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    Personal equation in timed observations
    From: Paul Hirose
    Date: 2018 Oct 22, 22:30 -0700

    In 1945 Popular Astronomy magazine ran a three-part series by Raynor L.
    Duncombe on the history of the "personal equation" in observations with
    transit instruments. He begins with the case of the Greenwich
    Observatory assistant who persistently observed meridian transits .5 to
    .8 second late relative to Maskelyne, who fired the man in 1796 for his
    "vicious" habit.
    However, by the early 19th century there was growing awareness of
    systematic individual differences in "eye and ear" transit timings by
    experienced observers. (The observer listens to the ticks of the clock
    and keeps mental count of the seconds while watching the star cross the
    vertical wire of the telescope.) For instance, a series of tests showed
    a 0.8 to 1.0 second offset in the transit timings of eminent astronomers
    Bessel and Struve.
    Development of the electrical art gave an alternative to eye and ear:
    the recording chronograph, in which a pen traced a helical path on
    paper, wrapped around a cylinder and rotated at constant speed. An
    electromagnet wired to contacts in a clock deflected the pen once per
    second. It also recorded the observer's tap on an electrical key at the
    moment of transit.
    This was an improvement. Early tests of personal equation were purely
    relative: one man with respect to another. But now absolute measurements
    were possible, via an apparatus which drove an artificial star across
    the field of view and recorded the true crossing of the central wire vs.
    the observer's key tap. Thus each observer's work could be made free of
    his personal equation.
    At least, that was the theory. But the growing body of chronograph data
    began to show a systematic error as a function of declination in the
    work of some observers, but not others. The fault lay in the lack of
    standardization in the tapping technique. Some observers were proactive
    — they thought it proper to anticipate the instant of transit and begin
    the muscular impulse early so the tap occurred exactly on the wire.
    Others were reactive. They waited until the star was on the wire, then
    tapped. Of course this tap was always late, but reaction time would be
    included in that observer's personal equation.
    It turned out the latter gave more consistent results. Proactive tappers
    had a tendency to develop a timing optimized for one particular
    declination. At any other declination the star would move at a different
    rate, and despite the observer's best effort the tap would be early or late.
    The next weapon against personal equation was the impersonal Repsold
    micrometer. In this the wire was movable, driven by a screw operated by
    the observer, who tracked the star continuously. A disc with electrical
    contacts was attached to the screw. This transmitted pulses to the
    chronograph. In some cases a motor rotated the screw, and the observer
    controlled its rate.
    With this device the transit instrument attained unprecedented accuracy.
    In fact, even recent JPL ephemerides depend in part on transit
    observations of the outer planets as far back as 1911. (This coincides
    with the introduction of the impersonal micrometer at the USNO.)
    Nevertheless, eye and ear is still the way we check a clock with a
    shortwave radio. When I find a time page on the Web dead accurate (or
    not) with respect to ticks from my radio, I wonder how much personal
    equation is present. Some of the values measured in the heyday of eye
    and ear are almost unbelievably large.

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