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  1. #1
    Philip Clarke's Avatar
    Philip Clarke Guest

    Default "The Calendar" by David Ewing Duncan: Numerous Errors?

    I have recently read "The Calendar" by David Ewing Duncan. It is an
    excellent book, and one that often had me going back over the pages to
    check or compare what I was currently reading with what I had read
    earlier. In doing so, however, I found several discrepancies that I
    couldn't explain. The question is, are these errors, or have I simply

    My copy is a paperback edition published by Fourth Estate, London, in
    1999. I can only quote page numbers from my book, so my apologies if
    your page numbers are different. In the order that they appear in the
    book, my queries are as follows;

    1. Calendar Index, page vi - The year as amended by Pope Gregory XIII
    (the Gregorian calendar): 365 days, 5 hours, 48 minutes, 20 seconds.
    Shouldn't this be 365 days, 5 hours, 49 minutes, 12 seconds?

    2. Calendar Index, page vi - Length of time the Gregorian calendar is
    off from the true solar year: 25.96768 seconds. Deducting this from
    the figure I have assumed in item 1 above, the true solar year would
    be 365 days, 5 hours, 48 minutes, 46.03232 seconds. Why be so
    precise, and then get it wrong? According to some sources, this
    figure corresponds to the 1840's, not 1900, 1996, 1999 or 2000 (all
    years considered to be current at various locations in the book).

    3. Calendar Index, page vi - The year as measured in oscillations of
    atomic cesium: 290,091,200,500,000,000. If Cesium oscillates
    9,192,631,770 times per second, then there are 794,243,384,928,000
    oscillations in a day. Is the year really an exact multiple of
    500,000,000 oscillations?

    4. Timeline, page xxi, Year 1100 - The year by Omar Khayyam is given
    as 365d 5h 49m 12s (and the same again on page 278), but on page 190
    it is given as 365.24219858156 days. This converts to 365d 5h 48m
    45.96s, so why the difference? I believe that the first figure is
    actually the Gregorian year. The second figure is 99.99999% of that
    given for the atomic year.

    5. Time Stands Still, page 97 - In the table, 6 Kalends April is given
    as 26th March, whereas other sources give this as 27th March. Which
    is correct?

    6. Time Stands Still, page 98. The formula 22 + 11 + 33 - 30 + 3,
    should read 22 + 11 = 33 - 30 = 3?

    7. The Strange Journey of 365.242199, page 154 - He (Aryabhata)
    estimates the length of the solar year at 365.3586805 days, some 2
    hours 47 minutes and 44 seconds off from the true year in Aryabhata's
    era, which equalled 365.244583 days. The footnote says that this is
    about 7 seconds shorter than our current year. Only three errors
    here! These are (i) 365.3586805 days is 2 hours 47 minutes and 44
    seconds off our era, not the year in 499; (ii) 365.244583 days equals
    365 days, 5 hours, 52 minutes, 12 seconds, which is actually 3 minutes
    26 seconds longer than 365.242199 days; and (iii) In 499, the year
    would have been about 7 seconds longer, not shorter, than our current

    8. From the House of Wisdom to Darkest Europe, page 190 - Omar Khayyam
    appears to have calculated the year to within 4 seconds of what it was
    in 1079. Duncan doesn't make this point, but just brushes it of as
    'overly precise'. Any comments?

    9. From the House of Wisdom to Darkest Europe, page 190-191 - Ulugh
    Beg gave a measurement for the length of the year that came to 365
    days, 5 hours, 49 minutes and 15 seconds, just 25 seconds too long. I
    make this figure about 29 seconds longer than our time, and 27 seconds
    longer than in 1440. Where does the 25 seconds come from?

    10. Solving the Riddle of Time, page 277-278 - The table contains two
    differences from what is given elsewhere in the book. The
    measurements for Omar Khayyam and the Gregorian calendar are not as
    quoted on pages 190 and 277 respectively. See items 4 and 1 above for
    further details.

    My conclusions? It's a great book, that probably took Duncan many
    years to research. However, next time, he should get somebody to
    check his mathematics!


    Philip Clarke

  2. #2
    Tom Rankin's Avatar
    Tom Rankin Guest

    Default "The Calendar" by David Ewing Duncan: Numerous Errors?

    I can take a shot at #3.

    Since the oscillation of Cesium is not known to 18 places, there is most
    likely a round off taking place here.

    It is interesting though, that this seems to imply that the length of
    the year is only defined to roughly .05 seconds.

    Philip Clarke wrote:

    Tom Rankin - Programmer by day, amateur astronomer by night!
    Mid-Hudson Astronomy Association -
    Views and Brews -

    When replying, remove the capital letters from my email address.

  3. #3
    Philip Clarke's Avatar
    Philip Clarke Guest

    Default "The Calendar" by David Ewing Duncan: Numerous Errors?


    Thanks for your response. Yes, I'm sure you're right that rounding
    has taken place.

    On page 322, Duncan defines the year as 31,556,925.9747 seconds (the
    standard up until 1967). Multiplying this by the Cesium rate gives
    290,091,200,278,565,436 oscillations. What I don't understand,
    though, is why this is rounded UP to 290,091,200,500,000,000. I would
    have been quite happy with 290,091,200,278,000,000, though.


    Philip Clarke

    Tom Rankin <> wrote in message news:<1XNMc.42187$>. ..

  4. #4
    Dr John Stockton's Avatar
    Dr John Stockton Guest

    Default "The Calendar" by David Ewing Duncan: Numerous Errors?

    JRS: In article <1XNMc.42187$>, dated
    Sun, 25 Jul 2004 12:44:45, seen in news:sci.astro.amateur, Tom Rankin
    <> posted :

    Please put responses after (trimmed) quotes.

    The figure is not for oscillations of caesium; it is for the frequency
    of radiation corresponding with a hyperfine transition of caesium.

    More importantly, the figure is exact; it defines the SI second :

    "La seconde est la durée de 9 192 631 770 périodes de la radiation
    correspondant à la transition entre les deux niveaux hyperfins de l'état
    fondamental de l'atome de cesium 133 (CGPM 13, 1967, Resolution 1). "

    One cannot speak of the length of the year without defining which year -
    Gregorian Calendar, UTC, Tropical, Sidereal, Anomalistic, Eclipse, etc.

    There appear to be 290,091,439,519,565,040 oscillations in an average
    UTC year disregarding leap-seconds - EXACTLY. For an ordinary year,
    289,898,835,498,720,000; for a leap year, 290,693,078,883,648,000; also

    Philip :

    Q1, yes, ... 12 seconds; easily worked out.

    Does the information in Duncan suffice to pin down, with certainty and
    allowing for days starting early, the exact date and time in the
    Gregorian or Julian Calendars of the first moment of Year 1 Month 1 Day
    1 of the Islamic Calendar (disregarding variation of local time with

    I considered the book to be quite good, but prefer

    <URL:> E.G.Richards,
    "Mapping Time - The Calendar and its History",
    OUP 1998, ISBN 0-19-850413-6 (now 2nd Edn, and pbk.).
    Book &amp; site include algorithms; site has errata.

    I've not seen the second edition; one does need to deal with the errata,
    though they are mostly typos.

    See <URL:> .

    © John Stockton, Surrey, UK. ? Turnpike v4.00 MIME. ©
    Web <URL:> - w. FAQish topics, links, acronyms
    PAS EXE etc : <URL:> - see 00index.htm
    Dates - miscdate.htm moredate.htm js-dates.htm pas-time.htm critdate.htm etc.

  5. #5
    Philip Clarke's Avatar
    Philip Clarke Guest

    Default "The Calendar" by David Ewing Duncan: Numerous Errors?

    Dr John Stockton wrote:

    Sorry; I've just re-read the Posting Style Guide.

    Noted; for bevity I will use the term "caesium frequency".

    Oui, je comprends.

    Agreed. Unfortunately, I wasn't too clear here. I was actually
    looking to verify the accuracy of the mean solar year that I had
    originally referred to in the previous question.

    I can see that these figures relate to 365.2425, 365 and 366 days,
    respectively. Isn't the first figure the Gregorian year, or is this
    the same as the UTC year?

    Since I couldn't verify the exact length of the mean solar year, I was
    hoping to approach the problem from another angle. Of course, I could
    have multiplied the "caesium frequency" by 365 days, 5 hours, 48
    minutes, 46.03232 seconds, but it was this duration that I was trying
    to prove. Initially, I was struck by an internet article which
    described how the second was originally defined as 1 / 31,556,925.975
    of a year, and then after Scientists complained that this was not
    accurate enough, they re-defined the second as 1 / 31,556,925.9747 of
    a year. By definition, a (mean solar?) year is 31,556,925.9747
    seconds in duratin. The question is, if 0.003 of a second made a
    difference to Scientists in 1967, then why was the "caesium frequency"
    of the current year only defined to the nearest 0.5 seconds? I have
    looked at formulae by Newcomb and others without success.

    I thought so, thanks.

    I'm sorry, but I don't really understand this question.

    Thanks, I will try to get a copy.

    Many thanks for your reponse.


    Philip Clarke

  6. #6
    Dr John Stockton's Avatar
    Dr John Stockton Guest

    Default "The Calendar" by David Ewing Duncan: Numerous Errors?

    JRS: In article < >,
    dated Wed, 28 Jul 2004 16:36:33, seen in news:sci.astro.amateur, Philip
    Clarke <> posted :

    Yes; no, except if leap-seconds are disregarded. The difference between
    Greg & UTC year varies according to the antics of our globe. UTC has
    never been less than Greg since current rules started, has certainly
    never exceeded it by more than two seconds, and AFAIR never by two, but

    Well, anyone else is free to answer it; or indeed to pin down the exact
    date ant time in any other trustworthy and cite-able manner. Anyone
    care to ask their Imam?

    P.S. Actually, since writing that, I've borrowed a Duncan - which does
    not address the point; it says little about Islamic calendars.

    © John Stockton, Surrey, UK. ? Turnpike v4.00 MIME. ©
    Web <URL:> - w. FAQish topics, links, acronyms
    PAS EXE etc : <URL:> - see 00index.htm
    Dates - miscdate.htm moredate.htm js-dates.htm pas-time.htm critdate.htm etc.

  7. #7
    Oriel36's Avatar
    Oriel36 Guest

    Default "The Calendar" by David Ewing Duncan: Numerous Errors? (Philip Clarke) wrote in message news:< com>...

    You will have to rely on your own commonsense in the absense of any
    worthwhile response and you need not go too far before you recognise
    why contemporary explanations are misleading and ineffective.

    To determine the annual orbital cycle as 365 day 5 hours 49 min you
    are required to determine the equable 24 hour day First whereby the
    equable hour,minute and second are determined as subdivisions of the
    24 hour day.

    If you agree that it is not possible to calculate the annual cycle
    without first determining the equable 24 hour day you will be half way
    to developing a far better appreceation of the calendar system as an
    offshoot of the principles which determine the equable day.

    Using the Sun as a reference for the motions of the Earth,the combined
    constant axial and variable orbital motion generates a change from
    one rotation for a given longitude meridian to the next complete
    rotation.The brilliance of our ancestors was to equalise the variation
    by adding and subtracting appropriate minutes and seconds to
    longitudinal noon to smooth out the variations and facilitate the
    seamless transition from one 24 hour day to the next 24 hour
    day,Monday into Tuesday,ect.

    This correction is known as the Equation of Time.

    In 1677,Flamsteed altered the 24 hour/360 degree equivalency and
    linked the rotation of the Earth directly to stellar circumpolar
    motion giving the value for rotation through 360 degrees as the
    sidereal 23 hours 56 min 04 sec.He screwed up the ancient exquisite
    reasoning that benefited humanity with the 24 hour day and
    subsequently the calendar year based on that equable day.

    The other responses you received so far indicate that in the 21st
    century,men are incapable of telling what the rotation rate of the
    Earth is through 360 degrees choosing as their value the sidereal
    value.The correct value is and always will be 24 hours insofar as the
    Equation of Time correction is the exquisite equalising method to
    screen out all the variables introduced by variable orbital
    motion,finite light distance or indeed variations in the rotation rate
    of the Earth itself to facilitate the difference of 1 degree rotation
    per 4 min, 15 degrees per 1 hour and ultimately 360 degrees per 24

    Initially, I was struck by an internet article which

  8. #8
    Ernie Wright's Avatar
    Ernie Wright Guest

    Default "The Calendar" by David Ewing Duncan: Numerous Errors?

    Philip Clarke wrote:

    I'm not sure this is what you're getting at, but the length of the mean
    tropical year isn't constant. It's getting shorter, and the measurement
    is getting more accurate. 31556925.9747 sec is the canonical length of
    a specific year (1900). The J2000 mean tropical year is 31556925.187488

    It's not defined as a number of seconds. The year 1900 was in effect
    defined to be this length, but in general, the mean tropical year is the
    mean amount of time it takes the sun to return to a given longitude on
    the ecliptic, and the ecliptic changes over time.

    The "caesium frequency" was just rounded off, possibly because the
    length of a year isn't constant. I don't think there's any deeper
    explanation than that.

    Giving this number to greater precision would have implied a specific
    measurement of a particular year, and it seems clear from the context
    you've quoted that the number was merely an approximation derived from
    the current definition of the SI second.

    If you're hoping to use a higher precision version of this number to
    to get "the" length of a year, you've been misled.

    The Newcomb formula gives the longitude of the sun on a given date.

    L = L0 + 129602768".13 C + 1".089 C^2 + ...

    where L0 = 279° 41' 48".04 is the longitude of the sun on 1 Jan 1900 at
    12:00Z, and C is the number of Julian centuries since that date. (A
    Julian century is exactly 36525 days.)

    Hopefully somebody will correct me if I'm wrong about this, since I'm
    not an expert on how the definition of the ephemeris second was derived,
    but I believe a version of Newcomb's formula with only the linear term
    was used,

    L = L0 + 129602768".13 C

    and following this truncated version of the formula, the length of the
    tropical year beginning 1 Jan 1900 12:00Z is just the value of C for
    which L = L0 + 360°. Solving for C,

    C = 1296000" / 129602768".13
    = 0.0099997864142842054588143772543... Julian centuries
    = 365.24219878173060438319512921348... days
    = 31556925.974741524218708059164045... seconds

    There's no physical justification for the extra precision--the year 1900
    wasn't "really" precisely this long. The value 31556925.9747 arises
    simply from rounding at the number of significant digits in the formula.
    It also depends on ignoring the higher order terms. If those are added,
    the number differs by on the order of 0.003 sec.

    - Ernie

  9. #9
    Jonathan Silverlight's Avatar
    Jonathan Silverlight Guest

    Default "The Calendar" by David Ewing Duncan: Numerous Errors?

    In message < >, Oriel36
    <> writes

    The same old BS.

    But the day is defined as the time between meridian passages of the sun,
    and it's divided up into hours, minutes, and seconds. In Civil Time the
    day is assumed to be of constant length. What's so difficult about that

    Why not post the Flamsteed statement, or post a link to it? I'd be
    interested to hear from someone who actually knows what they are talking
    about, but AFAICS Flamsteed was responsible for the idea of the equation
    of time.
    BTW, either you have a virus or you are deliberately sending me
    unsolicited emails.
    What have they got to hide? Release the full Beagle 2 report.
    Remove spam and invalid from address to reply.

  10. #10
    Oriel36's Avatar
    Oriel36 Guest

    Default "The Calendar" by David Ewing Duncan: Numerous Errors?

    Jonathan Silverlight <> wrote in message news:<1pdtJQDJ$>...

    To be fair to you,the mistake is a really old one and precedes the
    gravitational agenda (which makes use of the mistake) by a decade.The
    first professional astronomer was Flamsteed who set out to prove that
    the Earth rotates constantly on its axis through the motion of the
    fixed stars thereby making use of this observation for determining
    planetary longitude.

    Flamsteed was incorrect.

    I did many times -

    .... our clocks kept so good a correspondence with the Heavens that I
    doubt it not but they would prove the revolutions of the Earth to be

    A direct consequence of that statement can be found in any website
    refering to the sidereal value -

    I'd be

    You won't find any,there is just myself.

    You can however appeal to those who are familiar with the equable 24
    hour clock day,the Equation of Time correction from the noon
    determination and how one 24 hour day elapses seamlessly into the next
    24 hour day by the 'Equation of Time' method but then you will
    encounter those who are aware that the precise value for axial
    rotation through 360 degrees,is and always will be 24 hours.


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