julian calendar. This system is largely the Julian
calendar with two changes. Firstly the leap year rule was changed so that
centurial years (for instance: 1600, 1700, and 1800) must be evenly
divisible by 400 to be leap years. In a 400year period 3 leap days would
be lost compared to the Julian calendar. Recall that the Julian calendar
would gain 3.12 days in this time period. This difference limits the gain
in 400 years to 0.12 days for the Gregorian calendar: it will take 3300
years to gain a permanent day. (This is such an achievement that I wonder
why there were no worldwide festivities to mark the 400th anniversary of
the calendar in 1982?)
Secondly, ten days were dropped so that the seasons would occur as they
did in 325 AD. This was probably done because the First Council of Nicaea
had set the rules for determining the date of Easter in that year. Where
the Pope had sway, the day after October 4th 1582 (Julian) was October
15th 1582 (Gregorian). Other countries held on to the Julian calendar much
longer and had to drop a few more days when they switched. England and the
American colonies converted in 1752, Japan adopted this Western calendar
in 1873, Russia had to wait until the government changed in 1918, and
Turkey held out until the 192628 period when reformers took power. A recently
published book: Mapping Time: The Calendar and its History by E. G.
Richards gives a global survey of calendars from the prehistoric
to modern. While not must reading for the average amateur, if you
see it in a library or bookstore, peruse chapter 19 for a fascinating look
at the multicentury struggle to reform the Julian calendar into the
Gregorian calendar.
Calendrics
Civil calendars are unsatisfactory for carrying out date calculations (calendrics)
and comparing astronomical data gathered under different calendars. The
Julian day count is a common astronomical calendar that facilitates
comparison and manipulation of dates. It is a continuous count of dates
since January 1, 4713 BC; this start date was chosen to encompass all
dates within recorded history.
Date Formulas Usage Example
The typical amateur astronomer may not have a great need to translate
between Julian and Gregorian dates. On the other hand, it is very useful
for dating old documents such as used in genealogy research. Here is an
example of converting a Julian birthday to Gregorian, by way of Julian day
count:
Julian Calendar Date input 

Julian Day intermediate 

Gregorian Calendar Date output 

This is George Washington's birthday. But for an historian or
genealogist there is a peculiar twist to this result. In the period that
Washington lived, the English New Year was on the Feast of the Annunciation
on March 25. So, for the first twenty years of his life Washington's date
of birthday was 1731. Calendar reform that adopted the Gregorian calendar
in 1752 shifted the start of the year to January and his birthday to 1732.
Since the formulas presented here can't take into account all
machinations to the Julian/Gregorian calendar switch prior to the modern age,
research is advised before taking a calculated result as historical fact.
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