Jonathan Silverlight wrote in message ...

the 23 hour 56 minute 04 second value is measured, and the 24 hour value is a convention to allow days and hours of constant length.

The length of the mean solar day is measured to be 24 hours, and not
assigned by convention. If the mean solar day were significantly
different from 24 hours, then with respect to our good clocks that
repeat their indications every 24 hours, we would soon see the Sun
rising and setting at strange hours.

Of course, the mean solar day is not *exactly* 24 hours, i.e., 86400
seconds where the second is defined in terms of the frequency of a
certain atomic vibration. The difference is small, so that after
roughly 100 intervals of exactly 24 hours each, an angular discrepancy
corresponding to one second of time will have accrued ("leap second").

For the benefit of the original poster, the shortness of the sideral
day with respect to the mean solar day can be calculated by noting
that in a given amount of time, namely one year, the Earth makes
365.25 turns from the point of view of the Sun, and 366.25 turns from
the point of view of the distant stars. The extra turn in the stars'
viewpoint is the turn the Earth makes by orbiting the Sun. According
to the same effect, in one month the Moon makes one more turn in the
view of the stars than it does in the view of the Earth. (For a total
of one turn per month in the view of the stars: as all know, the Moon
makes zero turns per month in the view of the Earth because its
rotation has been stopped by tidal effects.) So, (3 min, 56 s per day)
x 366.25 days = 24.010 hours.

The "equation of time" referred to by the original poster is somewhat
unrelated. The amount of time from noon to noon, i.e., the solar day,
varries throughout the year. Somes days are shorter and some longer
than 24 hours, while 24 hours is the average taken over one year. The
discrepancy is as large as a few minutes. The variation is caused, in
roughly equal amounts, by the ellipticity of the Earth's orbit and the
inclination of the Earth's rotation axis with respect to the plane of
its orbit. These irregularities are taken into account by the equation
of time. Sundial readings, corrected with the equation of time, give
local mean time. With an additional adjustment for longitude (and
daylight savings time if it is in effect), sundial readings then agree
with the civil time kept by 24 hour, atomic-second clocks.

The amount of time from one meridian transit of a star to the next
transit of that star (this would be "noon" as defined by a star) shows
very little variation. So little as to be not possible to detect
directly until the advent of atomic clocks. With the greatest
regularity, this time is 23h 56m 4s.

If the Earth's axis were not inclined and its orbit not eccentric,
there would be no equation of time effect, but the solar day would
still be longer than the sideral day.

-Arnie