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    Re: Eqn. of time
    From: George Huxtable
    Date: 2007 Jan 9, 18:26 -0000

    Bill had asked-
    | "That caused me to wonder if at some time in the past there was
    | a  conscious effort to link the equation of time to some celestial
    event."
    
    And Frank answered-
    | er... how could there be? Its numerical value follows directly  from
    its
    | definition. The values on specific dates do change over the
    centuries  and
    | millennia. Is that what you were asking about?
    
    It's quite possible to define equation of time in different ways, and
    historically, it has indeed been defined in different ways.
    
    The first printed version of an equation of time came from Christian
    Huyghens, in "Kort Onderwys ...", 1665, which has been reproduced in
    "The Quest for Longitude". It became necessary, in Huyghens'
    development of an accurate pendulum clock, to provide a way for that
    "mean-time" clock to be checked from observations of the Sun, using a
    sundial or some other noon sightline. Remember, in those days, sundial
    time, from the apparent Sun, was "the time". Equation of time was
    different from what we know today, in that instead of being split
    halfway, as it is at present, about equally one way and the other over
    the year, Huyghens put his zero-point at one extreme value, then at 10
    Feb. In that way, it made arithmetic simpler, the correction being
    always in the same direction. It provided an amount, ranging from zero
    to 32 minutes, to add to sundial time to establish what a "mean-time"
    precise clock should read. I put "mean time" in quotation marks for
    reasons you will see.
    
    In 1676, two Tompion "regulator" clocks, each with an enormous
    pendulum 13 feet long, were got going at Greenwich, showing sidereal
    time from the stars, and mean solar time from the Sun. They still
    exist. They were adjusted according to a special fixed telescope that
    could see Sirius as it crossed the meridian, even in daytime. They
    provided the working time-scale for the observatory, which would then
    observe, and predict, the moment of the Sun's meridian passage on that
    basis. So the purpose of the equation-of-time table had been reversed;
    instead of its use for adjusting a "mean-time" clock from the Sun, it
    became a matter of predicting the position of the Sun from a mean-time
    clock.
    
    That solar clock was set to keep what was called "Greenwich Mean
    Time", and the "Mean" part of the name gets us to the answer to Bill's
    question. It was taken to be, on average, exactly as much behind the
    apparent Sun as it was ahead of it. So now, the Equation of Time was
    measured from a zero-point that was somewhere in the middle of it's
    range. Not just roughly, but precisely so,  splitting the EoT curve,
    such that the area above it exactly equals the area below it. That's
    what Bill should find if he looks at the "Total" curve provided by
    Frank. It's implied in the definition of "Mean". It's implied, also,
    in the symmetry about zero of the two individual nearly-sine curves,
    that combine to make up the total. From that zero, the dates of the
    four zero-crossings follow. They follow a similar pattern, year to
    year, but change a bit over centuries, as the date of the Earth's
    perihelion slowly drifts.
    
    So, going back to Huyghens, his pendulum clocks had been set, from his
    own EoT table, to read a steady time at The Hague: not  "Mean Time at
    the Hague", but getting on for a quarter-hour different. You could
    think of it as being a mean time, I suppose, but not local mean time
    there, but somewhere else, nearly 4 degrees away in longitude.
    
    Although Greenwich "worked" on Greenwich Mean Time, from the first
    Nautical Almanac in 1767, nearly all predictions were given in terms
    of Apparent Time, until 1834, when they finally recognised that
    significant numbers of mariners possessed chronometers and could use
    mean time.
    
    ============================
    
    So how was the EoT table tabulated, to allow the conversion between
    mean and apparent times? Which way round do you present the sign of
    the change, when converting one timescale to the other? That's been a
    source of confusion, and obscurity, ever since.
    
    Consider one extreme EoT value, that in mid February, which Huyghens
    took as his zero. Maskeyne's table, in the Nautical almanac, gives it
    as 14m 42s, heading the column "add". He tells us in his explanation,
    that this, "when applied to the apparent time, ... gives the mean
    ...time".
    
    In the modern almanac it's stated differently. The EoT is shown, for
    each day, at noon and midnight, and the entry is shown either with a
    shaded background, or without. For February, it's shown shaded. An
    explanation is given as follows-
    
    "The sign is positive for unshaded vales and negative for shaded
    values. To obtain apparent time, add the equation of time to mean time
    when the sign is positive" And vice versa. When you have worked out
    the convolutions of that, it turns out to be the same as for 1767; as
    it should, of course.
    
    The 1864 almanac headed the relevant column, for February, "Equation
    of time, to be added to apparent time". For other months, it would say
    "subtracted". Sometimes, that designation switched mid-month.
    
    Simplest to understand was that in the old Reed's, which simply
    attached a + or a - to each entry, and on each page states "Equation
    of Time is the excess of Mean Time over Apparent time". I think that's
    also the way round that it's quoted in some European almanacs.
    
    Why all this confusion then? Mostly, it's in the adoption of a silly
    name, "equation of time", which gives no clue as what's to be applied
    to what, and which way. Much better would be to adopt a simple name
    that explained itself, leaving no room for confusion, such as "Sun
    Lag", which would be positive in February and negative in December.
    Pity that never happened.
    
    George.
    
    contact George Huxtable at george---.u-net.com
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    
    
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