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    Re: Watches as chronometers
    From: Brad Morris
    Date: 2013 Jun 14, 15:02 -0400

    I gave this a deep think over the past few days.  In responding, I
    will take that trip to the adjective laden location, formerly known as
    �crazy town�.
    
    Let me suppose that Gary isn�t comparing his chronometers to the
    standard time chronometer, but rather to the angular orientation of
    the earth to celestial objects that the NIST standard time represents.
     The insertion of leap seconds is to account for the change in angular
    position as a function of the change velocity of the earth about its
    axis of rotation.
    
    That angular velocity is a function of the mass moment of inertia of
    the rotating object (the earth) multiplied by its acceleration over
    time.  The mass moment of inertia is strictly a sum of (the inertial
    mass of all the objects that the earth represents multiplied by the
    radius of gyration, squared, of each object).
    
    Here�s a very small change to the mass moment of inertia.  When
    Shackleton was at the equator in Endurance, his radius of gyration is
    the radius of the earth.  When Shackleton was at the South Pole (or
    thereabouts), his radius of gyration much smaller. This represents a
    change to the mass moment of inertia, and as a function of the
    conservation of momentum, the earth rotated an infinitesimally faster
    when he was at the South Pole (or there abouts) compared to when he
    was at the equator.  That�s a random change.
    
    Too small to notice, I�m sure you�ll say.  Perhaps, but still true
    none the less.  What if all 7.2 billion people managed to stand on the
    poles, and then on the equator?  Still too small a random change (but
    quite silly to visualize!).
    
    Here�s a slightly larger random change.  As volcanos spew lava to the
    surface, the distribution of mass changes and as a function of the
    radius of gyration squared, the earth still slows.  Its random.
    
    Still too small?  Okay, in a subduction zone, earthquakes occur as one
    tectonic plate slips under another.  We may have a net zero change in
    the MMI, a gain or a loss.  Its random.  There is another component to
    this change here.  Due to the sudden release of energy, we have an
    accelerative force, which will act upon the MMI, yielding a change in
    the angular rate.  Again random.  That force could make us go faster
    or slower.  Not frequent enough?  In the Canary Islands, earthquakes
    can occur as frequently as 450 events in a single 24 hour period
    (March 2011).  Those �quakes not large enough?  The recent earthquake
    near Honshu certainly provided an accelerative force and a small
    change to the angular velocity, as was well documented in the media.
    We also have the rise of the tectonic plates, now that the major
    glaciation of the Ice Ages have melted.  We have the retarding effect
    of the moon�s drag.  Ditto the sun�s retardation.  These are longer
    term, more readily modeled changes to the MMI and thus to the angular
    velocity.
    
    But wait a minute, Gary isn�t measuring any of this.  I sincerely
    doubt that Gary is measuring his orientation versus the celestial
    objects and then correcting his chronometer.  That�s the job of the
    folks at NIST.  They have an increment counter, and the face value of
    that increment counter is adjusted when they see fit to bring NIST
    standard time (by whatever name you want to call it) in alignment with
    celestial objects.  They account for the random effects.  They account
    for the slow steady state effects on the angular velocity.  They
    provide that face value to us as standard time.  The claim is that the
    time (and therefore the orientation) is kept within a one second
    increment.
    
    The purpose of Gary�s chronometer is to also provide that reference to
    the celestial objects, such that he can navigate via celestial
    navigation.  He compares his chronometer to NIST standard time such
    that he can generate rate and performance data.   If his chronometer
    is slowing at the exact rate of the earth, then he can still have an
    error in his chronometer based upon WHEN the leap second is injected.
    That is random injected discontinuity.  Compare Gary�s chronometer for
    rate just before the discontinuity yields  a different rate than if
    compared just after the discontinuity, but only if the discontinuity
    is included as part of the rate calculation.  If you treat the
    discontinuities as a separate data point, not subject to the rate
    calculation, then the rate before and after the discontinuity is the
    same.
    
    I do get the point that over very long term rate and performance
    measurements, that the difference in rate (should we include the
    discontinuity in the rate calculation) will be small and probably not
    yield differences over 1 second, which is the celestial navigation
    threshold.  Perhaps I just seek mathematical purity in the treatment
    of the discontinuity, such that we treat the discontinuity as an
    external adjustment for both.  After all, both time keepers are
    attempting to count 1 second increments.
    
    I have come to the view that, perhaps, the term �crazy town� is a bit
    harsh.  Its inclusion on very long term performance and rating
    exercises will not yield differences significant to practical
    celestial navigation�s quantized 1 second increment.  The inclusion of
    the discontinuity will yield different rates than if the discontinuity
    is treated as an addendum.  I�ve been bothered by that.  Not bothered
    anymore.
    
    It just so happens that Paul has explained, much more eloquently than
    I can, exactly what I was trying to express.  Treat the leap seconds
    excluded from rate.
    
    Brad
    
    
    On 6/14/13, Paul Hirose  wrote:
    > Geoffrey Kolbe wrote:
    >> Gary was comparing his clocks against WWV, which
    >> is UTC or "broadcast time". But UTC is itself
    >> being constantly compared to UT1 and periodically
    >> a second of time is inserted (or taken away) from
    >> UTC so that UTC continues to agree with UT1 to
    >> within +/- 0.9 seconds. So, what Gary is actually
    >> comparing his clocks against is UT1, not UTC.
    >
    > I disagree, Geoffrey. Like Gary, I periodically compare clocks to UTC
    > (WWV) and log the results. It is not the same as comparing to UT1. Logs
    > of clock performance with respect to UT1 and UTC would would have
    > noticeable differences. Clock error could be up to 0.8 second different.
    >
    > Daily rate would be the same except after a leap second, when the UTC
    > log would show a momentary deviation from normal. By adjusting for the
    > leap second as I explained in a previous message, the rate discontinuity
    > can be eliminated. However, the discrepancy in clock error remains.
    >
    > To compare a clock to UT1, Gary can first note its error relative to
    > UTC. Then, by listening to the double ticks in the WWV audio, determine
    > DUT1 (= UT1-UTC rounded to 0.1 second). Algebraically subtract DUT1 from
    > clock error (with respect to UTC) to obtain error with respect to UT1.
    > For example, if clock error (UTC) is +0.1 s, and DUT1 = +0.1 s, clock
    > error (UT1) = 0.
    >
    > That can be done retroactively if records of clock error relative to UTC
    > exist. Daily precise values of UT1-UTC are in the IERS Bulletin B archive.
    >
    > No special procedure is required for leap seconds, because there is a
    > step adjustment to UT1-UTC at the same time. See Bulletin B at the end
    > of June 2012:
    > ftp://hpiers.obspm.fr/iers/bul/bulb_new/bulletinb.294
    >
    > Nevertheless, I prefer to compare clocks to UTC. The main reason is that
    > there's no UT1 time standard. UT1 must be derived from UTC every time
    > the clock is checked. It's less trouble to use UTC directly and apply an
    > adjustment for the occasional leap second.
    >
    > In effect, my log shows clock error relative to UTC, and rate relative
    > to atomic time.
    >
    > Back in the 1970s when I was a shortwave listening hobbyist there was a
    > time station (BPM in China?) which broadcast UT1. It was on or close to
    > the WWV frequency. You could hear them simultaneously, and the offset in
    > the ticks was obvious. With such a station it would be easy to compare a
    > clock to UT1.
    >
    > --
    > 
    >
    > : http://fer3.com/arc/m2.aspx?i=124350
    

       
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