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    Re: Measuring dip
    From: George Huxtable
    Date: 2006 May 16, 23:26 +0100

    Alex wrote-
    | Dip by backsight.
    | Some time ago we discussed the dip of the horizon
    | on the old list, and a possibility of measuring dip
    | by a back sight was mentioned. After a recent hint
    | from Frank J., that modern sextants do permit back
    | sights under certain conditions, I worked the details.
    | The method should also work if you want to determine
    | the hight of a mountain while standing on the peak,
    | if you see the horizon in all directions.
    | It is a common opinion that uncertainty of the dip is the major
    | factor affecting the accuracy of altitude measurements.
    | Both Schufeldt and Russian theorists recommend to use dipmeters.
    | However I have never seen a dipmeter "alive" or on e-bay.
    | So the method using only ordinary sextant might be of some
    | interest.
    | The method is applicable if two conditions are satisfied:
    | a) The Sun altitude is more than 60 d.
    | (If your sextant measures angles up to 140 d, as SNO-T
    | does, you can use Sun at smaller altitudes down to 40).
    | b) You can see the horizon under the Sun and in the opposite
    | Here are the simple steps.
    | 1. Measure the Sun altitude in the usual way, say lower limb,
    | and record the time of the observation. Let the altitude be H1 and
    time T1.
    | 2. Put your sextant arm at approximately 180d minus altitude
    | you just measured. Turn back to the Sun and take a back sight.
    | Measure the upper limb. It will LOOK LIKE LOWER LIMB through
    | your sextant: you will see the Sun touching the horizon from above,
    | if your scope is a straight one. Let the altitude by back sight
    | be H2 and time T2.
    | 3. Compute the dip by the formula:
    | DIP=90d-(H1+H2)/2-SD+TC.
    | Here H1 and H2 are your altitudes, both corrected for the IC.
    | SD is the Sun semidiameter from the almanac.
    | TC is a "time correction" computed by the formula
    | TC=(T2-T1)cos(LAT)cos(DEC)sin(LHA)/cos(H1),
    | where T2-T1 is the elapsed time between the observations,
    | translated into ANGULAR units. (So if the elapsed time is 2 min 3
    | you use (15 times 2)+3/4=30'.8 as T2-T1.
    | The quantities LAT, DEC and LHA have the usual meaning.
    | The TC correction is positive after noon and negative before noon.
    | (The formula takes this into account automatically)
    | DIP is always negative.
    | The time between observations has to be measured very accurately, as
    you do
    | with ordinary Sun sights.
    Comment from George-
    It seems to me that Alex has got everything right.
    The Sun is just being used as a marker in the sky, and if you measured
    to the SAME edge of the Sun for both sights, then its semidiameter
    wouldn't enter into it, and wouldn't need to be subtracted. It's
    rather confusing to refer to upper and lower limbs in that case, when
    one is up behind your head, so think of it as either observing the
    Eastern edge of the Sun in both cases, or the Western in both cases.
    It's the edge that's furthest from one of your horizons, and nearest
    to the other.
    If you make the observation at local apparent noon, when the Sun is
    neither rising or falling, then the TC correction can also be left out
    of the equation, as it will be zero. Alex's strictures about accurate
    timing apply only to measurements away from noon.
    Alex didn't mention refraction, because there's no correction for
    refraction required.
    In the latitudes where I usually sail, near 51 degrees North, Alex's
    proposal is a trick that would be useful with the Sun only over a
    7-week period around midsummer, when its noon altitude exceeds 60
    degrees, if a 120-degree sextant was being used. In fact, many
    sextants can handle a few degrees more than that. Alex's instrument
    can measure 140; a true quintant can measure 144.
    However, if it was acceptable to wait for dawn or dusk, a pair of such
    altitudes of a suitable star with a high enough declination, as it
    crossed the meridian, ought to work if such a bright star is on offer
    at the right time.
    Observations made facing away from the Sun, so it's behind your head
    at a high angle, could sometimes be useful in other contexts. In 1790
    the well-equipped Malaspina expedition was surveying the West coast of
    South America, North of Callao. Being too close to the coast to get a
    true horizon under the morning Sun, a quintant was used to measure Sun
    altitude, up-and-over from the Western horizon, behind the observer's
    head as he faced West. This must have been one of the very first
    A version of Alex's proposal could be used in a rather different way,
    when setting up an octant. Many octants were fitted with an extra peep
    and mirror, for use as a backsight, which could measure angles right
    behind your head, right down to the horizon. Trouble was that the
    normal index-check procedure, of aligning some body with itself,
    couldn't be used with a backsight. A common way of checking the zero
    of the backsight mode, at sea, was to align the horizon, seen forward,
    with the image of the back-horizon, in the opposite direction, seen
    via the mirrors, behind the observer's head. Those horizons should be
    180 degrees apart, measured in altitude over the zenith. Or very
    nearly so, because twice the dip had to be added as well. That dip
    value had to be assumed, to set the zero correctly, so because the
    zero had been set in that way, the instrument couldn't then be used as
    a way to measure the dip.
    contact George Huxtable at george@huxtable.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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