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    Re: Longitude by calculator -theodolite
    From: Brad Morris
    Date: 2013 Jul 1, 23:32 -0400

    Hi Bruce

    Here's a trick I used with my dark field autocollimator, when I tried to use it in a dark space.  I couldn't see the cross hairs either.  So I placed a small light such that it was down the throat of the autocollimator, yet off axis.  It brightened up the entire field of view and the cross hairs, while not disturbing the desired light.  Of course, you may have to experiment a bit to get the right amount.  This will completely free you up for nocturnal observations, independent of time.


    On Jul 1, 2013 10:54 PM, "Bruce J. Pennino" <bpennino.ce@charter.net> wrote:

    Hello Paul, Antoine, and All:

    The stop watch idea is a good one, and I'll look  for one. But I like just reading my digital watch; simple. Someone please recommend a stop watch of the variety described by Paul.  It would make tabulating data easier!

     I want to take data in some daylight because I can see the cross hairs easily without using a flashlight. Adjusting the theodolite, reading time and recording data is complicated enough.   The moon is big, convenient and just easy.

    Because my theodolite body  has a low height (a short pivot, hard to describe), I must select a celestial body at relatively small Hs (large zenith angle). Say it another way, I can't get my eye to instrument if I want to sight a large Hs. My maximum Hs is 30-35 degrees. I read the angle to nearest second, but the merest touch moves the hairline. So the value is realistically only good to a second or so. Deflection of the vertical is one of those errors that I just "lump into small errors difficult to quantify".  That is why my accuracy as perceived by me can't be plus or minus three seconds. Any measurement where I am within 3 seconds , Hc-Ho, is just plain luck or happenstance. Averaging balances various errors, but good luck is difficult to trump. There are just too many embedded places where errors can result.  I now believe I can probably, on average,  measure a Hs to within 6 seconds, but I said 12 seconds just to give myself " some slack" and have confidence in the results. 

    For my measurements, I think recording normal weather or water conditions does not add much on any practical basis. Unusual conditions should be recorded. When I make dip measurements, I do record weather and water conditions.Antoine, when I did the moon celestial measurements, I did not bother to record any conditions. There was no significant wind ; it was a pleasant New England evening and I was standing in shirt sleeves 65-70 F. Normal air pressure conditions.

    Thank you for data analysis.  For the past three days we have had rain, fog, haze and mist.  I'll try to sight some stars in near future and analyze; Hc-Ho.

    Best regards,

    On Sat, Jun 29, 2013 at 7:33 PM, Paul Hirose wrote:


    Bruce J. Pennino wrote:
    > Actually, for my
    > next set of sights I'm going to use some early rising stars at twilight.
    > Should work ok.  Someone asked  about my using the moon. I used the moon
    > because I can't put any shades on the theodolite, and there would be
    > optical distortion (maybe) as suggested.

    Wouldn't it be more convenient to work in full darkness? Then you
    wouldn't have to observe within a specific time window. The selection of
    stars would be better too.

    > I am measuring time to nearest whole second. So I'm probably accurate to
    > plus or minus 1/2 second for a single measurement, at very best .

    It helps to use a stopwatch with a split-action feature (to stop the
    display without stopping the watch). Record the start time. Take a split
    at each observation. After all the observations, take a final split
    against your time standard to verify the start time.

    I used to own a dedicated stopwatch with 10 memories to record the
    splits. Sadly, it quit working several years ago. My wristwatch simply
    displays the split for 10 seconds then resumes running. That's not as
    convenient, but still usable.

    > The theodolite is a "6 second gun", which
    > means I can directly read to 3 seconds, and maybe estimate to the
    > nearest second or so.

    To realize the potential of that instrument, altitudes should be
    computed to 1 second or better. By careful choice of stars you
    can minimize refraction error. A stable temperature helps. That's
    another reason to observe when the sky is fully dark. You avoid the
    rapid temperature decrease around sunset.

    I wonder if you have considered deflection of the vertical. At your
    location, xi = -4.26 and eta = 1.37 seconds, according to the National
    Geodetic Survey calculator:

    That means an instrument, exactly level with respect to gravity,
    actually has its vertical axis inclined 4.26 seconds south and 1.37
    seconds east with respect to the ellipsoid. Its observations yield
    astronomic latitude and longitude, different from the geodetic
    coordinates on a map or GPS receiver.

    At the precision to which you are working, I believe deflection of the
    vertical will be a significant part of your error budget unless corrected.

    For example, at 2013 June 30 0200 UTC, Antares is observed from N42
    W072, 0 height above ellipsoid. UT1-UTC = +0.05773 s. Computed
    unrefracted altitude from the Tinyac program:

    20°45'10.0" no deflection of vertical
    20°45'14.4" with deflection of vertical

    One solution is to compute altitude at the geodetic position where a
    perpendicular to the ellipsoid is parallel with the deflected plumb line
    at the true position. The adjusted position is north latitude plus xi,
    and east longitude plus (eta divided by cosine latitude). In this case,
    the adjusted position is N41 59 55.74 W071 59 58.16.

    The Tinyac program uses that simple method. I later realized it is
    effective for altitude only. Azimuths are inaccurate, the error
    increasing with latitude. Lunar3 does it right, though. Compare azimuth
    and unrefracted altitude of Antares, including deflection of the vertical:

    169°13'36.2"  20°45'14.4"  Tinyac
    169°13′35.0″  20°45′14.4″  Lunar3

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