Why are there 24 hours in a day, and 60 minutes in an hour and 60 seconds in a minute?

[ Editor: from the notes to the Earth and Sky radio program "Twenty-Four
Hours" (Friday, January 12, 1996), as given on its web page; the notes
are by LeRoy E. Doggett of the U.S. Naval Observatory, dated October
23, 1995. ]

The Hour

Why are there 24 hours in a day?  For this we have to blame the
Egyptians.  The explanation is a bit complicated, but the Egyptians had
plenty of time to develop the system.  Although we don't have a
detailed, step-by-step chronology of events, significant stages are
documented in monuments and tombs.

About the 30th century B.C., the Egyptians developed a calendar of 365
days per year (with no leap years).  It consisted of 12 months of 30
days, plus 5 holidays at the end of the year.  Each month was divided
into 3 "decades" of 10 days.  As you'll see, this early example of a
metric calendrical unit is crucial to the creation of the hour.

Keeping that in mind, let's consider a bright star that rises at the
same time as the Sun.  The star is not seen because the sky is too
bright.  During the day, the Sun and star cross the sky together,
though the Sun crosses slightly more slowly than the star.  Next
morning the star rises a few minutes before the Sun, but is still
swamped by the glare of sunlight.  After several days, however, the
star is seen briefly in the morning twilight.  This first appearance
is known as heliacal rise.

Each morning the star rises about 4 minutes earlier than the day
before, so it is visible a little longer before the Sun rises.
Gradually, it becomes visible for a significant part of the night.
Meanwhile a new bright star has risen heliacally.

The Egyptians found they could associate the heliacal rising of a
particular star with each of their 10-day decades.  Since there were 36
(=360/10 or 3x12) decades in a year, they had a system of 36 stars, the
"decans."  The decan stars were not distributed perfectly evenly across
the sky, of course, but the Egyptians were tolerant of imperfection.

Let us say Star A has its heliacal rise during Decade 1 of the year.
During that decade, Star A is also associated with the short period of
time before sunrise, the last period of the night.  We'll call this
period an hour.  (And you wondered if you'd ever see that word again!)
During Decade 2, Star B rises heliacally and becomes associated with
the last hour of the night.  Now the rising of Star A is associated
with the hour before the last hour of night.  And so it goes.

How many decan stars will rise during the course of a given night?
With a total of 36 stars, we expect half of them will rise during the
daytime.  Off hand, it would seem that 18 will rise during the night,
give or take a couple because they are not evenly spaced.  However,
because there is a period of twilight before sunrise and another one
after sunset, the period of darkness is shorter than the period of
daylight.  Furthermore, the periods of daylight and darkness change
with the seasons.  The punch line is that, during the summer when
nights are short, 12 decans could be seen rising during the night.
Evidence for this division of nighttime is actually found on coffin
lids of the 2nd millennium B.C.

Okay, we've explained 12 hours at night.  What about daytime?  The
Egyptians divided the period from sunrise to sunset into 10 parts.
Then they added an hour before sunrise and an hour after sunset for
twilight periods.  This gives a total of 24 hours for a day/night
period.  These hours are not of equal length, of course.  Daytime
hours generally were not the same length as nighttime hours.  Since
their duration varied with the seasons; they were called "seasonal"
hours.  The "equinoctial" hours of equal length were introduced by
Greek astronomers for theoretical use.  Even in the Middle Ages, when
mechanical clocks were coming into use, seasonal hours were used in
everyday life.

Minutes and Seconds

For dividing the hour - and the circle - into 60 units, we can blame
the Babylonians, who got the idea from the Sumerians.  We do not know
how the number 60 was chosen, but we know what to call the system:
sexagesimal.  We also know why it was adopted for use in astronomy and
time keeping: the Babylonians used place notation.  It is because of
them that we use place notation.

Consider a number such as 325.82.  This is really a condensed notation
for 3x10^2 + 2x10^1 + 5x10^0 + 8x10^-1 + 2x10^-2.  The Babylonians
used the same system, except that instead of powers of 10, they used
powers of 60.  But the point is that they developed the system.  Then
it was picked up by Greek astronomers who used it to divide the hour
and the circle.

The scheme with the hours and minutes is actually a hybrid, of course.
We count whole hours in decimal notation, but shift to sexagesimal for
the fraction.  Thus 15 hours, 44 minutes, 13 seconds could be written
in place notation as 1x10^1 + 5x10^0 + 44x60^-1 + 13x60^-2.
Historians of astronomy write it 15;44,13 [Editor: "15;44,33" in the
original] -- where the semicolon separates the whole number from the
fraction and the comma separates sexagesimal units of the fraction.

-- LeRoy E. Doggett, U.S. Naval Observatory

[ Editor: the program's script thanks LeRoy Doggett for assistance and
refers to the related Earth and Sky program "Noon and Midnight"
(January 11, 1996).  Earth and Sky: http://www.earthsky.com/ ]