hen the clock is gaining on the sundial, the Sun
rises and sets later each day, and when the sundial is
gaining on the clock, the Sun rises and sets earlier each
day. If the two effects which give us the equation of time
were solely responsible for sunrise and sunset times, these
times would be late in summer and winter and early in spring
and fall. Most of us would say at once that, of course
this is not true. But it is true for anyone living on the
On a standard meridian at the equator one might
expect the Sun to rise at 6:00 A.M. and set at 6:00 P.M.,
but the Sun rises at 6:03 A.M. in July, a summer month, and
also rises late, at 6:11 A.M. in February, a winter month. It rises seven
minutes before 6:00 A.M. in mid-May, and 20 minutes before
6:00 A.M. at the end of October. At the equator these
effects are entirely accounted for by the equation of time.
The daily path of the Sun as seen at the equator on
the first day of spring, summer, fall, and winter is
illustrated in Figures 7 and 7a .
At the equator the Sun rises
perpendicularly from the horizon and sets perpendicularly,
regardless of the season. Also, the total path of the Sun,
day and night, is divided equally by the horizon. There are
always twelve hours of daytime and twelve hours of
night-time at the equator, except for two minor effects that
increase daytime by about eight minutes. First, since we
mark the instant of sunrise as the time the Sun's upper edge
or "limb" just touches the horizon, the actual center of the Sun is still
below the horizon by half the diameter of the Sun, 16 arc
minutes or ¼ degree.. It will take an additional minute
for the Sun's center to be on the horizon. At sunset the
same thing happens and so an additional two minutes are
gained for daytime. Second, when the Sun's limb appears at
the horizon, it is actually still 43 arc minutes below the
horizon but only appears to be at the horizon due to the
refraction or bending of the Sun's rays by the Earth's
atmosphere. This effect causes the sunrise to appear about
three minutes early and sunset late by the same amount.
Taking both effects together, the length of daytime is about
8 minutes more than 12 hours, and so, of course, night-time
will be 8 minutes less than 12 hours, resulting in daytime
being 16 minutes more than night-time at the equator, or for
that matter, anywhere during the equinoxes (March 21 and September 21).
Figure 7. The daily or diurnal paths of the Sun during the solstices(21 December
and 21 June) and the equinoxes (21 March and 21 September) as seen by an
observer at the equator. Solid lines are daytime, dashed lines are night-time.
At all seasons on the equator, the daily paths of the Sun are divided
equally above and below the horizon.
The same information shown in Figure 7 is presented in Figure 7a, below, in the
form of a polar plot of the position of the Sun in the coordinates of the
azimuth and altitude of the Sun as seen by an observer at that latitude.
Figure 8 and 8a show the apparent paths of the Sun as seen from Hawai'i,
the southernmost State of the United States,
21 degrees north of the equator. The paths are all parallel
to each other, but are slanting at 21 degrees to the
horizon. It will also be noticed that the horizon
divides the total path of the Sun into equal periods only
on the first days of spring and fall, i.e., the equinoxes.
In summer, the portion of the Sun's path above the horizon
is much greater than the night portion, and the reverse is
true in the winter. This illustrates the geographical
effect, which depends on the observer's latitude.
Figure 8 and 8a (below). The daily path of the Sun as seen from Hawai'i on
the first day of spring, summer, fall, and winter.
extreme situation is shown in Figures 9 aand 9a for a location at the
Arctic Circle, latitude 66½ o north. The Sun is above the
horizon all day at the beginning of summer, barely touching
the horizon at midnight.
At the beginning of winter the Sun's path is entirely below the
horizon. This latter situation is modified by the
refraction of sunlight by the Earth's atmosphere which
causes the Sun to appear a little higher at the horizon than
it actually is. Because of this refraction, the Sun
appears briefly above the southern horizon at noon on the
first day of winter at the Arctic Circle.
Figures 9 and 9a (below). The daily path of the Sun as seen at 66.5 degrees
north latitude (the Arctic Circle) on the first day of spring, summer, fall,