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    Re: longitude and time: was [NAV-L] Star-sight discrepancy
    From: George Huxtable
    Date: 2005 Aug 29, 12:24 +0100

    I recently sent the following message-
    >Fred Hebard asked-
    >>  In this
    >>post, I'm returning to the land-based observations, repeating the
    >>following question:
    >>How did astronomers arrange their telescopes to swing precisely in a
    >>North-South plane?  What technique did they use to achieve the
    >>alignment?  I know it's off topic, although similar technique also was
    >>used by surveyors, who might be regarded as navigators on land, to
    >>bring it slightly back on topic.
    >In W.Chauvenet, "Spherical and Practical Astronomy", vol. II, chapter V is
    >all about Transit Instruments. It occupies pages  131 to 282 in my 5th
    >edition (University Edition). Plate IV shows an observatory instrument and
    >plate V a portable one (which is probably most relevant to Fred's
    >question). That portable transit has its two bearings, along an azimuth
    >V,carried on an iron frame which sits on three pointed adjusing-screw
    >feet, and Chauvenet suggests that it should be placed on the stump of a
    >cut-down tree.
    >In para 125, which starts on page 141, Chauvenet having previously defined
    >the quantity a as the error of the axis of rotation from true East-West
    >(which is what Fred is after, I think) states-
    >"To reduce a to a small quantity, or to place the instrument very near to
    >the meridian, we must have recourse to the observation of stars. The
    >following process will be found as simple as any other with a portable
    >Compute the mean time of transit of a slow moving star (one near the
    >pole), and bring the telescope upon it at that time. For the first
    >approximation, the time may be given by a common watch, and the telescope
    >may be brought upon the star by moving the frame of the instrument
    >horizontally. Then level the axis [this is done by adjusting the screw
    >feet according to a sensitive striding spirit-level placed across the two
    >bearings - George], and note the time by the clock of the transit of a
    >star near the zenith over the middle thread. It is evident that the time
    >of transit of a star near the zenith will not be much affected by a
    >deviation of the instrument in azimuth, and therefore the difference
    >between the star's right ascension and the clock time will be the
    >approximate error of the clock on sidereal time. With this error, we are
    >prepared to repeat the process with another slow-moving star, this time
    >employing the clock and causing the middle thread to follow the star by
    >moving only the azimuth N. When the clock correction has been previously
    >found by other means (as with the sextant), the first approximation will
    >usually be found sufficient. The instrument is now sufficiently near the
    >meridian, and the outstanding small deviations can be found and allowed
    >for as explained below."
    >I'm doubt if I understand all of that text, and hope that it makes more
    >sense to Fred. I can't decide whether that procedure requires a precise
    >knownedge of lat and long, and GMT, or not. If anyone can enlighten me,
    >please do.
    >Chauvenet goes on to point out that it's not necessary to remove all error
    >a from the azimuth of the East-West bearings, but shows how such error can
    >be measured and used to correct observations.
    Since sending that message, I've given the matter a bit more thought, and
    can suggest the following "idiot's explanation" of Chauvenet's procedure
    for aligning a transit instrument.
    If there happened to be a star exactly at the Pole, completely stationary,
    alignment would be very simple. You would simply raise the telescope until
    that star appeared in view, and then turn the frame on its tree-trunk base
    until the star was exactly on the central thread of the telescope,
    levelling its bearings with the striding spirit level. There the star would
    stay, as the Earth rotated beneath it. Job done.
    But unfortunately, there isn't such a star, readily visible. In the
    Northern hemisphere, the observer would probably substitute Polaris, which
    in Chauvenet's day was something of the order of a degree away from the
    Polar axis. So Polaris is never far from the observer's meridian circle,
    and is exactly on it twice a day, once above the pole and once below it. If
    the observer has a rough idea of time by his watch,, he can work out when
    that moment is, and set the azimuth of the transit so that the cental
    thread is then aligned. That will have done the job reasonably well, but
    depends on how good that assessment of time was. The alignment is not very
    senstive to that timing, because Polaris moves in such a small circle.
    However, alignment of the transit needs to be done rather better than that.
    Now observe another star, Sirius, say, when it crosses the plane that the
    transit is now set to, and note that time with a clock running at an
    accurately-known rate. The clock can then give a measure of local sidereal
    time, to some reasonable accuracy. Knowing the difference in Right
    Ascension between Sirius and Polaris (which has been well-determined
    beforehand by astronomers) this allows the next crossing of the observer's
    meridian by Polaris to be well predicted, much better than it was by the
    watch in the first instance. At that precise time, perfect the alignment of
    the telescope central thread with Polaris, and the job is completed, though
    further iterations can be done if thought necessary.
    If that's all correct (and it may not be) then the alignment procedure does
    not require any initial knowledge of time, or latitude or longitude. If
    anyone can confirm whether my understanding is correct, or explain where
    it's wrong, it would be appreciated.
    I doubt if such alignment procedures would have changed much since
    Chauvenet's day, but it's possible.
    I can see one potential snag. There are only two possible moments, in the
    24 hours, when Polaris is in the right position, on an observer's meridian.
    In Summer, when nights are short, the sky may not be dark at either of
    those times. In which case, another star near the pole, with a different
    Right Ascension, would have to be chosen instead.
    Contact George at george@huxtable.u-net.com ,or by phone +44 1865 820222,
    or from within UK 01865 820222.
    Or by post- George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13
    5HX, UK.

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