he Equation of Time (ET) allows one to calculate the Standard Time at which the
Sun will be found in a particular part of the sky. For example, if it is asked at what time
does the Sun rise in Hilo, Hawaii, on March 21, we must know the ET on March 21 and
the longitude of Hilo. The ET can be read from the graph and is approximately 8 min. .
The longitude of Hilo is 155o W, corresponding to the example under Equation of Time.
First, let us determine the time of sunrise at the Standard Meridian of 150^{o} W, and then
make the correction for Hilo's longitude. The apparent time at sunrise must be 4 minutes
before 6 a.m. (The explanation of the 4 minutes is found under Sunrise and Sunset). From the
definition of ET = Apparent time  Mean (or Standard) time, we see that the Standard
time in this case is the App. time  ET, or, 5h 56min  (8 min) = 6h 4min. This is now
corrected for Hilo's longitude by adding 20 minutes, giving sunrise as 6h 24min or
6:24 a.m., HST (Hawaii Standard Time).
Another example: at what time will the Sun be on the local meridian to an
observer in Boston on October 31? Remember that the local meridian is the great circle
from north to south passing through the zenith. The ET on October 31 is approximately
+16 minutes, and Boston is situated at longitude 71^{o} W. The Apparent time when the Sun
is on the meridian is 12 noon. Thus, Standard time = 12h 00min  (+16 min) = 11h 44min.
This is the correct time at the Standard Meridian of 75^{o}W, but Boston is 4^{o} east of this, so
the Sun crosses the Boston meridian 16 minutes before the 75th meridian. Hence, the
answer is that the Sun crosses the meridian of Boston on October 31 at 11h 28min or
11:28 a.m., EST (Eastern Standard Time).
An interesting problem for the Hawaii student is to determine on what day and at
what time the Sun passes directly overhead, i.e., through the local zenith. (Note that
Hawaii is the only place in the United States where this can happen!) This requires the use
of a table of the declination of the Sun for every day of the year and for the particular year
in question, and such a table can be found in the American Ephemeris and Nautical
Almanac (see REFERENCES). The declination of the Sun corresponds to latitude on the
Earth, so that, when the declination of the Sun equals the latitude of the observer, the Sun
will pass through the observer's zenith. Since the latitude of Hilo is 19^{o} 43', we need to
look for the day on which the Sun has a declination of 19^{o} 43'. We then need to find the
ET on that day and proceed to determine, as above, the HST at which that zenith crossing
occurs. We like to call this a "shadowless" noon, for indeed, a flagpole has no shadow at
that instant!
