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    Re: Measure of All Things
    From: Brooke Clarke
    Date: 2003 Sep 30, 11:36 -0700

    Hi Kieran:
    When making any measurement there is a limit to the number of digits in
    the result.  If the measurement is of an angle the instrument used may
    only be able to read out minutes of angle.  The person using the
    instrument may guess the fraction of a minute.  Assuming that the
    technique of using the instrument is perfect and no blunders are made
    there will be some noise in the measurement.  Averaging the measurements
    improves the result by the square root of the number of measurements.
    I mention blunders because they do happen.  Yesterday I was looking at
    the design of a K&E Alidade, which was the primary surveying instrument
    used in the field for map making prior to GPS and total stations.  The
    5093A has a scale graduated in degrees to measure vertical angles for
    the scope in the range of -30 to +30 degrees from level but the
    graduations run from 0 to 60 degrees.  In a like manner there is a
    couple of scales that have a factor to convert from the slant distance
    measured using the stadia method into the horizontal and vertical
    distances.  When the instrument is level the HOR scale reads 100 (i.e.
    the horizontal distance is 100% of the slant distance), but the VERT
    scale reads 50 when the scope if level, NOT 0.  So the three readings on
    the instrument for a level scope are: 30 (to get vertical angle subtract
    30), 100 (the true HOR %), and 50 (subtract 50 to get the VERT %
    factor).  Note that all the readings are different and seem designed to
    minimize blunders.
    Of all the things that can be measured time and/or time interval is the
    most precise.  For example a state of the art instrument like the
    Agilent E1710A Angle encoder can resolve 0.0033 arc seconds which is
    2.54E-9 of a circle.  Time can be measured to 1E-15 or about a million
    times more accurately.  Measuring time is the basis of the GPS system.
    Map making prior to GPS was based on surveying from some benchmark to
    the unknown location and was referenced to some local datum.  The
    accuracy of the instruments is expressed as some absolute value plus an
    error that is a function of distance.  So as a survey gets further and
    further away from the benchmark the accuracy of the result also
    degrades.  So if GPS is used to measure some landmark on an early map
    the location GPS reports may be different from the Lon and Lat on the
    map (after correcting for a different datum) because of the error
    accumulation when the map was made.
    Today high quality survey grade GPS receivers can find the relative
    location of some unknown point in relation to a bench mark with a
    precision on the order of a millimeter.  Note this is a relative
    location, not an absolute.  Who's to say what the absolute location of
    any bench mark is?
    I hope this helps answer your question.
    Have Fun,
    Brooke Clarke, N6GCE
    Kieran Kelly wrote:
    >I recently read Ken Alder's excellent work The Measure of All Things and was
    >struck by Delambre's struggle to improve the accuracy of celestial sights
    >and transit observations for the French metric survey. In the book there is
    >a discussion of the difference between Precision i.e. random errors and
    >Accuracy i.e. constant errors when making a celestial observation either
    >with a theodolite, sextant or transit circle.
    >I am still a bit confused. Is a random error-precision-a human error either
    >in the sighting technique or in the calculation such as an arithmetic error?
    >These errors would presumably be expressed as a bell shaped curve. If so
    >then the accuracy must relate to the instrument and would always be
    >constant. Thus errors of accuracy would be expressed as a straight line when
    >plotted. Those who use sextants are familiar with errors such as index
    >error, collimation error or the errors along the arc. But I thought these
    >errors could be eliminated. Apparently not completely eliminated. Is this
    >interpretation correct?
    >Does it mean that because of random errors no observation is ever completely
    >precise as minute human variables come into play? Similarly if there was to
    >be no errors of accuracy then the measuring instrument - sextant, theodolite
    >etc would need to be perfect. On the basis that no man made machine is
    >perfect it would appear that all navigational fixes and surveying
    >triangulations are ultimately only approximations.
    >This was certainly the case with the French metric survey which was found to
    >be inaccurate with the advent of satellite navigation. What I don't
    >understand is how do scientists know it is inaccurate when there appears to
    >be no absolute standard if Delamere is to be believed. Is it possible that
    >in future a further technological development will prove the satellite
    >survey to be inaccurate?
    >Any assistance would be appreciated.
    >Kieran Kelly

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