
             SUPPLEMENTAL INFORMATION FOR SETTIME.MAC
             ========================================

                             Contents

A.  DESCRIPTION OF THE NIST AUTOMATED COMPUTER TIME SERVICE (ACTS)
B.  DESCRIPTION OF US NAVAL OBSERVATORY (USNO) SYSTEM
C.  MODIFIED JULIAN DATE
D.  THE JULIAN AND THE GREGORIAN CALENDARS


 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
A.  DESCRIPTION OF THE NIST AUTOMATED COMPUTER TIME SERVICE (ACTS)

The service uses multi_speed modems which should automatically adapt to
the speed of the originating modem.  All messages are sent using standard
ASCII characters with 8 bits, no parity and 1 stop bit.

Format of the time message:

                          D  L D
   MJD  YR MO DA H  M  S  ST S UT1 msADV        <OTM>
  47999 90_04_18 21:39:17 50 0 +.1 045.0 UTC(NIST) *
  47999 90_04_18 21:39:18 50 0 +.1 045.0 UTC(NIST) *
  etc...

     The message transmits Universal Coordinated Time (UTC), the
official world time referred to the zero meridian of longitude.

The MJD is the modified Julian Day number, which advances by 1 at 0000
UTC every day.

The DST parameter provides information about Daylight Saving Time, using
the model valid for the continental US:

  00 = US is on standard time (ST).

  50 = US is on DST.

  82 to 51 = 50 plus number of days until DST goes into effect. Count
             starts on April 1.  Go to DST when your local time is 2:00 am
             and the count is 51.  The count is decremented daily at 00
             (UTC).

  31 to 01 = Number of days until ST goes into effect.  This count starts
             on October 1.  Go to ST when your local time is 2:00 am and
             the count is 01. The count is decremented daily at 00 (UTC).

LS = Leap second flag is set to "1" to indicate that a leap second is to be
added as 23:59:60 UTC on the last day of the current month (usually June or
December).  The flag will be set to "2" if the last second of the current
month is to be dropped. The second following 23:59:58 UTC on the last day
of the month will be 00:00:00 of the next day in that case.  The flag will
remain on for the entire month before a leap_second event; it will be 0
otherwise.

DUT1 = Approximate difference between earth rotation time (UT1) and UTC, in
steps of 0.1 second.         DUT1 = UT1 - UTC

The specified time is valid when the "*" on-time marker is received.  This
character will be transmitted 45 ms early to compensate for the nominal
delay in the modems and the telephone connection.

The maximum connection time will be 40 seconds unless you transmit a
"%" character before then.  If this character is received, the transmitter
will break the connection at the next on_time marker.

For more information write:
NIST-ACTS
Time and Frequency Division
Mail Stop 847
325 Broadway
Boulder, CO  80303

e-mail: time@time.nist.gov

Software for setting (PC)DOS compatible machines is available
on a 360-kbyte diskette for $42 from:

    Office of Standard Reference Materials
    NIST, Gaithersburg, MD, 20899, (301) 975-6776

The software and additional information are also available on the internet
via anonymous ftp from time-a.timefreq.bldrdoc.gov and from
http:/www.bldrdoc.gov/timefreq/service/acts.htm

 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
B.  DESCRIPTION OF US NAVAL OBSERVATORY (USNO) SYSTEM


Time Service provides USNO Master Clock time via dialin modem on line:
(202) 762-1594

The communications parameters are: 1200 Baud, 8-bit ASCII, no parity

The format of data is:
MJD DOY HHMMSS UTC cr/lf
* cr/lf

MJD is the 5-digit Modified Julian Day.  DOY is the 3-digit day of the
year.  HH is the current hour; MM, current minutes; and SS, current
seconds.  UTC is the three characters "UTC".

The MJD of the last day of the year from 1997 to 2100 is given by

    MJD = 50448 + INT(365.25*(YEAR-1997)),

where INT(x) means the integer part of x.

The "*" is the on-time mark for the preceding time information, and is
delayed by .0017 seconds (+/- .0004 sec.) from UTC(USNO).

The timing generator which produces this data stream is driven directly by
the Master Clock's reference signals without computer intervention.

The modems on line are compatible with Bell 212A and CCITT V.22 standards.
They also support CCITT V.54 Remote Digital Loopback (RDLB). The Hayes
command for RDLB is AT&T6. After the RDLB command is sent, any characters
sent will be returned to the sender. Count the time it takes for a
character to return, divided by two, and you will have the time delay
between the two locations. This correction can be added to the time mark
for high accuracy synchronization.

The Julian Day (JD) is a continuous day count from 4712 BC. The Modified
Julian Day is the Julian Day minus 2400000.5.

 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
C.  MODIFIED JULIAN DATE

"L'amour faite passer les temps. Les temps faite passer l'amour."
-- from an old French sundial

The Modified Julian Day (MJD) is an abbreviated version of the
old Julian Day (JD) dating method which has been in use for
centuries by astronomers, geophysicists, chronologers and others
who needed to have an unambiguous dating system based on
continuing day counts.

The JD counts have very little to do with the Julian calendar
which was introduced by Julius Caesar (44 BC) and in force until
1582 when Pope Gregory directed the use of an improved calendar,
now known as the Gregorian Calendar. In the case of the Julian
day count, the name was given because at the time, the Julian
calendar was in use and, therefore, the epoch of the day count
was fixed in respect to it. The JD counts days within one Julian
Period of exactly 7980 Julian years of 365.25 days.

Start of the JD count is 12 NOON 1 JAN -4712, Julian proleptic
Calendar. Note that this day count conforms with the astronomical
convention starting the day at noon, in contrast with the civil
practice where the day starts with midnight (in popular use the
belief is widespread that the day ends with midnight but this is
not the proper scientific use).

The Julian Period is given by the time it takes from one
coincidence to the next of a solar cycle (28), a lunar cycle
(19), and the Roman Indiction (a tax cycle of 15 years). At any
rate, this period is of interest only in regard to the adoption
of the start, at which time all periods counted backwards were in
coincidence.

The Modified Julian Day, on the other hand, was introduced by
space scientists in the late 50's of this century. It is defined
as

    MJD = JD - 2400000.5

The half day is subtracted so that the day starts at midnight in
conformance with civil time reckoning. This MJD has been
sanctioned by various international commissions such as IAU,
CCIR, and others who recommend it as a decimal day count which is
independent of the civil calendar in use. To give dates in this
system is convenient in all cases where data are collected over
long periods of time. Examples are double star and variable star
observations, the computation of time differences over long
periods of time such as in the computation of small rate
differences of atomic clocks, etc.

The MJD is a convenient dating system with only 5 digits,
sufficient for most modern purposes. The days of the week can
easily be computed because the same weekday is obtained for the
same remainder of the MJD after division by 7.

EXAMPLE: MJD 49987 = MON., 27 SEPT, 1995

Division of the MJD by 7 gives a remainder of 0. All Mondays in
1995 have this same remainder of 0.

Note that for 1993 the MJD = 48987 + DOY
          For 1994 the MJD = 49352 + DOY   previous + 365 days
          For 1995 the MJD = 49717 + DOY   previous + 365 days
          For 1996 the MJD = 50082 + DOY   previous + 365 days
          For 1997 the MJD = 50448 + DOY   previous + 366 days

where DOY is the Day of the respective Year.

The MJD (and even more so the JD) has to be well distinguished
from this day of the year (DOY). This is also often but
erroneously called Julian Date, when in fact it is a Gregorian
Date expressed as number of days in the year. This is a grossly
misleading practice that was introduced by some who were simply
ignorant and too careless to learn the proper terminology. It
creates a confusion which should not be taken lightly. Moreover,
a continuation of the use of expressions "Julian" or "J" day in
the sense of a Gregorian Date will make matters even worse. It
will inevitably lead to dangerous mistakes, increased confusion,
and it will eventually destroy whatever standard practices exist.

The MJD has been officially recognized by the International
Astronomical Union (IAU), and by the Consultative Committe for
Radio (CCIR), the advisory committee to the International
Telecommunications Union (ITU). The pertinent document is

CCIR RECOMMENDATION 457-1, USE OF THE MODIFIED JULIAN DATE BY THE
STANDARD FREQUENCY AND TIME-SIGNAL SERVICES.

This document is contained in the CCIR "Green Book" Volume VII.
Additional, extensive documentation regarding the JD is contained
in the Explanatory Supplement to the Astronomical Ephemeris and
Nautical Almanac, and in the yearbooks themselves, now called The
Astronomical Almanac. The Almanac for Computers also provides
information on such matters.

NOTE: The MJD is always referred to as a time reckoned in
Universal Time (UT). The same is not true for the DOY. This is
usually meant in a local time sense, but in all data which are
given here at the observatory, we refer the DOY to UT also,
except where specifically noted. One could call it then something
like Universal Day of the Year to emphasize the point. However,
this would introduce a completely new term, not authorized by any
convention. Moreover, it is not really necessary to use a
different term because we simply follow logically the same
practice of extending a time and date measure to the UT reference
as we do when we give any date or hour.

NASA sometimes uses what they call the Truncated MJD or TJD. It
is simply the MJD less the first digit. The above used date would
be 6324 Note, however, that in this case the remainder for the
days of the week comes out differently (3 for Mondays).

LITERATURE:

Gordon Moyer, "The Origin of the Julian Day System", Sky and
Telescope, vol. 61, pp. 311-313 (April 1981).   See also a
subsequent letter by R.H. van Gent, Sky and Telescope, vol.62,
p.16 (July 1981).

Last but not least, see also the Explanatory Supplement to the
Astronomical Almanac pp. 600 etc.  This is the current, revised
issue published by University Science Books, FAX 415-383-3167,
ISBN 0-935702-68-7.

Gernot M. R. Winkler
formerly with
U.S. NAVAL OBSERVATORY
3450 MASSACHUSETTS AVENUE NW
WASHINGTON DC  20392-5420

 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
D.  THE JULIAN AND THE GREGORIAN CALENDARS

by Peter Meyer
Last modified: October 21, 1997
11-03-97 Minor format editing by David Rife


1.  The Julian Calendar

2.  The Gregorian Reform

3.  Adoption of the Gregorian Calendar

4.  Astronomical Year Numbering

5.  The Julian and the Gregorian Proleptic Calendars

6.  Variation in the Tropical Year

7.  Accuracy of the Gregorian and Orthodox Calendars

8.  True Length of the Tropical Year

------------------------------------------------------------------------

(1) The Julian Calendar

For many European (now often worldwide) institutions, we can
thank the Romans (for good or for bad, though they too had their
predecessors). So with the solar calendar currently in widespread
use.

Originally the Romans numbered years ab urbe condita, that is,
"from the founding of the city" (of Rome, where much of the
character of the modern world had its beginnings). Had this old
calendar remained in use, 1996-01-14 would have been New Years
Day in the year 2749 a.u.c.

Following his conquest of Egypt in 48 B.C. Julius Caesar
consulted the Alexandrian astronomer Sosigenes about calendar
reform (since the a.u.c. calendar then used by the Romans was
completely inadequate to the needs of the emerging empire, which
Caesar was poised to command, briefly as it turned out). The
calendar which Julius Caesar adopted in the year 709 a.u.c. (what
we now call 46 B.C.) was identical to the Alexandrian
Aristarchus' calendar of 239 B.C., and consisted of a solar year
of twelve months and of 365 days with an extra day every fourth
year. It is unclear as to where or how Aristarchus arrived at
this calendar, but one may speculate that Babylonian data or
theory was involved.

As we can read in the excellent article, "The Western Calendar
and Calendar Reforms" in the Encyclopedia Brittanica, Sosigenes
decided that the year known in modern times as 46 B.C. should
have two intercalations. The first was the customary
intercalation of 23 days following February 23, the second, "to
bring the calendar in step with the equinoxes, was achieved by
inserting two additional months between the end of November and
the beginning of December. This insertion amounted to an addition
of 67 days, making a year of no less than 445 days and causing
the beginning of March, 45 B.C. in the Roman republican calendar,
to fall on what is still called January 1 of the Julian
Calendar."

The Roman date-keepers at first erroneously added a leap day
every third year, rather than every fourth, as we do today. This
practice was continued to 9 B.C., when the Emperor Augustus
(Caesar's nephew Octavian) decreed that leap years should not be
observed for awhile (they were resumed in 8 A.D.).

Another source of uncertainty regarding exact dating of days at
this time derives from changes made by Augustus to the lengths of
the months. According to some accounts, originally the month of
February had 29 days and in leap years 30 days (unlike 28 and 29
now). It lost a day because at some point the fifth and six
months of the old Roman calendar were renamed as Julius and
Augustus respectively, in honor of their eponyms, and the number
of days in August, previously 30, now became 31 (the same as the
number of days in July), so that Augustus Caesar would not be
regarded as inferior to Julius Caesar. The extra day needed for
August was taken from the end of February. However there is still
no certainty regarding these matters, so all dates prior to A.D.
8, when the Julian Calendar finally stabilized, are uncertain.

Subsequently the Julian Calendar became widespread as a result of
its use throughout the Roman Empire and later by the Christian
Church, which inherited many of the institutions of the Roman
world.

The system of numbering years A.D. (for Anno Domini, "in the year
of Our Lord") was instituted in the year 525 by the Roman abbot
Dionysus Exiguus, and endured for more than a millennium. Because
of its specifically Christian meaning this designation is now
often replaced by the more neutral C.E. (for Common Era), and
B.C. is now often written B.C.E. (for Before Common Era).


(2) The Gregorian Reform

The average length of a year in the Julian Calendar is 365.25
days (one additional day being added every four years). The
length of the year in the Julian Calendar exceeds the length of
the mean solar year (365.24219 mean solar days to five decimal
places) by 11.2 minutes. This error accumulates so that after 128
years the calendar is out of sync with the equinoxes and
solstices by one day. Thus as the centuries passed the Julian
Calendar became increasingly inaccurate with respect to the
seasons. This was especially troubling to the Christian Church
because it affected the determination of the date of Easter,
which, by the 16th Century, was well on the way to slipping into
Summer.

Pope Paul III recruited several astronomers to come up with a
solution, principally the Jesuit Christopher Clavius (1537-1612)
who built upon calendar reform proposals by the astronomer and
physician Luigi Lilio (d. 1576). When Pope Gregory XIII was
elected he found various proposals for calendar reform before
him, and decided in favor of that of Clavius. On 1582-02-24 he
issued a papal bull, Inter Gravissimas, establishing what is now
called the Gregorian Calendar reform. The Gregorian Calendar is
the calendar which is currently in use in all Western and
Westernized countries.

The Gregorian reform consisted of the following:

    Ten days were omitted from the calendar, and it was decreed
    that the day following (Thursday) October 4, 1582 (which is
    October 5, 1582, in the old calendar) would thenceforth be
    known as (Friday) October 15, 1582.

    The rule for leap years was changed. In the Julian Calendar a
    year is a leap year if it is divisible by 4. In the Gregorian
    Calendar a year is a leap year if (a) it is divisible by 4
    and (b) if it is divisible by 100 then it is divisible by
    400. In other words, a year which is divisible by 4 is a leap
    year unless it is divisible by 100 but not by 400 (in which
    case it is not a leap year). Thus the years 1600 and 2000 are
    leap years, but 1700, 1800, 1900 and 2100 are not.

	New rules for the determination of the date of Easter were
    adopted (the old rule relied on the Jewish calendar).

	The first day of the year (New Years Day) was set at January
    1st.

	The position of the extra day in a leap year was moved from
    the day before February 25th to the day following February
    28th.

The term "leap year" derives from the fact that the day of the
week on which certain festivals were held normally advanced by
one day (since 365 = 7*52 + 1), but in years with an extra day
the festivals would "leap" to the weekday following that.

It may be noted that there was no necessity for ten days, rather
than, say, twelve days to have been omitted from the calendar. In
fact, the calendar could have been reformed without omitting any
days at all, since only the new rule for leap years is required
to keep the calendar synchronized with the vernal equinoxes. The
number of days omitted determines the date for the Spring
equinox, an omission of ten days resulting in a date usually of
March 20th.

The average length of the vernal equinox year during the last
2000 years is 365.242 days. The average length of the Julian year
(365.25 days) differs from this value by 0.008 days. So from the
year 1 to the year 1582 the calendar drifted off the mean solar
year by 1581*0.008 = 12.6 days. Why didn't Pope Gregory remove
twelve days, instead of just ten? It has to do with the First
Council of Nicea, which was held in Nicea (now Iznik, Turkey) in
the year 325. One of the matters settled by this council was the
method for determining the date of Easter. From the 325 to 1582
the calendar diverged by 1257*0.008 = 10.1 days, so ten days were
removed so as to restore the date of Easter to the same time of
the year at which it had occurred at the time of the Council of
Nicea.


(3) Adoption of the Gregorian Calendar

The Gregorian Calendar was adopted immediately upon the
promulgation of Pope Gregory's decree in the Catholic countries
of Italy, Spain, Portugal and Poland, and shortly thereafter in
France and Luxembourg. During the next two years most Catholic
regions of Germany, Belgium, Switzerland and the Netherlands came
on board. Hungary followed in 1587. The rest of the Netherlands,
Denmark, Germany and Switzerland made the change during 1699 to
1701.

By the time the British were ready to go along with the rest of
Europe, the old calendar had drifted off by one more day,
requiring a correction of eleven days, rather than ten, to locate
the Spring equinox at March 21. The Gregorian calendar was
adopted in Britain (and in the British colonies) in 1752, with
September 2, 1752, being followed immediately by September 14,
1752.

In many countries the Julian Calendar was used by the general
population long after the official introduction of the Gregorian
Calendar. Thus events were recorded in the 16th - 18th Centuries
with various dates, depending on which calendar was used. Dates
recorded in the Julian Calendar were marked "O.S." for "Old
Style", and those in the Gregorian Calendar were marked "N.S."
for "New Style".

To complicate matters further New Year's Day, the first day of
the new year, was celebrated in different countries, and
sometimes by different groups of people within the same country,
on either January 1, March 1, March 25 or December 25. January 1
(decreed by Pope Gregory) seems to have been the usual date but
there was no standard observed. With the introduction of the
Gregorian Calendar in Britain and the colonies New Year's Day was
generally observed on January 1. Previously in the colonies it
was common for March 24 of one year to be followed by March 25 of
the next year. This explains why, with the calendrical reform,
the year of George Washington's birth changed from 1731 to 1732.
In the Julian Calendar he was born on 2/11/1731 but in the
Gregorian Calendar his birthdate is 2/22/1732.

Sweden adopted the Gregorian Calendar in 1753, Japan in 1873,
Egypt in 1875, Easterm Europe during 1912 to 1919 and Turkey in
1927. Following the Bolshevik Revolution in Russia it was decreed
that thirteen days would be omitted from the calendar, the day
following January 31, 1918, O.S. becoming February 14, 1918, N.S.
Further information can be found in The Perpetual Calendar.

In 1923 the Eastern Orthodox Churches adopted a modified form of
the Gregorian calendar in an attempt to render the calendar more
accurate (see below). October 1, 1923, in the Julian Calendar
became October 14, 1923, in the Eastern Orthodox calendar. The
date of Easter is determined by reference to modern lunar
astronomy (in contrast to the more approximate lunar model of the
Gregorian system).


(4) Astronomical Year Numbering

Astronomers designate years B.C. by means of negative numbers. In
order to avoid a hiatus between the year 1 and the year -1, there
has to be a year 0. Thus astronomers adopt the following
convention:

1 A.D. = year 11 B.C. = year 02 B.C. = year -1 and so on

More generally, a year popularly designated n B.C. is designated
by astronomers as the year -(n-1).

The rules for leap years, in both calendars, are valid for the
year 0 and for negative years as well as for positive years.

Note that the rules for leap years in the two calendars work for
years prior to 1 A.D. only if those years are expressed according
to the astronomical system, not if expressed as years B.C.  4 A.D
is a leap year in both calendars, 1 B.C = astronomical year 0, 5
B.C = year -4, 9 B.C = year -8, and so on, are all leap years.
101 B.C. = year -100 is a leap year in the (proleptic) Julian
Calendar but not in the (proleptic) Gregorian Calendar. These
statements, however, are only abstractly true, because (as noted
above) prior to 8 A.D. the leap years were not observed correctly
by the Roman calendrical authorities.


(5) The Julian and the Gregorian Proleptic Calendars

Every date recorded in history prior to October 15, 1582
(Gregorian), such as the coronation of Charlemagne as Holy Roman
Emperor on Christmas day in the year 800, is a date in the Julian
Calendar, since on those dates the Gregorian calendar had not yet
been invented.

We can, however, identify particular days prior to October 15,
1582 (Gregorian), by means of dates in the Gregorian Calendar
simply by projecting the Gregorian dating system back beyond the
time of its implementation. A calendar obtained by extension
earlier in time than its invention or implementation is called
the "proleptic" version of the calendar, and thus we obtain the
Gregorian proleptic calendar. The Julian Calendar also can be
extended backward as the Julian proleptic calendar.

For example, even though the Gregorian Calendar was implemented
on October 15, 1582 (Gregorian) we can still say that the date of
the day one year before was October 15, 1581 (Gregorian), even
though people alive on that day would have said that the date was
October 5, 1581 (the Julian date at that time). As another
example, the date of the coronation of Charlemagne, December 25,
800, in the Julian Calendar, was December 29, 800, in the
Gregorian proleptic calendar.

Similarly, dates after October 15, 1582 (Gregorian) have
equivalent, but different, dates in the Julian Calendar. For
example, this article was completed on October 10, 1992, in the
Gregorian Calendar, but we could equally well say that it was
completed on September 28, 1992, in the Julian Calendar. As
another example, the date of the winter solstice in the year 2012
is December 21, 2012 (Gregorian), which is December 8, 2012
(Julian).

Thus any day in the history of the Earth, either in the past or
in the future, can be specified as a date in either of these two
calendrical systems. The dates will generally be different; in
fact they will be the same only for dates from March 1st, 200, to
February 28, 300. The dates in neither calendar will coincide
with the seasons in the distant past or distant future, but that
does not affect the validity of these calendars as systems for
uniquely identifying particular days.


(6) Variation in the Tropical Year

The tropical year (a.k.a. the mean solar year) corresponds to the
cycle of the seasons. The exact definition of this concept is
currently a matter of debate among some astronomers (see Simon
Cassidy's Error in Statement of Tropical Year). All agree,
however, that due to the gravitational dynamics of the
Sun-Earth-Moon system the length of the tropical year (however
defined) is changing slowly. The length of the tropical year on
2000-01-01 is calculated by some astronomers to be 365.24218967
days, but at this level of precision the value depends on the
definition of the concept. The value changes significantly with
the millennia, however, as follows (according to a formula in
common use among astronomers):

  Year           Length of tropical year in days
 -5000           365.24253
 -4000           365.24250
 -3000           365.24246
 -2000           365.24242
 -1000           365.24237
     0           365.24231
  1000           365.24225
  2000           365.24219
  3000           365.24213
  4000           365.24207
  5000           365.24201

Thus the value of the tropical year varies over this 10,000-year
timespan by as much as .00052 days (about 45 seconds).


(7) Accuracy of the Gregorian and Orthodox Calendars

As in any completely rule-based (or determinate) calendar, the
Gregorian Calendar is not absolutely accurate. As noted above,
the average mean solar year at 2000-01-01 is 365.24219 days,
compared to the average length of the year in the Gregorian
Calendar of 365.2425 days. The average length of the year in the
Gregorian Calendar thus exceeds the mean solar value at present
by about 11.23 seconds (compared to 11.2 minutes for the Julian).
Were the length of the mean solar year to be constant this error
would accumulate to one day after about 3,200 years. However, by
the year 5000 the value of the mean solar year will have
decreased from 365.24219 days to 365.24201 days. Since the value
of the mean solar year during the period of -5000 to 5000 ranges
from 365.24253 to 365.24201 it is difficult to estimate
calendrical error precisely, but we can say that the Gregorian
calendar is becoming less accurate (with respect to the mean
solar year) in the short term (a few thousand years) but may
become more accurate in the long term (about 20,000 years), with
further variations thereafter.

However, astronomers distinguish between the mean solar year and
the average vernal equinox year (a distinction considered by some
to have not only astronomical but also political significance)
and the Gregorian Calendar, according to some acute
investigators, was intended to follow the latter rather than the
former, a fact which has resulted in confusion among scholars who
study the question of its accuracy.

Whereas in the Gregorian Calendar a century year is a leap year
only if division of the century number by 4 leaves a remainder of
0, in the Eastern Orthodox system a century year is a leap year
only if division of the century number by 9 leaves a remainder of
2 or 6. This implies an average calendar year length in the
Orthodox calendar of 365.24222 days. This is very close to the
present mean solar value of 365.24219, and the Eastern Orthodox
calendar is at present significantly more accurate in this
respect than the Gregorian. Were the mean solar year to remain
constant, the Orthodox calendar would be off by one day only
after about 33,000 years. However over the next few millennia the
Orthodox calendar, like the Gregorian, will become increasingly
inaccurate with respect to the mean solar year until possibly
recovering around 10,000 years from now. However, in terms of the
vernal equinox year the Gregorian Calendar is more accurate than
the Orthodox and will become more accurate in the near future.


(8) True Length of the Tropical Year

There is currently some controversy over the accuracy of
calendars and the true length of the tropical year (and, as noted
above, there is even controversy as to how this notion should be
defined). Those interested in diving into the conceptual
complexities of this debate should consult the following:

Royal Greenwich Observatory  Information leaflets

Royal Greenwich Observatory  Information Leaflet No. 48:

Leap Years  L. E. Doggett  Calendars  Simon Cassidy  Error in
Statement of Tropical Year  Simon Cassidy

The Tropical and the Anomalistic Year  Simon Cassidy
Re 4-1/8 yr.

Leap Rule responses of Richard, Jim and Amos  Simon Cassidy

Implementing a correct 33-year calendar reform  Chris Carrier


