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    Re: Lunars using Bennett
    From: Ken Muldrew
    Date: 2008 Jul 03, 16:35 -0600

    On 3 Jul 2008 at 22:58, George Huxtable wrote:
    
    > I might not have expressed myself clearly, but the altitude measurements
    > I
    > was referring to were those necessary for clearing the lunar, to get
    > Greenwich time
    
    Right, I was just adding that although you need the altitudes of the moon
    and
    the other body used in the lunar distance measurement, those can be
    calculated
    rather than measured if you know your latitude and local time. I was only
    talking
    about clearing the lunar to find Greenwich time.
    
    >  "Even when the lunar was a sun-moon measurement (so that the time sight
    > used a sun altitude), the lunar was cleared with a calculated altitude
    > for
    > the sun (i.e. no effort was made to extrapolate the measured sun altitude
    > to
    > make it coincident with the measured lunar distance)."
    >
    > Could Ken explain further, please? I think I can see how that might
    > arise,
    > especially if a Sun-Moon lunar was taken near noon in Summer, inland. In
    > that case, with no sea horizon, altitudes would have to be measured by
    > reflection, and the doubled Sun altitude might well put it out of range
    > of
    > an octant, or even of a sextant.
    
    Even when the sun was in range (as it always was in every case that I've
    seen in the journals of David Thompson and Peter Fidler - literally
    hundreds of sun-moon lunars) they would calculate the sun's altitude for
    clearing the lunar despite having measured it within a few minutes (or
    tens of minutes) of taking the lunar.
    
    > It was, as Ken implies, possible to work a lunar by calculating the two
    > altitudes, rather than measuring them. The problem arises that in order
    > to
    > do that, you have to make an initial guess at your GMT, by making a guess
    > at
    > your longitude. Then, if you work the lunar on that basis, it will give
    > you
    > a better GMT, and therefore a longitude, that's much closer to your
    > initial
    > guess (about 30x closer, I think). That's fine if you have a good idea of
    > your longitude already, as a land-navigator might well have.
    
    These land-navigators were more map-makers than navigators and so they
    always knew approximately where they were.
    
    > Ken raises the intriguing possibility (if I understand him right) that
    > for
    > the lunar, perhaps only the Moon altitude might be measured, and the Sun
    > altitude could be calculated instead. I've not come across that notion
    > before, but perhaps it would work. The Sun's contribution to correcting
    > the
    > lunar, mainly the effect of refraction, is small, especially when the Sun
    > is
    > high. The Moon's contribution, mainly its parallax, is much greater. and
    > more dependent on its altitude. Perhaps, then, a precise value for Sun
    > altitude isn't really needed, and it can be estimated instead. I haven't
    > quite convinced myself of the validity of that argument, and offer it up,
    > for what it's worth, for someone else to knock down.
    
    In fact I have never seen a single instance of either Thompson or Fidler
    measuring the moon's altitude. At night they measure the altitude of a
    convenient star that is either rising in the East or setting in the West
    for a time sight, and a different convenient star that crosses the
    meridian while they're out taking observations, and then the lunar
    distance (not necessarily in that order). During the day they will use a
    time sight from the morning or evening, the meridian altitude of the sun,
    and the sun-moon lunar distance.
    
    Both of these navigators were taught by Philip Turnor who had himself been
    taught by William Wales. After Turnor left Canada he worked for Maskelyne
    as one of the computers for the Nautical Almanac. Neither Thompson nor
    Fidler were using a technique that was outside of the mainstream.
    
    My point was just to say that to get Greenwich time from a lunar you need
    to measure two altitudes and the lunar distance, they just don't need to
    be the altitudes of the moon and the other body used for the lunar
    distance.
    
    Ken Muldrew.
    
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